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.
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.
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.
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
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.
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.
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.
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.
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.
Erokhin, N. S. Zakharov, V. E.; Zol’nikova, N. N.; Mikhailovskaya, L. A.
2015-02-15
Different variants of resonance tunneling of a transverse electromagnetic wave through a plasma layer containing short-scale (subwavelength) inhomogeneities, including evanescence regions to which approximate methods are inapplicable, are analyzed in the framework of an exactly solvable one-dimensional model. Complex plasma density profiles described by a number of free parameters determining the permittivity modulation depth, the characteristic scale lengths of plasma structures, their number, and the thickness of the inhomogeneous plasma layer are considered. It is demonstrated that reflection-free propagation of the wave incident on the layer from vacuum (the effect of wave-barrier transillumination) can be achieved for various sets of such structures, including plasma density profiles containing a stochastic component. Taking into account cubic nonlinearity, it is also possible to obtain an exact solution to the one-dimensional problem on the nonlinear transillumination of nonuniform plasma. In this case, the thicknesses of the evanescence regions decrease appreciably. The problem of resonance tunneling of electromagnetic waves through such barriers is of interest for a number of practical applications.
NASA Astrophysics Data System (ADS)
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.
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
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
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…
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.
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.
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.
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.
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.
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.
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
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
Some analytical models of radiating collapsing spheres
Herrera, L.; Di Prisco, A; Ospino, J.
2006-08-15
We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each solution, using a hyperbolic transport equation, which permits to exhibit the influence of relaxational effects on the dynamics of the system.
Analytical 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)
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.
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.
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.
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 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.
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 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.
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.
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.
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.
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.
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.
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.
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.
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
FACTOR ANALYTIC MODELS OF CLUSTERED MULTIVARIATE DATA WITH INFORMATIVE CENSORING
This paper describes a general class of factor analytic models for the analysis of clustered multivariate data in the presence of informative missingness. We assume that there are distinct sets of cluster-level latent variables related to the primary outcomes and to the censorin...
Analytical 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.
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
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.
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…
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.
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.
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
An Analytical Thermal Model for Autonomous Soaring Research
NASA Technical Reports Server (NTRS)
Allen, Michael
2006-01-01
A viewgraph presentation describing an analytical thermal model used to enable research on autonomous soaring for a small UAV aircraft is given. The topics include: 1) Purpose; 2) Approach; 3) SURFRAD Data; 4) Convective Layer Thickness; 5) Surface Heat Budget; 6) Surface Virtual Potential Temperature Flux; 7) Convective Scaling Velocity; 8) Other Calculations; 9) Yearly trends; 10) Scale Factors; 11) Scale Factor Test Matrix; 12) Statistical Model; 13) Updraft Strength Calculation; 14) Updraft Diameter; 15) Updraft Shape; 16) Smoothed Updraft Shape; 17) Updraft Spacing; 18) Environment Sink; 19) Updraft Lifespan; 20) Autonomous Soaring Research; 21) Planned Flight Test; and 22) Mixing Ratio.
Peat pyrolysis and the analytical semi-empirical model
Feng, J.; Green, A.E.S.
2007-07-01
Pyrolysis of peat could convert this material into useful fuels and valuable hydrocarbons. A study of peat pyrolysis can also serve as a useful bridge between studies of coal pyrolysis and biomass pyrolysis. Using an analytical model of pyrolysis that has previously been applied to biomass and to coal, we present here the results of applications of this model to a representative peat. The analysis suggests means of organizing and processing rate and yield data that should be useful in applications of pyrolysis for the production of fuels and chemicals.
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
Analytical dynamics models for space missions around minor bodies
NASA Astrophysics Data System (ADS)
Cardoso dos Santos, Josué; dos Santos Carvalho, Jean Paulo; Vilhena de Moraes, Rodolpho; Bertachini de Almeida Prado, Antônio Fernando
2015-08-01
In recent years, the dynamics of orbits around minor bodies and icy moons in our solar system has become important in planning future missions that intend to visit dwarf planets, planetary moons, asteroids and comets. Due to their special characteristics, Europa, Ganymede, Callisto, Enceladus, Titan and Triton are among the group of objects with greater potential to receive missions in a near future. In order to provide a semi-analytical theory for tuture space exploration of these celestial bodies, this work aims to present two analytical models to describe and evaluate gravitational disturbances over a spacecrat's orbit around a minor body. A search for these less perturbed orbits is performed. An analytical model for the third-body perturbation is presented and consideres it in an eccentric-inclined orbit. Some harmonic terms due to the non-uniform distribuition of mass are considered according they are available in the literature. The dynamic of these orbits is explored by numerical simulations. The results are in accordance with the requirements for missions present in the literature.
An 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.
An analytic model for buoyancy resonances in protoplanetary disks
Lubow, Stephen H.; Zhu, Zhaohuan E-mail: zhzhu@astro.princeton.edu
2014-04-10
Zhu et al. found in three-dimensional shearing box simulations a new form of planet-disk interaction that they attributed to a vertical buoyancy resonance in the disk. We describe an analytic linear model for this interaction. We adopt a simplified model involving azimuthal forcing that produces the resonance and permits an analytic description of its structure. We derive an analytic expression for the buoyancy torque and show that the vertical torque distribution agrees well with the results of the Athena simulations and a Fourier method for linear numerical calculations carried out with the same forcing. The buoyancy resonance differs from the classic Lindblad and corotation resonances in that the resonance lies along tilted planes. Its width depends on damping effects and is independent of the gas sound speed. The resonance does not excite propagating waves. At a given large azimuthal wavenumber k{sub y} > h {sup –1} (for disk thickness h), the buoyancy resonance exerts a torque over a region that lies radially closer to the corotation radius than the Lindblad resonance. Because the torque is localized to the region of excitation, it is potentially subject to the effects of nonlinear saturation. In addition, the torque can be reduced by the effects of radiative heat transfer between the resonant region and its surroundings. For each azimuthal wavenumber, the resonance establishes a large scale density wave pattern in a plane within the disk.
Universal analytic model for tunnel FET circuit simulation
NASA Astrophysics Data System (ADS)
Lu, Hao; Esseni, David; Seabaugh, Alan
2015-06-01
A simple analytic model based on the Kane-Sze formula is used to describe the current-voltage characteristics of tunnel field-effect transistors (TFETs). This model captures the unique features of the TFET including the decrease in subthreshold swing with drain current and the superlinear onset of the output characteristic. The model also captures the ambipolar current characteristic at negative gate-source bias and the negative differential resistance for negative drain-source biases. A simple empirical capacitance model is also included to enable circuit simulation. The model has fairly general validity and is not specific to a particular TFET geometry. Good agreement is shown with published atomistic simulations of an InAs double-gate TFET with gate perpendicular to the tunnel junction and with numerical simulations of a broken-gap AlGaSb/InAs TFET with gate in parallel with the tunnel junction.
Analytical modeling of glucose biosensors based on carbon nanotubes
2014-01-01
In recent years, carbon nanotubes have received widespread attention as promising carbon-based nanoelectronic devices. Due to their exceptional physical, chemical, and electrical properties, namely a high surface-to-volume ratio, their enhanced electron transfer properties, and their high thermal conductivity, carbon nanotubes can be used effectively as electrochemical sensors. The integration of carbon nanotubes with a functional group provides a good and solid support for the immobilization of enzymes. The determination of glucose levels using biosensors, particularly in the medical diagnostics and food industries, is gaining mass appeal. Glucose biosensors detect the glucose molecule by catalyzing glucose to gluconic acid and hydrogen peroxide in the presence of oxygen. This action provides high accuracy and a quick detection rate. In this paper, a single-wall carbon nanotube field-effect transistor biosensor for glucose detection is analytically modeled. In the proposed model, the glucose concentration is presented as a function of gate voltage. Subsequently, the proposed model is compared with existing experimental data. A good consensus between the model and the experimental data is reported. The simulated data demonstrate that the analytical model can be employed with an electrochemical glucose sensor to predict the behavior of the sensing mechanism in biosensors. PMID:24428818
Analytical model of reactive transport processes with spatially variable coefficients.
Simpson, Matthew J; Morrow, Liam C
2015-05-01
Analytical solutions of partial differential equation (PDE) models describing reactive transport phenomena in saturated porous media are often used as screening tools to provide insight into contaminant fate and transport processes. While many practical modelling scenarios involve spatially variable coefficients, such as spatially variable flow velocity, v(x), or spatially variable decay rate, k(x), most analytical models deal with constant coefficients. Here we present a framework for constructing exact solutions of PDE models of reactive transport. Our approach is relevant for advection-dominant problems, and is based on a regular perturbation technique. We present a description of the solution technique for a range of one-dimensional scenarios involving constant and variable coefficients, and we show that the solutions compare well with numerical approximations. Our general approach applies to a range of initial conditions and various forms of v(x) and k(x). Instead of simply documenting specific solutions for particular cases, we present a symbolic worksheet, as supplementary material, which enables the solution to be evaluated for different choices of the initial condition, v(x) and k(x). We also discuss how the technique generalizes to apply to models of coupled multispecies reactive transport as well as higher dimensional problems. PMID:26064648
An analytical model of a longitudinal-torsional ultrasonic transducer
NASA Astrophysics Data System (ADS)
Al-Budairi, Hassan; Lucas, Margaret
2012-08-01
The combination of longitudinal and torsional (LT) vibrations at high frequencies finds many applications such as ultrasonic drilling, ultrasonic welding, and ultrasonic motors. The LT mode can be obtained by modifications to the design of a standard bolted Langevin ultrasonic transducer driven by an axially poled piezoceramic stack, by a technique that degenerates the longitudinal mode to an LT motion by a geometrical alteration of the wave path. The transducer design is developed and optimised through numerical modelling which can represent the geometry and mechanical properties of the transducer and its vibration response to an electrical input applied across the piezoceramic stack. However, although these models can allow accurate descriptions of the mechanical behaviour, they do not generally provide adequate insights into the electrical characteristics of the transducer. In this work, an analytical model is developed to present the LT transducer based on the equivalent circuit method. This model can represent both the mechanical and electrical aspects and is used to extract many of the design parameters, such as resonance and anti-resonance frequencies, the impedance spectra and the coupling coefficient of the transducer. The validity of the analytical model is demonstrated by close agreement with experimental results.
Analytical model of reactive transport processes with spatially variable coefficients
Simpson, Matthew J.; Morrow, Liam C.
2015-01-01
Analytical solutions of partial differential equation (PDE) models describing reactive transport phenomena in saturated porous media are often used as screening tools to provide insight into contaminant fate and transport processes. While many practical modelling scenarios involve spatially variable coefficients, such as spatially variable flow velocity, v(x), or spatially variable decay rate, k(x), most analytical models deal with constant coefficients. Here we present a framework for constructing exact solutions of PDE models of reactive transport. Our approach is relevant for advection-dominant problems, and is based on a regular perturbation technique. We present a description of the solution technique for a range of one-dimensional scenarios involving constant and variable coefficients, and we show that the solutions compare well with numerical approximations. Our general approach applies to a range of initial conditions and various forms of v(x) and k(x). Instead of simply documenting specific solutions for particular cases, we present a symbolic worksheet, as supplementary material, which enables the solution to be evaluated for different choices of the initial condition, v(x) and k(x). We also discuss how the technique generalizes to apply to models of coupled multispecies reactive transport as well as higher dimensional problems. PMID:26064648
Analytical model for contaminant mass removal by air sparging
Rabideau, A.J.; Blayden, J.M.
1998-12-31
An analytical model was developed to predict the removal of volatile organic compounds (VOCs) from ground water by air sparging (AS). The model treats the air sparging zone as a completely mixed reactor subject to the removal of dissolved contaminants by volatilization, advection, and first-order decay. Nonequilibrium desorption is approximated as a first-order mass transfer process. The model reproduces the tailing and rebound behavior often observed at AS sites, and would normally require the estimation of three site-specific parameters. Dimensional analysis demonstrates that predicting tailing can be interpreted in terms of kinetic desorption or diffusion of aqueous phase contaminants into discrete air channels. Related work is ongoing to test the model against field data.
Laser satellite constellations for strategic defense - an analytic model
Parmentola, J.A.; Milton, A.F.
1987-10-01
Using mainly geometric reasoning, an analytic model is constructed that predicts the required characteristics of an orbiting constellation of laser battle stations, each of which is designed to destroy ballistic missiles during their boost phase. The geometry of the constellation configuration and some general aspects of the coverage problem are discussed. The determination of the absentee ratio falls into two main categories that depend upon whether the Soviet ICBM threat is concentrated at a single location or whether it is distributed as it is now. A point-threat model and a distributive threat model are considered, the determination of the respective kill rates for these models is discussed, and the scaling properties of the laser constellation with respect to a change in the quantitative nature of the two types of ICBM threats are considered.
A semi-analytic model of magnetized liner inertial fusion
McBride, Ryan D.; Slutz, Stephen A.
2015-05-15
Presented is a semi-analytic model of magnetized liner inertial fusion (MagLIF). This model accounts for several key aspects of MagLIF, including: (1) preheat of the fuel (optionally via laser absorption); (2) pulsed-power-driven liner implosion; (3) liner compressibility with an analytic equation of state, artificial viscosity, internal magnetic pressure, and ohmic heating; (4) adiabatic compression and heating of the fuel; (5) radiative losses and fuel opacity; (6) magnetic flux compression with Nernst thermoelectric losses; (7) magnetized electron and ion thermal conduction losses; (8) end losses; (9) enhanced losses due to prescribed dopant concentrations and contaminant mix; (10) deuterium-deuterium and deuterium-tritium primary fusion reactions for arbitrary deuterium to tritium fuel ratios; and (11) magnetized α-particle fuel heating. We show that this simplified model, with its transparent and accessible physics, can be used to reproduce the general 1D behavior presented throughout the original MagLIF paper [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)]. We also discuss some important physics insights gained as a result of developing this model, such as the dependence of radiative loss rates on the radial fraction of the fuel that is preheated.
Comparison between analytical and numerical solution of mathematical drying model
NASA Astrophysics Data System (ADS)
Shahari, N.; Rasmani, K.; Jamil, N.
2016-02-01
Drying is often related to the food industry as a process of shifting heat and mass inside food, which helps in preserving food. Previous research using a mass transfer equation showed that the results were mostly concerned with the comparison between the simulation model and the experimental data. In this paper, the finite difference method was used to solve a mass equation during drying using different kinds of boundary condition, which are equilibrium and convective boundary conditions. The results of these two models provide a comparison between the analytical and the numerical solution. The result shows a close match between the two solution curves. It is concluded that the two proposed models produce an accurate solution to describe the moisture distribution content during the drying process. This analysis indicates that we have confidence in the behaviour of moisture in the numerical simulation. This result demonstrated that a combined analytical and numerical approach prove that the system is behaving physically. Based on this assumption, the model of mass transfer was extended to include the temperature transfer, and the result shows a similar trend to those presented in the simpler case.
A two-dimensional analytical model of petroleum vapor intrusion
NASA Astrophysics Data System (ADS)
Yao, Yijun; Verginelli, Iason; Suuberg, Eric M.
2016-02-01
In this study we present an analytical solution of a two-dimensional petroleum vapor intrusion model, which incorporates a steady-state diffusion-dominated vapor transport in a homogeneous soil and piecewise first-order aerobic biodegradation limited by oxygen availability. This new model can help practitioners to easily generate two-dimensional soil gas concentration profiles for both hydrocarbons and oxygen and estimate hydrocarbon indoor air concentrations as a function of site-specific conditions such as source strength and depth, reaction rate constant, soil characteristics and building features. The soil gas concentration profiles generated by this new model are shown in good agreement with three-dimensional numerical simulations and two-dimensional measured soil gas data from a field study. This implies that for cases involving diffusion dominated soil gas transport, steady state conditions and homogenous source and soil, this analytical model can be used as a fast and easy-to-use risk screening tool by replicating the results of 3-D numerical simulations but with much less computational effort.
Generalized Analytical Model for the Radio-Frequency Sheath
NASA Astrophysics Data System (ADS)
Czarnetzki, Uwe
2014-10-01
An analytical model for the planar radio frequency (RF) sheath in capacitive discharges is developed based on the applied RF voltage as the boundary condition. The model applies to all kind of waveforms for the applied RF voltage, includes both sheaths in a discharge of arbitrary symmetry, and allows for an arbitrary degree of ion collisionallity in the sheaths (charge-exchange collisions). Further, effects of the finite floating potential during sheath collapse are included. The model can even be extended to electronegative plasmas with low bulk conductivity. The individual sheath voltages, the self-bias, and the RF floating potentials are explicitly calculated by a voltage balance equation using a cubic-charge voltage relation for the sheaths. In particular, the RF-phase as a function of the sheath voltage is determined. This is an input for a single second order non-linear integro-differential equation which is governing the ion flow velocity in the sheath. Fast numerical integration is straight forward and in many cases approximate analytical solutions can be obtained. Based on the solution for the ion flow velocity, densities, electric fields, currents, and charge-voltage relations are calculated. Further, the Child-Langmuir laws for the collisionless as well as the highly collisional case are derived. Very good agreement between model and experiments is obtained.
Analytical model for flow duration curves in seasonally dry climates
NASA Astrophysics Data System (ADS)
Müller, Marc F.; Dralle, David N.; Thompson, Sally E.
2014-07-01
Flow duration curves (FDC) display streamflow values against their relative exceedance time. They provide critical information for watershed management by representing the variation in the availability and reliability of surface water to supply ecosystem services and satisfy anthropogenic needs. FDCs are particularly revealing in seasonally dry climates, where surface water supplies are highly variable. While useful, the empirical computation of FDCs is data intensive and challenging in sparsely gauged regions, meaning that there is a need for robust, predictive models to evaluate FDCs with simple parameterization. Here, we derive a process-based analytical expression for FDCs in seasonally dry climates. During the wet season, streamflow is modeled as a stochastic variable driven by rainfall, following the stochastic analytical model of Botter et al. (2007a). During the dry season, streamflow is modeled as a deterministic recession with a stochastic initial condition that accounts for the carryover of catchment storage across seasons. The resulting FDC model is applied to 38 catchments in Nepal, coastal California, and Western Australia, where FDCs are successfully modeled using five physically meaningful parameters with minimal calibration. A Monte Carlo analysis revealed that the model is robust to deviations from its assumptions of Poissonian rainfall, exponentially distributed response times and constant seasonal timing. The approach successfully models period-of-record FDCs and allows interannual and intra-annual sources of variations in dry season streamflow to be separated. The resulting median annual FDCs and confidence intervals allow the simulation of the consequences of interannual flow variations for infrastructure projects. We present an example using run-of-river hydropower in Nepal as a case study.
Analytical model of solute transport by unsteady unsaturated gravitational infiltration.
Lessoff, S C; Indelman, P
2004-08-01
Penetration of reactive solute into a soil during a cycle of water infiltration and redistribution is investigated by deriving analytical closed form solutions for fluid flux, moisture content and contaminant concentration. The solution is developed for gravitational flow and advective transport and is applied to two scenarios of solute applications encountered in the applications: a finite pulse of solute dissolved in irrigation water and an instantaneous pulse broadcasted onto the soil surface. Through comparison to simulations of Richards' flow, capillary suction is shown to have contrasting effects on the upper and lower boundaries of the fluid pulse, speeding penetration of the wetting front and reducing the rate of drying. This leads to agreement between the analytical and numerical solutions for typical field and experimental conditions. The analytical solution is further incorporated into a stochastic column model of flow and transport to compute mean solute concentration in a heterogeneous field. An unusual phenomenon of plume contraction is observed at long times of solute propagation during the drying stage. The mean concentration profiles match those of the Monte-Carlo simulations for capillary length scales typical of sandy soils. PMID:15240168
Analytic Thermoelectric Couple Modeling: Variable Material Properties and Transient Operation
NASA Technical Reports Server (NTRS)
Mackey, Jonathan A.; Sehirlioglu, Alp; Dynys, Fred
2015-01-01
To gain a deeper understanding of the operation of a thermoelectric couple a set of analytic solutions have been derived for a variable material property couple and a transient couple. Using an analytic approach, as opposed to commonly used numerical techniques, results in a set of useful design guidelines. These guidelines can serve as useful starting conditions for further numerical studies, or can serve as design rules for lab built couples. The analytic modeling considers two cases and accounts for 1) material properties which vary with temperature and 2) transient operation of a couple. The variable material property case was handled by means of an asymptotic expansion, which allows for insight into the influence of temperature dependence on different material properties. The variable property work demonstrated the important fact that materials with identical average Figure of Merits can lead to different conversion efficiencies due to temperature dependence of the properties. The transient couple was investigated through a Greens function approach; several transient boundary conditions were investigated. The transient work introduces several new design considerations which are not captured by the classic steady state analysis. The work helps to assist in designing couples for optimal performance, and also helps assist in material selection.
A hybrid finite-difference and analytic element groundwater model.
Haitjema, H M; Feinstein, D T; Hunt, R J; Gusyev, M A
2010-01-01
Regional finite-difference models tend to have large cell sizes, often on the order of 1-2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW-MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models. PMID:20132324
Solvability of initial boundary value problem for the equations of filtration in poroelastic media
NASA Astrophysics Data System (ADS)
Tokareva, M. A.
2016-06-01
The study is devoted to the mathematical model of fluid filtration in poroelastic media. The laws of conservation of mass for each phase, Darcy's law for fluid phase, the rheological law and the general equation of conservation of momentum for system describe this process. The local solvability of the problem is proved in this paper for the case in which the density of the mass forces is equal to zero and the fluid is compressible.
Digital forensics: an analytical crime scene procedure model (ACSPM).
Bulbul, Halil Ibrahim; Yavuzcan, H Guclu; Ozel, Mesut
2013-12-10
In order to ensure that digital evidence is collected, preserved, examined, or transferred in a manner safeguarding the accuracy and reliability of the evidence, law enforcement and digital forensic units must establish and maintain an effective quality assurance system. The very first part of this system is standard operating procedures (SOP's) and/or models, conforming chain of custody requirements, those rely on digital forensics "process-phase-procedure-task-subtask" sequence. An acceptable and thorough Digital Forensics (DF) process depends on the sequential DF phases, and each phase depends on sequential DF procedures, respectively each procedure depends on tasks and subtasks. There are numerous amounts of DF Process Models that define DF phases in the literature, but no DF model that defines the phase-based sequential procedures for crime scene identified. An analytical crime scene procedure model (ACSPM) that we suggest in this paper is supposed to fill in this gap. The proposed analytical procedure model for digital investigations at a crime scene is developed and defined for crime scene practitioners; with main focus on crime scene digital forensic procedures, other than that of whole digital investigation process and phases that ends up in a court. When reviewing the relevant literature and interrogating with the law enforcement agencies, only device based charts specific to a particular device and/or more general perspective approaches to digital evidence management models from crime scene to courts are found. After analyzing the needs of law enforcement organizations and realizing the absence of crime scene digital investigation procedure model for crime scene activities we decided to inspect the relevant literature in an analytical way. The outcome of this inspection is our suggested model explained here, which is supposed to provide guidance for thorough and secure implementation of digital forensic procedures at a crime scene. In digital forensic
Improved analytical model for residual stress prediction in orthogonal cutting
NASA Astrophysics Data System (ADS)
Qi, Zhaoxu; Li, Bin; Xiong, Liangshan
2014-09-01
The analytical model of residual stress in orthogonal cutting proposed by Jiann is an important tool for residual stress prediction in orthogonal cutting. In application of the model, a problem of low precision of the surface residual stress prediction is found. By theoretical analysis, several shortages of Jiann's model are picked out, including: inappropriate boundary conditions, unreasonable calculation method of thermal stress, ignorance of stress constraint and cyclic loading algorithm. These shortages may directly lead to the low precision of the surface residual stress prediction. To eliminate these shortages and make the prediction more accurate, an improved model is proposed. In this model, a new contact boundary condition between tool and workpiece is used to make it in accord with the real cutting process; an improved calculation method of thermal stress is adopted; a stress constraint is added according to the volumeconstancy of plastic deformation; and the accumulative effect of the stresses during cyclic loading is considered. At last, an experiment for measuring residual stress in cutting AISI 1045 steel is conducted. Also, Jiann's model and the improved model are simulated under the same conditions with cutting experiment. The comparisons show that the surface residual stresses predicted by the improved model is closer to the experimental results than the results predicted by Jiann's model.
Improved analytical model for residual stress prediction in orthogonal cutting
NASA Astrophysics Data System (ADS)
Qi, Zhaoxu; Li, Bin; Xiong, Liangshan
2014-09-01
The analytical model of residual stress in orthogonal cutting proposed by Jiann is an important tool for residual stress prediction in orthogonal cutting. In application of the model, a problem of low precision of the surface residual stress prediction is found. By theoretical analysis, several shortages of Jiann's model are picked out, including: inappropriate boundary conditions, unreasonable calculation method of thermal stress, ignorance of stress constraint and cyclic loading algorithm. These shortages may directly lead to the low precision of the surface residual stress prediction. To eliminate these shortages and make the prediction more accurate, an improved model is proposed. In this model, a new contact boundary condition between tool and workpiece is used to make it in accord with the real cutting process; an improved calculation method of thermal stress is adopted; a stress constraint is added according to the volume-constancy of plastic deformation; and the accumulative effect of the stresses during cyclic loading is considered. At last, an experiment for measuring residual stress in cutting AISI 1045 steel is conducted. Also, Jiann's model and the improved model are simulated under the same conditions with cutting experiment. The comparisons show that the surface residual stresses predicted by the improved model is closer to the experimental results than the results predicted by Jiann's model.
Analytical and numerical modeling of surface morphologies in thin films
Genin, F.Y.
1995-05-01
Experimental studies have show that strains due to thermal expansion mismatch between a film and its substrate can produce very large stresses in the film that can lead to the formation of holes and hillocks. Based on a phenomenological description of the evolution of a solid surface under both capillary and stress driving forces and for surface and grain boundary self-diffusion, this article provides analytical and numerical solutions for surface profiles of model geometries in polycrystalline thin films. Results can explain a variety of surface morphologies commonly observed experimentally and are discussed to give some practical insights on how to control the growth of holes and hillocks in thin films.
HTS axial flux induction motor with analytic and FEA modeling
NASA Astrophysics Data System (ADS)
Li, S.; Fan, Y.; Fang, J.; Qin, W.; Lv, G.; Li, J. H.
2013-11-01
This paper presents a high-temperature superconductor (HTS) axial-flux induction motor, which can output levitation force and torque simultaneously. In order to analyze the character of the force, analytic method and finite element method are adopted to model the motor. To make sure the HTS can carry sufficiently large current and work well, the magnetic field distribution in HTS coil is calculated. An effective method to improve the critical current of HTS coil is presented. Then, AC losses in HTS windings in the motor are estimated and tested.
"Violent Intent Modeling: Incorporating Cultural Knowledge into the Analytical Process
Sanfilippo, Antonio P.; Nibbs, Faith G.
2007-08-24
While culture has a significant effect on the appropriate interpretation of textual data, the incorporation of cultural considerations into data transformations has not been systematic. Recognizing that the successful prevention of terrorist activities could hinge on the knowledge of the subcultures, Anthropologist and DHS intern Faith Nibbs has been addressing the need to incorporate cultural knowledge into the analytical process. In this Brown Bag she will present how cultural ideology is being used to understand how the rhetoric of group leaders influences the likelihood of their constituents to engage in violent or radicalized behavior, and how violent intent modeling can benefit from understanding that process.
Shear mechanical properties of the spleen: experiment and analytical modelling.
Nicolle, S; Noguer, L; Palierne, J-F
2012-05-01
This paper aims at providing the first shear mechanical properties of spleen tissue. Rheometric tests on porcine splenic tissues were performed in the linear and nonlinear regime, revealing a weak frequency dependence of the dynamic moduli in linear regime and a distinct strain-hardening effect in nonlinear regime. These behaviours are typical of soft tissues such as kidney and liver, with however a less pronounced strain-hardening for the spleen. An analytical model based on power laws is then proposed to describe the general shear viscoelastic behaviour of the spleen. PMID:22498291
Analytical model of ionospheric convection at subauroral latitudes
NASA Astrophysics Data System (ADS)
Deminov, M. G.; Kim, V. P.; Shubin, V. N.; Khegai, V. V.
An analytical model of plasma convection in the subauroral ionosphere is developed, assuming that the electric shielding of the inner magnetosphere is controlled by polarization of the hot ion zone situated behind the inner boundary of the plasma sheet. It is shown that, at subauroral latitudes at night, the plasma drifts eastward, while during the day it shifts westward. Thus, in the predmidnight sector, the direction of convection in the subauroral ionosphere is opposite to that of auroral convection. In general, the electric field, with a strength of 10 mV/m, has a meridional direction.
Analytical model for the radio-frequency sheath
NASA Astrophysics Data System (ADS)
Czarnetzki, Uwe
2013-12-01
A simple analytical model for the planar radio-frequency (rf) sheath in capacitive discharges is developed that is based on the assumptions of a step profile for the electron front, charge exchange collisions with constant cross sections, negligible ionization within the sheath, and negligible ion dynamics. The continuity, momentum conservation, and Poisson equations are combined in a single integro-differential equation for the square of the ion drift velocity, the so called sheath equation. Starting from the kinetic Boltzmann equation, special attention is paid to the derivation and the validity of the approximate fluid equation for momentum balance. The integrals in the sheath equation appear in the screening function which considers the relative contribution of the temporal mean of the electron density to the space charge in the sheath. It is shown that the screening function is quite insensitive to variations of the effective sheath parameters. The two parameters defining the solution are the ratios of the maximum sheath extension to the ion mean free path and the Debye length, respectively. A simple general analytic expression for the screening function is introduced. By means of this expression approximate analytical solutions are obtained for the collisionless as well as the highly collisional case that compare well with the exact numerical solution. A simple transition formula allows application to all degrees of collisionality. In addition, the solutions are used to calculate all static and dynamic quantities of the sheath, e.g., the ion density, fields, and currents. Further, the rf Child-Langmuir laws for the collisionless as well as the collisional case are derived. An essential part of the model is the a priori knowledge of the wave form of the sheath voltage. This wave form is derived on the basis of a cubic charge-voltage relation for individual sheaths, considering both sheaths and the self-consistent self-bias in a discharge with arbitrary
An analytical model of accretion onto white dwarfs
NASA Astrophysics Data System (ADS)
Ospina, N.; Hernanz, M.
