Soft modes in the perceptron model for jamming.

NASA Astrophysics Data System (ADS)

Franz, Silvio

I will show how a well known neural network model \\x9Dthe perceptro provides a simple solvable model of glassy behavior and jamming. The glassy minima of the energy function of this model can be studied in full analytic detail. This allows the identification of two kind of soft modes the first ones associated to the existence a marginal glass phase and a hierarchical structure of the energy landscape, the second ones associated to isostaticity and marginality of jamming. These results highlight the universality of the spectrum of normal modes in disordered systems, and open the way toward a detailed analytical understanding of the vibrational spectrum of low-temperature glasses. This work was supported by a Grant from the Simons Foundation (454941 to Silvio Franz).

The quest for solvable multistate Landau-Zener models

DOE PAGES

Sinitsyn, Nikolai A.; Chernyak, Vladimir Y.

2017-05-24

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

Intermittency inhibited by transport: An exactly solvable model

NASA Astrophysics Data System (ADS)

Zanette, Damián H.

1994-04-01

Transport is incorporated in a discrete-time stochastic model of a system undergoing autocatalytic reactions of the type A-->2A and A-->0, whose population field is known to exhibit spatiotemporal intermittency. The temporal evolution is exactly solved, and it is shown that if the transport process is strong enough, intermittency is inhibited. This inhibition is nonuniform, in the sense that, as transport is strengthened, low-order population moments are affected before the high-order ones. Numerical simulations are presented to support the analytical results.

A performability solution method for degradable nonrepairable systems

NASA Technical Reports Server (NTRS)

Furchtgott, D. G.; Meyer, J. F.

1984-01-01

The present performability model-solving algorithm identifies performance with 'reward', representing the state behavior of a system S by a finite-state stochastic process and determining reward by means of reward rates that are associated with the states of the base model. A general method is obtained for determining the probability distribution function of the performance (reward) variable, and therefore the performability, of the corresponding system. This is done for bounded utilization periods, and the result is an integral expression which is either analytically or numerically solvable.

General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks.

PubMed

Reis, Matthias; Kromer, Justus A; Klipp, Edda

2018-01-20

Multimodality is a phenomenon which complicates the analysis of statistical data based exclusively on mean and variance. Here, we present criteria for multimodality in hierarchic first-order reaction networks, consisting of catalytic and splitting reactions. Those networks are characterized by independent and dependent subnetworks. First, we prove the general solvability of the Chemical Master Equation (CME) for this type of reaction network and thereby extend the class of solvable CME's. Our general solution is analytical in the sense that it allows for a detailed analysis of its statistical properties. Given Poisson/deterministic initial conditions, we then prove the independent species to be Poisson/binomially distributed, while the dependent species exhibit generalized Poisson/Khatri Type B distributions. Generalized Poisson/Khatri Type B distributions are multimodal for an appropriate choice of parameters. We illustrate our criteria for multimodality by several basic models, as well as the well-known two-stage transcription-translation network and Bateman's model from nuclear physics. For both examples, multimodality was previously not reported.

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

NASA Astrophysics Data System (ADS)

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

2012-05-01

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

Responses to applied forces and the Jarzynski equality in classical oscillator systems coupled to finite baths: an exactly solvable nondissipative nonergodic model.

PubMed

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.

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

NASA Astrophysics Data System (ADS)

Mayo, Michael; Pfeifer, Peter; Gheorghiu, Stefan

2008-03-01

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

Theory of ground state factorization in quantum cooperative systems.

PubMed

Giampaolo, Salvatore M; Adesso, Gerardo; Illuminati, Fabrizio

2008-05-16

We introduce a general analytic approach to the study of factorization points and factorized ground states in quantum cooperative systems. The method allows us to determine rigorously the existence, location, and exact form of separable ground states in a large variety of, generally nonexactly solvable, spin models belonging to different universality classes. The theory applies to translationally invariant systems, irrespective of spatial dimensionality, and for spin-spin interactions of arbitrary range.

Collision problems treated with the Generalized Hyperspherical Sturmian method

NASA Astrophysics Data System (ADS)

Mitnik, D. M.; Gasaneo, G.; Ancarani, L. U.; Ambrosio, M. J.

2014-04-01

An hyperspherical Sturmian approach recently developed for three-body break-up processes is presented. To test several of its features, the method is applied to two simplified models. Excellent agreement is found when compared with the results of an analytically solvable problem. For the Temkin-Poet model of the double ionization of He by high energy electron impact, the present method is compared with the Spherical Sturmian approach, and again excellent agreement is found. Finally, a study of the channels appearing in the break-up three-body wave function is presented.

Analytical expressions for the evolution of many-body quantum systems quenched far from equilibrium

NASA Astrophysics Data System (ADS)

Santos, Lea F.; Torres-Herrera, E. Jonathan

2017-12-01

Possible strategies to describe analytically the dynamics of many-body quantum systems out of equilibrium include the use of solvable models and of full random matrices. None of the two approaches represent actual realistic systems, but they serve as references for the studies of these ones. We take the second path and obtain analytical expressions for the survival probability, density imbalance, and out-of-time-ordered correlator. Using these findings, we then propose an approximate expression that matches very well numerical results for the evolution of realistic finite quantum systems that are strongly chaotic and quenched far from equilibrium. In the case of the survival probability, the expression proposed covers all different time scales, from the moment the system is taken out of equilibrium to the moment it reaches a new equilibrium. The realistic systems considered are described by one-dimensional spin-1/2 models.

Exact solution for a non-Markovian dissipative quantum dynamics.

PubMed

Ferialdi, Luca; Bassi, Angelo

2012-04-27

We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

Black holes by analytic continuation

NASA Astrophysics Data System (ADS)

Amati, D.; Russo, J. G.

1997-07-01

In the context of a two-dimensional exactly solvable model, the dynamics of quantum black holes is obtained by analytically continuing the description of the regime where no black hole is formed. The resulting spectrum of outgoing radiation departs from the one predicted by the Hawking model in the region where the outgoing modes arise from the horizon with Planck-order frequencies. This occurs early in the evaporation process, and the resulting physical picture is unconventional. The theory predicts that black holes will only radiate out an energy of Planck mass order, stabilizing after a transitory period. The continuation from a regime without black hole formation-accessible in the 1+1 gravity theory considered-is implicit in an S-matrix approach and suggests in this way a possible solution to the problem of information loss.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sinitsyn, Nikolai A.

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

Integration within the Felsenstein equation for improved Markov chain Monte Carlo methods in population genetics

PubMed Central

Hey, Jody; Nielsen, Rasmus

2007-01-01

In 1988, Felsenstein described a framework for assessing the likelihood of a genetic data set in which all of the possible genealogical histories of the data are considered, each in proportion to their probability. Although not analytically solvable, several approaches, including Markov chain Monte Carlo methods, have been developed to find approximate solutions. Here, we describe an approach in which Markov chain Monte Carlo simulations are used to integrate over the space of genealogies, whereas other parameters are integrated out analytically. The result is an approximation to the full joint posterior density of the model parameters. For many purposes, this function can be treated as a likelihood, thereby permitting likelihood-based analyses, including likelihood ratio tests of nested models. Several examples, including an application to the divergence of chimpanzee subspecies, are provided. PMID:17301231

Solvable model of spiral wave chimeras.

PubMed

Martens, Erik A; Laing, Carlo R; Strogatz, Steven H

2010-01-29

Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coupled locally by diffusion. At the center of such spirals is a phase singularity, a topological defect where the oscillator amplitude drops to zero. But if the coupling is nonlocal, a new kind of spiral can occur, with a circular core consisting of desynchronized oscillators running at full amplitude. Here, we provide the first analytical description of such a spiral wave chimera and use perturbation theory to calculate its rotation speed and the size of its incoherent core.

Integrable models of quantum optics

NASA Astrophysics Data System (ADS)

Yudson, Vladimir; Makarov, Aleksander

2017-10-01

We give an overview of exactly solvable many-body models of quantum optics. Among them is a system of two-level atoms which interact with photons propagating in a one-dimensional (1D) chiral waveguide; exact eigenstates of this system can be explicitly constructed. This approach is used also for a system of closely located atoms in the usual (non-chiral) waveguide or in 3D space. Moreover, it is shown that for an arbitrary atomic system with a cascade spontaneous radiative decay, the fluorescence spectrum can be described by an exact analytic expression which accounts for interference of emitted photons. Open questions related with broken integrability are discussed.

Continual Lie algebras and noncommutative counterparts of exactly solvable models

NASA Astrophysics Data System (ADS)

Zuevsky, A.

2004-01-01

Noncommutative counterparts of exactly solvable models are introduced on the basis of a generalization of Saveliev-Vershik continual Lie algebras. Examples of noncommutative Liouville and sin/h-Gordon equations are given. The simplest soliton solution to the noncommutative sine-Gordon equation is found.

A solvable model of Vlasov-kinetic plasma turbulence in Fourier-Hermite phase space

NASA Astrophysics Data System (ADS)

Adkins, T.; Schekochihin, A. A.

2018-02-01

A class of simple kinetic systems is considered, described by the one-dimensional Vlasov-Landau equation with Poisson or Boltzmann electrostatic response and an energy source. Assuming a stochastic electric field, a solvable model is constructed for the phase-space turbulence of the particle distribution. The model is a kinetic analogue of the Kraichnan-Batchelor model of chaotic advection. The solution of the model is found in Fourier-Hermite space and shows that the free-energy flux from low to high Hermite moments is suppressed, with phase mixing cancelled on average by anti-phase-mixing (stochastic plasma echo). This implies that Landau damping is an ineffective route to dissipation (i.e. to thermalisation of electric energy via velocity space). The full Fourier-Hermite spectrum is derived. Its asymptotics are -3/2$ at low wavenumbers and high Hermite moments ( ) and -1/2k-2$ at low Hermite moments and high wavenumbers ( ). These conclusions hold at wavenumbers below a certain cutoff (analogue of Kolmogorov scale), which increases with the amplitude of the stochastic electric field and scales as inverse square of the collision rate. The energy distribution and flows in phase space are a simple and, therefore, useful example of competition between phase mixing and nonlinear dynamics in kinetic turbulence, reminiscent of more realistic but more complicated multi-dimensional systems that have not so far been amenable to complete analytical solution.

Canonical Formulation of Supermechanics

NASA Astrophysics Data System (ADS)

Matsumoto, S.

1990-07-01

The canonical formulation of a theory of dynamical systems with both Grassmann even and odd variables is investigated. The sufficient condition for the system being analytically solvable is given. The geodesic motion of a particle in the super Poincaré upper half plane is solved as an example.

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.

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.