2013-05-01
The analytical model of Frank et al. (2002) has been used to investigate the structure of the accretion stream onto white dwarfs (WD). In particular, the post-shock region (temperature, density and gas velocity distributions) and X-ray spectrum emitted by this region. We have obtained the temperature, density and gas velocity distributions of the emission region for different masses of white dwarfs and at different positions in the shock coordinate. Also, we calculated the emitted spectrum for different WD masses and at different positions of the shock with the principal objective of study the accretion at different points of the emission region.
Analytical modeling of turbine wakes in yawed conditions
NASA Astrophysics Data System (ADS)
Bastankhah, Majid; Porté-Agel, Fernando
2016-04-01
Increasing wind energy production has become a unanimous plan for virtually all the developed countries. In addition to constructing new wind farms, this goal can be achieved by making wind farms more efficient. Control strategies in wind farms, such as manipulating the yaw angle of the turbines, have the potential to make wind farms more efficient. Costly numerical simulations or measurements cannot be, however, employed to assess the viability of this strategy in the numerous different scenarios happening in real wind farms. In this study, we aim to develop an inexpensive and simple analytical model that is able for the first time to predict the whole wake of a yawed turbine with an acceptable accuracy. The proposed analytical model is built upon the simplified version of the Reynolds-averaged Navier-Stokes equations. Apart from the ability of the model to predict wake flows in yawed conditions, it can provide a better understanding of turbine wakes in this complex situation. For example, it can give valuable insights on how the wake deflection varies by changing turbine and incoming flow characteristics, such as the thrust coefficient of the turbine or the ambient turbulence.
An Analytical Model for the Radio-Frequency Sheath
NASA Astrophysics Data System (ADS)
Czarnetzki, Uwe
2013-09-01
An analytical model for the planar radio frequency (RF) sheath in capacitive discharges is developed based on the applied RF voltage as the boundary condition. In a first step, the individual sheath voltages and the self-bias are calculated using a cubic-charge voltage relation. In the second step, a single integro-differential equation is derived to describe the ion flow velocity in the sheath under all conditions of collisionality. Central to the model is the screening function that describes the screening of the ion density by the mean electron density in the sheath. Numerical integration of the sheath equation is straight forward. However, for the collisionless as well as the collisional case explicit, simple, and precise analytical approximations can be found. Drift velocities, densities, fields, currents, and charge-voltage relations are calculated. Further, the Child-Langmuir laws for both cases of collisonality are derived. These solutions are in very good agreement with experimental data from the literature based on laser electric field measurements, the Brinkmann sheath model, and PIC simulations. The technique works well also for other waveforms, e.g. the electrical asymmetry effect or tailored pulse waveforms.
Experimental, numerical and analytical models of mantle starting plumes
NASA Astrophysics Data System (ADS)
Coulliette, D. L.; Loper, D. E.
1995-12-01
The results of a combined experimental, numerical and analytical investigation of starting thermal plumes are described, to obtain a better perspective on plumes within the Earth's mantle. Thermal plumes were generated experimentally in a tank of corn syrup by means of an electrical heater. Viscosity ratios of 400, 30 000, and 10 8 were generated by varying the temperature of the tank. Plumes for the smaller ratios had the traditional 'balloon-on-astring' shape, but that at the highest ratio had a novel morphology. The plume heads in the first two cases were observed to rise at roughly a constant speed, in contrast to most previous studies which found the plume heads to accelerate. Loss of buoyancy from the plume head owing to heat loss is believed to be responsible for this difference. Starting plumes were simulated numerically using an axisymmetric, finite-element code to solve the Boussinesq equations at finite Prandtl numbers. The constant rise speed observed experimentally was confirmed by the numerical simulation for the viscosity ratios of 400 and 30 000, but numerical instability prevented simulation of the case with a viscosity ratio of 10 8. There was very good agreement between the experimental and numerical rise speeds. An analytical model was developed which reduces to previous models in limiting cases. This parameterization gives better agreement with the experimental and numerical results than does any previous model.
Analytic modeling of antibody versus nanocell delivery of photosensitizer
NASA Astrophysics Data System (ADS)
Pogue, Brian W.; Srinivasan, Subhadra; Samkoe, Kimberley; Zheng, Lei Zak; Rai, Prakash; Mai, Zhiming; Verma, Sarika; Hasan, Tayyaba
2010-02-01
Delivery of therapeutic agents to solid tumors is challenging, and the issues that govern this can be distilled down into parameters which allow computational modeling. In this paper, the basic rate equations and diffusion kernel for the time and space modeling of delivery are developed, along with an analytical solution to this equation. The model is then used to compare delivery of Avastin antibody relative to delivery encapsulated in a nanocell delivery vehicle. The key factors are the plasma clearance or excretion rates, and the binding, or not, as it transports into the tumor tissue. A reduction in the plasma clearance rate inherently increases available delivery over time, and additionally the reduction in binding from antibody to nanocell allows higher penetration into the tumor at the longer circulation times.
Urban stormwater management planning with analytical probabilistic models
Adams, B.J.
2000-07-01
Understanding how to properly manage urban stormwater is a critical concern to civil and environmental engineers the world over. Mismanagement of stormwater and urban runoff results in flooding, erosion, and water quality problems. In an effort to develop better management techniques, engineers have come to rely on computer simulation and advanced mathematical modeling techniques to help plan and predict water system performance. This important book outlines a new method that uses probability tools to model how stormwater behaves and interacts in a combined- or single-system municipal water system. Complete with sample problems and case studies illustrating how concepts really work, the book presents a cost-effective, easy-to-master approach to analytical modeling of stormwater management systems.
Semi-analytical model of cosmic ray electron transport
NASA Astrophysics Data System (ADS)
Ivascenko, A.; Spanier, F.
2011-07-01
We present a numerical extension to the analytical propagation model introduced in Hein and Spanier (2008) to describe the leptonic population in the galactic disc. The model is used to derive a possible identification of the components that contribute to the leptonic cosmic ray spectrum, as measured by PAMELA, Fermi and HESS, with an emphasis on secondary e+-e- production in collisions of cosmic ray particles with ambient interstellar medium (ISM). We find that besides secondaries, an additional source symmetric in e+ and e- production is needed to explain both the PAMELA anomaly and the Fermi bump, assuming a power-law primary electron spectrum. Our model also allows us to derive constraints for some properties of the ISM.
Analytic Modeling of Collector Current and Delay Time in Hbts
NASA Astrophysics Data System (ADS)
Jung, Hee-Bum
1992-01-01
Collector current in abrupt Al_ {0.48}In_{0.52} As/In_{0.53}Ga _{0.47}As HBTs is investigated. Because tunneling plays an important role for abrupt heterojunctions, thermionic field emission (TF) mechanism is included, as a part of the model, in addition to thermionic emission (TE) theory. To model the modulation of the effective barrier height correctly, non-ideal doping profile across the heterojunction is considered. Calculations showed that under nominal operating conditions, TF is dominant over TE in determining the collector current. Furthermore, modulation of the effective barrier height manifests itself in the collector ideality factor that is greater than unity. It is shown that, by calculating the above mentioned transport mechanisms and including the barrier height modulation, the collector current and its temperature dependence in abrupt AlInAs/InGaAs HBTs can be predicted correctly. The detailed calculation is reduced to an analytical closed -form model by assuming a Gaussian energy spectrum for TF current. The model is determined to be accurate over a wide range of bias and temperatures. A simple TE/TF Ebers -Moll model for abrupt HBTs is derived. The classical expression for collector small signal delay time is inadequate for vertically scaled transistors where transient velocity effects can no longer be ignored. Analytical expressions for collector transit time and small signal delay time are proposed for circuit simulation. These models use a general non-uniform velocity profile described entirely in terms of five physical parameters: momentum and energy relaxation times, and initial, peak, and saturated velocities. A C_infty-continuous function approximation for the transit time is used to obtain analytical closed-form expressions for collector small signal delay time in terms of physically meaningful transport parameters. An accurate empirical two-piece model is also proposed. As the collector thickness is scaled down, the ratio of small signal
A Mechanistic Stochastic Ricker Model: Analytical and Numerical Investigations
NASA Astrophysics Data System (ADS)
Gadrich, Tamar; Katriel, Guy
The Ricker model is one of the simplest and most widely-used ecological models displaying complex nonlinear dynamics. We study a discrete-time population model, which is derived from simple assumptions concerning individual organisms’ behavior, using the “site-based” approach, developed by Brännström, Broomhead, Johansson and Sumpter. In the large-population limit the model converges to the Ricker model, and can thus be considered a mechanistic version of the Ricker model, derived from basic ecological principles, and taking into account the demographic stochasticity inherent to finite populations. We employ several analytical and precise numerical methods to study the model, showing how each approach contributes to understanding the model’s dynamics. Expressing the model as a Markov chain, we employ the concept of quasi-stationary distributions, which are computed numerically, and used to examine the interaction between complex deterministic dynamics and demographic stochasticity, as well as to calculate mean times to extinction. A Gaussian Markov chain approximation is used to obtain quantitative asymptotic approximations for the size of fluctuations of the stochastic model’s time series around the deterministic trajectory, and for the correlations between successive fluctuations. Results of these approximations are compared to results obtained from quasi-stationary distributions and from direct simulations, and are shown to be in good agreement.
Analytical aerodynamic model of a high alpha research vehicle wind-tunnel model
NASA Technical Reports Server (NTRS)
Cao, Jichang; Garrett, Frederick, Jr.; Hoffman, Eric; Stalford, Harold
1990-01-01
A 6 DOF analytical aerodynamic model of a high alpha research vehicle is derived. The derivation is based on wind-tunnel model data valid in the altitude-Mach flight envelope centered at 15,000 ft altitude and 0.6 Mach number with Mach range between 0.3 and 0.9. The analytical models of the aerodynamics coefficients are nonlinear functions of alpha with all control variable and other states fixed. Interpolation is required between the parameterized nonlinear functions. The lift and pitching moment coefficients have unsteady flow parts due to the time range of change of angle-of-attack (alpha dot). The analytical models are plotted and compared with their corresponding wind-tunnel data. Piloted simulated maneuvers of the wind-tunnel model are used to evaluate the analytical model. The maneuvers considered are pitch-ups, 360 degree loaded and unloaded rolls, turn reversals, split S's, and level turns. The evaluation finds that (1) the analytical model is a good representation at Mach 0.6, (2) the longitudinal part is good for the Mach range 0.3 to 0.9, and (3) the lateral part is good for Mach numbers between 0.6 and 0.9. The computer simulations show that the storage requirement of the analytical model is about one tenth that of the wind-tunnel model and it runs twice as fast.
A physically based analytical spatial air temperature and humidity model
NASA Astrophysics Data System (ADS)
Yang, Yang; Endreny, Theodore A.; Nowak, David J.
2013-09-01
Spatial variation of urban surface air temperature and humidity influences human thermal comfort, the settling rate of atmospheric pollutants, and plant physiology and growth. Given the lack of observations, we developed a Physically based Analytical Spatial Air Temperature and Humidity (PASATH) model. The PASATH model calculates spatial solar radiation and heat storage based on semiempirical functions and generates spatially distributed estimates based on inputs of topography, land cover, and the weather data measured at a reference site. The model assumes that for all grids under the same mesoscale climate, grid air temperature and humidity are modified by local variation in absorbed solar radiation and the partitioning of sensible and latent heat. The model uses a reference grid site for time series meteorological data and the air temperature and humidity of any other grid can be obtained by solving the heat flux network equations. PASATH was coupled with the USDA iTree-Hydro water balance model to obtain evapotranspiration terms and run from 20 to 29 August 2010 at a 360 m by 360 m grid scale and hourly time step across a 285 km2 watershed including the urban area of Syracuse, NY. PASATH predictions were tested at nine urban weather stations representing variability in urban topography and land cover. The PASATH model predictive efficiency R2 ranged from 0.81 to 0.99 for air temperature and 0.77 to 0.97 for dew point temperature. PASATH is expected to have broad applications on environmental and ecological models.
An analytically tractable model for community ecology with many species
NASA Astrophysics Data System (ADS)
Dickens, Benjamin; Fisher, Charles; Mehta, Pankaj; Pankaj Mehta Biophysics Theory Group Team
A fundamental problem in community ecology is to understand how ecological processes such as selection, drift, and immigration yield observed patterns in species composition and diversity. Here, we present an analytically tractable, presence-absence (PA) model for community assembly and use it to ask how ecological traits such as the strength of competition, diversity in competition, and stochasticity affect species composition in a community. In our PA model, we treat species as stochastic binary variables that can either be present or absent in a community: species can immigrate into the community from a regional species pool and can go extinct due to competition and stochasticity. Despite its simplicity, the PA model reproduces the qualitative features of more complicated models of community assembly. In agreement with recent work on large, competitive Lotka-Volterra systems, the PA model exhibits distinct ecological behaviors organized around a special (``critical'') point corresponding to Hubbell's neutral theory of biodiversity. Our results suggest that the concepts of ``phases'' and phase diagrams can provide a powerful framework for thinking about community ecology and that the PA model captures the essential ecological dynamics of community assembly. Pm was supported by a Simons Investigator in the Mathematical Modeling of Living Systems and a Sloan Research Fellowship.
Stochastic analytical modeling of the biodegradation of steady plumes
NASA Astrophysics Data System (ADS)
Zarlenga, A.; Fiori, A.
2014-02-01
We present a stochastic analytical framework to assess the contaminant concentration of a steady plume undergoing biodegradation. The method is focused on heterogeneous formations, and it embeds both fringe and core degradation. The Lagrangian concentration approach of Fiori (2001) was employed, which is suited for describing the interplay between the large scale advection caused by heterogeneity and the local dispersion processes. The principal scope of the model is to provide a relatively simple tool for a quick assessment of the contamination level in aquifers, as function of a few relevant, physically based dimensionless parameters. The solution of the analytical model is relatively simple and generalizes previous approaches developed for homogeneous formations. It is found that heterogeneity generally enhances mixing and degradation; in fact, the plume shear and distortion operated by the complex, heterogeneous velocity field facilitates local dispersion in diluting the contaminant and mixing it with the electron acceptor. The decay of the electron donor concentration, and so the plume length, is proportional to the transverse pore-scale dispersivity, which is indeed the parameter ruling mixing and hence degradation. While the theoretical plume length is controlled by the fringe processes, the core degradation may determine a significant decay of concentration along the mean flow direction, thus affecting the length of the plume. The method is applied to the crude oil contamination event at the Bemijdi site, Minnesota (USA).
Validated Analytical Model of a Pressure Compensation Drip Irrigation Emitter
NASA Astrophysics Data System (ADS)
Shamshery, Pulkit; Wang, Ruo-Qian; Taylor, Katherine; Tran, Davis; Winter, Amos
2015-11-01
This work is focused on analytically characterizing the behavior of pressure-compensating drip emitters in order to design low-cost, low-power irrigation solutions appropriate for off-grid communities in developing countries. There are 2.5 billion small acreage farmers worldwide who rely solely on their land for sustenance. Drip, compared to flood, irrigation leads to up to 70% reduction in water consumption while increasing yields by 90% - important in countries like India which are quickly running out of water. To design a low-power drip system, there is a need to decrease the pumping pressure requirement at the emitters, as pumping power is the product of pressure and flow rate. To efficiently design such an emitter, the relationship between the fluid-structure interactions that occur in an emitter need to be understood. In this study, a 2D analytical model that captures the behavior of a common drip emitter was developed and validated through experiments. The effects of independently changing the channel depth, channel width, channel length and land height on the performance were studied. The model and the key parametric insights presented have the potential to be optimized in order to guide the design of low-pressure, clog-resistant, pressure-compensating emitters.
A Three Level Analytic Model for Alkali Vapor Lasers
Hager, Gordon D.; Perram, Glen P.
2010-10-08
A three level analytic model for optically pumped alkali metal vapor lasers is developed considering the steady-state rate equations for the longitudinally averaged number densities of the ground {sup 2}S{sub 1/2} and first excited {sup 2}P{sub 1/2} and {sup 2}P{sub 3/2} states. The threshold pump intensity includes both the requirements to fully bleach the pump transition and exceed optical losses, typically about 200 W/cm{sup 2}. Slope efficiency depends critically on the fraction of incident photons absorbed and the overlap of pump and resonator modes, approaching the quantum efficiency of 0.95-0.98, depending on alkali atom. For efficient operation, the collisional relaxation between the two upper levels should be fast relative to stimulated emission. By assuming a statistical distribution between the upper levels, the limiting analytic solution for the quasi-two level system is achieved. Application of the model and comparisons to recent laser demonstrations is presented.
Characterization of uniform scanning proton beams with analytical models
NASA Astrophysics Data System (ADS)
Demez, Nebi
Tissue equivalent phantoms have an important place in radiation therapy planning and delivery. They have been manufactured for use in conventional radiotherapy. Their tissue equivalency for proton beams is currently in active investigation. The Bragg-Kleeman rule was used to calculate water equivalent thickness (WET) for available tissue equivalent phantoms from CIRS (Norfolk, VA, USA). WET's of those phantoms were also measured using proton beams at Hampton University Proton Therapy Institute (HUPTI). WET measurements and calculations are in good agreement within ˜1% accuracy except for high Z phantoms. Proton beams were also characterized with an analytical proton dose calculation model, Proton Loss Model (PLM) [26], to investigate protons interactions in water and those phantoms. Depth-dose and lateral dose profiles of protons in water and in those phantoms were calculated, measured, and compared. Water Equivalent Spreadness (WES) was also investigated for those phantoms using the formula for scattering power ratio. Because WES is independent of incident energy of protons, it is possible to estimate spreadness of protons in different media by just knowing WES. Measurements are usually taken for configuration of the treatment planning system (TPS). This study attempted to achieve commissioning data for uniform scanning proton planning with analytical methods, PLM, which have been verified with published measurements and Monte Carlo calculations. Depth doses and lateral profiles calculated by PLM were compared with measurements via the gamma analysis method. While gamma analysis shows that depth doses are in >90% agreement with measured depth doses, the agreement falls to <80% for some lateral profiles. PLM data were imported into the TPS (PLM-TPS). PLM-TPS was tested with different patient cases. The PLM-TPS treatment plans for 5 prostate cases show acceptable agreement. The Planning Treatment Volume (PTV) coverage was 100 % with PLM-TPS except for one case in
Strong field coherent control of molecular torsions—Analytical models
Ashwell, Benjamin A.; Ramakrishna, S.; Seideman, Tamar
2015-08-14
We introduce analytical models of torsional alignment by moderately intense laser pulses that are applicable to the limiting cases of the torsional barrier heights. Using these models, we explore in detail the role that the laser intensity and pulse duration play in coherent torsional dynamics, addressing both experimental and theoretical concerns. Our results suggest strategies for minimizing the risk of off-resonant ionization, noting the qualitative differences between the case of torsional alignment subject to a field-free torsional barrier and that of torsional alignment of a barrier-less system (equivalent to a 2D rigid rotor). We also investigate several interesting torsional phenomena, including the onset of impulsive alignment of torsions, field-driven oscillations in quantum number space, and the disappearance of an alignment upper bound observed for a rigid rotor in the impulsive torsional alignment limit.
Streaming instability of slime mold amoebae: An analytical model
NASA Astrophysics Data System (ADS)
Höfer, Thomas; Maini, Philip K.
1997-08-01
During the aggregation of amoebae of the cellular slime mould Dictyostelium, the interaction of chemical waves of the signaling molecule cAMP with cAMP-directed cell movement causes the breakup of a uniform cell layer into branching patterns of cell streams. Recent numerical and experimental investigations emphasize the pivotal role of the cell-density dependence of the chemical wave speed for the occurrence of the streaming instability. A simple, analytically tractable, model of Dictyostelium aggregation is developed to test this idea. The interaction of cAMP waves with cAMP-directed cell movement is studied in the form of coupled dynamics of wave front geometries and cell density. Comparing the resulting explicit instability criterion and dispersion relation for cell streaming with the previous findings of model simulations and numerical stability analyses, a unifying interpretation of the streaming instability as a cAMP wave-driven chemotactic instability is proposed.
Modeling superhelical DNA: recent analytical and dynamic approaches.
Schlick, T
1995-04-01
During the past year, a variety of diverse and complementary approaches have been presented for modeling superhelical DNA, offering new physical and biological insights into fundamental functional processes of DNA. Analytical approaches have probed deeper into the effects of entropy and thermal fluctuations on DNA structure and on various topological constraints induced by DNA-binding proteins. In tandem, new kinetic approaches--by molecular, Langevin and Brownian dynamics, as well as extensions of elastic-rod theory--have begun to offer dynamic information associated with supercoiling. Such dynamic approaches, along with other equilibrium studies, are refining the basic elastic-rod and polymer framework and incorporating more realistic treatments of salt and sequence-specific features. These collective advances in modeling large DNA molecules, in concert with technological innovations, are pointing to an exciting interplay between theory and experiment on the horizon. PMID:7648328
Strong field coherent control of molecular torsions--Analytical models.
Ashwell, Benjamin A; Ramakrishna, S; Seideman, Tamar
2015-08-14
We introduce analytical models of torsional alignment by moderately intense laser pulses that are applicable to the limiting cases of the torsional barrier heights. Using these models, we explore in detail the role that the laser intensity and pulse duration play in coherent torsional dynamics, addressing both experimental and theoretical concerns. Our results suggest strategies for minimizing the risk of off-resonant ionization, noting the qualitative differences between the case of torsional alignment subject to a field-free torsional barrier and that of torsional alignment of a barrier-less system (equivalent to a 2D rigid rotor). We also investigate several interesting torsional phenomena, including the onset of impulsive alignment of torsions, field-driven oscillations in quantum number space, and the disappearance of an alignment upper bound observed for a rigid rotor in the impulsive torsional alignment limit. PMID:26277138
Model for analytical calculation of nuclear photoabsorption at intermediate energies
NASA Astrophysics Data System (ADS)
Hütt, M.-Th.; Milstein, A. I.; Schumacher, M.
1997-02-01
The universal curve {σ}/{A} of nuclear photoabsorption is investigated within a Fermi gas model of nuclear matter. An energy range from pion threshold up to 400 MeV is considered. The interactions between nucleon, pion, Δ-isobar and photon are considered in the non-relativistic approximation with corrections of the order {1}/{M} taken into account with respect to proton mass. Analytical expressions are obtained, in which the influence of nuclear correlations and two-nucleon contributions is studied explicitly. The contributions of real and virtual pions are found to be sufficient to obtain agreement with experimental data in this energy range. An extension of the model calculation to nucleon knock-out reactions is discussed.
Analytical modeling requirements for tilting proprotor aircraft dynamics
NASA Technical Reports Server (NTRS)
Johnson, W.
1975-01-01
Proprotor and cantilever wing aeroelastic behavior is applied to a gimballed rotor and a hingeless rotor to develop an analytical model for prediction of tilting proprotor aircraft dynamics. Particular attention is given to: the influence of coupled flap/lag bending modes; the influence of rotor blade torsion degrees of freedom on proprotor dynamics; and, to a constant coefficient approximation representing the dynamics in nonaxial flow through the rotor. The following are also examined: the number of blade bending and torsion modes required; the influence of the rotor aerodynamic model; the influence of the blade trim bending deflection; the importance of the rotor rotational speed degree of freedom; and the effect of the wing aerodynamic forces. The origin of the significant influence of the blade pitch motion on the proprotor dynamics is discussed.
Analytical model for macromolecular partitioning during yeast cell division
2014-01-01
Background Asymmetric cell division, whereby a parent cell generates two sibling cells with unequal content and thereby distinct fates, is central to cell differentiation, organism development and ageing. Unequal partitioning of the macromolecular content of the parent cell — which includes proteins, DNA, RNA, large proteinaceous assemblies and organelles — can be achieved by both passive (e.g. diffusion, localized retention sites) and active (e.g. motor-driven transport) processes operating in the presence of external polarity cues, internal asymmetries, spontaneous symmetry breaking, or stochastic effects. However, the quantitative contribution of different processes to the partitioning of macromolecular content is difficult to evaluate. Results Here we developed an analytical model that allows rapid quantitative assessment of partitioning as a function of various parameters in the budding yeast Saccharomyces cerevisiae. This model exposes quantitative degeneracies among the physical parameters that govern macromolecular partitioning, and reveals regions of the solution space where diffusion is sufficient to drive asymmetric partitioning and regions where asymmetric partitioning can only be achieved through additional processes such as motor-driven transport. Application of the model to different macromolecular assemblies suggests that partitioning of protein aggregates and episomes, but not prions, is diffusion-limited in yeast, consistent with previous reports. Conclusions In contrast to computationally intensive stochastic simulations of particular scenarios, our analytical model provides an efficient and comprehensive overview of partitioning as a function of global and macromolecule-specific parameters. Identification of quantitative degeneracies among these parameters highlights the importance of their careful measurement for a given macromolecular species in order to understand the dominant processes responsible for its observed partitioning. PMID
Analytically tractable model for community ecology with many species.
Dickens, Benjamin; Fisher, Charles K; Mehta, Pankaj
2016-08-01
A fundamental problem in community ecology is understanding how ecological processes such as selection, drift, and immigration give rise to observed patterns in species composition and diversity. Here, we analyze a recently introduced, analytically tractable, presence-absence (PA) model for community assembly, and we use it to ask how ecological traits such as the strength of competition, the amount of diversity, and demographic and environmental stochasticity affect species composition in a community. In the PA model, species are treated as stochastic binary variables that can either be present or absent in a community: species can immigrate into the community from a regional species pool and can go extinct due to competition and stochasticity. Building upon previous work, we show that, despite its simplicity, the PA model reproduces the qualitative features of more complicated models of community assembly. In agreement with recent studies of large, competitive Lotka-Volterra systems, the PA model exhibits distinct ecological behaviors organized around a special ("critical") point corresponding to Hubbell's neutral theory of biodiversity. These results suggest that the concepts of ecological "phases" and phase diagrams can provide a powerful framework for thinking about community ecology, and that the PA model captures the essential ecological dynamics of community assembly. PMID:27627348
A macroscopic analytical model of collaboration in distributed robotic systems.
Lerman, K; Galstyan, A; Martinoli, A; Ijspeert, A
2001-01-01
In this article, we present a macroscopic analytical model of collaboration in a group of reactive robots. The model consists of a series of coupled differential equations that describe the dynamics of group behavior. After presenting the general model, we analyze in detail a case study of collaboration, the stick-pulling experiment, studied experimentally and in simulation by Ijspeert et al. [Autonomous Robots, 11, 149-171]. The robots' task is to pull sticks out of their holes, and it can be successfully achieved only through the collaboration of two robots. There is no explicit communication or coordination between the robots. Unlike microscopic simulations (sensor-based or using a probabilistic numerical model), in which computational time scales with the robot group size, the macroscopic model is computationally efficient, because its solutions are independent of robot group size. Analysis reproduces several qualitative conclusions of Ijspeert et al.: namely, the different dynamical regimes for different values of the ratio of robots to sticks, the existence of optimal control parameters that maximize system performance as a function of group size, and the transition from superlinear to sublinear performance as the number of robots is increased. PMID:11911788
A semi-analytic dynamical friction model for cored galaxies
NASA Astrophysics Data System (ADS)
Petts, J. A.; Read, J. I.; Gualandris, A.
2016-08-01
We present a dynamical friction model based on Chandrasekhar's formula that reproduces the fast inspiral and stalling experienced by satellites orbiting galaxies with a large constant density core. We show that the fast inspiral phase does not owe to resonance. Rather, it owes to the background velocity distribution function for the constant density core being dissimilar from the usually-assumed Maxwellian distribution. Using the correct background velocity distribution function and the semi-analytic model from Petts et al. (2015), we are able to correctly reproduce the infall rate in both cored and cusped potentials. However, in the case of large cores, our model is no longer able to correctly capture core-stalling. We show that this stalling owes to the tidal radius of the satellite approaching the size of the core. By switching off dynamical friction when rt(r) = r (where rt is the tidal radius at the satellite's position) we arrive at a model which reproduces the N-body results remarkably well. Since the tidal radius can be very large for constant density background distributions, our model recovers the result that stalling can occur for Ms/Menc ≪ 1, where Ms and Menc are the mass of the satellite and the enclosed galaxy mass, respectively. Finally, we include the contribution to dynamical friction that comes from stars moving faster than the satellite. This next-to-leading order effect becomes the dominant driver of inspiral near the core region, prior to stalling.
Analytical Modeling of Variable Density Multilayer Insulation for Cryogenic Storage
NASA Technical Reports Server (NTRS)
Hedayat, A.; Hastings, L. J.; Brown, T.; Cruit, Wendy (Technical Monitor)
2001-01-01
A unique foam/Multilayer Insulation (MLI) combination concept for orbital cryogenic storage was experimentally evaluated at NASA Marshall Space Flight Center (MSFC) using the Multipurpose Hydrogen Test Bed (MHTB). The MLI was designed for an on-orbit storage period of 45 days and included several unique features such as: a variable layer density and larger but fewer perforations for venting during ascent to orbit. Test results with liquid hydrogen indicated that the MLI weight or heat leak is reduced by about half in comparison with standard MLI. The focus of this paper is on analytical modeling of the Variable Density MLI (VD-MLI) on-orbit performance (i.e. vacuum/low pressure environment). The foam/VD-MLI combination model is considered to have five segments. The first segment represents the optional foam layer. The second, third, and fourth segments represent three MLI segments with different layer densities. The last segment is considered to be a shroud that surrounds the last MLI layer. Two approaches are considered. In the first approach, the variable density MLI is modeled layer by layer while in the second approach, a semi-empirical model is applied. Both models account for thermal radiation between shields, gas conduction, and solid conduction through the layer separator materials.