Valuing options in shot noise market

NASA Astrophysics Data System (ADS)

Laskin, Nick

2018-07-01

A new exactly solvable option pricing model has been introduced and elaborated. It is assumed that a stock price follows a Geometric shot noise process. An arbitrage-free integro-differential option pricing equation has been obtained and solved. The new Greeks have been analytically calculated. It has been shown that in diffusion approximation the developed option pricing model incorporates the well-known Black-Scholes equation and its solution. The stochastic dynamic origin of the Black-Scholes volatility has been uncovered. To model the observed market stock price patterns consisting of high frequency small magnitude and low frequency large magnitude jumps, the superposition of two Geometric shot noises has been implemented. A new generalized option pricing equation has been obtained and its exact solution was found. Merton's jump-diffusion formula for option price was recovered in diffusion approximation. Despite the non-Gaussian nature of probability distributions involved, the new option pricing model has the same degree of analytical tractability as the Black-Scholes model and the Merton jump-diffusion model. This attractive feature allows one to derive exact formulas to value options and option related instruments in the market with jump-like price patterns.

Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models

NASA Astrophysics Data System (ADS)

Ghosh, Pijush K.; Sinha, Debdeep

2018-01-01

A Hamiltonian formulation of generic many-body systems with balanced loss and gain is presented. It is shown that a Hamiltonian formulation is possible only if the balancing of loss and gain terms occurs in a pairwise fashion. It is also shown that with the choice of a suitable co-ordinate, the Hamiltonian can always be reformulated in the background of a pseudo-Euclidean metric. If the equations of motion of some of the well-known many-body systems like Calogero models are generalized to include balanced loss and gain, it appears that the same may not be amenable to a Hamiltonian formulation. A few exactly solvable systems with balanced loss and gain, along with a set of integrals of motion are constructed. The examples include a coupled chain of nonlinear oscillators and a many-particle Calogero-type model with four-body inverse square plus two-body pair-wise harmonic interactions. For the case of nonlinear oscillators, stable solution exists even if the loss and gain parameter has unbounded upper range. Further, the range of the parameter for which the stable solutions are obtained is independent of the total number of the oscillators. The set of coupled nonlinear equations are solved exactly for the case when the values of all the constants of motions except the Hamiltonian are equal to zero. Exact, analytical classical solutions are presented for all the examples considered.

Disturbance accommodating control design for wind turbines using solvability conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

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

Disturbance accommodating control design for wind turbines using solvability conditions

DOE PAGES

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

2017-02-07

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

On the exact solvability of the anisotropic central spin model: An operator approach

NASA Astrophysics Data System (ADS)

Wu, Ning

2018-07-01

Using an operator approach based on a commutator scheme that has been previously applied to Richardson's reduced BCS model and the inhomogeneous Dicke model, we obtain general exact solvability requirements for an anisotropic central spin model with XXZ-type hyperfine coupling between the central spin and the spin bath, without any prior knowledge of integrability of the model. We outline basic steps of the usage of the operators approach, and pedagogically summarize them into two Lemmas and two Constraints. Through a step-by-step construction of the eigen-problem, we show that the condition gj‧2 - gj2 = c naturally arises for the model to be exactly solvable, where c is a constant independent of the bath-spin index j, and {gj } and { gj‧ } are the longitudinal and transverse hyperfine interactions, respectively. The obtained conditions and the resulting Bethe ansatz equations are consistent with that in previous literature.

Analytically solvable model of an electronic Mach-Zehnder interferometer

NASA Astrophysics Data System (ADS)

Ngo Dinh, Stéphane; Bagrets, Dmitry A.; Mirlin, Alexander D.

2013-05-01

We consider a class of models of nonequilibrium electronic Mach-Zehnder interferometers built on integer quantum Hall edges states. The models are characterized by the electron-electron interaction being restricted to the inner part of the interferometer and transmission coefficients of the quantum quantum point contacts, defining the interferometer, which may take arbitrary values from zero to one. We establish an exact solution of these models in terms of single-particle quantities, determinants and resolvents of Fredholm integral operators. In the general situation, the results can be obtained numerically. In the case of strong charging interaction, the operators acquire the block Toeplitz form. Analyzing the corresponding Riemann-Hilbert problem, we reduce the result to certain singular single-channel determinants (which are a generalization of Toeplitz determinants with Fisher-Hartwig singularities) and obtain an analytic result for the interference current (and, in particular, for the visibility of Aharonov-Bohm oscillations). Our results, which are in good agreement with experimental observations, show an intimate connection between the observed “lobe” structure in the visibility of Aharonov-Bohm oscillations and multiple branches in the asymptotics of singular integral determinants.

On the Complexity of Delaying an Adversary’s Project

DTIC Science & Technology

2005-01-01

interdiction models for such problems and show that the resulting problem com- plexities run the gamut : polynomially solvable, weakly NP-complete, strongly...problems and show that the resulting problem complexities run the gamut : polynomially solvable, weakly NP-complete, strongly NP-complete or NP-hard. We

Noise effects in nonlinear biochemical signaling

NASA Astrophysics Data System (ADS)

Bostani, Neda; Kessler, David A.; Shnerb, Nadav M.; Rappel, Wouter-Jan; Levine, Herbert

2012-01-01

It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it is a priori obvious that this approximation can violate physical constraints, such as the positivity of chemical concentrations. Here, we show that even when such nonphysical fluctuations are rare, an exact solution of the Gaussian model shows that the model can yield unphysical results. This is done in the context of a simple incoherent-feedforward model which exhibits perfect adaptation in the deterministic limit. We show how one can use the natural separation of time scales in this model to yield an approximate model, that is analytically solvable, including its dynamical response to an environmental change. Alternatively, one can employ a cutoff procedure to regularize the Gaussian result.

Quantum square-well with logarithmic central spike

NASA Astrophysics Data System (ADS)

Znojil, Miloslav; Semorádová, Iveta

2018-01-01

Singular repulsive barrier V (x) = -gln(|x|) inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction ℒeff(x) = -gln[ψ∗(x)ψ(x)] in nonlinear Schrödinger equation. In the linearized case, Rayleigh-Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small g or after an amendment of the unperturbed Hamiltonian. At any spike strength g, the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables x = expy which interchanges the roles of the asymptotic and central boundary conditions.

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.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schulze-Halberg, Axel, E-mail: xbataxel@gmail.com; García-Ravelo, Jesús; Pacheco-García, Christian

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 inmore » closed form. ► Relation to delta-doped semiconductors is discussed. ► Explicit subband bottom energies are calculated and compared to results obtained in a previous study.« less

On non-homogeneous tachyon condensation in closed string theory

NASA Astrophysics Data System (ADS)

Giribet, Gaston; Rado, Laura

2017-08-01

Lorentzian continuation of the Sine-Liouville model describes non-homogeneous rolling closed string tachyon. Via T-duality, this relates to the gauged H + 3 Wess-Zumino-Witten model at subcritical level. This model is exactly solvable. We give a closed formula for the 3-point correlation functions for the model at level k within the range 0 < k < 2, which relates to the analogous quantity for k > 2 in a similar way as how the Harlow-Maltz-Witten 3-point function of timelike Liouville field theory relates to the analytic continuation of the Dorn-Otto-Zamolodchikov-Zamolodchikov structure constants: we find that the ratio between both 3-point functions can be written in terms of quotients of Jacobi's θ-functions, while their product exhibits remarkable cancellations and eventually factorizes. Our formula is consistent with previous proposals made in the literature.

Fate of classical solitons in one-dimensional quantum systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pustilnik, M.; Matveev, K. A.

We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, andmore » argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.« less

The Sensitivity of Atmospheric Water Isotopes to Entrainment and Precipitation Efficiency in a Bulk Plume Model of Convection

NASA Astrophysics Data System (ADS)

Duan, S.; Wright, J. S.; Romps, D. M.

2016-12-01

Atmospheric water isotopes have been proposed as potentially powerful constraints on the physics of convective clouds and parameterizations of convective processes in models. We have previously derived an analytical model of water vapor (H2O) and one of its heavy isotopes (HDO) in convective environments based on a bulk-plume convective water budget in radiative convective equilibrium. This analytical model provides a useful starting point for examining the joint responses of water vapor and its isotopic composition to changes in convective parameters; however, certain idealistic assumptions are required to make the model analytically solvable. Here, we develop a more flexible numerical framework that enables a wider range of model configurations and includes additional isotopic tracers. This model provides a bridge between Rayleigh distillation, which is simple but inflexible, and more complicated convection schemes and cloud resolving models, which are more realistic but also more difficult to perturb and interpret. Application of realistic in-cloud water profiles in our model produces vertical distributions of δD that qualitatively match satellite observations from the Tropospheric Emission Spectrometer (TES). We test the sensitivity of water vapor and its isotopic composition to a wide range of perturbations in the model parameters and their vertical profiles. In this presentation, we focus especially on establishing constraints for convective entrainment and precipitation efficiency. We conclude by discussing the potential application of this model as part of a larger water isotope toolkit for use with offline diagnostics provided by reanalyses and GCMs.

Gradient structure and transport coefficients for strong particles

NASA Astrophysics Data System (ADS)

Gabrielli, Davide; Krapivsky, P. L.

2018-04-01

We introduce and study a simple and natural class of solvable stochastic lattice gases. This is the class of strong particles. The name is due to the fact that when they try to jump to an occupied site they succeed in pushing away a pile of particles. For this class of models we explicitly compute the transport coefficients. We also discuss some generalizations and the relations with other classes of solvable models.

Singularity resolution in string theory and new quantum condensed matter phases

NASA Astrophysics Data System (ADS)

Fidkowski, Lukasz

2007-12-01

In the first part of this thesis (chapters 1 through 4) we study singularity resolution in string theory. We employ an array of techniques, including the AdS-CFT correspondence, exact solvability of low dimensional models, and supersymmetry. We are able to detect a signature of the black hole singularity by analytically continuing certain AdS-CFT correlators. Also in AdS-CFT, we are able to study a D-brane snapping transition on both sides of the correspondence. In the second part (chapters 5 through 7) we study topological phases in condensed matter systems. We investigate theoretical lattice models realizing such phases, use these to derive nontrivial mathematical physics results, and study an idealized quantum interferometer designed to detect such a phase in quantum Hall systems.

Quasi-exact solvability and entropies of the one-dimensional regularised Calogero model

NASA Astrophysics Data System (ADS)

Pont, Federico M.; Osenda, Omar; Serra, Pablo

2018-05-01

The Calogero model can be regularised through the introduction of a cutoff parameter which removes the divergence in the interaction term. In this work we show that the one-dimensional two-particle regularised Calogero model is quasi-exactly solvable and that for certain values of the Hamiltonian parameters the eigenfunctions can be written in terms of Heun’s confluent polynomials. These eigenfunctions are such that the reduced density matrix of the two-particle density operator can be obtained exactly as well as its entanglement spectrum. We found that the number of non-zero eigenvalues of the reduced density matrix is finite in these cases. The limits for the cutoff distance going to zero (Calogero) and infinity are analysed and all the previously obtained results for the Calogero model are reproduced. Once the exact eigenfunctions are obtained, the exact von Neumann and Rényi entanglement entropies are studied to characterise the physical traits of the model. The quasi-exactly solvable character of the model is assessed studying the numerically calculated Rényi entropy and entanglement spectrum for the whole parameter space.

Nonminimally coupled massive scalar field in a 2D black hole: Exactly solvable model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frolov, V.; Zelnikov, A.