Fuzzy modeling of analytical redundancy for sensor failure detection
Tsai, T.M.; Chou, H.P. )
1991-01-01
Failure detection and isolation (FDI) in dynamic systems may be accomplished by testing the consistency of the system via analytically redundant relations. The redundant relation is basically a mathematical model relating system inputs and dissimilar sensor outputs from which information is extracted and subsequently examined for the presence of failure signatures. Performance of the approach is often jeopardized by inherent modeling error and noise interference. To mitigate such effects, techniques such as Kalman filtering, auto-regression-moving-average (ARMA) modeling in conjunction with probability tests are often employed. These conventional techniques treat the stochastic nature of uncertainties in a deterministic manner to generate best-estimated model and sensor outputs by minimizing uncertainties. In this paper, the authors present a different approach by treating the effect of uncertainties with fuzzy numbers. Coefficients in redundant relations derived from first-principle physical models are considered as fuzzy parameters and on-line updated according to system behaviors. Failure detection is accomplished by examining the possibility that a sensor signal occurred in an estimated fuzzy domain. To facilitate failure isolation, individual FDI monitors are designed for each interested sensor.
Star formation in Herschel's Monsters versus semi-analytic models
NASA Astrophysics Data System (ADS)
Gruppioni, C.; Calura, F.; Pozzi, F.; Delvecchio, I.; Berta, S.; De Lucia, G.; Fontanot, F.; Franceschini, A.; Marchetti, L.; Menci, N.; Monaco, P.; Vaccari, M.
2015-08-01
We present a direct comparison between the observed star formation rate functions (SFRFs) and the state-of-the-art predictions of semi-analytic models (SAMs) of galaxy formation and evolution. We use the PACS Evolutionary Probe Survey and Herschel Multi-tiered Extragalactic Survey data sets in the COSMOS and GOODS-South fields, combined with broad-band photometry from UV to sub-mm, to obtain total (IR+UV) instantaneous star formation rates (SFRs) for individual Herschel galaxies up to z ˜ 4, subtracted of possible active galactic nucleus (AGN) contamination. The comparison with model predictions shows that SAMs broadly reproduce the observed SFRFs up to z ˜ 2, when the observational errors on the SFR are taken into account. However, all the models seem to underpredict the bright end of the SFRF at z ≳ 2. The cause of this underprediction could lie in an improper modelling of several model ingredients, like too strong (AGN or stellar) feedback in the brighter objects or too low fallback of gas, caused by weak feedback and outflows at earlier epochs.
Model choice considerations and information integration using analytical hierarchy process
Langenbrunner, James R; Hemez, Francois M; Booker, Jane M; Ross, Timothy J.
2010-10-15
Using the theory of information-gap for decision-making under severe uncertainty, it has been shown that model output compared to experimental data contains irrevocable trade-offs between fidelity-to-data, robustness-to-uncertainty and confidence-in-prediction. We illustrate a strategy for information integration by gathering and aggregating all available data, knowledge, theory, experience, similar applications. Such integration of information becomes important when the physics is difficult to model, when observational data are sparse or difficult to measure, or both. To aggregate the available information, we take an inference perspective. Models are not rejected, nor wasted, but can be integrated into a final result. We show an example of information integration using Saaty's Analytic Hierarchy Process (AHP), integrating theory, simulation output and experimental data. We used expert elicitation to determine weights for two models and two experimental data sets, by forming pair-wise comparisons between model output and experimental data. In this way we transform epistemic and/or statistical strength from one field of study into another branch of physical application. The price to pay for utilizing all available knowledge is that inferences drawn for the integrated information must be accounted for and the costs can be considerable. Focusing on inferences and inference uncertainty (IU) is one way to understand complex information.
Analytical model of diffuse reflectance spectrum of skin tissue
Lisenko, S A; Kugeiko, M M; Firago, V A; Sobchuk, A N
2014-01-31
We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions. (biophotonics)
Analytical Perturbative Treatment of Multiterminal Nonequilibrium Anderson Impurity Models
NASA Astrophysics Data System (ADS)
Taniguchi, Nobuhiko
2015-03-01
We investigate analytically the nonequilibrium Anderson impurity model connecting with multiterminal leads. Within the validity of the second-order perturbation regarding the interaction strength, the full dependence on frequency and bias voltage of the nonequilibrium self-energy and spectral function is determined for a generic multiterminal setting where the current preservation has been an issue. Our analytical perturbative treatment respects the current conservation as well as the spectral sum rule, and it encompasses Fermi-liquid and non-Fermi liquid behaviors, showing that increasing finite-bias voltage leads to a crossover from the Kondo resonance to the Coulomb blockade phenomena. Analysis on two-terminal and multiterminal settings shows that finite-bias voltage does not split the Kondo resonance in this order; no specific structure due to multiple leads emerges in the spectral function. Overall bias dependence is quite similar to finite-temperature effect, which could be understood by help of the Ward identity and the limit of N >> 1 terminals. Grant-in-Aid for Scientific Research (No. 26400382, MEXT, Japan).
Analytical model of diffuse reflectance spectrum of skin tissue
NASA Astrophysics Data System (ADS)
Lisenko, S. A.; Kugeiko, M. M.; Firago, V. A.; Sobchuk, A. N.
2014-01-01
We have derived simple analytical expressions that enable highly accurate calculation of diffusely reflected light signals of skin in the spectral range from 450 to 800 nm at a distance from the region of delivery of exciting radiation. The expressions, taking into account the dependence of the detected signals on the refractive index, transport scattering coefficient, absorption coefficient and anisotropy factor of the medium, have been obtained in the approximation of a two-layer medium model (epidermis and dermis) for the same parameters of light scattering but different absorption coefficients of layers. Numerical experiments on the retrieval of the skin biophysical parameters from the diffuse reflectance spectra simulated by the Monte Carlo method show that commercially available fibre-optic spectrophotometers with a fixed distance between the radiation source and detector can reliably determine the concentration of bilirubin, oxy- and deoxyhaemoglobin in the dermis tissues and the tissue structure parameter characterising the size of its effective scatterers. We present the examples of quantitative analysis of the experimental data, confirming the correctness of estimates of biophysical parameters of skin using the obtained analytical expressions.
Analytical Modeling of Shale Hydraulic Fracturing and Gas Production
NASA Astrophysics Data System (ADS)
Xu, W.
2012-12-01
Shale gas is abundant all over the world. Due to its extremely low permeability, extensive stimulation of a shale reservoir is always required for its economic production. Hydraulic fracturing has been the primary method of shale reservoir stimulation. Consequently the design and optimization of a hydraulic fracturing treatment plays a vital role insuring job success and economic production. Due to the many variables involved and the lack of a simple yet robust tool based on fundamental physics, horizontal well placement and fracturing job designs have to certain degree been a guessing game built on previous trial and error experience. This paper presents a method for hydraulic fracturing design and optimization in these environments. The growth of a complex hydraulic fracture network (HFN) during a fracturing job is equivalently represented by a wiremesh fracturing model (WFM) constructed on the basis of fracture mechanics and mass balance. The model also simulates proppant transport and placement during HFN growth. Results of WFM simulations can then be used as the input into a wiremesh production model (WPM) constructed based on WFM. WPM represents gas flow through the wiremesh HFN by an elliptic flow and the flow of gas in shale matrix by a novel analytical solution accounting for contributions from both free and adsorbed gases stored in the pore space. WPM simulation is validated by testing against numerical simulations using a commercially available reservoir production simulator. Due to the analytical nature of WFM and WPM, both hydraulic fracturing and gas production simulations run very fast on a regular personal computer and are suitable for hydraulic fracturing job design and optimization. A case study is presented to demonstrate how a non-optimized hydraulic fracturing job might have been optimized using WFM and WPM simulations.Fig. 1. Ellipsoidal representation of (a) stimulated reservoir and (b) hydraulic fracture network created by hydraulic
Hydrogeologic role of geologic structures. Part 2: analytical models
NASA Astrophysics Data System (ADS)
Levens, Russell L.; Williams, Roy E.; Ralston, Dale R.
1994-04-01
This paper is the second of two papers that address the influence of geologic structures on ground water flow at various scales in fractured rocks. The ultimate purpose of this research is to investigate the feasibility of grouting preferentially permeable zones as a strategy to minimize the production of acid mine drainage in underground hard rock mines in which the major permeability is structure and fracture controlled. The aim of grouting is to reduce permeability around mined-out openings, to minimize the rate of inflow of ground water into such openings via the structurally controlled preferentially permeable pathways. A series of hydraulic stress tests were conducted to help characterize the role of geologic structures in controlling the ground water flow system in the vicinity of the Bunker Hill Mine in north Idaho. The results of these tests indicate that most of the ground water that flows from the underground drillholes used for hydraulic stress testing is derived from a few discrete, structurally produced fracture zones that are more or less connected through smaller-scale fractures. Four types of analytical models are considered as a means of analyzing the results of multiple drillhole hydraulic stress tests, as follows: cross-hole equivalent porous media; double-porosity equivalent porous media; a solution to flow in and around a single vertical fracture; leaky equivalent porous media, partial penetration. The estimation of hydraulic coefficients in complex fractured rock environments involves the combined application of a number of deterministic analytical models. The models to be used are selected dependent on the location of the drawdown observations relative to the water-producing zone and the length of the test. The result of the tests can be related to the permeability hierarchy discussed in our first paper.
Analytic model and frequency characteristics of plasma synthetic jet actuator
NASA Astrophysics Data System (ADS)
Zong, Hao-hua; Wu, Yun; Li, Ying-hong; Song, Hui-min; Zhang, Zhi-bo; Jia, Min
2015-02-01
This paper reports a novel analytic model of a plasma synthetic jet actuator (PSJA), considering both the heat transfer effect and the inertia of the throat gas. Both the whole cycle characteristics and the repetitive working process of PSJA can be predicted with this model. The frequency characteristics of a PSJA with 87 mm3 volume and different orifice diameters are investigated based on the analytic model combined with experiments. In the repetitive working mode, the actuator works initially in the transitional stage with 20 cycles and then in the dynamic balanced stage. During the transitional stage, major performance parameters of PSJA experience stepped growth, while during the dynamic balanced stage, these parameters are characterized by periodic variation. With a constant discharge energy of 6.9 mJ, there exists a saturated frequency of 4 kHz/6 kHz for an orifice diameter of 1 mm/1.5 mm, at which the time-averaged total pressure of the pulsed jet reaches a maximum. Between 0.5 mm and 1.5 mm, a larger orifice diameter leads to a higher saturated frequency due to the reduced jet duration time. As the actuation frequency increases, both the time-averaged cavity temperature and the peak jet velocity initially increase and then remain almost unchanged at 1600 K and 280 m/s, respectively. Besides, with increasing frequency, the mechanical energy incorporated in single pulsed jet, the expelled mass per pulse, and the time-averaged density in the cavity, decline in a stair stepping way, which is caused by the intermittent decrease of refresh stage duration in one period.
Analytic model for coaxial helicity injection in tokamak plasmas
Weening, R. H.
2011-12-15
Using a partial differential equation for the time evolution of the mean-field poloidal magnetic flux that incorporates resistivity {eta} and hyper-resistivity {Lambda} terms, an exact analytic solution is obtained for steady-state coaxial helicity injection (CHI) in force-free large aspect ratio tokamaks. The analytic mean-field Ohm's law model allows for calculation of the tokamak CHI current drive efficiency and the plasma inductances at arbitrary levels of magnetic fluctuations, or dynamo activity. The results of the mean-field model suggest that CHI approaching Ohmic efficiency is only possible in tokamaks when the size of the effective current drive boundary layer, {delta}{identical_to}({Lambda}/{eta}){sup 1/2}, becomes greater than half the size of the plasma, {delta}>a/2, with a the plasma minor radius. The electron thermal diffusivity due to magnetic fluctuation induced transport is obtained from the expression {chi}{sub e}={Lambda}/{mu}{sub 0}d{sub e}{sup 2}, with {mu}{sub 0} the permeability of free space and d{sub e} the electron skin depth, which for typical tokamak fusion plasma parameters is on the order of a millimeter. Thus, the ratio of the energy confinement time to the resistive diffusion time in a tokamak plasma driven by steady-state CHI approaching Ohmic efficiency is shown to be constrained by the relation {tau}{sub E}/{tau}{sub {eta}}<(d{sub e}/a){sup 2}{approx_equal}10{sup -6}. The mean-field model suggests that steady-state CHI can be viewed most simply as a boundary layer of stochastically wandering magnetic field lines.
Analytic model for the bispectrum of galaxies in redshift space
Smith, Robert E.; Sheth, Ravi K.; Scoccimarro, Roman
2008-07-15
We develop an analytic theory for the redshift space bispectrum of dark matter, haloes, and galaxies. This is done within the context of the halo model of structure formation, as this allows for the self-consistent inclusion of linear and nonlinear redshift-space distortions and also for the nonlinearity of the halo bias. The model is applicable over a wide range of scales: on the largest scales the predictions reduce to those of the standard perturbation theory (PT); on smaller scales they are determined primarily by the nonlinear virial velocities of galaxies within haloes, and this gives rise to the U-shaped anisotropy in the reduced bispectrum--a finger print of the Finger-Of-God distortions. We then confront the predictions with measurements of the redshift-space bispectrum of dark matter from an ensemble of numerical simulations. On very large scales, k=0.05h Mpc{sup -1}, we find reasonably good agreement between our halo model, PT and the data, to within the errors. On smaller scales, k=0.1h Mpc{sup -1}, the measured bispectra differ from the PT at the level of {approx}10%-20%, especially for colinear triangle configurations. The halo model predictions improve over PT, but are accurate to no better than 10%. On smaller scales k=0.5-1.0h Mpc{sup -1}, our model provides a significant improvement over PT, which breaks down. This implies that studies which use the lowest order PT to extract galaxy bias information are not robust on scales k > or approx. 0.1h Mpc{sup -1}. The analytic and simulation results also indicate that there is no observable scale for which the configuration dependence of the reduced bispectrum is constant--hierarchical models for the higher-order correlation functions in redshift space are unlikely to be useful. It is hoped that our model will facilitate extraction of information from large-scale structure surveys of the Universe, because different galaxy populations are naturally included into our description.
BLEDNYKH, A.; WANG, J.M.
2005-05-15
The vertical impedances of the preliminary designs of National Synchrotron Light Source II (NSLS-II) Mini Gap Undulators (MGU) are calculated by means of GdfidL code. The Transverse Mode Coupling Instability (TMCI) thresholds corresponding to these impedances are estimated using an analytically solvable model.
Numerical-analytical modeling of the Earth's pole oscillations
NASA Astrophysics Data System (ADS)
Markov, Y.; Filippova, A.
2015-08-01
For the purpose of more accurate forecasting the oscillatory process of the Earth pole in time periods with significant anomalies (irregular deviations) a numerical-analytical approach is presented for the combined modeling of the interdependent dynamical processes - the oscillatory-rotational motion of the Earth and the time dependent coefficients of the geopotential. The oscillations of the inertia tensor components of the Earth depend on various factors such as mechanical and physical parameters of the planet, the motions of the tide-generating bodies and observed large scale natural events. Time variations of these and some other factors affect the Earth orientation parameters. The generalization of the previously researched mathematical model of Chandler and annual oscillations of the Earth pole is being held with the use of celestial mechanics methods and the mathematical description of the Earth gravitational field's temporal variations. The latter makes possible to improve the forecast precision of the Earth pole trajectory. Also the more precise model is to have small number of parameters and to agree with the previously developed one (to have the same structural features and to have a correspondence between the averaged dynamical parameters and the parameters of the basic model).
Analytical model for CO(2) laser ablation of fused quartz.
Nowak, Krzysztof M; Baker, Howard J; Hall, Denis R
2015-10-10
This paper reports the development of an analytical model, with supporting experimental data, which quite accurately describes the key features of CO_{2} laser ablation of fused silica glass. The quantitative model of nonexplosive, evaporative material removal is shown to match the experimental data very well, to the extent that it can be used as a tool for ablative measurements of absorption coefficient and vaporization energy. The experimental results indicated that a minimum of 12 MJ kg^{-1} is required to fully vaporize fused quartz initially held at room temperature, which is in good agreement with the prediction of the model supplied with input data available in the literature. An optimal window for the machining of fused quartz was revealed in terms of pulse duration 20-80 μs and CO_{2} laser wavelength optimized for maximum absorption coefficient. Material removal rates of 0.33 μm per J cm^{-2} allow for a high-precision depth control with modest laser stability. The model may also be used as a parameter selection guide for CO_{2} laser ablation of fused silica or other materials of similar thermophysical properties. PMID:26479800
Analytical Modelling Of Milling For Tool Design And Selection
Fontaine, M.; Devillez, A.; Dudzinski, D.
2007-05-17
This paper presents an efficient analytical model which allows to simulate a large panel of milling operations. A geometrical description of common end mills and of their engagement in the workpiece material is proposed. The internal radius of the rounded part of the tool envelope is used to define the considered type of mill. The cutting edge position is described for a constant lead helix and for a constant local helix angle. A thermomechanical approach of oblique cutting is applied to predict forces acting on the tool and these results are compared with experimental data obtained from milling tests on a 42CrMo4 steel for three classical types of mills. The influence of some tool's geometrical parameters on predicted cutting forces is presented in order to propose optimisation criteria for design and selection of cutting tools.
Analytic model of aurorally coupled magnetospheric and ionospheric electrostatic potentials
NASA Astrophysics Data System (ADS)
Cornwall, John M.
1993-09-01
This paper describes modest but significant improvements on earlier studies of electrostatic potential structure in the auroral region, using the adiabatic auroral arc model. With certain simplifying assumptions, new analytic nonlinear solutions fully exhibiting the parametric dependence of potentials on magnetospheric (e.g., cross-tail potential) and ionospheric (e.g., recombination rate) parameters are found. No purely phenomenological parameters are introduced. The results are in reasonable agreement with observed average auroral potential drops, inverted-V scale sizes, and dissipation rates. The dissipation rate is quite comparable to tail energization and transport rates and should have a major effect on tail and magnetospheric dynamics. Various relations between the cross-tail potential and auroral parameters (e.g., total parallel currents and potential drops) are given which can be studied with existing data sets.
An analytical model of joule heating in piezoresistive microcantilevers.
Ansari, Mohd Zahid; Cho, Chongdu
2010-01-01
The present study investigates Joule heating in piezoresistive microcantilever sensors. Joule heating and thermal deflections are a major source of noise in such sensors. This work uses analytical and numerical techniques to characterise the Joule heating in 4-layer piezoresistive microcantilevers made of silicon and silicon dioxide substrates but with the same U-shaped silicon piezoresistor. A theoretical model for predicting the temperature generated due to Joule heating is developed. The commercial finite element software ANSYS Multiphysics was used to study the effect of electrical potential on temperature and deflection produced in the cantilevers. The effect of piezoresistor width on Joule heating is also studied. Results show that Joule heating strongly depends on the applied potential and width of piezoresistor and that a silicon substrate cantilever has better thermal characteristics than a silicon dioxide cantilever. PMID:22163433
An Analytical Model of Joule Heating in Piezoresistive Microcantilevers
Ansari, Mohd Zahid; Cho, Chongdu
2010-01-01
The present study investigates Joule heating in piezoresistive microcantilever sensors. Joule heating and thermal deflections are a major source of noise in such sensors. This work uses analytical and numerical techniques to characterise the Joule heating in 4-layer piezoresistive microcantilevers made of silicon and silicon dioxide substrates but with the same U-shaped silicon piezoresistor. A theoretical model for predicting the temperature generated due to Joule heating is developed. The commercial finite element software ANSYS Multiphysics was used to study the effect of electrical potential on temperature and deflection produced in the cantilevers. The effect of piezoresistor width on Joule heating is also studied. Results show that Joule heating strongly depends on the applied potential and width of piezoresistor and that a silicon substrate cantilever has better thermal characteristics than a silicon dioxide cantilever. PMID:22163433
Analytic model of aurorally coupled magnetospheric and ionospheric electrostatic potentials
NASA Technical Reports Server (NTRS)
Cornwall, John M.
1993-01-01
This paper describes modest but significant improvements on earlier studies of electrostatic potential structure in the auroral region, using the adiabatic auroral arc model. With certain simplifying assumptions, new analytic nonlinear solutions fully exhibiting the parametric dependence of potentials on magnetospheric (e.g., cross-tail potential) and ionospheric (e.g., recombination rate) parameters are found. No purely phenomenological parameters are introduced. The results are in reasonable agreement with observed average auroral potential drops, inverted-V scale sizes, and dissipation rates. The dissipation rate is quite comparable to tail energization and transport rates and should have a major effect on tail and magnetospheric dynamics. Various relations between the cross-tail potential and auroral parameters (e.g., total parallel currents and potential drops) are given which can be studied with existing data sets.
Analytical Deriving of the Field Capacity through Soil Bundle Model
NASA Astrophysics Data System (ADS)
Arnone, E.; Viola, F.; Antinoro, C.; Noto, L. V.
2015-12-01
The concept of field capacity as soil hydraulic parameter is widely used in many hydrological applications. Althought its recurring usage, its definition is not univocal. Traditionally, field capacity has been related to the amount of water that remains in the soil after the excess water has drained away and the water downward movement experiences a significant decresase. Quantifying the drainage of excess of water may be vague and several definitions, often subjective, have been proposed. These definitions are based on fixed thresholds either of time, pressure, or flux to which the field capacity condition is associated. The flux-based definition identifies the field capacity as the soil moisture value corresponding to an arbitrary fixed threshold of free drainage flux. Recently, many works have investigated the flux-based definition by varying either the drainage threshold, the geometry setting and mainly the description of the drainage flux. Most of these methods are based on the simulation of the flux through a porous medium by using the Darcy's law or Richard's equation. Using the above-mentioned flux-based definition, in this work we propose an alternative analytical approach for deriving the field capacity based on a bundle-of-tubes model. The pore space of a porous medium is conceptualized as a bundle of capillary tubes of given length of different radii, derived from a known distribution. The drainage from a single capillary tube is given by the analytical solution of the differential equation describing the water height evolution within the capillary tube. This equation is based on the Poiseuille's law and describes the drainage flux with time as a function of tube radius. The drainage process is then integrated for any portion of soil taking into account the tube radius distribution which in turns depends on the soil type. This methodology allows to analytically derive the dynamics of drainage water flux for any soil type and consequently to define the
An analytical phase-space model for tidal caustics
NASA Astrophysics Data System (ADS)
Sanderson, Robyn E.; Helmi, Amina
2013-10-01
The class of tidal features around galaxies known as `shells' or `umbrellas' comprises debris that has arisen from high-mass-ratio mergers with low-impact parameter; the nearly radial orbits of the debris give rise to a unique morphology, a universal density profile and a tight correlation between positions and velocities of the material. As such they are accessible to analytical treatment, and can provide a relatively clean system for probing the gravitational potential of the host galaxy. In this work, we present a simple analytical model that describes the density profile, phase-space distribution, and geometry of a shell and whose parameters are directly related to physical characteristics of the interacting galaxies. The model makes three assumptions: the orbit of the interacting galaxies is radial, the potential of the host galaxy at the shell radius is spherical and the satellite galaxy's initial velocity distribution is Maxwellian. We quantify the error introduced by the first two assumptions and show that selecting shells by their appearance on the sky is a sufficient basis to assume that these simplifications are valid. We further demonstrate that (1) given only an image of a shell, the radial gravitational force at the shell edge and the phase-space density of the satellite are jointly constrained, (2) combining the image with measurements of either point line-of-sight velocities or integrated-light spectra will yield an independent estimate of the gravitational force at a shell and (3) an independent measurement of this force is obtained for each shell observed around a given galaxy, potentially enabling a determination of the galactic mass distribution.
Distributed-Channel Bipolar Device: Experimentation, Analytical Modeling and Applications.
NASA Astrophysics Data System (ADS)
Jiang, Fenglai
Experimental results and theoretical modeling for four terminal distributed channel bipolar devices (DCBD) are presented. The DCBD device is comprised of an interwoven BJT and MOSFET. The device may be characterized as a MOSFET with a bipolar transistor source distributed under the MOSFET channel. Alternatively, the device may be represented as a BJT where a MOSFET channel provides the current collection function. The physical layout of the device is that of a n-channel MOSFET placed above a p-Si epitaxial base region which was grown on an n^+-Si substrate emitter. Distributed electronic behavior exhibits itself through self-biasing influences of the channel-collected current on the channel-base junction bias. For appropriate biasing, the MOSFET channel divides itself into two regions exhibiting forward active and saturation BJT behavior. Both experimental results and theoretical modeling are provided. Experimental results for "large area" rectangular gate, circular gate and trapezoidal gate DCBD are reported. The experimental results exhibit the transconductance threshold voltage, beta fall off and transconductance fall-off features reported previously by others. A "large area" trapezoidal gate structure is incorporated to illustrate the gate area influences on the electrical characteristics and to provide a model sensitive structure for evaluating the validity of the theory developed in the dissertation. An analytical model based on conventional MOSFET and bipolar theories is developed. The analytical model is applied to the large gate area devices (example: 0.127 mm rectangular gate length) and smaller dimensional gate devices down to 0.9 micron rectangular gate length. The theoretical results show good agreement with the large gate area experimental results. Application examples are provided. The use of the base current invariant transconductance threshold voltage as a reference voltage is discussed. Comparison of the transconductance threshold voltage
An analytically enriched finite element method for cohesive crack modeling.
Cox, James V.
2010-04-01
Meaningful computational investigations of many solid mechanics problems require accurate characterization of material behavior through failure. A recent approach to fracture modeling has combined the partition of unity finite element method (PUFEM) with cohesive zone models. Extension of the PUFEM to address crack propagation is often referred to as the extended finite element method (XFEM). In the PUFEM, the displacement field is enriched to improve the local approximation. Most XFEM studies have used simplified enrichment functions (e.g., generalized Heaviside functions) to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack. As such, the mesh had to be sufficiently fine for the FEM basis functions to capture these gradients.In this study enrichment functions based upon two analytical investigations of the cohesive crack problem are examined. These functions have the potential of representing displacement gradients in the vicinity of the cohesive crack with a relatively coarse mesh and allow the crack to incrementally advance across each element. Key aspects of the corresponding numerical formulation are summarized. Analysis results for simple model problems are presented to evaluate if quasi-static crack propagation can be accurately followed with the proposed formulation. A standard finite element solution with interface elements is used to provide the accurate reference solution, so the model problems are limited to a straight, mode I crack in plane stress. Except for the cohesive zone, the material model for the problems is homogenous, isotropic linear elasticity. The effects of mesh refinement, mesh orientation, and enrichment schemes that enrich a larger region around the cohesive crack are considered in the study. Propagation of the cohesive zone tip and crack tip, time variation of the cohesive zone length, and crack profiles are presented. The analysis
NASA Technical Reports Server (NTRS)
Groom, N. J.
1979-01-01
An analytical model of an Annular Momentum Control Device (AMCD) laboratory test model magnetic bearing actuator with permanent magnet fluxbiasing is presented. An AMCD consists of a spinning annular rim which is suspended by a noncontacting linear electromagnetic spin motor. The actuator is treated as a lumped-parameter electromechanical system in the development of the model.
Analytical thermal model validation for Cassini radioisotope thermoelectric generator
Lin, E.I.
1997-12-31
The Saturn-bound Cassini spacecraft is designed to rely, without precedent, on the waste heat from its three radioisotope thermoelectric generators (RTGs) to warm the propulsion module subsystem, and the RTG end dome temperature is a key determining factor of the amount of waste heat delivered. A previously validated SINDA thermal model of the RTG was the sole guide to understanding its complex thermal behavior, but displayed large discrepancies against some initial thermal development test data. A careful revalidation effort led to significant modifications and adjustments of the model, which result in a doubling of the radiative heat transfer from the heat source support assemblies to the end domes and bring up the end dome and flange temperature predictions to within 2 C of the pertinent test data. The increased inboard end dome temperature has a considerable impact on thermal control of the spacecraft central body. The validation process offers an example of physically-driven analytical model calibration with test data from not only an electrical simulator but also a nuclear-fueled flight unit, and has established the end dome temperatures of a flight RTG where no in-flight or ground-test data existed before.
Machine learning and cosmological simulations - I. Semi-analytical models
NASA Astrophysics Data System (ADS)
Kamdar, Harshil M.; Turk, Matthew J.; Brunner, Robert J.
2016-01-01
We present a new exploratory framework to model galaxy formation and evolution in a hierarchical Universe by using machine learning (ML). Our motivations are two-fold: (1) presenting a new, promising technique to study galaxy formation, and (2) quantitatively analysing the extent of the influence of dark matter halo properties on galaxies in the backdrop of semi-analytical models (SAMs). We use the influential Millennium Simulation and the corresponding Munich SAM to train and test various sophisticated ML algorithms (k-Nearest Neighbors, decision trees, random forests, and extremely randomized trees). By using only essential dark matter halo physical properties for haloes of M > 1012 M⊙ and a partial merger tree, our model predicts the hot gas mass, cold gas mass, bulge mass, total stellar mass, black hole mass and cooling radius at z = 0 for each central galaxy in a dark matter halo for the Millennium run. Our results provide a unique and powerful phenomenological framework to explore the galaxy-halo connection that is built upon SAMs and demonstrably place ML as a promising and a computationally efficient tool to study small-scale structure formation.
More on analytic bootstrap for O( N) models
NASA Astrophysics Data System (ADS)
Dey, Parijat; Kaviraj, Apratim; Sen, Kallol
2016-06-01
This note is an extension of a recent work on the analytical bootstrapping of O( N) models. An additonal feature of the O( N) model is that the OPE contains trace and antisymmetric operators apart from the symmetric-traceless objects appearing in the OPE of the singlet sector. This in addition to the stress tensor ( T μν ) and the ϕ i ϕ i scalar, we also have other minimal twist operators as the spin-1 current J μ and the symmetric-traceless scalar in the case of O( N). We determine the effect of these additional objects on the anomalous dimensions of the corresponding trace, symmetric-traceless and antisymmetric operators in the large spin sector of the O( N) model, in the limit when the spin is much larger than the twist. As an observation, we also verified that the leading order results for the large spin sector from the ɛ-expansion are an exact match with our n = 0 case. A plausible holographic setup for the special case when N = 2 is also mentioned which mimics the calculation in the CFT.