2001-06-15

We study a nonminimal massive scalar field in the background of a two-dimensional black hole spacetime. We consider the black hole which is the solution of the 2D dilaton gravity derived from string-theoretical models. We find an explicit solution in a closed form for all modes and the Green function of the scalar field with an arbitrary mass and a nonminimal coupling to the curvature. Greybody factors, the Hawking radiation, and 2>{sup ren} are calculated explicitly for this exactly solvable model.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turbiner, Alexander; Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado, Postal 70-543, 04510 Mexico, D. F.

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.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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.}

Solvable Model of a Generic Trapped Mixture of Interacting Bosons: Many-Body and Mean-Field Properties

NASA Astrophysics Data System (ADS)

Klaiman, S.; Streltsov, A. I.; Alon, O. E.

2018-04-01

A solvable model of a generic trapped bosonic mixture, N 1 bosons of mass m 1 and N 2 bosons of mass m 2 trapped in an harmonic potential of frequency ω and interacting by harmonic inter-particle interactions of strengths λ 1, λ 2, and λ 12, is discussed. It has recently been shown for the ground state [J. Phys. A 50, 295002 (2017)] that in the infinite-particle limit, when the interaction parameters λ 1(N 1 ‑ 1), λ 2(N 2 ‑ 1), λ 12 N 1, λ 12 N 2 are held fixed, each of the species is 100% condensed and its density per particle as well as the total energy per particle are given by the solution of the coupled Gross-Pitaevskii equations of the mixture. In the present work we investigate properties of the trapped generic mixture at the infinite-particle limit, and find differences between the many-body and mean-field descriptions of the mixture, despite each species being 100%. We compute analytically and analyze, both for the mixture and for each species, the center-of-mass position and momentum variances, their uncertainty product, the angular-momentum variance, as well as the overlap of the exact and Gross-Pitaevskii wavefunctions of the mixture. The results obtained in this work can be considered as a step forward in characterizing how important are many-body effects in a fully condensed trapped bosonic mixture at the infinite-particle limit.

Exact BPS domain walls at finite gauge coupling

NASA Astrophysics Data System (ADS)

Blaschke, Filip

2017-01-01

Bogomol'nyi-Prasad-Sommerfield solitons in models with spontaneously broken gauge symmetry have been intensively studied at the infinite gauge coupling limit, where the governing equation-the so-called master equation-is exactly solvable. Except for a handful of special solutions, the standing impression is that analytic results at finite coupling are generally unavailable. The aim of this paper is to demonstrate, using domain walls in Abelian-Higgs models as the simplest example, that exact solitons at finite gauge coupling can be readily obtained if the number of Higgs fields (NF ) is large enough. In particular, we present a family of exact solutions, describing N domain walls at arbitrary positions in models with at least NF≥2 N +1 . We have also found that adding together any pair of solutions can produce a new exact solution if the combined tension is below a certain limit.

Generalized squeezing rotating-wave approximation to the isotropic and anisotropic Rabi model in the ultrastrong-coupling regime

NASA Astrophysics Data System (ADS)

Zhang, Yu-Yu

2016-12-01

Generalized squeezing rotating-wave approximation (GSRWA) is proposed by employing both the displacement and the squeezing transformations. A solvable Hamiltonian is reformulated in the same form as the ordinary RWA ones. For a qubit coupled to oscillators experiment, a well-defined Schrödinger-cat-like entangled state is given by the displaced-squeezed oscillator state instead of the original displaced state. For the isotropic Rabi case, the mean photon number and the ground-state energy are expressed analytically with additional squeezing terms, exhibiting a substantial improvement of the GSRWA. And the ground-state energy in the anisotropic Rabi model confirms the effectiveness of the GSRWA. Due to the squeezing effect, the GSRWA improves the previous methods only with the displacement transformation in a wide range of coupling strengths even for large atom frequency.

Adaptive-Grid Methods for Phase Field Models of Microstructure Development

NASA Technical Reports Server (NTRS)

Provatas, Nikolas; Goldenfeld, Nigel; Dantzig, Jonathan A.

1999-01-01

In this work the authors show how the phase field model can be solved in a computationally efficient manner that opens a new large-scale simulational window on solidification physics. Our method uses a finite element, adaptive-grid formulation, and exploits the fact that the phase and temperature fields vary significantly only near the interface. We illustrate how our method allows efficient simulation of phase-field models in very large systems, and verify the predictions of solvability theory at intermediate undercooling. We then present new results at low undercoolings that suggest that solvability theory may not give the correct tip speed in that regime. We model solidification using the phase-field model used by Karma and Rappel.

The microscopic structure of an exactly solvable model binary solution that exhibits two closed loops in the phase diagram.

PubMed

Lungu, Radu P; Huckaby, Dale A

2008-07-21

An exactly solvable lattice model describing a binary solution is considered where rodlike molecules of types AA and BB cover the links of a honeycomb lattice, the neighboring molecular ends having three-body and orientation-dependent bonding interactions. At phase coexistence of AA-rich and BB-rich phases, the average fraction of each type of triangle of neighboring molecular ends is calculated exactly. The fractions of the different types of triangles are then used to deduce the local microscopic structure of the coexisting phases for a case of the model that contains two closed loops in the phase diagram.

CRE Solvability, Nonlocal Symmetry and Exact Interaction Solutions of the Fifth-Order Modified Korteweg-de Vries Equation

NASA Astrophysics Data System (ADS)

Cheng, Wen-Guang; Qiu, De-Qin; Yu, Bo

2017-06-01

This paper is concerned with the fifth-order modified Korteweg-de Vries (fmKdV) equation. It is proved that the fmKdV equation is consistent Riccati expansion (CRE) solvable. Three special form of soliton-cnoidal wave interaction solutions are discussed analytically and shown graphically. Furthermore, based on the consistent tanh expansion (CTE) method, the nonlocal symmetry related to the consistent tanh expansion (CTE) is investigated, we also give the relationship between this kind of nonlocal symmetry and the residual symmetry which can be obtained with the truncated Painlevé method. We further study the spectral function symmetry and derive the Lax pair of the fmKdV equation. The residual symmetry can be localized to the Lie point symmetry of an enlarged system and the corresponding finite transformation group is computed. Supported by National Natural Science Foundation of China under Grant No. 11505090, and Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009

Continuous-Time Random Walk with multi-step memory: an application to market dynamics

NASA Astrophysics Data System (ADS)

Gubiec, Tomasz; Kutner, Ryszard

2017-11-01

An extended version of the Continuous-Time Random Walk (CTRW) model with memory is herein developed. This memory involves the dependence between arbitrary number of successive jumps of the process while waiting times between jumps are considered as i.i.d. random variables. This dependence was established analyzing empirical histograms for the stochastic process of a single share price on a market within the high frequency time scale. Then, it was justified theoretically by considering bid-ask bounce mechanism containing some delay characteristic for any double-auction market. Our model appeared exactly analytically solvable. Therefore, it enables a direct comparison of its predictions with their empirical counterparts, for instance, with empirical velocity autocorrelation function. Thus, the present research significantly extends capabilities of the CTRW formalism. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

Hydrodynamic-to-ballistic crossover in Dirac materials

NASA Astrophysics Data System (ADS)

Svintsov, D.

2018-03-01

We develop an analytically solvable classical kinetic model of spatially dispersive transport in Dirac materials accounting for strong electron-electron (e-e) and electron-hole (e-h) collisions. We use this model to track the evolution of graphene conductivity and properties of its collective excitations across the hydrodynamic-to-ballistic crossover. We find the relaxation rate of electric current by e-e collisions that is possible due to the lack of Galilean invariance and introduce a universal numerical measure of this noninvariance. We find the two branches of collective excitations in the Dirac fluid: plasmons and electron-hole sound. The sound waves persist at frequencies exceeding the e-e collision frequency, have a small viscous damping at the neutrality point, but acquire large damping due to e-h friction even at slight doping. On the contrary, plasmons acquire strong frictional damping at the neutrality point and become well defined in doped samples.

Pattern Storage, Bifurcations, and Groupwise Correlation Structure of an Exactly Solvable Asymmetric Neural Network Model.

PubMed

Fasoli, Diego; Cattani, Anna; Panzeri, Stefano

2018-05-01

Despite their biological plausibility, neural network models with asymmetric weights are rarely solved analytically, and closed-form solutions are available only in some limiting cases or in some mean-field approximations. We found exact analytical solutions of an asymmetric spin model of neural networks with arbitrary size without resorting to any approximation, and we comprehensively studied its dynamical and statistical properties. The network had discrete time evolution equations and binary firing rates, and it could be driven by noise with any distribution. We found analytical expressions of the conditional and stationary joint probability distributions of the membrane potentials and the firing rates. By manipulating the conditional probability distribution of the firing rates, we extend to stochastic networks the associating learning rule previously introduced by Personnaz and coworkers. The new learning rule allowed the safe storage, under the presence of noise, of point and cyclic attractors, with useful implications for content-addressable memories. Furthermore, we studied the bifurcation structure of the network dynamics in the zero-noise limit. We analytically derived examples of the codimension 1 and codimension 2 bifurcation diagrams of the network, which describe how the neuronal dynamics changes with the external stimuli. This showed that the network may undergo transitions among multistable regimes, oscillatory behavior elicited by asymmetric synaptic connections, and various forms of spontaneous symmetry breaking. We also calculated analytically groupwise correlations of neural activity in the network in the stationary regime. This revealed neuronal regimes where, statistically, the membrane potentials and the firing rates are either synchronous or asynchronous. Our results are valid for networks with any number of neurons, although our equations can be realistically solved only for small networks. For completeness, we also derived the network equations in the thermodynamic limit of infinite network size and we analytically studied their local bifurcations. All the analytical results were extensively validated by numerical simulations.

Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability

NASA Astrophysics Data System (ADS)

Turbiner, Alexander V.; Miller, Willard; Escobar-Ruiz, M. A.

2018-02-01

As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., "Three-body problem in 3D space: Ground state, (quasi)-exact-solvability," J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi-exactly solvable problems. The extension to the case of non-equal masses is straightforward and is briefly discussed.

Pattern selection and tip perturbations in the Saffman-Taylor problem

NASA Technical Reports Server (NTRS)

Hong, D. C.; Langer, J. S.

1987-01-01

An analytic approach to the Saffman-Taylor problem of predicting the width of a viscous finger in a Hele-Shaw cell is presented. The first purpose is to provide a systematic description of the way in which the singular perturbation introduced by capillary forces leads to a solvability mechanism for pattern selection. It is then shown how recent experimental observations by Couder et al. (1986) may be interpreted in terms suggested by this mechanism.

Two solvable problems of planar geometrical optics.

PubMed

Borghero, Francesco; Bozis, George

2006-12-01

In the framework of geometrical optics we consider a two-dimensional transparent inhomogeneous isotropic medium (dispersive or not). We show that (i) for any family belonging to a certain class of planar monoparametric families of monochromatic light rays given in the form f(x,y)=c of any definite color and satisfying a differential condition, all the refractive index profiles n=n(x,y) allowing for the creation of the given family can be found analytically (inverse problem) and that (ii) for any member of a class of two-dimensional refractive index profiles n=n(x,y) satisfying a differential condition, all the compatible families of light rays can be found analytically (direct problem). We present appropriate examples.