Computational and analytical modeling of eye refractive surgery
NASA Astrophysics Data System (ADS)
Cabrera, Delia
As the number of corneal refractive procedures increases annually, concerns about their long-term stability and predictability have become the center of attention in the ophthalmic community. This thesis focuses on developing quantitative biomechanical models of the cornea that will overcome shortcomings of previous models and incorporate new observations of corneal elastic properties. Our intent is to provide a more accurate model of the corneal structure to guide current and future developments. The second chapter shows that neural networks could rapidly prototype practical solutions to obtain a better estimate of the average corneal power using the contrast and image size parameters provided by the topographic systems. After establishing improved measurements of the corneal shape the thesis focuses on the development of various corneal models. The analytical model proposed shows that geometric optics, corneal structural properties and surgical nomograms could be used to gain a better understanding of corneal response to surgical interventions. The predictions of this model are closer to the values provided by the published nomograms and clinical data than that obtained by the traditional geometric model. Three surgical procedures (Ultrafast Laser-Automated Lamellar Keratomileusis, Corneal Transplant and Intrastromal Refractive Keratectomy) were simulated using the finite element method. A new formulation was developed that simulates the changes on corneal curvature after refractive surgery when the stiffness inhomogeneities across the corneal thickness are considered. It has been shown that the predictability of the surgical outcome is improved when the stiffness inhomogeneities and nonlinearities of the deformations are included in the finite element simulations. Moreover, a finite element formulation has been developed first time to characterize the intrastromal refractive keratectomy procedure. An inhomogeneous (small displacements) model was identified as an
Simple analytical model of evapotranspiration in the presence of roots
NASA Astrophysics Data System (ADS)
Cejas, Cesare M.; Hough, L. A.; Castaing, Jean-Christophe; Frétigny, Christian; Dreyfus, Rémi
2014-10-01
Evaporation of water out of a soil involves complicated and well-debated mechanisms. When plant roots are added into the soil, water transfer between the soil and the outside environment is even more complicated. Indeed, plants provide an additional process of water transfer. Water is pumped by the roots, channeled to the leaf surface, and released into the surrounding air by a process called transpiration. Prediction of the evapotranspiration of water over time in the presence of roots helps keep track of the amount of water that remains in the soil. Using a controlled visual setup of a two-dimensional model soil consisting of monodisperse glass beads, we perform experiments on actual roots grown under different relative humidity conditions. We record the total water mass loss in the medium and the position of the evaporating front that forms within the medium. We then develop a simple analytical model that predicts the position of the evaporating front as a function of time as well as the total amount of water that is lost from the medium due to the combined effects of evaporation and transpiration. The model is based on fundamental principles of evaporation fluxes and includes empirical assumptions on the quantity of open stomata in the leaves, where water transpiration occurs. Comparison between the model and experimental results shows excellent prediction of the position of the evaporating front as well as the total mass loss from evapotranspiration in the presence of roots. The model also provides a way to predict the lifetime of a plant.
On solvability of some boundary value problems for a biharmonic equation with periodic conditions
NASA Astrophysics Data System (ADS)
Karachik, Valery V.; Massanov, Saparbay K.; Turmetov, Batirkhan Kh.
2016-08-01
In the paper we study questions about solvability of some boundary value problems with periodic conditions for an inhomogeneous biharmonic equation. The exact conditions for solvability of the problems are found.
Enabling analytical and Modeling Tools for Enhanced Disease Surveillance
Dawn K. Manley
2003-04-01
Early detection, identification, and warning are essential to minimize casualties from a biological attack. For covert attacks, sick people are likely to provide the first indication of an attack. An enhanced medical surveillance system that synthesizes distributed health indicator information and rapidly analyzes the information can dramatically increase the number of lives saved. Current surveillance methods to detect both biological attacks and natural outbreaks are hindered by factors such as distributed ownership of information, incompatible data storage and analysis programs, and patient privacy concerns. Moreover, because data are not widely shared, few data mining algorithms have been tested on and applied to diverse health indicator data. This project addressed both integration of multiple data sources and development and integration of analytical tools for rapid detection of disease outbreaks. As a first prototype, we developed an application to query and display distributed patient records. This application incorporated need-to-know access control and incorporated data from standard commercial databases. We developed and tested two different algorithms for outbreak recognition. The first is a pattern recognition technique that searches for space-time data clusters that may signal a disease outbreak. The second is a genetic algorithm to design and train neural networks (GANN) that we applied toward disease forecasting. We tested these algorithms against influenza, respiratory illness, and Dengue Fever data. Through this LDRD in combination with other internal funding, we delivered a distributed simulation capability to synthesize disparate information and models for earlier recognition and improved decision-making in the event of a biological attack. The architecture incorporates user feedback and control so that a user's decision inputs can impact the scenario outcome as well as integrated security and role-based access-control for communicating between
Two novel classes of solvable many-body problems of goldfish type with constraints
NASA Astrophysics Data System (ADS)
Calogero, F.; Gómez-Ullate, D.
2007-05-01
Two novel classes of many-body models with nonlinear interactions 'of goldfish type' are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints), i.e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited, i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.
INCAS: an analytical model to describe displacement cascades
NASA Astrophysics Data System (ADS)
Jumel, Stéphanie; Claude Van-Duysen, Jean
2004-07-01
REVE (REactor for Virtual Experiments) is an international project aimed at developing tools to simulate neutron irradiation effects in Light Water Reactor materials (Fe, Ni or Zr-based alloys). One of the important steps of the project is to characterise the displacement cascades induced by neutrons. Accordingly, the Department of Material Studies of Electricité de France developed an analytical model based on the binary collision approximation. This model, called INCAS (INtegration of CAScades), was devised to be applied on pure elements; however, it can also be used on diluted alloys (reactor pressure vessel steels, etc.) or alloys composed of atoms with close atomic numbers (stainless steels, etc.). INCAS describes displacement cascades by taking into account the nuclear collisions and electronic interactions undergone by the moving atoms. In particular, it enables to determine the mean number of sub-cascades induced by a PKA (depending on its energy) as well as the mean energy dissipated in each of them. The experimental validation of INCAS requires a large effort and could not be carried out in the framework of the study. However, it was verified that INCAS results are in conformity with those obtained from other approaches. As a first application, INCAS was applied to determine the sub-cascade spectrum induced in iron by the neutron spectrum corresponding to the central channel of the High Flux Irradiation Reactor of Oak Ridge National Laboratory.
New analytic solutions for modeling vertical gravity gradient anomalies
NASA Astrophysics Data System (ADS)
Kim, Seung-Sep; Wessel, Paul
2016-05-01
Modern processing of satellite altimetry for use in marine gravimetry involves computing the along-track slopes of observed sea-surface heights, projecting them into east-west and north-south deflection of the vertical grids, and using Laplace's equation to algebraically obtain a grid of the vertical gravity gradient (VGG). The VGG grid is then integrated via overlapping, flat Earth Fourier transforms to yield a free-air anomaly grid. Because of this integration and associated edge effects, the VGG grid retains more short-wavelength information (e.g., fracture zone and seamount signatures) that is of particular importance for plate tectonic investigations. While modeling of gravity anomalies over arbitrary bodies has long been a standard undertaking, similar modeling of VGG anomalies over oceanic features is not commonplace yet. Here we derive analytic solutions for VGG anomalies over simple bodies and arbitrary 2-D and 3-D sources. We demonstrate their usability in determining mass excess and deficiency across the Mendocino fracture zone (a 2-D feature) and find the best bulk density estimate for Jasper seamount (a 3-D feature). The methodologies used herein are implemented in the Generic Mapping Tools, available from gmt.soest.hawaii.edu.
Analytic model of electromagnetic ion-cyclotron anisotropy instability
Yoon, P. H.; Seough, J. J.; Khim, K. K.; Kim, Hyunnam; Kwon, Hyuck-Jin; Park, Jongsun; Parkh, Sarah; Park, Kyung Sun
2010-08-15
In the present paper, the real frequency and growth rate associated with the electromagnetic ion cyclotron instability driven by temperature anisotropy are analytically modeled on the basis of conjecture and upon comparison with numerical roots of the dispersion relation. The ions are assumed to have an anisotropic distribution function with Maxwellian parallel distribution. Under such an assumption complex roots of the dispersion relation depend only on two dimensionless parameters, namely, the temperature anisotropy factor A=T{sub perpendiculari}/T{sub ||}i-1, where T{sub perpendiculari} and T{sub ||i} are the perpendicular and parallel ion temperatures, respectively, and the parallel ion beta, {beta}=(8{pi}nT{sub i}/B{sup 2}){sup 1/2}, where n and B are the plasma density and magnetic field intensity, respectively. The ion-cyclotron instability is thus heuristically modeled by complex frequency which is parametrically dependent on A and {beta}. The present result constitutes a useful shortcut research tool that may be employed in a wide variety of applications.
Analytic Modeling of Neural Tissue: I. A Spherical Bidomain.
Schwartz, Benjamin L; Chauhan, Munish; Sadleir, Rosalind J
2016-12-01
Presented here is a model of neural tissue in a conductive medium stimulated by externally injected currents. The tissue is described as a conductively isotropic bidomain, i.e. comprised of intra and extracellular regions that occupy the same space, as well as the membrane that divides them, and the injection currents are described as a pair of source and sink points. The problem is solved in three spatial dimensions and defined in spherical coordinates [Formula: see text]. The system of coupled partial differential equations is solved by recasting the problem to be in terms of the membrane and a monodomain, interpreted as a weighted average of the intra and extracellular domains. The membrane and monodomain are defined by the scalar Helmholtz and Laplace equations, respectively, which are both separable in spherical coordinates. Product solutions are thus assumed and given through certain transcendental functions. From these electrical potentials, analytic expressions for current density are derived and from those fields the magnetic flux density is calculated. Numerical examples are considered wherein the interstitial conductivity is varied, as well as the limiting case of the problem simplifying to two dimensions due to azimuthal independence. Finally, future modeling work is discussed. PMID:27613652
Analytic model of aurorally coupled magnetospheric and ionospheric electrostatic potentials
NASA Technical Reports Server (NTRS)
Cornwall, J. M.
1994-01-01
This paper describes modest but significant improvements on earlier studies of electrostatic potential structure in the auroral region using the adiabatic auroral arc model. This model has crucial nonlinearities (connected, for example. with aurorally produced ionization) which have hampered analysis; earlier work has either been linear, which I will show is a poor approximation or, if nonlinear, either numerical or too specialized to study parametric dependencies. With certain simplifying assumptions I find new analytic nonlinear solutions fully exhibiting the parametric dependence of potentials on magnetospheric (e.g.. cross-tail potential) and ionospheric (e.g., recombination rate) parameters. No purely phenomenological parameters are introduced. The results are in reasonable agreement with observed average auroral potential drops, inverted-V scale sizes, and dissipation rates. The dissipation rate is quite comparable to tail energization and transport rates and should have a major effect on tail and magnetospheric dynamics. This paper gives various relations between the cross-tail potential and auroral parameters (e.g., total parallel currents and potential drops) which can be studied with existing data sets.
Analytical examples, measurement models, and classical limit of quantum backflow
NASA Astrophysics Data System (ADS)
Yearsley, J. M.; Halliwell, J. J.; Hartshorn, R.; Whitby, A.
2012-10-01
We investigate the backflow effect in elementary quantum mechanics—the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. We compute the current and flux for states consisting of superpositions of Gaussian wave packets. These are experimentally realizable but the amount of backflow is small. Inspired by the numerical results of Penz [Penz, Grübl, Kreidl, and Wagner, J. Phys. AJPHAC50305-447010.1088/0305-4470/39/2/012 39, 423 (2006)], we find two nontrivial wave functions whose current at any time may be computed analytically and which have periods of significant backflow, in one case with a backward flux equal to about 70% of the maximum possible backflow, a dimensionless number cbm≈0.04, discovered by Bracken and Melloy [Bracken and Melloy, J. Phys. AJPHAC50305-447010.1088/0305-4470/27/6/040 27, 2197 (1994)]. This number has the unusual property of being independent of ℏ (and also of all other parameters of the model), despite corresponding to an obviously quantum-mechanical effect, and we shed some light on this surprising property by considering the classical limit of backflow. We discuss some specific measurement models in which backflow may be identified in certain measurable probabilities.
The use of analytical models in human-computer interface design
NASA Technical Reports Server (NTRS)
Gugerty, Leo
1991-01-01
Some of the many analytical models in human-computer interface design that are currently being developed are described. The usefulness of analytical models for human-computer interface design is evaluated. Can the use of analytical models be recommended to interface designers? The answer, based on the empirical research summarized here, is: not at this time. There are too many unanswered questions concerning the validity of models and their ability to meet the practical needs of design organizations.
Model Misspecification and Invariance Testing Using Confirmatory Factor Analytic Procedures
ERIC Educational Resources Information Center
French, Brian F.; Finch, W. Holmes
2011-01-01
Confirmatory factor analytic procedures are routinely implemented to provide evidence of measurement invariance. Current lines of research focus on the accuracy of common analytic steps used in confirmatory factor analysis for invariance testing. However, the few studies that have examined this procedure have done so with perfectly or near…
A semi-analytical model for semiconductor solar cells
NASA Astrophysics Data System (ADS)
Ding, D.; Johnson, S. R.; Yu, S.-Q.; Wu, S.-N.; Zhang, Y.-H.
2011-12-01
A semi-analytical model is constructed for single- and multi-junction solar cells. This model incorporates the key performance aspects of practical devices, including nonradiative recombination, photon recycling within a given junction, spontaneous emission coupling between junctions, and non-step-like absorptance and emittance with below-bandgap tail absorption. Four typical planar structures with the combinations of a smooth/textured top surface and an absorbing/reflecting substrate (or backside surface) are investigated, through which the extracted power and four types of fundamental loss mechanisms, transmission, thermalization, spatial-relaxation, and recombination loss are analyzed for both single- and multi-junction solar cells. The below-bandgap tail absorption increases the short-circuit current but decreases the output and open-circuit voltage. Using a straightforward formulism this model provides the initial design parameters and the achievable efficiencies for both single- and multiple-junction solar cells over a wide range of material quality. The achievable efficiency limits calculated using the best reported materials and AM1.5 G one sun for GaAs and Si single-junction solar cells are, respectively, 27.4 and 21.1% for semiconductor slabs with a flat surface and a non-reflecting index-matched absorbing substrate, and 30.8 and 26.4% for semiconductor slabs with a textured surface and an ideal 100% reflecting backside surface. Two important design rules for both single- and multi-junction solar cells are established: i) the optimal junction thickness decreases and the optimal bandgap energy increases when nonradiative recombination increases; and ii) the optimal junction thickness increases and the optimal bandgap energy decreases for higher solar concentrations.
Analytical model for minority games with evolutionary learning
NASA Astrophysics Data System (ADS)
Campos, Daniel; Méndez, Vicenç; Llebot, Josep E.; Hernández, Germán A.
2010-06-01
In a recent work [D. Campos, J.E. Llebot, V. Méndez, Theor. Popul. Biol. 74 (2009) 16] we have introduced a biological version of the Evolutionary Minority Game that tries to reproduce the intraspecific competition for limited resources in an ecosystem. In comparison with the complex decision-making mechanisms used in standard Minority Games, only two extremely simple strategies ( juveniles and adults) are accessible to the agents. Complexity is introduced instead through an evolutionary learning rule that allows younger agents to learn taking better decisions. We find that this game shows many of the typical properties found for Evolutionary Minority Games, like self-segregation behavior or the existence of an oscillation phase for a certain range of the parameter values. However, an analytical treatment becomes much easier in our case, taking advantage of the simple strategies considered. Using a model consisting of a simple dynamical system, the phase diagram of the game (which differentiates three phases: adults crowd, juveniles crowd and oscillations) is reproduced.
An analytical model of eddy current ferrite-core probes
NASA Astrophysics Data System (ADS)
Lu, Y.; Bowler, J. R.
2012-05-01
An analytical model of an axisymmetric eddy current probe with a cylindrical ferrite core above a layered conductive half-space is developed. Initially we consider the magnetic vector potential of a circular filament coaxial with a ferrite core over a layered conducting half-space. The principle of superposition is then used to derive close-form expressions for both the electromagnetic field and the impedance of a coil from the filament field. Rather than locating the probe in infinite space, it is confined coaxially within a circularly cylindrical boundary on which the vector potential field is zero. The radius of this artificial boundary is large in order to ensure that does not interfere substantially with the field near the probe. By using a truncated region in this way, the vector potential in the probe region can be expanded as a series rather than an integral form. Thus the solution of the problem amounts to finding the expansion coeefficients in the series. The numerical predictions of probe impedance have been compared with experimental data showing good agreement.
Analytical models for total dose ionization effects in MOS devices.
Campbell, Phillip Montgomery; Bogdan, Carolyn W.
2008-08-01
MOS devices are susceptible to damage by ionizing radiation due to charge buildup in gate, field and SOI buried oxides. Under positive bias holes created in the gate oxide will transport to the Si / SiO{sub 2} interface creating oxide-trapped charge. As a result of hole transport and trapping, hydrogen is liberated in the oxide which can create interface-trapped charge. The trapped charge will affect the threshold voltage and degrade the channel mobility. Neutralization of oxidetrapped charge by electron tunneling from the silicon and by thermal emission can take place over long periods of time. Neutralization of interface-trapped charge is not observed at room temperature. Analytical models are developed that account for the principal effects of total dose in MOS devices under different gate bias. The intent is to obtain closed-form solutions that can be used in circuit simulation. Expressions are derived for the aging effects of very low dose rate radiation over long time periods.
Analytical model of coincidence resolving time in TOF-PET.
Wieczorek, H; Thon, A; Dey, T; Khanin, V; Rodnyi, P
2016-06-21
The coincidence resolving time (CRT) of scintillation detectors is the parameter determining noise reduction in time-of-flight PET. We derive an analytical CRT model based on the statistical distribution of photons for two different prototype scintillators. For the first one, characterized by single exponential decay, CRT is proportional to the decay time and inversely proportional to the number of photons, with a square root dependence on the trigger level. For the second scintillator prototype, characterized by exponential rise and decay, CRT is proportional to the square root of the product of rise time and decay time divided by the doubled number of photons, and it is nearly independent of the trigger level. This theory is verified by measurements of scintillation time constants, light yield and CRT on scintillator sticks. Trapping effects are taken into account by defining an effective decay time. We show that in terms of signal-to-noise ratio, CRT is as important as patient dose, imaging time or PET system sensitivity. The noise reduction effect of better timing resolution is verified and visualized by Monte Carlo simulation of a NEMA image quality phantom. PMID:27245232
Analytical model of coincidence resolving time in TOF-PET
NASA Astrophysics Data System (ADS)
Wieczorek, H.; Thon, A.; Dey, T.; Khanin, V.; Rodnyi, P.
2016-06-01
The coincidence resolving time (CRT) of scintillation detectors is the parameter determining noise reduction in time-of-flight PET. We derive an analytical CRT model based on the statistical distribution of photons for two different prototype scintillators. For the first one, characterized by single exponential decay, CRT is proportional to the decay time and inversely proportional to the number of photons, with a square root dependence on the trigger level. For the second scintillator prototype, characterized by exponential rise and decay, CRT is proportional to the square root of the product of rise time and decay time divided by the doubled number of photons, and it is nearly independent of the trigger level. This theory is verified by measurements of scintillation time constants, light yield and CRT on scintillator sticks. Trapping effects are taken into account by defining an effective decay time. We show that in terms of signal-to-noise ratio, CRT is as important as patient dose, imaging time or PET system sensitivity. The noise reduction effect of better timing resolution is verified and visualized by Monte Carlo simulation of a NEMA image quality phantom.
Analytical model for force prediction when machining metal matrix composites
NASA Astrophysics Data System (ADS)
Sikder, Snahungshu
Metal Matrix Composites (MMC) offer several thermo-mechanical advantages over standard materials and alloys which make them better candidates in different applications. Their light weight, high stiffness, and strength have attracted several industries such as automotive, aerospace, and defence for their wide range of products. However, the wide spread application of Meal Matrix Composites is still a challenge for industry. The hard and abrasive nature of the reinforcement particles is responsible for rapid tool wear and high machining costs. Fracture and debonding of the abrasive reinforcement particles are the considerable damage modes that directly influence the tool performance. It is very important to find highly effective way to machine MMCs. So, it is important to predict forces when machining Metal Matrix Composites because this will help to choose perfect tools for machining and ultimately save both money and time. This research presents an analytical force model for predicting the forces generated during machining of Metal Matrix Composites. In estimating the generated forces, several aspects of cutting mechanics were considered including: shearing force, ploughing force, and particle fracture force. Chip formation force was obtained by classical orthogonal metal cutting mechanics and the Johnson-Cook Equation. The ploughing force was formulated while the fracture force was calculated from the slip line field theory and the Griffith theory of failure. The predicted results were compared with previously measured data. The results showed very good agreement between the theoretically predicted and experimentally measured cutting forces.
An analytical study of various telecomminication networks using markov models
NASA Astrophysics Data System (ADS)
Ramakrishnan, M.; Jayamani, E.; Ezhumalai, P.
2015-04-01
The main aim of this paper is to examine issues relating to the performance of various Telecommunication networks, and applied queuing theory for better design and improved efficiency. Firstly, giving an analytical study of queues deals with quantifying the phenomenon of waiting lines using representative measures of performances, such as average queue length (on average number of customers in the queue), average waiting time in queue (on average time to wait) and average facility utilization (proportion of time the service facility is in use). In the second, using Matlab simulator, summarizes the finding of the investigations, from which and where we obtain results and describing methodology for a) compare the waiting time and average number of messages in the queue in M/M/1 and M/M/2 queues b) Compare the performance of M/M/1 and M/D/1 queues and study the effect of increasing the number of servers on the blocking probability M/M/k/k queue model.
An analytical model of axial compressor off-design performance
Camp, T.R.; Horlock, J.H. . Whittle Lab.)
1994-07-01
An analysis is presented of the off-design performance of multistage axial-flow compressors. It is based on an analytical solution, valid for small perturbations in operating conditions from the design point, and provides an insight into the effects of choices made during the compressor design process on performance and off-design stage matching. It is shown that the mean design value of stage loading coefficient ([psi] = [Delta]h[sub 0]/U[sup 2]) has a dominant effect on off-design performance, whereas the stage-wise distribution of stage loading coefficient and the design value of flow coefficient have little influence. The powerful effects of variable stator vanes on stage-matching are also demonstrated and these results are shown to agree well with previous work. The slope of the working line of a gas turbine engine, overlaid on overall compressor characteristics, is shown to have a strong effect on the off-design stage-matching through the compressor. The model is also used to analyze design changes to the compressor geometry and to show how errors in estimates of annulus blockage, decided during the design process, have less effect on compressor performance than has previously been thought.
Analysis of structural dynamic data from Skylab. Volume 2: Skylab analytical and test model data
NASA Technical Reports Server (NTRS)
Demchak, L.; Harcrow, H.
1976-01-01
The orbital configuration test modal data, analytical test correlation modal data, and analytical flight configuration modal data are presented. Tables showing the generalized mass contributions (GMCs) for each of the thirty tests modes are given along with the two dimensional mode shape plots and tables of GMCs for the test correlated analytical modes. The two dimensional mode shape plots for the analytical modes and uncoupled and coupled modes of the orbital flight configuration at three development phases of the model are included.
Analytical model of impact disruption of satellites and asteroids
NASA Astrophysics Data System (ADS)
Leliwa-Kopystyński, J.; Włodarczyk, I.; Burchell, M. J.
2016-04-01
A model of impact disruption of the bodies with sizes from the laboratory scale to that of an order of 100 km is developed. On the lowermost end of the target size the model is based on the numerous laboratory data related to the mass-velocity distribution of the impact produced fragments. On the minor-planets scale the model is supported by the data related to the largest observed craters on small icy satellites and on some asteroids (Leliwa-Kopystynski, J., Burchell, M.J., Lowen, D. [2008]. Icarus 195, 817-826). The model takes into account the target disruption and the dispersion of the impact produced fragments against the intermolecular forces acting on the surfaces of the contacts of the fragments and against self-gravitation of the target. The head-on collisions of non-rotating and non-porous targets and impactors are considered. The impactor delivers kinetic energy but its mass is neglected in comparison to mass of the target. For this simple case the analytical formulae for specific disruption energy as well as for specific energy of formation of the largest craters are found. They depend on a set of parameters. Of these the most important (i.e. with the greatest influence on the final result) are three rather weakly known parameters. They are: (i) The exponent γ in the distribution function of the fragments. (ii) The characteristic velocity v0 that appears in the velocity distribution of the ejected fragments. (iii) The exponent β in the mass-velocity distribution. The influence of the choice of the numerical values of these parameters on the final results has been studied. Another group of parameters contains the relevant material data. They are: (a) The energy σ of breaking of the intermolecular bonds of the target material per unit of the fragment surface and (b) the density ρ of the target. According to our calculations the transition between the strength regime and the gravitational regime is in the range of the target radius from ∼0.4 km to
Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach.
ERIC Educational Resources Information Center
Pronchik, Jeremy N.; Williams, Brian W.
2003-01-01
Describes an alternative approach to finding exactly solvable, one-dimensional quantum mechanical potentials. Differs from the usual approach in that instead of starting with a particular potential and seeking solutions to the related Schrodinger equations, it begins with known solutions to second-order ordinary differential equations and seeks to…
Design Protocols and Analytical Strategies that Incorporate Structural Reliability Models
NASA Technical Reports Server (NTRS)
Duffy, Stephen F.
1997-01-01
Ceramic matrix composites (CMC) and intermetallic materials (e.g., single crystal nickel aluminide) are high performance materials that exhibit attractive mechanical, thermal and chemical properties. These materials are critically important in advancing certain performance aspects of gas turbine engines. From an aerospace engineer's perspective the new generation of ceramic composites and intermetallics offers a significant potential for raising the thrust/weight ratio and reducing NO(x) emissions of gas turbine engines. These aspects have increased interest in utilizing these materials in the hot sections of turbine engines. However, as these materials evolve and their performance characteristics improve a persistent need exists for state-of-the-art analytical methods that predict the response of components fabricated from CMC and intermetallic material systems. This need provided the motivation for the technology developed under this research effort. Continuous ceramic fiber composites exhibit an increase in work of fracture, which allows for "graceful" rather than catastrophic failure. When loaded in the fiber direction, these composites retain substantial strength capacity beyond the initiation of transverse matrix cracking despite the fact that neither of its constituents would exhibit such behavior if tested alone. As additional load is applied beyond first matrix cracking, the matrix tends to break in a series of cracks bridged by the ceramic fibers. Any additional load is born increasingly by the fibers until the ultimate strength of the composite is reached. Thus modeling efforts supported under this research effort have focused on predicting this sort of behavior. For single crystal intermetallics the issues that motivated the technology development involved questions relating to material behavior and component design. Thus the research effort supported by this grant had to determine the statistical nature and source of fracture in a high strength, Ni
Design Protocols and Analytical Strategies that Incorporate Structural Reliability Models
NASA Technical Reports Server (NTRS)
Duffy, Stephen F.
1997-01-01
Ceramic matrix composites (CMC) and intermetallic materials (e.g., single crystal nickel aluminide) are high performance materials that exhibit attractive mechanical, thermal, and chemical properties. These materials are critically important in advancing certain performance aspects of gas turbine engines. From an aerospace engineers perspective the new generation of ceramic composites and intermetallics offers a significant potential for raising the thrust/weight ratio and reducing NO(sub x) emissions of gas turbine engines. These aspects have increased interest in utilizing these materials in the hot sections of turbine engines. However, as these materials evolve and their performance characteristics improve a persistent need exists for state-of-the-art analytical methods that predict the response of components fabricated from CMC and intermetallic material systems. This need provided the motivation for the technology developed under this research effort. Continuous ceramic fiber composites exhibit an increase in work of fracture, which allows for 'graceful' rather than catastrophic failure. When loaded in the fiber direction these composites retain substantial strength capacity beyond the initiation of transverse matrix cracking despite the fact that neither of its constituents would exhibit such behavior if tested alone. As additional load is applied beyond first matrix cracking, the matrix tends to break in a series of cracks bridged by the ceramic fibers. Any additional load is born increasingly by the fibers until the ultimate strength of the composite is reached. Thus modeling efforts supported under this research effort have focused on predicting this sort of behavior. For single crystal intermetallics the issues that motivated the technology development involved questions relating to material behavior and component design. Thus the research effort supported by this grant had to determine the statistical nature and source of fracture in a high strength, Ni
An Analytical Model for the Influence of Contact Resistance on Thermoelectric Efficiency
NASA Astrophysics Data System (ADS)
Bjørk, Rasmus
2016-03-01
An analytical model is presented that can account for both electrical and hot and cold thermal contact resistances when calculating the efficiency of a thermoelectric generator. The model is compared to a numerical model of a thermoelectric leg for 16 different thermoelectric materials, as well as to the analytical models of Ebling et al. (J Electron Mater 39:1376, 2010) and Min and Rowe (J Power Sour 38:253, 1992). The model presented here is shown to accurately calculate the efficiency for all systems and all contact resistances considered, with an average difference in efficiency between the numerical model and the analytical model of -0.07 ± 0.35pp. This makes the model more accurate than previously published models. The maximum absolute difference in efficiency between the analytical model and the numerical model is 1.14pp for all materials and all contact resistances considered.
Liquid contact resonance AFM: analytical models, experiments, and limitations
NASA Astrophysics Data System (ADS)
Parlak, Zehra; Tu, Qing; Zauscher, Stefan
2014-11-01
Contact resonance AFM (CR-AFM) is a scanning probe microscopy technique that utilizes the contact resonances of the AFM cantilever for concurrent imaging of topography and surface stiffness. The technique has not been used in liquid until recently due to analytical and experimental difficulties, associated with viscous damping of cantilever vibrations and fluid loading effects. To address these difficulties, (i) an analytical approach for contact resonances in liquid is developed, and (ii) direct excitation of the contact resonances is demonstrated by actuating the cantilever directly in a magnetic field. By implementing the analytical approach and the direct actuation through magnetic particles, quantitative stiffness imaging on surfaces with a wide range of stiffness can be achieved in liquid with soft cantilevers and low contact forces.
Analytical model for electromagnetic cascades in rotating electric field
Nerush, E. N.; Bashmakov, V. F.; Kostyukov, I. Yu.
2011-08-15
Electromagnetic cascades attract a lot of attention as an important quantum electrodynamics effect that will reveal itself in various electromagnetic field configurations at ultrahigh intensities. We study cascade dynamics in rotating electric field analytically and numerically. The kinetic equations for the electron-positron plasma and gamma-quanta are formulated. The scaling laws are derived and analyzed. For the cascades arising far above the threshold the dependence of the cascade parameters on the field frequency is derived. The spectra of high-energy cascade particles are calculated. The analytical results are verified by numerical simulations.
Dubský, Pavel; Müllerová, Ludmila; Dvořák, Martin; Gaš, Bohuslav
2015-03-01
The model of electromigration of a multivalent weak acidic/basic/amphoteric analyte that undergoes complexation with a mixture of selectors is introduced. The model provides an extension of the series of models starting with the single-selector model without dissociation by Wren and Rowe in 1992, continuing with the monovalent weak analyte/single-selector model by Rawjee, Williams and Vigh in 1993 and that by Lelièvre in 1994, and ending with the multi-selector overall model without dissociation developed by our group in 2008. The new multivalent analyte multi-selector model shows that the effective mobility of the analyte obeys the original Wren and Row's formula. The overall complexation constant, mobility of the free analyte and mobility of complex can be measured and used in a standard way. The mathematical expressions for the overall parameters are provided. We further demonstrate mathematically that the pH dependent parameters for weak analytes can be simply used as an input into the multi-selector overall model and, in reverse, the multi-selector overall parameters can serve as an input into the pH-dependent models for the weak analytes. These findings can greatly simplify the rationale method development in analytical electrophoresis, specifically enantioseparations. PMID:25637010
Exactly solvable chaos in an electromechanical oscillator.
Owens, Benjamin A M; Stahl, Mark T; Corron, Ned J; Blakely, Jonathan N; Illing, Lucas
2013-09-01
A novel electromechanical chaotic oscillator is described that admits an exact analytic solution. The oscillator is a hybrid dynamical system with governing equations that include a linear second order ordinary differential equation with negative damping and a discrete switching condition that controls the oscillatory fixed point. The system produces provably chaotic oscillations with a topological structure similar to either the Lorenz butterfly or Rössler's folded-band oscillator depending on the configuration. Exact solutions are written as a linear convolution of a fixed basis pulse and a sequence of discrete symbols. We find close agreement between the exact analytical solutions and the physical oscillations. Waveform return maps for both configurations show equivalence to either a shift map or tent map, proving the chaotic nature of the oscillations. PMID:24089945
Exactly solvable chaos in an electromechanical oscillator
NASA Astrophysics Data System (ADS)
Owens, Benjamin A. M.; Stahl, Mark T.; Corron, Ned J.; Blakely, Jonathan N.; Illing, Lucas
2013-09-01
A novel electromechanical chaotic oscillator is described that admits an exact analytic solution. The oscillator is a hybrid dynamical system with governing equations that include a linear second order ordinary differential equation with negative damping and a discrete switching condition that controls the oscillatory fixed point. The system produces provably chaotic oscillations with a topological structure similar to either the Lorenz butterfly or Rössler's folded-band oscillator depending on the configuration. Exact solutions are written as a linear convolution of a fixed basis pulse and a sequence of discrete symbols. We find close agreement between the exact analytical solutions and the physical oscillations. Waveform return maps for both configurations show equivalence to either a shift map or tent map, proving the chaotic nature of the oscillations.
CTE Solvability, Nonlocal Symmetry and Explicit Solutions of Modified Boussinesq System
NASA Astrophysics Data System (ADS)
Ren, Bo; Cheng, Xue-Ping
2016-07-01
A consistent tanh expansion (CTE) method is used to study the modified Boussinesq equation. It is proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a nonanto-BT theorem. Furthermore, the nonlocal symmetry for the modified Boussinesq equation is obtained by the Painlevé analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing one auxiliary dependent variable. The finite symmetry transformation related with the nonlocal symemtry is obtained by solving the initial value problem of the prolonged systems. Thanks to the localization process, many interaction solutions among solitons and other complicated waves are computed through similarity reductions. Some special concrete soliton-cnoidal wave interaction behaviors are studied both in analytical and graphical ways. Supported by the National Natural Science Foundation of China under Grant Nos. 11305106 and 11505154
Analytical Model of Nano-Electromechanical (NEM) Nonvolatile Memory Cells
NASA Astrophysics Data System (ADS)
Han, Boram; Choi, Woo Young
The fringe field effects of nano-electromechanical (NEM) nonvolatile memory cells have been investigated analytically for the accurate evaluation of NEM memory cells. As the beam width is scaled down, fringe field effect becomes more severe. It has been observed that pull-in, release and hysteresis voltage decrease more than our prediction. Also, the fringe field on cell characteristics has been discussed.
An Analytical Model for Vertical Profiles in Submarine Channels
NASA Astrophysics Data System (ADS)
Bolla Pittaluga, M.; Imran, J.
2011-12-01
Turbidity currents are the primary agents carrying sediments from the continental shelf to the deep-sea. They are the counterpart of fluvial currents in the deep-sea environment and are responsible for the shaping of submarine channels. Due to the unpredictability of events and to their ability to destroy installed monitoring instruments, only a few attempts to directly measure the properties of turbidity currents in submarine channels has proved to be successful (Xu et al., 2004; Xu, 2010). Consequently the vast majority of the studies concerning the vertical structure of turbidity currents were either laboratory experiments or numerical models. In spite of the relevance of the problem, related to the consequences of flow field on sedimentary deposits, at present an ongoing debate still exist on similarities and differences between submarine and fluvial channels related in particular to the orientation of the helical flow in channel bends. Here we expand on the above ideas and develop an analytical theory for flow and suspended sediment transport in submarine channels able to describe vertical profiles of both flow field and suspendend sediment concentration. The turbulence closure needed to account for density stratification is adapted from the model of Mellor and Yamada (1982). Solutions are found for both straight and constant curvature channels. In the latter case, in order to evaluate the secondary flow induced by curvature, we take advantage of the fact that the ratio of flow depth to radius of curvature is typically small in the field, which leads to a solution of the governing equations through an appropriate asymptotic expansion. Steady fully developed flow conditions in a bend of constant width are considered. Results for longitudinal velocity and concentration profiles in straight channels are then compared with experimental observations of Sequeiros et al. (2010) providing good agreement. We also expect to find under which values of the controlling
Xu, Zhijie; Fang, Yilin; Scheibe, Timothy D.; Bonneville, Alain
2012-05-15
We present a hydro-mechanical model for geological sequestration of carbon dioxide. The model considers the poroelastic effects by taking into account the coupling between the geomechanical response and the fluid flow in greater detail. The simplified hydro-mechanical model includes the geomechanical part that relies on the linear elasticity, while the fluid flow is based on the Darcy’s law. Two parts were coupled using the standard linear poroelasticity. Analytical solutions for pressure field were obtained for a typical geological sequestration scenario. The model predicts the temporal and spatial variation of pressure field and effects of permeability and elastic modulus of formation on the fluid pressure distribution.
Modelling a flows in supply chain with analytical models: Case of a chemical industry
NASA Astrophysics Data System (ADS)
Benhida, Khalid; Azougagh, Yassine; Elfezazi, Said
2016-02-01
This study is interested on the modelling of the logistics flows in a supply chain composed on a production sites and a logistics platform. The contribution of this research is to develop an analytical model (integrated linear programming model), based on a case study of a real company operating in the phosphate field, considering a various constraints in this supply chain to resolve the planning problems for a better decision-making. The objectives of this model is to determine and define the optimal quantities of different products to route, to and from the various entities in the supply chain studied.
An analytic model of neutron ambient dose equivalent and equivalent dose for proton radiotherapy
Zhang, Rui; Pérez-Andújar, Angélica; Fontenot, Jonas D; Taddei, Phillip J; Newhauser, Wayne D
2010-01-01
Stray neutrons generated in passively scattered proton therapy are of concern because they increase the risk that a patient will develop a second cancer. Several investigations characterized stray neutrons in proton therapy using experimental measurements and Monte Carlo simulations, but capabilities of analytical methods to predict neutron exposures are less well developed. The goal of this study was to develop a new analytical model to calculate neutron ambient dose equivalent in air and equivalent dose in phantom based on Monte Carlo modeling of a passively scattered proton therapy unit. The accuracy of the new analytical model is superior to a previous analytical model and comparable to the accuracy of typical Monte Carlo simulations and measurements. Predictions from the new analytical model agreed reasonably well with corresponding values predicted by a Monte Carlo code using an anthropomorphic phantom. PMID:21076197
Analytical Model of Water Flow in Coal with Active Matrix
NASA Astrophysics Data System (ADS)
Siemek, Jakub; Stopa, Jerzy
2014-12-01
This paper presents new analytical model of gas-water flow in coal seams in one dimension with emphasis on interactions between water flowing in cleats and coal matrix. Coal as a flowing system, can be viewed as a solid organic material consisting of two flow subsystems: a microporous matrix and a system of interconnected macropores and fractures. Most of gas is accumulated in the microporous matrix, where the primary flow mechanism is diffusion. Fractures and cleats existing in coal play an important role as a transportation system for macro scale flow of water and gas governed by Darcy's law. The coal matrix can imbibe water under capillary forces leading to exchange of mass between fractures and coal matrix. In this paper new partial differential equation for water saturation in fractures has been formulated, respecting mass exchange between coal matrix and fractures. Exact analytical solution has been obtained using the method of characteristics. The final solution has very simple form that may be useful for practical engineering calculations. It was observed that the rate of exchange of mass between the fractures and the coal matrix is governed by an expression which is analogous to the Newton cooling law known from theory of heat exchange, but in present case the mass transfer coefficient depends not only on coal and fluid properties but also on time and position. The constant term of mass transfer coefficient depends on relation between micro porosity and macro porosity of coal, capillary forces, and microporous structure of coal matrix. This term can be expressed theoretically or obtained experimentally. W artykule zaprezentowano nowy model matematyczny przepływu wody i gazu w jednowymiarowej warstwie węglowej z uwzględnieniem wymiany masy między systemem szczelin i matrycą węglową. Węgiel jako system przepływowy traktowany jest jako układ o podwójnej porowatości i przepuszczalności, składający się z mikroporowatej matrycy węglowej oraz z
A model for analytical performance prediction of hypervapotron
Baxi, C.B.; Falter, H.
1992-07-01
A hypervapotron is a water-cooled device which combines the advantages of finned surfaces with the large heat transfer rates possible during boiling heat transfer. Hypervapotrons have been used as beam dumps in the past and plans are under way to use them for divertor cooling in the Joint European Torus (JET). Experiments at JET have shows that a surface heat flux of 25 MW/m{sup 2} can be achieved in hypervapotrons. This performance makes such a device very attractive for cooling of divertor of the International Thermonuclear Experimental Reactor (ITER). This paper presents an analytical method to predict the thermal performance of the hypervapotrons. Preliminary results show an excellent agreement between experimental results and analytical prediction over a wide range of flow velocities, pressures, subcooling temperatures and heat fluxes. This paper also presents the predicted performance of hypervapotron made of materials other than copper. After further development and verification, the analytical method could be used for optimizing designs and performance prediction.
A simple analytical aerodynamic model of Langley Winged-Cone Aerospace Plane concept
NASA Technical Reports Server (NTRS)
Pamadi, Bandu N.
1994-01-01
A simple three DOF analytical aerodynamic model of the Langley Winged-Coned Aerospace Plane concept is presented in a form suitable for simulation, trajectory optimization, and guidance and control studies. The analytical model is especially suitable for methods based on variational calculus. Analytical expressions are presented for lift, drag, and pitching moment coefficients from subsonic to hypersonic Mach numbers and angles of attack up to +/- 20 deg. This analytical model has break points at Mach numbers of 1.0, 1.4, 4.0, and 6.0. Across these Mach number break points, the lift, drag, and pitching moment coefficients are made continuous but their derivatives are not. There are no break points in angle of attack. The effect of control surface deflection is not considered. The present analytical model compares well with the APAS calculations and wind tunnel test data for most angles of attack and Mach numbers.
NASA Astrophysics Data System (ADS)
Astashev, M. G.; Novikov, M. A.; Panfilov, D. I.; Rashitov, P. A.; Fedorova, M. I.
2015-12-01
In this paper, an approach to the development of a simplified analytical model for the analysis of electromagnetic processes of a thyristor-controlled phase angle regulator with an individual phase-controlled thyristor switch is considered. The analytical expressions for the calculation of electrical parameters in symmetrical and open-phase operating mode are obtained. With a concrete example, the verification of the developed analytical model is carried out. It is accomplished by means of comparison between current and voltage calculation results when the thyristor-controlled phase angle regulator is in an open-phase operating mode with the simulation results in the MatLab software environment. Adequacy check of the obtained analytical model is carried out by comparison between the analytical calculation and experimental data received from the actual physical model.
Some decidable results on reachability of solvable systems
NASA Astrophysics Data System (ADS)
Xu, Ming; Zhu, Jiaqi; Li, Zhi-Bin
2013-05-01
Reachability analysis plays an important role in verifying the safety of modern control systems. In the existing work, there are many decidable results on reachability of discrete systems. For continuous systems, however, the known decidable results are established merely for linear systems. In this paper, we propose a class of nonlinear systems (named solvable systems) extending linear systems. We first show that their solutions are of closed form. On the basis of it, we study a series of reachability problems for various subclasses of solvable systems. Our main results are that these reachability problems are decidable by manipulations in number theory, real root isolation, and quantifier elimination. Finally the decision procedures are implemented in a Maple package REACH to solve several non-trivial examples.
The use of analytical models in human-computer interface design
NASA Technical Reports Server (NTRS)
Gugerty, Leo
1993-01-01
Recently, a large number of human-computer interface (HCI) researchers have investigated building analytical models of the user, which are often implemented as computer models. These models simulate the cognitive processes and task knowledge of the user in ways that allow a researcher or designer to estimate various aspects of an interface's usability, such as when user errors are likely to occur. This information can lead to design improvements. Analytical models can supplement design guidelines by providing designers rigorous ways of analyzing the information-processing requirements of specific tasks (i.e., task analysis). These models offer the potential of improving early designs and replacing some of the early phases of usability testing, thus reducing the cost of interface design. This paper describes some of the many analytical models that are currently being developed and evaluates the usefulness of analytical models for human-computer interface design. This paper will focus on computational, analytical models, such as the GOMS model, rather than less formal, verbal models, because the more exact predictions and task descriptions of computational models may be useful to designers. The paper also discusses some of the practical requirements for using analytical models in complex design organizations such as NASA.
IT vendor selection model by using structural equation model & analytical hierarchy process
NASA Astrophysics Data System (ADS)
Maitra, Sarit; Dominic, P. D. D.
2012-11-01
Selecting and evaluating the right vendors is imperative for an organization's global marketplace competitiveness. Improper selection and evaluation of potential vendors can dwarf an organization's supply chain performance. Numerous studies have demonstrated that firms consider multiple criteria when selecting key vendors. This research intends to develop a new hybrid model for vendor selection process with better decision making. The new proposed model provides a suitable tool for assisting decision makers and managers to make the right decisions and select the most suitable vendor. This paper proposes a Hybrid model based on Structural Equation Model (SEM) and Analytical Hierarchy Process (AHP) for long-term strategic vendor selection problems. The five steps framework of the model has been designed after the thorough literature study. The proposed hybrid model will be applied using a real life case study to assess its effectiveness. In addition, What-if analysis technique will be used for model validation purpose.
NASA Astrophysics Data System (ADS)
Tiwari, Purushottam; Wang, Xuewen; Darici, Yesim; He, Jin; Uren, Aykut
Surface plasmon resonance (SPR) is a biophysical technique for the quantitative analysis of bimolecular interactions. Correct identification of the binding model is crucial for the interpretation of SPR data. Bivalent SPR model is governed by non-linear differential equations, which, in general, have no analytical solutions. Therefore, an analytical based approach cannot be employed in order to identify this particular model. There exists a unique signature in the bivalent analyte model, existence of an `optimal analyte concentration', which can distinguish this model from other biphasic models. The unambiguous identification and related analysis of the bivalent analyte model is demonstrated by using theoretical simulations and experimentally measured SPR sensorgrams. Experimental SPR sensorgrams were measured by using Biacore T200 instrument available in Biacore Molecular Interaction Shared Resource facility, supported by NIH Grant P30CA51008, at Georgetown University.
Analytical models of optical response in one-dimensional semiconductors
NASA Astrophysics Data System (ADS)
Pedersen, Thomas Garm
2015-09-01
The quantum mechanical description of the optical properties of crystalline materials typically requires extensive numerical computation. Including excitonic and non-perturbative field effects adds to the complexity. In one dimension, however, the analysis simplifies and optical spectra can be computed exactly. In this paper, we apply the Wannier exciton formalism to derive analytical expressions for the optical response in four cases of increasing complexity. Thus, we start from free carriers and, in turn, switch on electrostatic fields and electron-hole attraction and, finally, analyze the combined influence of these effects. In addition, the optical response of impurity-localized excitons is discussed.
ERIC Educational Resources Information Center
Budsankom, Prayoonsri; Sawangboon, Tatsirin; Damrongpanit, Suntorapot; Chuensirimongkol, Jariya
2015-01-01
The purpose of the research is to develop and identify the validity of factors affecting higher order thinking skills (HOTS) of students. The thinking skills can be divided into three types: analytical, critical, and creative thinking. This analysis is done by applying the meta-analytic structural equation modeling (MASEM) based on a database of…
An Analytic Hierarchy Process for School Quality and Inspection: Model Development and Application
ERIC Educational Resources Information Center
Al Qubaisi, Amal; Badri, Masood; Mohaidat, Jihad; Al Dhaheri, Hamad; Yang, Guang; Al Rashedi, Asma; Greer, Kenneth
2016-01-01
Purpose: The purpose of this paper is to develop an analytic hierarchy planning-based framework to establish criteria weights and to develop a school performance system commonly called school inspections. Design/methodology/approach: The analytic hierarchy process (AHP) model uses pairwise comparisons and a measurement scale to generate the…
Analytic model approach to the inversion of scattering data. [to obtain ozone profile
NASA Technical Reports Server (NTRS)
Green, A. E. S.; Klenk, K. F.
1977-01-01
An analytic model approach is applied to several simple atmospheric inversion problems. This method gives a sharp determination of aerosol size distribution parameters. It is shown that this analytic approach, together with ground level point sampling data measurements, can be used to infer information on the tropospheric ozone profile.
Promoting Active Learning by Practicing the "Self-Assembly" of Model Analytical Instruments
ERIC Educational Resources Information Center
Algar, W. Russ; Krull, Ulrich J.
2010-01-01
In our upper-year instrumental analytical chemistry course, we have developed "cut-and-paste" exercises where students "build" models of analytical instruments from individual schematic images of components. These exercises encourage active learning by students. Instead of trying to memorize diagrams, students are required to think deeply about…
Dike emplacement in layered media: analytical, numerical and analogous models
NASA Astrophysics Data System (ADS)
Rivalta, E.; Dahm, T.
2003-04-01
Strong heterogeneities are very common in volcanic areas, and are recognized to have a great influence on the stress field generated by magma intrusions. Layering, represented by strong discontinuities in the elastic parameters, is able to significantly concentrate and enhance stress. For instance, at Moho depth where elastic and viscoelastic parameters change, or beneath volcanic edifices, that are made up by a stiff basaltic basement covered by softer materials produced by repetitive activity. Numerical and (semi)analytical studies have shown how layering influences the shape of the intrusion and the surrounding stress field. However, it is important to quantify how layering influences the propagation of the dikes, in order to understand the physics controlling the dynamic of the interaction between the dike and the elastic parameters of the medium. The stress intensity factor is a measure of the tendency of the dike to break new rock and to propagate, and is therefore an useful parameter to analyse the migration process. It has been calculated with both semianalytic and numerical procedures and has been plotted as a function of the depth in relation to different rigidity contrasts. The stress intensity factor is found to increase when the dike is embedded in the stiffer medium and propagates towards a softer one, and to decrease in the opposite situation. This may produce stops, pauses or accelerations in the migration process that may be mirrored in the seismicity recorded during injection events. Additionally to analytical and numerical studies, analogue experiments have been conducted to verify the theoretical findings.
Evaluation of Analytical Modeling Functions for the Phonation Onset Process.
Petermann, Simon; Kniesburges, Stefan; Ziethe, Anke; Schützenberger, Anne; Döllinger, Michael
2016-01-01
The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO), called the voice onset time (VOT), is currently under investigation as a clinical indicator for correct laryngeal functionality. Different analytical approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps) was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six analytical functions were tested that approximate the envelope of the filtered or unfiltered glottal area waveform (GAW) during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1) reliability of the fit function for a correct approximation of VO; (2) consistency represented by the standard deviation of VOT; and (3) accuracy of the approximation of VO. The results suggest the computation of VOT by a fourth-order polynomial approximation in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW. PMID:27066108
Evaluation of Analytical Modeling Functions for the Phonation Onset Process
Petermann, Simon; Kniesburges, Stefan; Ziethe, Anke; Schützenberger, Anne; Döllinger, Michael
2016-01-01
The human voice originates from oscillations of the vocal folds in the larynx. The duration of the voice onset (VO), called the voice onset time (VOT), is currently under investigation as a clinical indicator for correct laryngeal functionality. Different analytical approaches for computing the VOT based on endoscopic imaging were compared to determine the most reliable method to quantify automatically the transient vocal fold oscillations during VO. Transnasal endoscopic imaging in combination with a high-speed camera (8000 fps) was applied to visualize the phonation onset process. Two different definitions of VO interval were investigated. Six analytical functions were tested that approximate the envelope of the filtered or unfiltered glottal area waveform (GAW) during phonation onset. A total of 126 recordings from nine healthy males and 210 recordings from 15 healthy females were evaluated. Three criteria were analyzed to determine the most appropriate computation approach: (1) reliability of the fit function for a correct approximation of VO; (2) consistency represented by the standard deviation of VOT; and (3) accuracy of the approximation of VO. The results suggest the computation of VOT by a fourth-order polynomial approximation in the interval between 32.2 and 67.8% of the saturation amplitude of the filtered GAW. PMID:27066108
Design Evaluation of Wind Turbine Spline Couplings Using an Analytical Model: Preprint
Guo, Y.; Keller, J.; Wallen, R.; Errichello, R.; Halse, C.; Lambert, S.
2015-02-01
Articulated splines are commonly used in the planetary stage of wind turbine gearboxes for transmitting the driving torque and improving load sharing. Direct measurement of spline loads and performance is extremely challenging because of limited accessibility. This paper presents an analytical model for the analysis of articulated spline coupling designs. For a given torque and shaft misalignment, this analytical model quickly yields insights into relationships between the spline design parameters and resulting loads; bending, contact, and shear stresses; and safety factors considering various heat treatment methods. Comparisons of this analytical model against previously published computational approaches are also presented.
Hunt, R.J.; Anderson, M.P.; Kelson, V.A.
1998-01-01
This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.
Analytic Expressions for the BCDMEM Model of Recognition Memory
Myung, Jay I.; Montenegro, Maximiliano; Pitt, Mark A.
2007-01-01
We introduce a Fourier Transformation technique that enables one to derive closed-form expressions of performance measures (e.g., hit and false alarm rates) of simulation-based models of recognition memory. Application of the technique is demonstrated using the bind cue decide model of episodic memory (BCDMEM; Dennis & Humphreys, 2001). In addition to reducing the time required to test the model, which for models like BCDMEM can be excessive, asymptotic expressions of the measures reveal heretofore unknown properties of the model, such as model predictions being dependent on vector length. PMID:18516213
The analytic structure of lattice models - Why can't we solve most models?
NASA Astrophysics Data System (ADS)
Guttmann, Anthony J.
2005-06-01
We investigate the solvability of a variety of well-known problems in lattice statistical mechanics. We provide a new numerical procedure which enables one to conjecture whether the solution falls into a class of functions called differentiably finite functions. Almost all solved problems fall into this class. The fact that one can conjecture whether a given problem is or is not D-finite then informs one as to whether the solution is likely to be tractable or not. We also show how, for certain problems, it is possible to prove that the solutions are not D-finite, based on the work of Rechnitzer [1-3].
An exactly solvable system from quantum optics
NASA Astrophysics Data System (ADS)
Maciejewski, Andrzej J.; Przybylska, Maria; Stachowiak, Tomasz
2015-07-01
We investigate a generalisation of the Rabi system in the Bargmann-Fock representation. In this representation the eigenproblem of the considered quantum model is described by a system of two linear differential equations with one independent variable. The system has only one irregular singular point at infinity. We show how the quantisation of the model is related to asymptotic behaviour of solutions in a vicinity of this point. The explicit formulae for the spectrum and eigenfunctions of the model follow from an analysis of the Stokes phenomenon. An interpretation of the obtained results in terms of differential Galois group of the system is also given.
NASA Astrophysics Data System (ADS)
Yuya, Philip A.; Patel, Nimitt G.
2014-08-01
In the last few decades, nanoindentation has gained widespread acceptance as a technique for materials properties characterization at micron and submicron length scales. Accurate and precise characterization of material properties with a nanoindenter is critically dependent on the ability to correctly model the response of the test equipment in contact with the material. In dynamic nanoindention analysis, a simple Kelvin-Voigt model is commonly used to capture the viscoelastic response. However, this model oversimplifies the response of real viscoelastic materials such as polymers. A model is developed that captures the dynamic nanoindentation response of a viscoelastic material. Indenter tip-sample contact forces are modelled using a generalized Maxwell model. The results on a silicon elastomer were analysed using conventional two element Kelvin-Voigt model and contrasted to analysis done using the Maxwell model. The results show that conventional Kelvin-Voigt model overestimates the storage modulus of the silicone elastomer by ~30%. Maxwell model represents a significant improvement in capturing the viscoelastic material behaviour over the Voigt model.
Process models: analytical tools for managing industrial energy systems
Howe, S O; Pilati, D A; Balzer, C; Sparrow, F T
1980-01-01
How the process models developed at BNL are used to analyze industrial energy systems is described and illustrated. Following a brief overview of the industry modeling program, the general methodology of process modeling is discussed. The discussion highlights the important concepts, contents, inputs, and outputs of a typical process model. A model of the US pulp and paper industry is then discussed as a specific application of process modeling methodology. Applications addressed with the case study results include projections of energy demand, conservation technology assessment, energy-related tax policies, and sensitivity analysis. A subsequent discussion of these results supports the conclusion that industry process models are versatile and powerful tools for managing industrial energy systems.
Simple analytic QCD model with perturbative QCD behavior at high momenta
Contreras, Carlos; Espinosa, Olivier; Cvetic, Gorazd; Martinez, Hector E.
2010-10-01
Analytic QCD models are those where the QCD running coupling has the physically correct analytic behavior, i.e., no Landau singularities in the Euclidean regime. We present a simple analytic QCD model in which the discontinuity function of the running coupling at high momentum scales is the same as in perturbative QCD (just like in the analytic QCD model of Shirkov and Solovtsov), but at low scales it is replaced by a delta function which parametrizes the unknown behavior there. We require that the running coupling agree to a high degree with the perturbative coupling at high energies, which reduces the number of free parameters of the model from four to one. The remaining parameter is fixed by requiring the reproduction of the correct value of the semihadronic tau decay ratio.
Automated refinement and inference of analytical models for metabolic networks
NASA Astrophysics Data System (ADS)
Schmidt, Michael D.; Vallabhajosyula, Ravishankar R.; Jenkins, Jerry W.; Hood, Jonathan E.; Soni, Abhishek S.; Wikswo, John P.; Lipson, Hod
2011-10-01
The reverse engineering of metabolic networks from experimental data is traditionally a labor-intensive task requiring a priori systems knowledge. Using a proven model as a test system, we demonstrate an automated method to simplify this process by modifying an existing or related model--suggesting nonlinear terms and structural modifications--or even constructing a new model that agrees with the system's time series observations. In certain cases, this method can identify the full dynamical model from scratch without prior knowledge or structural assumptions. The algorithm selects between multiple candidate models by designing experiments to make their predictions disagree. We performed computational experiments to analyze a nonlinear seven-dimensional model of yeast glycolytic oscillations. This approach corrected mistakes reliably in both approximated and overspecified models. The method performed well to high levels of noise for most states, could identify the correct model de novo, and make better predictions than ordinary parametric regression and neural network models. We identified an invariant quantity in the model, which accurately derived kinetics and the numerical sensitivity coefficients of the system. Finally, we compared the system to dynamic flux estimation and discussed the scaling and application of this methodology to automated experiment design and control in biological systems in real time.
Automated refinement and inference of analytical models for metabolic networks
Schmidt, Michael D; Vallabhajosyula, Ravishankar R; Jenkins, Jerry W; Hood, Jonathan E; Soni, Abhishek S; Wikswo, John P; Lipson, Hod
2013-01-01
The reverse engineering of metabolic networks from experimental data is traditionally a labor-intensive task requiring a priori systems knowledge. Using a proven model as a test system, we demonstrate an automated method to simplify this process by modifying an existing or related model – suggesting nonlinear terms and structural modifications – or even constructing a new model that agrees with the system’s time-series observations. In certain cases, this method can identify the full dynamical model from scratch without prior knowledge or structural assumptions. The algorithm selects between multiple candidate models by designing experiments to make their predictions disagree. We performed computational experiments to analyze a nonlinear seven-dimensional model of yeast glycolytic oscillations. This approach corrected mistakes reliably in both approximated and overspecified models. The method performed well to high levels of noise for most states, could identify the correct model de novo, and make better predictions than ordinary parametric regression and neural network models. We identified an invariant quantity in the model, which accurately derived kinetics and the numerical sensitivity coefficients of the system. Finally, we compared the system to dynamic flux estimation and discussed the scaling and application of this methodology to automated experiment design and control in biological systems in real-time. PMID:21832805
Lumb, Matthew P.; Steiner, Myles A.; Geisz, John F.; Walters, Robert J.