Characterization of topological phases of dimerized Kitaev chain via edge correlation functions

NASA Astrophysics Data System (ADS)

Wang, Yucheng; Miao, Jian-Jian; Jin, Hui-Ke; Chen, Shu

2017-11-01

We study analytically topological properties of a noninteracting modified dimerized Kitaev chain and an exactly solvable interacting dimerized Kitaev chain under open boundary conditions by analyzing two introduced edge correlation functions. The interacting dimerized Kitaev chain at the symmetry point Δ =t and the chemical potential μ =0 can be exactly solved by applying two Jordan-Wigner transformations and a spin rotation, which permits us to calculate the edge correlation functions analytically. We demonstrate that the two edge correlation functions can be used to characterize the trivial, Su-Schrieffer-Heeger-like topological and topological superconductor phases of both the noninteracting and interacting systems and give their phase diagrams.

Loss of adiabaticity with increasing tunneling gap in nonintegrable multistate Landau-Zener models

NASA Astrophysics Data System (ADS)

Malla, Rajesh K.; Raikh, M. E.

2017-09-01

We consider the simplest nonintegrable model of the multistate Landau-Zener transition. In this model, two pairs of levels in two tunnel-coupled quantum dots are swept past each other by the gate voltage. Although this 2 ×2 model is nonintegrable, it can be solved analytically in the limit when the interlevel energy distance is much smaller than their tunnel splitting. The result is contrasted to the similar 2 ×1 model, in which one of the dots contains only one level. The latter model does not allow interference of the virtual transition amplitudes, and it is exactly solvable. In the 2 ×1 model, the probability for a particle, residing at time t →-∞ in one dot, to remain in the same dot at t →∞ , falls off exponentially with tunnel coupling. By contrast, in the 2 ×2 model, this probability grows rapidly with tunnel coupling. The physical origin of this growth is the formation of the tunneling-induced collective states in the system of two dots. This can be viewed as a manifestation of the Dicke effect.

Two-Dimensional One-Component Plasma on Flamm's Paraboloid

NASA Astrophysics Data System (ADS)

Fantoni, Riccardo; Téllez, Gabriel

2008-11-01

We study the classical non-relativistic two-dimensional one-component plasma at Coulomb coupling Γ=2 on the Riemannian surface known as Flamm's paraboloid which is obtained from the spatial part of the Schwarzschild metric. At this special value of the coupling constant, the statistical mechanics of the system are exactly solvable analytically. The Helmholtz free energy asymptotic expansion for the large system has been found. The density of the plasma, in the thermodynamic limit, has been carefully studied in various situations.

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G

2011-09-28

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. © 2011 American Institute of Physics

Exact analytical modeling of lightwave propagation in planar media with arbitrarily graded index profiles

NASA Astrophysics Data System (ADS)

Krapez, J.-C.

2018-02-01

Applying the Darboux transformation in the optical-depth space allows building infinite chains of exact analytical solutions of the electromagnetic (EM) fields in planar 1D-graded dielectrics. As a matter of fact, infinite chains of solvable admittance profiles (e.g. refractive-index profiles, in the case of non-magnetic materials), together with the related EM fields are simultaneously and recursively obtained. The whole procedure has received the name "PROFIDT method" for PROperty and FIeld Darboux Transformation method. By repeating the Darboux transformations we can find out progressively more complex profiles and their EM solutions. An alternative is to stop after the first step and settle for a particular class of four-parameter admittance profiles that were dubbed of "sech(ξ)-type". These profiles are highly flexible. For this reason, they can be used as elementary bricks for building and modeling profiles of arbitrary shape. In addition, the corresponding transfer matrix involves only elementary functions. The sub-class of "sech(ξ)-type" profiles with horizontal end-slopes (S-shaped function) is particularly interesting: these can be used for high-level modeling of piecewise-sigmoidal refractive-index profiles encountered in various photonic devices such as matchinglayers, antireflection layers, rugate filters, chirped mirrors and photonic crystals. These simple analytical tools also allow exploring the fascinating properties of a new kind of structure, namely smooth quasicrystals. They can also be applied to model propagation of other types of waves in graded media such as acoustic waves and electric waves in tapered transmission lines.

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ho, C.-L.; Lee, C.-C., E-mail: chieh.no27@gmail.com

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

Numerical evidences of universal trap-like aging dynamics

NASA Astrophysics Data System (ADS)

Cammarota, Chiara; Marinari, Enzo

2018-04-01

Trap models have been initially proposed as toy models for dynamical relaxation in extremely simplified rough potential energy landscapes. Their importance has recently grown considerably thanks to the discovery that the trap-like aging mechanism directly controls the out-of-equilibrium relaxation processes of more sophisticated spin models, that are considered as the solvable counterpart of real disordered systems. Further establishing the connection between these spin models, out-of-equilibrium behavior and the trap like aging mechanism could shed new light on the properties, which are still largely mysterious, for the activated out-of-equilibrium dynamics of disordered systems. In this work we discuss numerical evidence based on the computations of the permanence times of an emergent trap-like aging behavior in a variety of very simple disordered models—developed from the trap model paradigm. Our numerical results are backed by analytic derivations and heuristic discussions. Such exploration reveals some of the tricks needed to reveal the trap behavior in spite of the occurrence of secondary processes, of the existence of dynamical correlations and of strong finite system’s size effects.

Quasi-soliton scattering in quantum spin chains

NASA Astrophysics Data System (ADS)

Vlijm, R.; Ganahl, M.; Fioretto, D.; Brockmann, M.; Haque, M.; Evertz, H. G.; Caux, J.-S.