2014-11-21
The analytical drift-diffusion formalism is able to accurately simulate a wide range of solar cell architectures and was recently extended to include those with back surface reflectors. However, as solar cells approach the limits of material quality, photon recycling effects become increasingly important in predicting the behavior of these cells. In particular, the minority carrier diffusion length is significantly affected by the photon recycling, with consequences for the solar cell performance. In this paper, we outline an approach to account for photon recycling in the analytical Hovel model and compare analytical model predictions to GaAs-based experimental devices operating close to the fundamental efficiency limit.
Simplified Analytical Model of a Six-Degree-of-Freedom Large-Gap Magnetic Suspension System
NASA Technical Reports Server (NTRS)
Groom, Nelson J.
1997-01-01
A simplified analytical model of a six-degree-of-freedom large-gap magnetic suspension system is presented. The suspended element is a cylindrical permanent magnet that is magnetized in a direction which is perpendicular to its axis of symmetry. The actuators are air core electromagnets mounted in a planar array. The analytical model consists of an open-loop representation of the magnetic suspension system with electromagnet currents as inputs.
Exactly solvable self-dual strings
Myers, R.C. ); Periwal, V. )
1990-06-25
Models of random surfaces defined by means of integrals over quaternion-real self-dual random matrices are solved exactly in a double-scaling limit. Coupled nonlinear ordinary differential equations are obtained for the specific heat, which takes the form {ital r}+{ital w}{prime}, where {ital r} is the specific heat of the corresponding Hermitian-matrix model, and {ital w} satisfies a nonlinear differential equation depending on {ital r}. It is shown that the {ital k}=2 theory, which may describe a new phase of two-dimensional quantum gravity, is unitary. An alternative method of solution, based on a set of symplectically orthogonal polynomials, is indicated.
An analytical prediction of pilot ratings utilizing human pilot model
NASA Technical Reports Server (NTRS)
Tanaka, K.; Washizu, K.
1982-01-01
In order to analytically predict pilot ratings, an evaluation method of a manual control system which consists of an aircraft and a human pilot, is proposed and examined. The method is constructed upon the assumptions that the control mission determines the critical frequency the pilot should bring to his focus, and that the degree of closed-loop stability and the human compensation necessary to attain the stability determine the human subjective evaluation of the system. As a result, a simple evaluation chart is introduced. The chart enables prediction of the subjective evaluation, if the controlled element dynamics and the mission are given. The chart is in good accord with almost all of the existing results of pilot ratings. This method has the following advantages: (1) simplicity, in a sense that the method needs to evaluate only two typical controlled element parameters, namely, the gain slope and the phase at the critical control frequency; (2) applicability to unstable controlled elements; (3) predictability of controllability limits of manual control; (4) possibility of estimating human compensatory dynamics.
Analytical solutions for extended surface electrochemical fin models
NASA Astrophysics Data System (ADS)
Cassenti, Brice N.; Nelson, George J.; DeGostin, Matthew B.; Peracchio, Aldo A.; Chiu, Wilson K. S.
2014-11-01
Exact solutions were obtained for variations in the potential and the current for three axisymmetric geometries, with positive, negative and zero curvatures, which simulate current transport in fuel cell electrodes. These solutions can be used to assess the influence of geometry on performance for three dimensional electrode microstructures. A solid oxide fuel cell (SOFC) electrode was selected as a test case for these studies. From the exact solutions, simulations of current flow and potential drop for one dimensional networks in SOFC electrodes were performed. Numerical tests demonstrated that surfaces with positive curvature have greater current flow for the same potential drop due to higher current losses through the lateral surface area. The study also showed that zero curvature solutions will be sufficiently accurate for positive or negative curvature geometries for moderate radius changes, but differ significantly from positive or negative curvature solutions for more extreme radius changes. Analytical solutions indicate fundamental differences in geometry and its influence on current flow. Based on the results of the simulations, an approximate solution, based on one non-dimensional parameter, was developed for estimating the effects of extreme changes in cross-section area.
Energy demand analytics using coupled technological and economic models
Impacts of a range of policy scenarios on end-use energy demand are examined using a coupling of MARKAL, an energy system model with extensive supply and end-use technological detail, with Inforum LIFT, a large-scale model of the us. economy with inter-industry, government, and c...
An Analytical Model for University Identity and Reputation Strategy Work
ERIC Educational Resources Information Center
Steiner, Lars; Sundstrom, Agneta C.; Sammalisto, Kaisu
2013-01-01
Universities face increasing global competition, pressuring them to restructure and find new identities. A multidimensional model: identity, image and reputation of strategic university identity and reputation work is developed. The model includes: organizational identity; employee and student attitudes; symbolic identity; influence from…
On the Development of Parameterized Linear Analytical Longitudinal Airship Models
NASA Technical Reports Server (NTRS)
Kulczycki, Eric A.; Johnson, Joseph R.; Bayard, David S.; Elfes, Alberto; Quadrelli, Marco B.
2008-01-01
In order to explore Titan, a moon of Saturn, airships must be able to traverse the atmosphere autonomously. To achieve this, an accurate model and accurate control of the vehicle must be developed so that it is understood how the airship will react to specific sets of control inputs. This paper explains how longitudinal aircraft stability derivatives can be used with airship parameters to create a linear model of the airship solely by combining geometric and aerodynamic airship data. This method does not require system identification of the vehicle. All of the required data can be derived from computational fluid dynamics and wind tunnel testing. This alternate method of developing dynamic airship models will reduce time and cost. Results are compared to other stable airship dynamic models to validate the methods. Future work will address a lateral airship model using the same methods.
An analytical model for hydraulic fracturing in shallow bedrock formations.
dos Santos, José Sérgio; Ballestero, Thomas Paul; Pitombeira, Ernesto da Silva
2011-01-01
A theoretical method is proposed to estimate post-fracturing fracture size and transmissivity, and as a test of the methodology, data collected from two wells were used for verification. This method can be employed before hydrofracturing in order to obtain estimates of the potential hydraulic benefits of hydraulic fracturing. Five different pumping test analysis methods were used to evaluate the well hydraulic data. The most effective methods were the Papadopulos-Cooper model (1967), which includes wellbore storage effects, and the Gringarten-Ramey model (1974), known as the single horizontal fracture model. The hydraulic parameters resulting from fitting these models to the field data revealed that as a result of hydraulic fracturing, the transmissivity increased more than 46 times in one well and increased 285 times in the other well. The model developed by dos Santos (2008), which considers horizontal radial fracture propagation from the hydraulically fractured well, was used to estimate potential fracture geometry after hydrofracturing. For the two studied wells, their fractures could have propagated to distances of almost 175 m or more and developed maximum apertures of about 2.20 mm and hydraulic apertures close to 0.30 mm. Fracturing at this site appears to have expanded and propagated existing fractures and not created new fractures. Hydraulic apertures calculated from pumping test analyses closely matched the results obtained from the hydraulic fracturing model. As a result of this model, post-fracturing geometry and resulting post-fracturing well yield can be estimated before the actual hydrofracturing. PMID:20572875
Health Informatics for Neonatal Intensive Care Units: An Analytical Modeling Perspective.
Khazaei, Hamzeh; Mench-Bressan, Nadja; McGregor, Carolyn; Pugh, James Edward
2015-01-01
The effective use of data within intensive care units (ICUs) has great potential to create new cloud-based health analytics solutions for disease prevention or earlier condition onset detection. The Artemis project aims to achieve the above goals in the area of neonatal ICUs (NICU). In this paper, we proposed an analytical model for the Artemis cloud project which will be deployed at McMaster Children's Hospital in Hamilton. We collect not only physiological data but also the infusion pumps data that are attached to NICU beds. Using the proposed analytical model, we predict the amount of storage, memory, and computation power required for the system. Capacity planning and tradeoff analysis would be more accurate and systematic by applying the proposed analytical model in this paper. Numerical results are obtained using real inputs acquired from McMaster Children's Hospital and a pilot deployment of the system at The Hospital for Sick Children (SickKids) in Toronto. PMID:27170907
Analytical modeling of irrigation and land use effects on streamflow in semi-arid conditions
NASA Astrophysics Data System (ADS)
Traylor, Jonathan P.; Zlotnik, Vitaly A.
2016-02-01
Availability and uncertainty in input data are the primary constraints of groundwater modeling. Analytical models assimilate the key and important data, but capture the major traits of the watershed. We study a baseflow-dominated stream, Frenchman Creek in southwestern Nebraska, USA, which has experienced large streamflow reductions since the 1960s and is a subject of various actions on water rights appropriation. The new element of the model is simultaneous analytical consideration of groundwater pumping and land use change effects. Analytical stream depletion rate calculations by various methods show that pumping from the 462 irrigation wells in the basin consumed a large amount of baseflow. The simulated streamflow at the outlet of Frenchman Creek with minimal calibration compares favorably with observed streamflow and indicates the viability of an analytical approach to watersheds with limited hydrogeologic data.
Analytical model of the combustion of multicomponent solid propellants
NASA Technical Reports Server (NTRS)
Cohen, N. S.; Price, C. F.; Strand, L. D.
1977-01-01
Multiple flame models derived for simple composite propellants are extended to describe the combustion of propellants containing multimodal particle sizes, mixed oxidizers and monopropellant binders. Models combining the component contributions to propellant surface structure, flame structure and energy distribution are based in part upon experimental observations and in part upon hypotheses constrained to provide reasonable agreement with measured burning rate characteristics. The methods employed consist of superposition, interaction and iteration. The computerized model is applied to explain the effects of multiple ingredients and to discuss burning rate tailoring problems of current interest.
Compact objects from gravitational collapse: an analytical toy model
NASA Astrophysics Data System (ADS)
Malafarina, Daniele; Joshi, Pankaj S.
2015-12-01
We develop here a procedure to obtain regular static configurations resulting from dynamical gravitational collapse of a massive matter cloud in general relativity. Under certain general physical assumptions for the collapsing cloud, we find the class of dynamical models that lead to an equilibrium configuration. To illustrate this, we provide a class of perfect fluid collapse models that lead to a static constant density object as limit. We suggest that similar models might possibly constitute the basis for the description of formation of compact objects in nature.
NASA Technical Reports Server (NTRS)
Oglebay, J. C.
1977-01-01
A thermal analytic model for a 30-cm engineering model mercury-ion thruster was developed and calibrated using the experimental test results of tests of a pre-engineering model 30-cm thruster. A series of tests, performed later, simulated a wide range of thermal environments on an operating 30-cm engineering model thruster, which was instrumented to measure the temperature distribution within it. The modified analytic model is described and analytic and experimental results compared for various operating conditions. Based on the comparisons, it is concluded that the analytic model can be used as a preliminary design tool to predict thruster steady-state temperature distributions for stage and mission studies and to define the thermal interface bewteen the thruster and other elements of a spacecraft.
Recent Analytical and Numerical Results for The Navier-Stokes-Voigt Model and Related Models
NASA Astrophysics Data System (ADS)
Larios, Adam; Titi, Edriss; Petersen, Mark; Wingate, Beth
2010-11-01
The equations which govern the motions of fluids are notoriously difficult to handle both mathematically and computationally. Recently, a new approach to these equations, known as the Voigt-regularization, has been investigated as both a numerical and analytical regularization for the 3D Navier-Stokes equations, the Euler equations, and related fluid models. This inviscid regularization is related to the alpha-models of turbulent flow; however, it overcomes many of the problems present in those models. I will discuss recent work on the Voigt-regularization, as well as a new criterion for the finite-time blow-up of the Euler equations based on their Voigt-regularization. Time permitting, I will discuss some numerical results, as well as applications of this technique to the Magnetohydrodynamic (MHD) equations and various equations of ocean dynamics.
Analytic model for assessing the thermal performance of scuba divers
NASA Technical Reports Server (NTRS)
Montgomery, L. D.
1974-01-01
A biothermal model with a physically-controlled subsystem and a dynamically-controlled subsystem is developed to simulate the thermoregulatory system of man under immersed conditions. The model is consistent with experimental data for seminude subjects immersed to neck in cool to temperate water and for 'wet-suited' subjects immersed to neck in cold water. Equations are derived for predicting body temperatures under various dive conditions.
Analytic model for the dynamic Z-pinch
Piriz, A. R. Sun, Y. B.; Tahir, N. A.
2015-06-15
A model is presented for describing the cylindrical implosion of a shock wave driven by an accelerated piston. It is based in the identification of the acceleration of the shocked mass with the acceleration of the piston. The model yields the separate paths of the piston and the shock. In addition, by considering that the shocked region evolves isentropically, the approximate profiles of all the magnitudes in the shocked region are obtained. The application to the dynamic Z-pinch is presented and the results are compared with the well known snowplow and slug models which are also derived as limiting cases of the present model. The snowplow model is seen to yield a trajectory in between those of the shock and the piston. Instead, the neglect of the inertial effects in the slug model is seen to produce a too fast implosion, and the pressure uniformity is shown to lead to an unphysical instantaneous piston stopping when the shock arrives to the axis.
Human performance modeling for system of systems analytics :soldier fatigue.
Lawton, Craig R.; Campbell, James E.; Miller, Dwight Peter
2005-10-01
The military has identified Human Performance Modeling (HPM) as a significant requirement and challenge of future systems modeling and analysis initiatives as can be seen in the Department of Defense's (DoD) Defense Modeling and Simulation Office's (DMSO) Master Plan (DoD 5000.59-P 1995). To this goal, the military is currently spending millions of dollars on programs devoted to HPM in various military contexts. Examples include the Human Performance Modeling Integration (HPMI) program within the Air Force Research Laboratory, which focuses on integrating HPMs with constructive models of systems (e.g. cockpit simulations) and the Navy's Human Performance Center (HPC) established in September 2003. Nearly all of these initiatives focus on the interface between humans and a single system. This is insufficient in the era of highly complex network centric SoS. This report presents research and development in the area of HPM in a system-of-systems (SoS). Specifically, this report addresses modeling soldier fatigue and the potential impacts soldier fatigue can have on SoS performance.
Compact analytical modeling of SOI partially depleted MOSFETs with LETISOI
NASA Astrophysics Data System (ADS)
Faynot, O.; Poiroux, T.; Pelloie, J. L.
2001-04-01
As SOI technology becomes very attractive for ULSI CMOS, a dedicated and accurate SOI model has to be developed in order to take into account all specific electrical effects related to the SOI structure. The LETISOI model has been developed for partially depleted SOI devices; current and charge equations are built on a physical basis. In addition to the classical MOS conduction, FB effects, self-heating and bipolar transistor action have to be accurately modeled. The transient behavior, very different from the static one, has to be analyzed and kept in mind by designers to take full benefit of SOI devices in circuits, while avoiding any design issue due to SOI. Both FB and body-contacted devices can be described with this model. This paper describes how the model is built with an emphasis on the specific SOI needs and the related strategy for parameter extraction. Typical simulation results are also presented, outlining the capability of the model to simulate SOI specific dynamic behavior like bipolar activation and history effects.
NASA Astrophysics Data System (ADS)
Ukaegbu, Ikechi Augustine; Sangirov, Jamshid; Cho, Mu Hee; Lee, Tae-Woo; Park, Hyo-Hoon
2011-07-01
In this paper, a crosstalk expression and equivalent circuit model have been proposed based on RLC line model and interconnect parameters for wire-bonded and flip-chip bonded multichannel optoelectronic modules. The analytical expression and model are accurate for computing crosstalk of interconnects used in chip packaging. In addition, full-wave simulation and experimental results from total crosstalk measurement are discussed.
A Meta-Analytic Investigation of Fiedler's Contingency Model of Leadership Effectiveness.
ERIC Educational Resources Information Center
Strube, Michael J.; Garcia, Joseph E.
According to Fiedler's Contingency Model of Leadership Effectiveness, group performance is a function of the leader-situation interaction. A review of past validations has found several problems associated with the model. Meta-analytic techniques were applied to the Contingency Model in order to assess the validation evidence quantitatively. The…
Fitting the Normal-Ogive Factor Analytic Model to Scores on Tests.
ERIC Educational Resources Information Center
Ferrando, Pere J.; Lorenzo-Seva, Urbano
2001-01-01
Describes how the nonlinear factor analytic approach of R. McDonald to the normal ogive curve can be used to factor analyze test scores. Discusses the conditions in which this model is more appropriate than the linear model and illustrates the applicability of both models using an empirical example based on data from 1,769 adolescents who took the…
The third exactly solvable hypergeometric quantum-mechanical potential
NASA Astrophysics Data System (ADS)
Ishkhanyan, Artur
2016-07-01
We introduce the third independent exactly solvable hypergeometric potential, after the Eckart and the Pöschl-Teller potentials, which is proportional to an energy-independent parameter and has a shape that is independent of this parameter. The general solution of the Schrödinger equation for this potential is written through fundamental solutions each of which presents an irreducible combination of two Gauss hypergeometric functions. The potential is an asymmetric step-barrier with variable height and steepness. Discussing the transmission above such a barrier, we derive a compact formula for the reflection coefficient.
SIRS Dynamics on Random Networks: Simulations and Analytical Models
NASA Astrophysics Data System (ADS)
Rozhnova, Ganna; Nunes, Ana
The standard pair approximation equations (PA) for the Susceptible-Infective-Recovered-Susceptible (SIRS) model of infection spread on a network of homogeneous degree k predict a thin phase of sustained oscillations for parameter values that correspond to diseases that confer long lasting immunity. Here we present a study of the dependence of this oscillatory phase on the parameter k and of its relevance to understand the behaviour of simulations on networks. For k = 4, we compare the phase diagram of the PA model with the results of simulations on regular random graphs (RRG) of the same degree. We show that for parameter values in the oscillatory phase, and even for large system sizes, the simulations either die out or exhibit damped oscillations, depending on the initial conditions. This failure of the standard PA model to capture the qualitative behaviour of the simulations on large RRGs is currently being investigated.
On loop equations in KdV exactly solvable string theory
Dalley, S. . Joseph Henry Labs.)
1992-05-10
In this paper, the non-perturbative behavior of macroscopic loop amplitudes in the exactly solvable string theories based on the KdV hierarchies is considered. Loop equations are presented for the real non-perturbative solutions living on the spectral half-line, allowed by the most general string equation ({bar P}, Q) = Q, where {bar P} generates scale transformations. In general the end of the half-line (the wall) is a non-perturbative parameter whose role is that of boundary cosmological constant. The properties are compared with the perturbative behavior and solutions of (P,Q) = 1. Detailed arguments are given for the (2,2m {minus} 1) models while generalization to the other (p,q) minimal models and c = 1 is briefly addressed.
Analytical and experimental study of control effort associated with model reference adaptive control
NASA Technical Reports Server (NTRS)
Messer, R. S.; Haftka, R. T.; Cudney, H. H.
1992-01-01
Numerical simulation results presently obtained for the performance of model reference adaptive control (MRAC) are experimentally verified, with a view to accounting for differences between the plant and the reference model after the control function has been brought to bear. MRAC is both experimentally and analytically applied to a single-degree-of-freedom system, as well as analytically to a MIMO system having controlled differences between the reference model and the plant. The control effort is noted to be sensitive to differences between the plant and the reference model.
Herrera-May, Agustín L.; Aguilera-Cortés, Luz A.; Plascencia-Mora, Hector; Rodríguez-Morales, Ángel L.; Lu, Jian
2011-01-01
Multilayered microresonators commonly use sensitive coating or piezoelectric layers for detection of mass and gas. Most of these microresonators have a variable cross-section that complicates the prediction of their fundamental resonant frequency (generally of the bending mode) through conventional analytical models. In this paper, we present an analytical model to estimate the first resonant frequency and deflection curve of single-clamped multilayered microresonators with variable cross-section. The analytical model is obtained using the Rayleigh and Macaulay methods, as well as the Euler-Bernoulli beam theory. Our model is applied to two multilayered microresonators with piezoelectric excitation reported in the literature. Both microresonators are composed by layers of seven different materials. The results of our analytical model agree very well with those obtained from finite element models (FEMs) and experimental data. Our analytical model can be used to determine the suitable dimensions of the microresonator’s layers in order to obtain a microresonator that operates at a resonant frequency necessary for a particular application. PMID:22164071
Analytical models integrated with satellite images for optimized pest management
Technology Transfer Automated Retrieval System (TEKTRAN)
The global field protection (GFP) was developed to protect and optimize pest management resources integrating satellite images for precise field demarcation with physical models of controlled release devices of pesticides to protect large fields. The GFP was implemented using a graphical user interf...
Time dependent turbulence modeling and analytical theories of turbulence
NASA Technical Reports Server (NTRS)
Rubinstein, R.
1993-01-01
By simplifying the direct interaction approximation (DIA) for turbulent shear flow, time dependent formulas are derived for the Reynolds stresses which can be included in two equation models. The Green's function is treated phenomenologically, however, following Smith and Yakhot, we insist on the short and long time limits required by DIA. For small strain rates, perturbative evaluation of the correlation function yields a time dependent theory which includes normal stress effects in simple shear flows. From this standpoint, the phenomenological Launder-Reece-Rodi model is obtained by replacing the Green's function by its long time limit. Eddy damping corrections to short time behavior initiate too quickly in this model; in contrast, the present theory exhibits strong suppression of eddy damping at short times. A time dependent theory for large strain rates is proposed in which large scales are governed by rapid distortion theory while small scales are governed by Kolmogorov inertial range dynamics. At short times and large strain rates, the theory closely matches rapid distortion theory, but at long times it relaxes to an eddy damping model.
Analytic model for assessing thermal performance of SCUBA divers
NASA Technical Reports Server (NTRS)
Montgomery, L. D.
1975-01-01
To assist design of adequate protective clothing, mathematical model of man's thermoregulatory system has been developed so that body thermal responses under immersed conditions can be predicted accurately. Experimental data encompassed wide range of water temperatures, protective clothing, breathing-gas mixtures, and durations of immersion.
A Meta-Analytic Review of Behavior Modeling Training
ERIC Educational Resources Information Center
Taylor, Paul J.; Russ-Eft, Darlene F.; Chan, Daniel W. L.
2005-01-01
A meta-analysis of 117 studies evaluated the effects of behavior modeling training (BMT) on 6 training outcomes, across characteristics of training design. BMT effects were largest for learning outcomes, smaller for job behavior, and smaller still for results outcomes. Although BMT effects on declarative knowledge decayed over time, training…
Canonical Correlation Analysis as a General Analytical Model.
ERIC Educational Resources Information Center
Fan, Xitao
This paper focuses on three aspects related to the conceptualization and application of canonical correlation analysis as a dominant statistical model: (1) partial canonical correlation analysis and its application in statistical testing; (2) the relation between canonical correlation analysis and discriminant analysis; and (3) the relation…
ANALYTICAL DIFFUSION MODEL FOR LONG DISTANCE TRANSPORT OF AIR POLLUTANTS
A steady-state two-dimensional diffusion model suitable for predicting ambient air pollutant concentrations averaged over a long time period (e.g., month, season, or year) and resulting from the transport of pollutants for distances greater than about 100 km from the source is de...
Analytical model of LDMOS with a single step buried oxide layer
NASA Astrophysics Data System (ADS)
Yuan, Song; Duan, Baoxing; Cao, Zhen; Guo, Haijun; Yang, Yintang
2016-09-01
In this paper, a two-dimensional analytical model is established for the Single-Step Buried Oxide SOI structure proposed by the authors. Based on the two-dimensional Poisson equation, the analytic expression of the surface electric field and potential distributions for the device is achieved. In the SBOSOI (Single-Step Buried Oxide Silicon On Insulator) structure, the buried oxide layer thickness changes stepwise along the drift region, and the electric field in the oxide layer also varies with the different buried oxide layer thickness. These variations will modulate the surface electric field distribution through the electric field modulation effects, which makes the surface electric field distribution more uniform. As a result, the breakdown voltage of the device is improved by 60% compared with the conventional SOI structure. To verify the accuracy of the analytical model, the device simulation software ISE TCAD is utilized, the analytical values are in good agreement with the simulation results by the simulation software. The results verified the established two-dimensional analytical model for SBOSOI structure is valid, and it also illustrates the breakdown voltage enhancement by the electric field modulation effect sufficiently. The established analytical models will provide the physical and mathematical basis for further analysis of the new power devices with the patterned buried oxide layer.
Analytical model of LDMOS with a double step buried oxide layer
NASA Astrophysics Data System (ADS)
Yuan, Song; Duan, Baoxing; Cao, Zhen; Guo, Haijun; Yang, Yintang
2016-09-01
In this paper, a two-dimensional analytical model is established for the Buried Oxide Double Step Silicon On Insulator structure proposed by the authors. Based on the two-dimensional Poisson equation, the analytic expressions of the surface electric field and potential distributions for the device are achieved. In the BODS (Buried Oxide Double Step Silicon On Insulator) structure, the buried oxide layer thickness changes stepwise along the drift region, and the positive charge in the drift region can be accumulated at the corner of the step. These accumulated charge function as the space charge in the depleted drift region. At the same time, the electric field in the oxide layer also varies with the different drift region thickness. These variations especially the accumulated charge will modulate the surface electric field distribution through the electric field modulation effects, which makes the surface electric field distribution more uniform. As a result, the breakdown voltage of the device is improved by 30% compared with the conventional SOI structure. To verify the accuracy of the analytical model, the device simulation software ISE TCAD is utilized, the analytical values are in good agreement with the simulation results by the simulation software. That means the established two-dimensional analytical model for BODS structure is valid, and it also illustrates the breakdown voltage enhancement by the electric field modulation effect sufficiently. The established analytical models will provide the physical and mathematical basis for further analysis of the new power devices with the patterned buried oxide layer.
Analytical and numerical models to predict the behavior of unbonded flexible risers under torsion
NASA Astrophysics Data System (ADS)
Ren, Shao-fei; Xue, Hong-xiang; Tang, Wen-yong
2016-04-01
This paper presents analytical and numerical models to predict the behavior of unbonded flexible risers under torsion. The analytical model takes local bending and torsion of tensile armor wires into consideration, and equilibrium equations of forces and displacements of layers are deduced. The numerical model includes lay angle, cross-sectional profiles of carcass, pressure armor layer and contact between layers. Abaqus/Explicit quasi-static simulation and mass scaling are adopted to avoid convergence problem and excessive computation time caused by geometric and contact nonlinearities. Results show that local bending and torsion of helical strips may have great influence on torsional stiffness, but stress related to bending and torsion is negligible; the presentation of anti-friction tapes may have great influence both on torsional stiffness and stress; hysteresis of torsion-twist relationship under cyclic loading is obtained by numerical model, which cannot be predicted by analytical model because of the ignorance of friction between layers.
About solvability of some boundary value problems for Poisson equation in a ball
NASA Astrophysics Data System (ADS)
Koshanova, Maira D.; Usmanov, Kairat I.; Turmetov, Batirkhan Kh.
2016-08-01
In the present paper, we study properties of some integro-differential operators of fractional order. As an application of the properties of these operators for Poisson equation we examine questions on solvability of a fractional analogue of the Neumann problem and analogues of periodic boundary value problems for circular domains. The exact conditions for solvability of these problems are found.
On the solvability of boundary value problems for the nonhomogeneous polyharmonic equation in a ball
NASA Astrophysics Data System (ADS)
Koshanov, Bakytbek Danebekovich
2014-08-01
In this paper we find necessary and sufficient conditions for the solvability of boundary value problems for the nonhomogeneous polyharmonic equation in a ball. We construct the explicit Green function of the Dirichlet problem for the polyharmonic equation in a ball. In particular, we find conditions for the solvability of Neumann problems for the biharmonic and 3- harmonic equations.
An analytical model for in situ extraction of organic vapors
Roy, W.R.; Griffin, R.A.
1991-01-01
This paper introduces a simple convective-flow model that can be used as a screening tool and for conducting sensitivity analyses for in situ vapor extraction of organic compounds from porous media. An assumption basic to this model was that the total mass of volatile organic chemicals (VOC) exists in three forms: as vapors, in the soil solution, and adsorbed to soil particles. The equilibrium partitioning between the vapor-liquid phase was described by Henry's law constants (K(H)) and between the liquid-soil phase by soil adsorption constants (K(d)) derived from soil organic carbon-water partition coefficients (K(oc)). The model was used to assess the extractability of 36 VOCs from a hypothetical site. Most of the VOCs appeared to be removable from soil by this technology, although modeling results suggested that rates for the alcohols and ketones may be very slow. In general, rates for weakly adsorbed compounds (K(oc) < 100 mL/g) were significantly higher when K(H) was greater than 10-4 atm??m3??mol-1. When K(oc) was greater than about 100 mL/g, the rates of extraction were sensitive to the amount of organic carbon present in the soil. The air permeability of the soil material (k) was a critical factor. In situ extraction needs careful evaluation when k is less than 10 millidarcies to determine its applicability. An increase in the vacuum applied to an extraction well accelerated removal rates but the diameter of the well had little effect. However, an increase in the length of the well screen open to the contaminated zone significantly affected removal rates, especially in low-permeability materials.This paper introduces a simple convective-flow model that can be used as a screening tool and for conducting sensitivity analyses for in situ vapor extraction of organic compounds from porous media. An assumption basic to this model was that the total mass of volatile organic chemicals (VOC) exists in three forms: as vapors, in the soil solution, and adsorbed to soil
An Analytic Model Of Thermal Drift In Piezoresistive Microcantilever Sensors
Loui, A; Elhadj, S; Sirbuly, D J; McCall, S K; Hart, B R; Ratto, T V
2009-08-26
A closed form semi-empirical model has been developed to understand the physical origins of thermal drift in piezoresistive microcantilever sensors. The two-component model describes both the effects of temperature-related bending and heat dissipation on the piezoresistance. The temperature-related bending component is based on the Euler-Bernoulli theory of elastic deformation applied to a multilayer cantilever. The heat dissipation component is based on energy conservation per unit time for a piezoresistive cantilever in a Wheatstone bridge circuit, representing a balance between electrical power input and heat dissipation into the environment. Conduction and convection are found to be the primary mechanisms of heat transfer, and the dependence of these effects on the thermal conductivity, temperature, and flow rate of the gaseous environment is described. The thermal boundary layer value which defines the length scale of the heat dissipation phenomenon is treated as an empirical fitting parameter. Using the model, it is found that the cantilever heat dissipation is unaffected by the presence of a thin polymer coating, therefore the residual thermal drift in the differential response of a coated and uncoated cantilever is the result of non-identical temperature-related bending. Differential response data shows that residual drift is eliminated under isothermal laboratory conditions but not the unregulated and variable conditions that exist in the outdoor environment (i.e., the field). The two-component model is then validated by simulating the thermal drifts of an uncoated and a coated piezoresistive cantilever under field conditions over a 24 hour period using only meteorological data as input.
An analytic model of thermal drift in piezoresistive microcantilever sensors
NASA Astrophysics Data System (ADS)
Loui, A.; Elhadj, S.; Sirbuly, D. J.; McCall, S. K.; Hart, B. R.; Ratto, T. V.
2010-03-01
A closed-form semiempirical model has been developed to understand the physical origins of thermal drift in piezoresistive microcantilever sensors. The two-component model describes both the effects of temperature-related bending and heat dissipation on the piezoresistance. The temperature-related bending component is based on the Euler-Bernoulli theory of elastic deformation applied to a multilayer cantilever. The heat dissipation component is based on energy conservation per unit time for a piezoresistive cantilever in a Wheatstone bridge circuit, representing a balance between electrical power input and heat dissipation into the environment. Conduction and convection are found to be the primary mechanisms of heat transfer, and the dependence of these effects on the thermal conductivity, temperature, and flow rate of the gaseous environment is described. The thermal boundary layer value that defines the length scale of the heat dissipation phenomenon is treated as an empirical fitting parameter. Using the model, it is found that the cantilever heat dissipation is unaffected by the presence of a thin polymer coating; therefore, the residual thermal drift in the differential response of a coated and uncoated cantilever is the result of nonidentical temperature-related bending. Differential response data show that residual drift is eliminated under isothermal laboratory conditions but not the unregulated and variable conditions that exist in the outdoor environment (i.e., the field). The two-component model is then validated by simulating the thermal drifts of an uncoated and a coated piezoresistive cantilever under field conditions over a 24 h period using only meteorological data as input variables.
Analytic Intermodel Consistent Modeling of Volumetric Human Lung Dynamics.
Ilegbusi, Olusegun; Seyfi, Behnaz; Neylon, John; Santhanam, Anand P
2015-10-01
Human lung undergoes breathing-induced deformation in the form of inhalation and exhalation. Modeling the dynamics is numerically complicated by the lack of information on lung elastic behavior and fluid-structure interactions between air and the tissue. A mathematical method is developed to integrate deformation results from a deformable image registration (DIR) and physics-based modeling approaches in order to represent consistent volumetric lung dynamics. The computational fluid dynamics (CFD) simulation assumes the lung is a poro-elastic medium with spatially distributed elastic property. Simulation is performed on a 3D lung geometry reconstructed from four-dimensional computed tomography (4DCT) dataset of a human subject. The heterogeneous Young's modulus (YM) is estimated from a linear elastic deformation model with the same lung geometry and 4D lung DIR. The deformation obtained from the CFD is then coupled with the displacement obtained from the 4D lung DIR by means of the Tikhonov regularization (TR) algorithm. The numerical results include 4DCT registration, CFD, and optimal displacement data which collectively provide consistent estimate of the volumetric lung dynamics. The fusion method is validated by comparing the optimal displacement with the results obtained from the 4DCT registration. PMID:26292034
Semi-analytical modeling of the NIO1 source
NASA Astrophysics Data System (ADS)
Cazzador, M.; Cavenago, M.; Serianni, G.; Veltri, P.
2015-04-01
NIO1 is a compact and versatile negative ion source, with a total current of 130 mA accelerated to 60 keV. Negative ions are created inside the plasma, which is inductively coupled to an external rf cylindrical coil operating in the range of 2 ± 0.2 MHz. The plasma is confined in the source chamber (a 50 mm radius cylinder) by a multipole magnetic field and the ions are extracted through a 3x3 matrix of apertures. The use of cesium, to enhance the negative ion production by H0 bombardment of the surfaces, is foreseen in a second stage of the operation, so that at present time the source is operating in pure volume configuration. This paper presents a model aimed to describe the main physical phenomena occurring in the source, focusing on the rf coupling with the plasma and the evolution of plasma parameters in the source. With respect to more sophisticated models of negative ion sources here we aimed to develop a fast tool capable of qualitatively describing the response of the system to variations in the basic operating parameters. The findings of this models is finally compared with the first experimental results of NIO1.
Semi-analytical modeling of the NIO1 source
Cazzador, M.; Cavenago, M.; Serianni, G.; Veltri, P.
2015-04-08
NIO1 is a compact and versatile negative ion source, with a total current of 130 mA accelerated to 60 keV. Negative ions are created inside the plasma, which is inductively coupled to an external rf cylindrical coil operating in the range of 2 ± 0.2 MHz. The plasma is confined in the source chamber (a 50 mm radius cylinder) by a multipole magnetic field and the ions are extracted through a 3x3 matrix of apertures. The use of cesium, to enhance the negative ion production by H{sub 0} bombardment of the surfaces, is foreseen in a second stage of the operation, so that at present time the source is operating in pure volume configuration. This paper presents a model aimed to describe the main physical phenomena occurring in the source, focusing on the rf coupling with the plasma and the evolution of plasma parameters in the source. With respect to more sophisticated models of negative ion sources here we aimed to develop a fast tool capable of qualitatively describing the response of the system to variations in the basic operating parameters. The findings of this models is finally compared with the first experimental results of NIO1.
International Space Station Microgravity Analytical Model Correlation And Update
NASA Technical Reports Server (NTRS)
DelBasso, Steve; Laible, Michael; OKeefe, Edmund; Scheer, Steven A.
2003-01-01
The acceleration environment aboard the completed International Space Station (ISS) is a key resource for scientific and technological endeavors. Hardware verification activIties and early measurements indicate that the ISS is well on the way of meeting these "Assembly Complete" "microgravity" provisions, however, the simulation models that compute these accelerations have, to date, lacked the high degree of empirical validation typical of standard aerospace industry practices. Assembly stage, on-orbit measurements are used to address this shortcoming and to develop higher confidence in the simulation models. The Phase I correlation results show the analyses to be consistently conservative, producing higher than measured levels. The 25 to 30% greater quasi-steady computations are deemed acceptable for verification. Updates are made to localized structural dynamic and vibroacoustic parameters that reduce responses in selected one-third octave bands by almost 50%. These models are then used for the Assembly Complete verification analysis which concludes that the ISS vehicle meets the ISS microgravity requirements with minor reservations. Two of the sixteen rack are marginally non-compliant in the quasi-steady regime, and operational constraints are needed on the U. S. Lab and ESA APM vacuum resource vents, and the Russian Resistive Exercise Device in the structural dynamic regime.
NASA Technical Reports Server (NTRS)
Gedge, M. R.
1979-01-01
Analytical models were developed to study the effect of flow contraction and screening on inflow distortions to identify qualitative design criteria. Results of the study are that: (1) static testing distortions are due to atmospheric turbulence, nacelle boundary layer, exhaust flow reingestion, flow over stand, ground plane, and engine casing; (2) flow contraction suppresses, initially, turbulent axial velocity distortions and magnifies turbulent transverse velocity distortions; (3) perforated plate and gauze screens suppress axial components of velocity distortions to a degree determined by the screen pressure loss coefficient; (4) honeycomb screen suppress transverse components of velocity distortions to a degree determined by the length to diameter ratio of the honeycomb; (5) acoustic transmission loss of perforated plate is controlled by the reactance of its acoustic impedance; (6) acoustic transmission loss of honeycomb screens is negligible; and (7) a model for the direction change due to a corner between honeycomb panels compares favorably with measured data.
Analytical, Experimental, and Modelling Studies of Lunar and Terrestrial Rocks
NASA Technical Reports Server (NTRS)
Haskin, Larry A.
1997-01-01
The goal of our research has been to understand the paths and the processes of planetary evolution that produced planetary surface materials as we find them. Most of our work has been on lunar materials and processes. We have done studies that obtain geological knowledge from detailed examination of regolith materials and we have reported implications for future sample-collecting and on-surface robotic sensing missions. Our approach has been to study a suite of materials that we have chosen in order to answer specific geologic questions. We continue this work under NAG5-4172. The foundation of our work has been the study of materials with precise chemical and petrographic analyses, emphasizing analysis for trace chemical elements. We have used quantitative models as tests to account for the chemical compositions and mineralogical properties of the materials in terms of regolith processes and igneous processes. We have done experiments as needed to provide values for geochemical parameters used in the models. Our models take explicitly into account the physical as well as the chemical processes that produced or modified the materials. Our approach to planetary geoscience owes much to our experience in terrestrial geoscience, where samples can be collected in field context and sampling sites revisited if necessary. Through studies of terrestrial analog materials, we have tested our ideas about the origins of lunar materials. We have been mainly concerned with the materials of the lunar highland regolith, their properties, their modes of origin, their provenance, and how to extrapolate from their characteristics to learn about the origin and evolution of the Moon's early igneous crust. From this work a modified model for the Moon's structure and evolution is emerging, one of globally asymmetric differentiation of the crust and mantle to produce a crust consisting mainly of ferroan and magnesian igneous rocks containing on average 70-80% plagioclase, with a large
Analytical modeling of squeeze air film damping of biomimetic MEMS directional microphone
NASA Astrophysics Data System (ADS)
Ishfaque, Asif; Kim, Byungki
2016-08-01
Squeeze air film damping is introduced in microelectromechanical systems due to the motion of the fluid between two closely spaced oscillating micro-structures. The literature is abundant with different analytical models to address the squeeze air film damping effects, however, there is a lack of work in modeling the practical sensors like directional microphones. Here, we derive an analytical model of squeeze air film damping of first two fundamental vibration modes, namely, rocking and bending modes, of a directional microphone inspired from the fly Ormia ochracea's ear anatomy. A modified Reynolds equation that includes compressibility and rarefaction effects is used in the analysis. Pressure distribution under the vibrating diaphragm is derived by using Green's function. From mathematical modeling of the fly's inspired mechanical model, we infer that bringing the damping ratios of both modes in the critical damping range enhance the directional sensitivity cues. The microphone parameters are varied in derived damping formulas to bring the damping ratios in the vicinity of critical damping, and to show the usefulness of the analytical model in tuning the damping ratios of both modes. The accuracy of analytical damping results are also verified by finite element method (FEM) using ANSYS. The FEM results are in full compliance with the analytical results.
Analytical models of calcium binding in a calcium channel
NASA Astrophysics Data System (ADS)
Liu, Jinn-Liang; Eisenberg, Bob
2014-08-01
The anomalous mole fraction effect of L-type calcium channels is analyzed using a Fermi like distribution with the experimental data of Almers and McCleskey [J. Physiol. 353, 585 (1984)] and the atomic resolution model of Lipkind and Fozzard [Biochemistry 40, 6786 (2001)] of the selectivity filter of the channel. Much of the analysis is algebraic, independent of differential equations. The Fermi distribution is derived from the configuration entropy of ions and water molecules with different sizes, different valences, and interstitial voids between particles. It allows us to calculate potentials and distances (between the binding ion and the oxygen ions of the glutamate side chains) directly from the experimental data using algebraic formulas. The spatial resolution of these results is comparable with those of molecular models, but of course the accuracy is no better than that implied by the experimental data. The glutamate side chains in our model are flexible enough to accommodate different types of binding ions in different bath conditions. The binding curves of Na+ and Ca2+ for [CaCl2] ranging from 10-8 to 10-2 M with a fixed 32 mM background [NaCl] are shown to agree with published Monte Carlo simulations. The Poisson-Fermi differential equation—that includes both steric and correlation effects—is then used to obtain the spatial profiles of energy, concentration, and dielectric coefficient from the solvent region to the filter. The energy profiles of ions are shown to depend sensitively on the steric energy that is not taken into account in the classical rate theory. We improve the rate theory by introducing a steric energy that lumps the effects of excluded volumes of all ions and water molecules and empty spaces between particles created by Lennard-Jones type and electrostatic forces. We show that the energy landscape varies significantly with bath concentrations. The energy landscape is not constant.
Analytical models of calcium binding in a calcium channel
Liu, Jinn-Liang; Eisenberg, Bob
2014-08-21
The anomalous mole fraction effect of L-type calcium channels is analyzed using a Fermi like distribution with the experimental data of Almers and McCleskey [J. Physiol. 353, 585 (1984)] and the atomic resolution model of Lipkind and Fozzard [Biochemistry 40, 6786 (2001)] of the selectivity filter of the channel. Much of the analysis is algebraic, independent of differential equations. The Fermi distribution is derived from the configuration entropy of ions and water molecules with different sizes, different valences, and interstitial voids between particles. It allows us to calculate potentials and distances (between the binding ion and the oxygen ions of the glutamate side chains) directly from the experimental data using algebraic formulas. The spatial resolution of these results is comparable with those of molecular models, but of course the accuracy is no better than that implied by the experimental data. The glutamate side chains in our model are flexible enough to accommodate different types of binding ions in different bath conditions. The binding curves of Na{sup +} and Ca{sup 2+} for [CaCl{sub 2}] ranging from 10{sup −8} to 10{sup −2} M with a fixed 32 mM background [NaCl] are shown to agree with published Monte Carlo simulations. The Poisson-Fermi differential equation—that includes both steric and correlation effects—is then used to obtain the spatial profiles of energy, concentration, and dielectric coefficient from the solvent region to the filter. The energy profiles of ions are shown to depend sensitively on the steric energy that is not taken into account in the classical rate theory. We improve the rate theory by introducing a steric energy that lumps the effects of excluded volumes of all ions and water molecules and empty spaces between particles created by Lennard-Jones type and electrostatic forces. We show that the energy landscape varies significantly with bath concentrations. The energy landscape is not constant.
Leasing vs. owning a medical office: an analytical model.
Tolbert, Samuel H; Wood, Carol P
2007-01-01
Physicians often face a major financial dilemma: To lease or own their medical office. This article takes a set of typical assumptions for a real estate market and analyzes the capital costs, cash flow, and investment implications of the option of leasing a medical office versus owning a similar property. The paper analyzes the financial aspects of each option and the impact on net physician income and potential return-on-investment. A model for analysis is presented that can be used by practitioners who advise physicians in such decision-making. PMID:18972995
Analytic Differentiation of Barlat's 2D Criteria for Inverse Modeling
Endelt, Benny; Nielsen, Karl Brian; Danckert, Joachim
2005-08-05
The demand for alternative identification schemes for identification of constitutive parameters is getting more pronounced as the complexity of the constitutive equations increases, i.e. the number of parameters subject to identification. A general framework for inverse identification of constitutive parameters associated with sheet metal forming is proposed in the article. The inverse problem is solved, through minimization of the least square error between an experimental punch force sampled from a deep drawing and a predicted punch force produced from a coherent finite element model.
Analytics For Distracted Driver Behavior Modeling in Dilemma Zone
Li, Jan-Mou; Malikopoulos, Andreas; Thakur, Gautam; Vatsavai, Raju
2014-01-01
In this paper, we present the results obtained and insights gained through the analysis of TRB contest data. We used exploratory analysis, regression, and clustering models for gaining insights into the driver behavior in a dilemma zone while driving under distraction. While simple exploratory analysis showed the distinguishing driver behavior patterns among different popu- lation groups in the dilemma zone, regression analysis showed statically signification relationships between groups of variables. In addition to analyzing the contest data, we have also looked into the possible impact of distracted driving on the fuel economy.
Analytical modeling of the mechanical properties of recycled plastics
MacBain, K.; Ala Saadeghvaziri, M.
1999-06-01
The widespread use of recycled plastics has been restricted in part because of the limited state of knowledge about the behavior of this recycled material and the lack of unified design procedures. The material behaves differently in tension and compression, and the nonlinear nature of recycled plastic makes traditional terminology such as modulus of elasticity difficult to determine because generally there is no clearly defined yield point. Furthermore, the modulus of rupture, a property determined from beam tests, can vary for different portions of a fabricated beam making these terms specific to the particular beam rather than exclusively a material property. This article investigates the properties of recycled thermoplastics and methods of testing and analyzing recycled thermoplastic members in both axial compression and flexure. In an effort to provide means for analysis of recycled plastic, material tests of discrete portions of beams were performed to develop a uniaxial material model. The model was used to predict member response based on section geometry alone. This enables prediction of member response of sections not yet tested or even constructed with greater accuracy than previously possible, regardless of the differences in tension-compression behavior and material nonlinearities or variations in material properties among manufacturers.
Loop quantum cosmology in Bianchi type I models: Analytical investigation
Chiou, D.-W.
2007-01-15
The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed. In this paper, the methods are extended to the anisotropic Bianchi I cosmology. Both the precursor and the improved strategies are applied and the expected results are established: (i) the scalar field again serves as an internal clock and is treated as emergent time; (ii) the total Hamiltonian constraint is derived by imposing the fundamental discreteness and gives the evolution as a difference equation; and (iii) the physical Hilbert space, Dirac observables, and semiclassical states are constructed rigorously. It is also shown that the state in the kinematical Hilbert space associated with the classical singularity is decoupled in the difference evolution equation, indicating that the big bounce may take place when any of the area scales undergoes the vanishing behavior. The investigation affirms the robustness of the framework used in the isotropic model by enlarging its domain of validity and provides foundations to conduct the detailed numerical analysis.
Semi-analytical modelling of positive corona discharge in air
NASA Astrophysics Data System (ADS)
Pontiga, Francisco; Yanallah, Khelifa; Chen, Junhong
2013-09-01
Semianalytical approximate solutions of the spatial distribution of electric field and electron and ion densities have been obtained by solving Poisson's equations and the continuity equations for the charged species along the Laplacian field lines. The need to iterate for the correct value of space charge on the corona electrode has been eliminated by using the corona current distribution over the grounded plane derived by Deutsch, which predicts a cos m θ law similar to Warburg's law. Based on the results of the approximated model, a parametric study of the influence of gas pressure, the corona wire radius, and the inter-electrode wire-plate separation has been carried out. Also, the approximate solutions of the electron number density has been combined with a simplified plasma chemistry model in order to compute the ozone density generated by the corona discharge in the presence of a gas flow. This work was supported by the Consejeria de Innovacion, Ciencia y Empresa (Junta de Andalucia) and by the Ministerio de Ciencia e Innovacion, Spain, within the European Regional Development Fund contracts FQM-4983 and FIS2011-25161.
Development of an analytical model for organic-fluid fouling
Panchal, C.B.; Watkinson, A.P.
1994-10-01
The research goal of this project is to determine ways to effectively mitigate fouling in organic fluids: hydrocarbons and derived fluids. The fouling research focuses on the development of methodology for determining threshold conditions for fouling. Initially, fluid containing chemicals known to produce foulant is analyzed; subsequently, fouling of industrial fluids is investigated. The fouling model developed for determining the effects of physical parameters is the subject of this report. The fouling model is developed on the premise that the chemical reaction for generation of precursor can take place in the bulk fluid, in the thermal-boundary layer, or at the fluid/wall interface, depending upon the interactive effects of fluid dynamics, heat and mass transfer, and the controlling chemical reaction. In the analysis, the experimental data are examined for fouling deposition of polyperoxide produced by autoxidation of indene in kerosene. The effects of fluid and wall temperatures for two flow geometries are analyzed. The results show that the relative effects of physical parameters on the fouling rate differ for the three fouling mechanisms. Therefore, to apply the closed-flow-loop data to industrial conditions, the controlling mechanism must be identified.
Analytical modeling and experimental validation of a V-shape piezoelectric ultrasonic transducer
NASA Astrophysics Data System (ADS)
Li, Xiaoniu; Yao, Zhiyuan
2016-07-01
In this paper, an analytical model of a V-shape piezoelectric ultrasonic transducer is presented. The V-shape piezoelectric ultrasonic transducer has been widely applied to the piezoelectric actuator (ultrasonic motor), ultrasonic aided fabrication, sensor, and energy harvesting device. The V-shape piezoelectric ultrasonic transducer consists of two Langevin-type transducers connected together through a coupling point with a certain coupling angle. Considering the longitudinal and lateral movements of a single beam, the symmetrical and asymmetrical modals of the V-shape piezoelectric ultrasonic transducer are calculated. By using Hamilton–Lagrange equations, the electromechanical coupling model of the V-shape piezoelectric ultrasonic transducer is proposed. The influence of the coupling angle and cross-section on modal characteristics and electromechanical coupling coefficient are analyzed by the analytical model. A prototype of the V-shape piezoelectric ultrasonic transducer is fabricated, and the results of the experiments are in good agreement with the analytical model.
Analytical modeling of structure-soil systems for lunar bases
NASA Technical Reports Server (NTRS)
Macari-Pasqualino, Jose Emir
1989-01-01
The study of the behavior of granular materials in a reduced gravity environment and under low effective stresses became a subject of great interest in the mid 1960's when NASA's Surveyor missions to the Moon began the first extraterrestrial investigation and it was found that Lunar soils exhibited properties quite unlike those on Earth. This subject gained interest during the years of the Apollo missions and more recently due to NASA's plans for future exploration and colonization of Moon and Mars. It has since been clear that a good understanding of the mechanical properties of granular materials under reduced gravity and at low effective stress levels is of paramount importance for the design and construction of surface and buried structures on these bodies. In order to achieve such an understanding it is desirable to develop a set of constitutive equations that describes the response of such materials as they are subjected to tractions and displacements. This presentation examines issues associated with conducting experiments on highly nonlinear granular materials under high and low effective stresses. The friction and dilatancy properties which affect the behavior of granular soils with low cohesion values are assessed. In order to simulate the highly nonlinear strength and stress-strain behavior of soils at low as well as high effective stresses, a versatile isotropic, pressure sensitive, third stress invariant dependent, cone-cap elasto-plastic constitutive model was proposed. The integration of the constitutive relations is performed via a fully implicit Backward Euler technique known as the Closest Point Projection Method. The model was implemented into a finite element code in order to study nonlinear boundary value problems associated with homogeneous as well as nonhomogeneous deformations at low as well as high effective stresses. The effect of gravity (self-weight) on the stress-strain-strength response of these materials is evaluated. The calibration
Fatigue of notched fiber composite laminates. Part 1: Analytical model
NASA Technical Reports Server (NTRS)
Mclaughlin, P. V., Jr.; Kulkarni, S. V.; Huang, S. N.; Rosen, B. W.
1975-01-01
A description is given of a semi-empirical, deterministic analysis for prediction and correlation of fatigue crack growth, residual strength, and fatigue lifetime for fiber composite laminates containing notches (holes). The failure model used for the analysis is based upon composite heterogeneous behavior and experimentally observed failure modes under both static and fatigue loading. The analysis is consistent with the wearout philosophy. Axial cracking and transverse cracking failure modes are treated together in the analysis. Cracking off-axis is handled by making a modification to the axial cracking analysis. The analysis predicts notched laminate failure from unidirectional material fatique properties using constant strain laminate analysis techniques. For multidirectional laminates, it is necessary to know lamina fatique behavior under axial normal stress, transverse normal stress and axial shear stress. Examples of the analysis method are given.
Analytical modeling of circuit aerodynamics in the new NASA Lewis wind tunnel
NASA Technical Reports Server (NTRS)
Towne, C. E.; Povinelli, L. A.; Kunik, W. G.; Muramoto, K. K.; Hughes, C. E.; Levy, R.
1985-01-01
Rehabilitation and extention of the capability of the altitude wind tunnel (AWT) was analyzed. The analytical modeling program involves the use of advanced axisymmetric and three dimensional viscous analyses to compute the flow through the various AWT components. Results for the analytical modeling of the high speed leg aerodynamics are presented; these include: an evaluation of the flow quality at the entrance to the test section, an investigation of the effects of test section bleed for different model blockages, and an examination of three dimensional effects in the diffuser due to reentry flow and due to the change in cross sectional shape of the exhaust scoop.
Analytical modeling of circuit aerodynamics in the new NASA Lewis Altitude Wind Tunnel
NASA Technical Reports Server (NTRS)
Towne, C. E.; Povinelli, L. A.; Kunik, W. G.; Muramoti, K. K.; Hughes, C. E.; Levy, R.
1985-01-01
Rehabilitation and extention of the capability of the altitude wind tunnel (AWT) was analyzed. The analytical modelling program involves the use of advanced axisymmetric and three dimensional viscous analyses to compute the flow through the various AWT components. Results for the analytical modelling of the high speed leg aerodynamics are presented; these include: an evaluation of the flow quality at the entrance to the test section, an investigation of the effects of test section bleed for different model blockages, and an examination of three dimensional effects in the diffuser due to reentry flow and due to the change in cross sectional shape of the exhaust scoop.
Analytical model study of dendrimer/DNA complexes.
Qamhieh, Khawla; Nylander, Tommy; Ainalem, Marie-Louise
2009-07-13
The interaction between positively charged poly(amido amine) (PAMAM) dendrimers of generation 4 and DNA has been investigated for two DNA lengths; 2000 basepairs (bp; L = 680 nm) and 4331 bp (L = 1472.5 nm) using a theoretical model by Schiessel for a semiflexible polyelectrolyte and hard spheres. The model was modified to take into account that the dendrimers are to be regarded as soft spheres, that is, the radius is not constant when the DNA interact with the dendrimer. For the shorter and longer DNA, the estimated optimal wrapping length, l(opt) is ≈15.69 and ≈12.25 nm, respectively, for dendrimers that retain their original size (R(o) = 2.25 nm) upon DNA interaction. However, the values of l(opt) for the dendrimers that were considered to have a radius of (R = 0.4R(o)) 0.9 nm were 9.3 and 9.4 nm for the short and long DNA, respectively, and the effect due to the DNA length is no longer observed. For l(opt) = 10.88 nm, which is the length needed to neutralize the 64 positive charges of the G4 dendrimer, the maximum number of dendrimers per DNA (N(max)) was ≈76 for the shorter DNA, which is larger than the corresponding experimental value of 35 for 2000 bp DNA. For the longer DNA, N(max) ≈ 160, which is close to the experimental value of 140 for the 4331 bp DNA. Charge inversion of the dendrimer is only observed when they retain their size or only slightly contract upon DNA interaction. PMID:19438230
Analytical and Numerical Modeling of Strongly Rotating Rarefied Gas Flows
NASA Astrophysics Data System (ADS)
Pradhan, Sahadev; Kumaran, Viswanathan
2015-11-01
Centrifugal gas separation processes effect separation by utilizing the difference in the mole fraction in a high speed rotating cylinder caused by the difference in molecular mass, and consequently the centrifugal force density. These have been widely used in isotope separation because chemical separation methods cannot be used to separate isotopes of the same chemical species. More recently, centrifugal separation has also been explored for the separation of gases such as carbon dioxide and methane. The efficiency of separation is critically dependent on the secondary flow generated due to temperature gradients at the cylinder wall or due to inserts, and it is important to formulate accurate models for this secondary flow. The widely used Onsager model for secondary flow is restricted to very long cylinders where the length is large compared to the diameter, the limit of high stratification parameter, where the gas is restricted to a thin layer near the wall of the cylinder, and it assumes that there is no mass difference in the two species while calculating the secondary flow. There are two objectives of the present analysis of the rarefied gas flow in a rotating cylinder. The first is to remove the restriction of high stratification parameter, and to generalize the solutions to low rotation speeds where the stratification parameter may be O(1), and to apply for dissimilar gases considering the difference in molecular mass of the two species. Secondly, we would like to compare the predictions with molecular simulations based on the direct simulation Monte Carlo (DSMC) method for rarefied gas flows, in order to quantify the errors resulting from the approximations at different aspect ratios, Reynolds number and stratification parameter.
Analytical solution for two-phase flow in a wellbore using the drift-flux model
Pan, L.; Webb, S.W.; Oldenburg, C.M.
2011-11-01
This paper presents analytical solutions for steady-state, compressible two-phase flow through a wellbore under isothermal conditions using the drift flux conceptual model. Although only applicable to highly idealized systems, the analytical solutions are useful for verifying numerical simulation capabilities that can handle much more complicated systems, and can be used in their own right for gaining insight about two-phase flow processes in wells. The analytical solutions are obtained by solving the mixture momentum equation of steady-state, two-phase flow with an assumption that the two phases are immiscible. These analytical solutions describe the steady-state behavior of two-phase flow in the wellbore, including profiles of phase saturation, phase velocities, and pressure gradients, as affected by the total mass flow rate, phase mass fraction, and drift velocity (i.e., the slip between two phases). Close matching between the analytical solutions and numerical solutions for a hypothetical CO{sub 2} leakage problem as well as to field data from a CO{sub 2} production well indicates that the analytical solution is capable of capturing the major features of steady-state two-phase flow through an open wellbore, and that the related assumptions and simplifications are justified for many actual systems. In addition, we demonstrate the utility of the analytical solution to evaluate how the bottomhole pressure in a well in which CO{sub 2} is leaking upward responds to the mass flow rate of CO{sub 2}-water mixture.
Integrability of the Rabi Model
Braak, D.
2011-09-02
The Rabi model is a paradigm for interacting quantum systems. It couples a bosonic mode to the smallest possible quantum model, a two-level system. I present the analytical solution which allows us to consider the question of integrability for quantum systems that do not possess a classical limit. A criterion for quantum integrability is proposed which shows that the Rabi model is integrable due to the presence of a discrete symmetry. Moreover, I introduce a generalization with no symmetries; the generalized Rabi model is the first example of a nonintegrable but exactly solvable system.
Nanoscale device modeling using a conserving analytic continuation technique
NASA Astrophysics Data System (ADS)
Mera, H.; Lannoo, M.; Cavassilas, N.; Bescond, M.
2013-08-01
We propose an alternative approach to self-consistency and conservation laws in the theory of nonequilibrium Green's functions (NEGF's), which provides an infinite family of conserving but, generally, non-self-consistent approximations. Within any Φ-derivable approximation the associated Born series for the NEGF is shown to be conserving. Expectation values calculated from the Born series are then used to build a Padé table of approximations, while conservation laws are naturally preserved. We implement this technique for the Φ-derivable self-consistent Born approximation (SCBA), for which we obtain a recursion relation that yields the Born series for the NEGF up to any desired order. The expectation values calculated from the Born series are then postprocessed to build a Padé table of conserving approximations. The calculation of the SCBA photocurrent in a biased molecular junction model provides an example where, in addition to conservation laws, a substantial convergence acceleration relative to standard techniques is achieved. The present reformulation of the SCBA might aid convergence to the fully self-consistent results in a wide variety of problems.
Analytical model of rotor wake aerodynamics in ground effect
NASA Technical Reports Server (NTRS)
Saberi, H. A.
1983-01-01
The model and the computer program developed provides the velocity, location, and circulation of the tip vortices of a two-blade helicopter in and out of the ground effect. Comparison of the theoretical results with some experimental measurements for the location of the wake indicate that there is excellent accuracy in the vicinity of the rotor and fair amount of accuracy far from it. Having the location of the wake at all times enables us to compute the history of the velocity and the location of any point in the flow. The main goal of out study, induced velocity at the rotor, can also be calculated in addition to stream lines and streak lines. Since the wake location close to the rotor is known more accurately than at other places, the calculated induced velocity over the disc should be a good estimate of the real induced velocity, with the exception of the blade location, because each blade was replaced only by a vortex line. Because no experimental measurements of the wake close to the ground were available to us, quantitative evaluation of the theoretical wake was not possible. But qualitatively we have been able to show excellent agreement. Comparison of flow visualization with out results has indicated the location of the ground vortex is estimated excellently. Also the flow field in hover is well represented.
Analytical model of infiltration under constant-concentration boundary conditions
NASA Astrophysics Data System (ADS)
Triadis, D.; Broadbridge, P.
2010-03-01
Known integrable models for 1D flow in unsaturated soil have a rescaled soil water diffusivity that is either constant or proportional to C(C - 1)/(C - Θ)2, where Θ is the degree of saturation and C > 1 is constant. With a wider more realistic range of hydraulic conductivity functions than has been used in this context before, a formal series solution is developed for infiltration, subject to constant-concentration boundary conditions. A readily programmed iteration algorithm, applicable for any value of C, is used to construct many coefficients of the infiltration series without requiring any numerical integration. In particular, for either C - 1 small or 1/C small, several infiltration series coefficients are constructed as formal power series in C - 1 or in 1/C, for which we construct a number of terms explicitly. In the limit as the diffusivity approaches a delta function, the infiltration coefficients are obtained in simpler closed form. All but the sorptivity depend on the form of the conductivity function.
Global sensitivity analysis of analytical vibroacoustic transmission models
NASA Astrophysics Data System (ADS)
Christen, Jean-Loup; Ichchou, Mohamed; Troclet, Bernard; Bareille, Olivier; Ouisse, Morvan
2016-04-01
Noise reduction issues arise in many engineering problems. One typical vibroacoustic problem is the transmission loss (TL) optimisation and control. The TL depends mainly on the mechanical parameters of the considered media. At early stages of the design, such parameters are not well known. Decision making tools are therefore needed to tackle this issue. In this paper, we consider the use of the Fourier Amplitude Sensitivity Test (FAST) for the analysis of the impact of mechanical parameters on features of interest. FAST is implemented with several structural configurations. FAST method is used to estimate the relative influence of the model parameters while assuming some uncertainty or variability on their values. The method offers a way to synthesize the results of a multiparametric analysis with large variability. Results are presented for transmission loss of isotropic, orthotropic and sandwich plates excited by a diffuse field on one side. Qualitative trends found to agree with the physical expectation. Design rules can then be set up for vibroacoustic indicators. The case of a sandwich plate is taken as an example of the use of this method inside an optimisation process and for uncertainty quantification.
Analytic modeling of soot nucleation under fuel rich conditions
NASA Technical Reports Server (NTRS)
Yang, C. H.
1983-01-01
The objective of the present research is to construct a soot nucleation model according to a proposed chemical kinetic scheme to delineate quantitatively the nucleation mechanism in the soot formation process. Instead of following the traditional views which generally associate sooting with the homogeneous nucleation process in phase transformation or polymerization, we choose a chemical kinetic approach. In our proposed scheme the number of carbon atoms in the intermediate species between the fuel molecule and soot nuclei is continuously increased by radical additions. The number of hydrogen atoms in the intermediate species on the other hand is steadily decreased by radical dehydrogenation. When the number of carbon atoms in each of the intermediate molecules has exceeded a certain limit and the number of hydrogen atoms has fallen below a certain level, they may coagulate with one and another to form a larger molecule which is regarded as the initial soot nuclei in the present theory. Further coagulation and surface growth of the nuclei will lead to observable soot particles.
33 CFR 385.33 - Revisions to models and analytical tools.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 33 Navigation and Navigable Waters 3 2010-07-01 2010-07-01 false Revisions to models and... Incorporating New Information Into the Plan § 385.33 Revisions to models and analytical tools. (a) In carrying... Management District, and other non-Federal sponsors shall rely on the best available science including...
33 CFR 385.33 - Revisions to models and analytical tools.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 33 Navigation and Navigable Waters 3 2011-07-01 2011-07-01 false Revisions to models and... Incorporating New Information Into the Plan § 385.33 Revisions to models and analytical tools. (a) In carrying... Management District, and other non-Federal sponsors shall rely on the best available science including...
33 CFR 385.33 - Revisions to models and analytical tools.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 33 Navigation and Navigable Waters 3 2013-07-01 2013-07-01 false Revisions to models and... Incorporating New Information Into the Plan § 385.33 Revisions to models and analytical tools. (a) In carrying... Management District, and other non-Federal sponsors shall rely on the best available science including...
33 CFR 385.33 - Revisions to models and analytical tools.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 33 Navigation and Navigable Waters 3 2014-07-01 2014-07-01 false Revisions to models and... Incorporating New Information Into the Plan § 385.33 Revisions to models and analytical tools. (a) In carrying... Management District, and other non-Federal sponsors shall rely on the best available science including...
Accurate analytical method for the extraction of solar cell model parameters
NASA Astrophysics Data System (ADS)
Phang, J. C. H.; Chan, D. S. H.; Phillips, J. R.
1984-05-01
Single diode solar cell model parameters are rapidly extracted from experimental data by means of the presently derived analytical expressions. The parameter values obtained have a less than 5 percent error for most solar cells, in light of the extraction of model parameters for two cells of differing quality which were compared with parameters extracted by means of the iterative method.
Mechanistic analytical models for long-distance seed dispersal by wind.
Katul, G G; Porporato, A; Nathan, R; Siqueira, M; Soons, M B; Poggi, D; Horn, H S; Levin, S A
2005-09-01
We introduce an analytical model, the Wald analytical long-distance dispersal (WALD) model, for estimating dispersal kernels of wind-dispersed seeds and their escape probability from the canopy. The model is based on simplifications to well-established three-dimensional Lagrangian stochastic approaches for turbulent scalar transport resulting in a two-parameter Wald (or inverse Gaussian) distribution. Unlike commonly used phenomenological models, WALD's parameters can be estimated from the key factors affecting wind dispersal--wind statistics, seed release height, and seed terminal velocity--determined independently of dispersal data. WALD's asymptotic power-law tail has an exponent of -3/2, a limiting value verified by a meta-analysis for a wide variety of measured dispersal kernels and larger than the exponent of the bivariate Student t-test (2Dt). We tested WALD using three dispersal data sets on forest trees, heathland shrubs, and grassland forbs and compared WALD's performance with that of other analytical mechanistic models (revised versions of the tilted Gaussian Plume model and the advection-diffusion equation), revealing fairest agreement between WALD predictions and measurements. Analytical mechanistic models, such as WALD, combine the advantages of simplicity and mechanistic understanding and are valuable tools for modeling large-scale, long-term plant population dynamics. PMID:16224691
A Bayesian Multi-Level Factor Analytic Model of Consumer Price Sensitivities across Categories
ERIC Educational Resources Information Center
Duvvuri, Sri Devi; Gruca, Thomas S.
2010-01-01
Identifying price sensitive consumers is an important problem in marketing. We develop a Bayesian multi-level factor analytic model of the covariation among household-level price sensitivities across product categories that are substitutes. Based on a multivariate probit model of category incidence, this framework also allows the researcher to…
ERIC Educational Resources Information Center
Cheung, Mike W. L.; Chan, Wai
2009-01-01
Structural equation modeling (SEM) is widely used as a statistical framework to test complex models in behavioral and social sciences. When the number of publications increases, there is a need to systematically synthesize them. Methodology of synthesizing findings in the context of SEM is known as meta-analytic SEM (MASEM). Although correlation…
Analytical models and system topologies for remote multispectral data acquisition and classification
NASA Technical Reports Server (NTRS)
Huck, F. O.; Park, S. K.; Burcher, E. E.; Kelly, W. L., IV
1978-01-01
Simple analytical models are presented of the radiometric and statistical processes that are involved in multispectral data acquisition and classification. Also presented are basic system topologies which combine remote sensing with data classification. These models and topologies offer a preliminary but systematic step towards the use of computer simulations to analyze remote multispectral data acquisition and classification systems.
Goals and Characteristics of Long-Term Care Programs: An Analytic Model.
ERIC Educational Resources Information Center
Braun, Kathryn L.; Rose, Charles L.
1989-01-01
Used medico-social analytic model to compare five long-term care programs: Skilled Nursing Facility-Intermediate Care Facility (SNF-ICF) homes, ICF homes, foster homes, day hospitals, and home care. Identified similarities and differences among programs. Preliminary findings suggest that model is useful in the evaluation and design of long-term…
Several advances in the analytic element method have been made to enhance its performance and facilitate three-dimensional ground-water flow modeling in a regional aquifer setting. First, a new public domain modular code (ModAEM) has been developed for modeling ground-water flow ...
Meta-Analytic Structural Equation Modeling (MASEM): Comparison of the Multivariate Methods
ERIC Educational Resources Information Center
Zhang, Ying
2011-01-01
Meta-analytic Structural Equation Modeling (MASEM) has drawn interest from many researchers recently. In doing MASEM, researchers usually first synthesize correlation matrices across studies using meta-analysis techniques and then analyze the pooled correlation matrix using structural equation modeling techniques. Several multivariate methods of…
Analytic models of ducted turbomachinery tone noise sources. Volume 1: Analysis
NASA Technical Reports Server (NTRS)
Clark, T. L.; Ganz, U. W.; Graf, G. A.; Westall, J. S.
1974-01-01
The analytic models developed for computing the periodic sound pressure of subsonic fans and compressors in an infinite, hardwall annular duct with uniform flow are described. The basic sound-generating mechanism is the scattering into sound waves of velocity disturbances appearing to the rotor or stator blades as a series of harmonic gusts. The models include component interactions and rotor alone.
anQCD: Fortran programs for couplings at complex momenta in various analytic QCD models
NASA Astrophysics Data System (ADS)
Ayala, César; Cvetič, Gorazd
2016-02-01
We provide three Fortran programs which evaluate the QCD analytic (holomorphic) couplings Aν(Q2) for complex or real squared momenta Q2. These couplings are holomorphic analogs of the powers a(Q2)ν of the underlying perturbative QCD (pQCD) coupling a(Q2) ≡αs(Q2) / π, in three analytic QCD models (anQCD): Fractional Analytic Perturbation Theory (FAPT), Two-delta analytic QCD (2 δanQCD), and Massive Perturbation Theory (MPT). The index ν can be noninteger. The provided programs do basically the same job as the Mathematica package anQCD.m published by us previously (Ayala and Cvetič, 2015), but are now written in Fortran.
Analytical Model for Pair Dispersion in Gaussian Models of Eulerian Turbulence
NASA Astrophysics Data System (ADS)
Eyink, Gregory; Benveniste, Damien
2012-11-01
Synthetic models of Eulerian turbulence are often used as computational shortcuts for studying Lagrangian properties of turbulence (e.g. Elliott & Majda, 1996). These models have been criticized by Thomson & Devenish (2005), who argued on physical grounds that their sweeping effects are very different from true turbulence. We give analytical results for Eulerian turbulence modeled by Gaussian fields. Our starting point is an exact integrodifferential equation for the particle pair separation distribution obtained from Gaussian integration-by-parts. When velocity correlation times are short, a Markovian approximation leads to a Richardson-type diffusion model. We obtain a time-dependent pair diffusivity tensor of the form Kij (r , t) =Sij (r) τ (r , t) where Sij (r) is the structure-function tensor and τ (r , t) is an effective correlation time of velocity increments. Crucially, this is found to be the minimum value of three times: the intrinsic turnover time τeddy (r) at separation r, the overall evolution time t , and the sweeping time r /v0 with v0 the rms velocity. We thus verify the main argument of Thomson & Devenish (2005), but we predict scaling laws for pair dispersion different from theirs for zero-mean velocity ensembles.
Comprehensive analytical model for CW laser induced heat in turbid media.
Erkol, Hakan; Nouizi, Farouk; Luk, Alex; Unlu, Mehmet Burcin; Gulsen, Gultekin
2015-11-30
In this work, we present a new analytical approach to model continuous wave laser induced temperature in highly homogeneous turbid media. First, the diffusion equation is used to model light transport and a comprehensive solution is derived analytically by obtaining a special Greens' function. Next, the time-dependent bio-heat equation is used to describe the induced heat increase and propagation within the medium. The bio-heat equation is solved analytically utilizing the separation of variables technique. Our theoretical model is successfully validated using numerical simulations and experimental studies with agarose phantoms and ex-vivo chicken breast samples. The encouraging results show that our method can be implemented as a simulation tool to determine important laser parameters that govern the magnitude of temperature rise within homogenous biological tissue or organs. PMID:26698736
An analytically resolved model of a potato's thermal processing using Heun functions
NASA Astrophysics Data System (ADS)
Vargas Toro, Agustín.
2014-05-01
A potato's thermal processing model is solved analytically. The model is formulated using the equation of heat diffusion in the case of a spherical potato processed in a furnace, and assuming that the potato's thermal conductivity is radially modulated. The model is solved using the method of the Laplace transform, applying Bromwich Integral and Residue Theorem. The temperatures' profile in the potato is presented as an infinite series of Heun functions. All computations are performed with computer algebra software, specifically Maple. Using the numerical values of the thermal parameters of the potato and geometric and thermal parameters of the processing furnace, the time evolution of the temperatures in different regions inside the potato are presented analytically and graphically. The duration of thermal processing in order to achieve a specified effect on the potato is computed. It is expected that the obtained analytical results will be important in food engineering and cooking engineering.
Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models
NASA Astrophysics Data System (ADS)
Luther, K.; Haitjema, H. M.
2000-04-01
We present methods for finding approximate analytic solutions to three-dimensional (3D) unconfined steady state groundwater flow near partially penetrating and horizontal wells, and for combining those solutions with regional two-dimensional (2D) models. The 3D solutions use distributed singularities (analytic elements) to enforce boundary conditions on the phreatic surface and seepage faces at vertical wells, and to maintain fixed-head boundary conditions, obtained from the 2D model, at the perimeter of the 3D model. The approximate 3D solutions are analytic (continuous and differentiable) everywhere, including on the phreatic surface itself. While continuity of flow is satisfied exactly in the infinite 3D flow domain, water balance errors can occur across the phreatic surface.
Anisotropic Multishell Analytical Modeling of an Intervertebral Disk Subjected to Axial Compression.
Demers, Sébastien; Nadeau, Sylvie; Bouzid, Abdel-Hakim
2016-04-01
Studies on intervertebral disk (IVD) response to various loads and postures are essential to understand disk's mechanical functions and to suggest preventive and corrective actions in the workplace. The experimental and finite-element (FE) approaches are well-suited for these studies, but validating their findings is difficult, partly due to the lack of alternative methods. Analytical modeling could allow methodological triangulation and help validation of FE models. This paper presents an analytical method based on thin-shell, beam-on-elastic-foundation and composite materials theories to evaluate the stresses in the anulus fibrosus (AF) of an axisymmetric disk composed of multiple thin lamellae. Large deformations of the soft tissues are accounted for using an iterative method and the anisotropic material properties are derived from a published biaxial experiment. The results are compared to those obtained by FE modeling. The results demonstrate the capability of the analytical model to evaluate the stresses at any location of the simplified AF. It also demonstrates that anisotropy reduces stresses in the lamellae. This novel model is a preliminary step in developing valuable analytical models of IVDs, and represents a distinctive groundwork that is able to sustain future refinements. This paper suggests important features that may be included to improve model realism. PMID:26833355
Comparison of a semi-analytic and a CFD model uranium combustion to experimental data.
Clarksean, R.
1998-04-01
Two numerical models were developed and compared for the analysis of uranium combustion and ignition in a furnace. Both a semi-analytical solution and a computational fluid dynamics (CFD) numerical solution were obtained. Prediction of uranium oxidation rates is important for fuel storage applications, fuel processing, and the development of spent fuel metal waste forms. The semi-analytical model was based on heat transfer correlations, a semi-analytical model of flow over a flat surface, and simple radiative heat transfer from the material surface. The CFD model numerically determined the flowfield over the object of interest, calculated the heat and mass transfer to the material of interest, and calculated the radiative heat exchange of the material with the furnace. The semi-analytical model is much less detailed than the CFD model, but yields reasonable results and assists in understanding the physical process. Short computation times allowed the analyst to study numerous scenarios. The CFD model had significantly longer run times, was found to have some physical limitations that were not easily modified, but was better able to yield details of the heat and mass transfer and flow field once code limitations were overcome.
NASA Astrophysics Data System (ADS)
Hopkins, Philip F.; Quataert, Eliot
2011-08-01
We present analytic calculations of angular momentum transport and gas inflow in galaxies, from scales of ˜ kpc to deep inside the potential of a central massive black hole (BH). We compare these analytic calculations to numerical simulations and use them to develop a sub-grid model of BH growth that can be incorporated into semi-analytic calculations or cosmological simulations. Motivated by both analytic calculations and simulations of gas inflow in galactic nuclei, we argue that the strongest torque on gas arises when non-axisymmetric perturbations to the stellar gravitational potential produce orbit crossings and shocks in the gas. This is true both at large radii ˜0.01-1 kpc, where bar-like stellar modes dominate the non-axisymmetric potential, and at smaller radii ≲10 pc, where a lopsided/eccentric stellar disc dominates. The traditional orbit-crossing criterion is not always adequate to predict the locations of, and inflow due to, shocks in gas+stellar discs with finite sound speeds. We derive a modified criterion that predicts the presence of shocks in stellar-dominated systems even absent formal orbit crossing. We then derive analytic expressions for the loss of angular momentum and the resulting gas inflow rates in the presence of such shocks. We test our analytic predictions using hydrodynamic simulations at a range of galactic scales, and show that they successfully predict the mass inflow rates and quasi-steady gas surface densities with a small scatter ≃0.3 dex. We use our analytic results to construct a new estimate of the BH accretion rate given galaxy properties at larger radii, for use in galaxy and cosmological simulations and semi-analytic models. While highly simplified, this accretion rate predictor captures the key scalings in the numerical simulations. By contrast, alternate estimates such as the local viscous accretion rate or the spherical Bondi rate fail systematically to reproduce the simulations and have significantly larger
A Semi-Analytical Model for Short Range Dispersion From Ground Sources
NASA Astrophysics Data System (ADS)
Gavze, E.; Fattal, E.; Reichman, R.
2014-12-01
A semi-analytical model for dispersion of passive scalars from ground sources up to distances of a few hundred meters is presented. Most widely used analytical models are Gaussian models which assume both a uniform wind field and homogeneous turbulence. These assumptions are not valid when ground sources are involved since both the wind and the turbulence depend on height. The model presented here is free of these two assumptions. The formulation of the vertical dispersion is based on approximating the vertical profiles of the wind and the the vertical diffusion coefficient, based on Monin Obukhov Similarity Theory, as power laws. One advantage of this approach is that it allows for non Gaussian vertical profiles of the concentration which better fit the experimental data. For the lateral dispersion the model still assumes a Gaussian form. A system of equations was developed to compute the cloud width. This system of equations is based on an analytical solution of a Langevin equation which takes into account the non-homogeneity of the wind and the turbulence in the vertical direction. The model was tested against two field experiments. Comparison with a Gaussian model showed that it performed much better in predicting both the integrated cross wind ground concentration and the cloud width. Analytical, or semi-analytical models are useful as they are simple to use and require only a short computation time, compared, for example, to Lagrangian Stochastic Models. The presented model is very efficient from the computational point of view. As such it is suitable for cases in which repeated computations of the concentration field are required, as for example in risk assessments and in the inverse problem of source determination.
Analytical and numerical modeling of non-collinear shear wave mixing at an imperfect interface.
Zhang, Ziyin; Nagy, Peter B; Hassan, Waled
2016-02-01
Non-collinear shear wave mixing at an imperfect interface between two solids can be exploited for nonlinear ultrasonic assessment of bond quality. In this study we developed two analytical models for nonlinear imperfect interfaces. The first model uses a finite nonlinear interfacial stiffness representation of an imperfect interface of vanishing thickness, while the second model relies on a thin nonlinear interphase layer to represent an imperfect interface region. The second model is actually a derivative of the first model obtained by calculating the equivalent interfacial stiffness of a thin isotropic nonlinear interphase layer in the quasi-static approximation. The predictions of both analytical models were numerically verified by comparison to COMSOL finite element simulations. These models can accurately predict the additional nonlinearity caused by interface imperfections based on the strength of the reflected and transmitted mixed longitudinal waves produced by them under non-collinear shear wave interrogation. PMID:26482394
Analytical and numerical modeling of non-collinear shear wave mixing at an imperfect interface
NASA Astrophysics Data System (ADS)
Zhang, Ziyin; Nagy, Peter B.; Hassan, Waled
2016-02-01
Non-collinear shear wave mixing at an imperfect interface between two solids can be exploited for nonlinear ultrasonic assessment of bond quality. In this study we developed two analytical models for nonlinear imperfect interfaces. The first model uses a finite nonlinear interfacial stiffness representation of an imperfect interface of vanishing thickness, while the second model relies on a thin nonlinear interphase layer to represent an imperfect interface region. The second model is actually a derivative of the first model obtained by calculating the equivalent interfacial stiffness of a thin isotropic nonlinear interphase layer in the quasi-static approximation. The predictions of both analytical models were numerically verified by comparison to COMSOL finite element simulations. These models can accurately predict the excess nonlinearity caused by interface imperfections based on the strength of the reflected and transmitted mixed longitudinal waves produced by them under non-collinear shear wave interrogation.
WFR-2D: an analytical model for PWAS-generated 2D ultrasonic guided wave propagation
NASA Astrophysics Data System (ADS)
Shen, Yanfeng; Giurgiutiu, Victor
2014-03-01
This paper presents WaveFormRevealer 2-D (WFR-2D), an analytical predictive tool for the simulation of 2-D ultrasonic guided wave propagation and interaction with damage. The design of structural health monitoring (SHM) systems and self-aware smart structures requires the exploration of a wide range of parameters to achieve best detection and quantification of certain types of damage. Such need for parameter exploration on sensor dimension, location, guided wave characteristics (mode type, frequency, wavelength, etc.) can be best satisfied with analytical models which are fast and efficient. The analytical model was constructed based on the exact 2-D Lamb wave solution using Bessel and Hankel functions. Damage effects were inserted in the model by considering the damage as a secondary wave source with complex-valued directivity scattering coefficients containing both amplitude and phase information from wave-damage interaction. The analytical procedure was coded with MATLAB, and a predictive simulation tool called WaveFormRevealer 2-D was developed. The wave-damage interaction coefficients (WDICs) were extracted from harmonic analysis of local finite element model (FEM) with artificial non-reflective boundaries (NRB). The WFR-2D analytical simulation results were compared and verified with full scale multiphysics finite element models and experiments with scanning laser vibrometer. First, Lamb wave propagation in a pristine aluminum plate was simulated with WFR-2D, compared with finite element results, and verified by experiments. Then, an inhomogeneity was machined into the plate to represent damage. Analytical modeling was carried out, and verified by finite element simulation and experiments. This paper finishes with conclusions and suggestions for future work.
Analytical model of the temperature dependent properties of microresonators immersed in a gas
Ilin, E. A.; Kehrbusch, J.; Radzio, B.; Oesterschulze, E.
2011-02-01
A comprehensive theoretical model of microresonators immersed in a viscous gas of varying temperature is presented and verified by experiments. Analytical expressions for both the temperature dependent resonant frequency and quality factor of the first flexural eigenmode were derived extending Sader's theory of viscous damping to small temperature variations. The model provides useful implications for the thermal stabilization of microresonators immersed in a gas as well as for the reduction in the influence of the temperature dependent gas properties on the resonant frequency. Finally, an analytical expression is deduced for the mass detection capability of a microresonator that undergoes temperature variations.
Analytical model of a five degree of freedom magnetic suspension and positioning system
NASA Technical Reports Server (NTRS)
Groom, Nelson J.
1989-01-01
An analytical model of a five degree of freedom magnetic suspension and positioning system is presented. The suspended element is a cylinder which is composed of permanent magnet material and the magnetic actuators are air core electromagnets mounted in a planar array. The analytical model consists of an open loop representation of the suspension and positioning system with electromagnet currents as inputs and displacements and rates in inertial coordinates as outputs. The uncontrolled degree of freedom is rotation about the long axis of the suspended cylinder.
Analytical surrogate model for the aberrations of an arbitrary GRIN lens.
Easum, John A; Campbell, Sawyer D; Nagar, Jogender; Werner, Douglas H
2016-08-01
Current analytical expressions between Gradient-Index (GRIN) lens parameters and optical aberrations are limited to paraxial approximations, which are not suitable for realizing GRIN lenses with wide fields of view or small f-numbers. Here, an analytical surrogate model of an arbitrary GRIN lens ray-trace evaluation is formulated using multivariate polynomial regressions to correlate input GRIN lens parameters with output Zernike coefficients, without the need for approximations. The time needed to compute the resulting surrogate model is over one order-of-magnitude faster than traditional ray trace simulations with very little losses in accuracy, which can enable previously infeasible design studies to be completed. PMID:27505748
Useful measures and models for analytical quality management in medical laboratories.
Westgard, James O
2016-02-01
The 2014 Milan Conference "Defining analytical performance goals 15 years after the Stockholm Conference" initiated a new discussion of issues concerning goals for precision, trueness or bias, total analytical error (TAE), and measurement uncertainty (MU). Goal-setting models are critical for analytical quality management, along with error models, quality-assessment models, quality-planning models, as well as comprehensive models for quality management systems. There are also critical underlying issues, such as an emphasis on MU to the possible exclusion of TAE and a corresponding preference for separate precision and bias goals instead of a combined total error goal. This opinion recommends careful consideration of the differences in the concepts of accuracy and traceability and the appropriateness of different measures, particularly TAE as a measure of accuracy and MU as a measure of traceability. TAE is essential to manage quality within a medical laboratory and MU and trueness are essential to achieve comparability of results across laboratories. With this perspective, laboratory scientists can better understand the many measures and models needed for analytical quality management and assess their usefulness for practical applications in medical laboratories. PMID:26426893
On Improving Analytical Models of Cosmic Reionization for Matching Numerical Simulations
Kaurov, Alexander A.
2016-01-01
The methods for studying the epoch of cosmic reionization vary from full radiative transfer simulations to purely analytical models. While numerical approaches are computationally expensive and are not suitable for generating many mock catalogs, analytical methods are based on assumptions and approximations. We explore the interconnection between both methods. First, we ask how the analytical framework of excursion set formalism can be used for statistical analysis of numerical simulations and visual representation of the morphology of ionization fronts. Second, we explore the methods of training the analytical model on a given numerical simulation. We present a new code which emerged from this study. Its main application is to match the analytical model with a numerical simulation. Then, it allows one to generate mock reionization catalogs with volumes exceeding the original simulation quickly and computationally inexpensively, meanwhile reproducing large scale statistical properties. These mock catalogs are particularly useful for CMB polarization and 21cm experiments, where large volumes are required to simulate the observed signal.
Towards an Analytical Age-Dependent Model of Contrast Sensitivity Functions for an Ageing Society
Joulan, Karine; Brémond, Roland
2015-01-01
The Contrast Sensitivity Function (CSF) describes how the visibility of a grating depends on the stimulus spatial frequency. Many published CSF data have demonstrated that contrast sensitivity declines with age. However, an age-dependent analytical model of the CSF is not available to date. In this paper, we propose such an analytical CSF model based on visual mechanisms, taking into account the age factor. To this end, we have extended an existing model from Barten (1999), taking into account the dependencies of this model's optical and physiological parameters on age. Age-dependent models of the cones and ganglion cells densities, the optical and neural MTF, and optical and neural noise are proposed, based on published data. The proposed age-dependent CSF is finally tested against available experimental data, with fair results. Such an age-dependent model may be beneficial when designing real-time age-dependent image coding and display applications. PMID:26078994
Frankle, S.C.; Fitzgerald, D.H.; Hutson, R.L.; Macek, R.J.; Wilkinson, C.A.
1992-12-31
A comparison of 800-MeV proton beam spill measurements at the Los Alamos Meson Physics Facility (LAMPF) with analytical model calculations of neutron dose equivalent rates (DER) show agreement within factors of 2-3 for simple shielding geometries. The DER estimates were based on a modified Moyer model for transverse angles and a Monte Carlo based forward angle model described in the proceeding paper.
A quasi-analytical breakdown voltage model in four-layer punch-through TVS devices
NASA Astrophysics Data System (ADS)
Urresti, Jesus; Hidalgo, Salvador; Flores, David; Roig, Jaume; Rebollo, José; Mazarredo, Imanol
2005-08-01
A quasi-analytical model addressed to predict the breakdown voltage in four-layer transient voltage suppressor (TVS) diodes based on the punch-through effect is reported in this paper. For breakdown voltage in excess of 1 V, a closed form expression is derived. In addition, the three-layer TVS diode can also be described with the developed model. Finally, results obtained from the model are in good agreement with simulation and experimental data.