2015-12-01

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time-evolution fits on the displacements. The time-evolved block decimation algorithm allows for the study of scattering displacements from spin-block states, showing similar scattering displacement features.

Quasi-soliton scattering in quantum spin chains

NASA Astrophysics Data System (ADS)

Fioretto, Davide; Vljim, Rogier; Ganahl, Martin; Brockmann, Michael; Haque, Masud; Evertz, Hans-Gerd; Caux, Jean-Sébastien

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time evolution fits on the displacements. The TEBD algorithm allows for the study of scattering displacements from spin-block states, showing similar displacement scattering features.

Apparent impact: the hidden cost of one-shot trades

NASA Astrophysics Data System (ADS)

Mastromatteo, Iacopo

2015-06-01

We study the problem of the execution of a moderate size order in an illiquid market within the framework of a solvable Markovian model. We suppose that in order to avoid impact costs, a trader decides to execute her order through a unique trade, waiting for enough liquidity to accumulate at the best quote. We find that despite the absence of a proper price impact, such trader faces an execution cost arising from a non-vanishing correlation among volume at the best quotes and price changes. We characterize analytically the statistics of the execution time and its cost by mapping the problem to the simpler one of calculating a set of first-passage probabilities on a semi-infinite strip. We finally argue that price impact cannot be completely avoided by conditioning the execution of an order to a more favorable liquidity scenario.

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

NASA Astrophysics Data System (ADS)

Nemoto, Ryo; Iguchi, Tatsuo

2017-09-01

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

Construction of sequences of exact analytical solutions for heat diffusion in graded heterogeneous materials by the Darboux transformation method. Examples for half-space

NASA Astrophysics Data System (ADS)

Krapez, J.-C.

2016-09-01

The Darboux transformation is a differential transformation which, like other related methods (supersymmetry quantum mechanics-SUSYQM, factorization method) allows generating sequences of solvable potentials for the stationary 1D Schrodinger equation. It was recently shown that the heat equation in graded heterogeneous media, after a Liouville transformation, reduces to a pair of Schrödinger equations sharing the same potential function, one for the transformed temperature and one for the square root of effusivity. Repeated joint PROperty and Field Darboux Transformations (PROFIDT method) then yield two sequences of solutions: one of new solvable effusivity profiles and one of the corresponding temperature fields. In this paper we present and discuss the outcome in the case of a graded half-space domain. The interest in this methodology is that it provides closed-form solutions based on elementary functions. They are thus easily amenable to an implementation in an inversion process aimed, for example, at retrieving a subsurface effusivity profile from a modulated or transient surface temperature measurement (photothermal characterization).

The Dirac-Moshinsky oscillator coupled to an external field and its connection to quantum optics

NASA Astrophysics Data System (ADS)

Torres, Juan Mauricio; Sadurní, Emerson; Seligman, Thomas H.

2010-12-01

The Dirac-Moshinsky oscillator is an elegant example of an exactly solvable quantum relativistic model that under certain circumstances can be mapped onto the Jaynes-Cummings model in quantum optics. In this work we show, how to do this in detail. Then we extend it by considering its coupling with an external (isospin) field and find the conditions that maintain solvability. We use this extended system to explore entanglement in relativistic systems and then identify its quantum optical analog: two different atoms interacting with an electromagnetic mode. We show different aspects of entanglement which gain relevance in this last system, which can be used to emulate the former.

Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c = m/2

NASA Astrophysics Data System (ADS)

Minami, Kazuhiko

2017-12-01

An infinite number of spin chains are solved and it is derived that the ground-state phase transitions belong to the universality classes with central charge c = m / 2, where m is an integer. The models are diagonalized by automatically obtained transformations, many of which are different from the Jordan-Wigner transformation. The free energies, correlation functions, string order parameters, exponents, central charges, and the phase diagram are obtained. Most of the examples consist of the stabilizers of the cluster state. A unified structure of the one-dimensional XY and cluster-type spin chains is revealed, and other series of solvable models can be obtained through this formula.

Solvable Family of Driven-Dissipative Many-Body Systems.

PubMed

Foss-Feig, Michael; Young, Jeremy T; Albert, Victor V; Gorshkov, Alexey V; Maghrebi, Mohammad F

2017-11-10

Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.

Solvable Family of Driven-Dissipative Many-Body Systems

NASA Astrophysics Data System (ADS)

Foss-Feig, Michael; Young, Jeremy T.; Albert, Victor V.; Gorshkov, Alexey V.; Maghrebi, Mohammad F.

2017-11-01

Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.

Innovation Rather than Improvement: A Solvable High-Dimensional Model Highlights the Limitations of Scalar Fitness

NASA Astrophysics Data System (ADS)

Tikhonov, Mikhail; Monasson, Remi

2018-01-01

Much of our understanding of ecological and evolutionary mechanisms derives from analysis of low-dimensional models: with few interacting species, or few axes defining "fitness". It is not always clear to what extent the intuition derived from low-dimensional models applies to the complex, high-dimensional reality. For instance, most naturally occurring microbial communities are strikingly diverse, harboring a large number of coexisting species, each of which contributes to shaping the environment of others. Understanding the eco-evolutionary interplay in these systems is an important challenge, and an exciting new domain for statistical physics. Recent work identified a promising new platform for investigating highly diverse ecosystems, based on the classic resource competition model of MacArthur. Here, we describe how the same analytical framework can be used to study evolutionary questions. Our analysis illustrates how, at high dimension, the intuition promoted by a one-dimensional (scalar) notion of fitness can become misleading. Specifically, while the low-dimensional picture emphasizes organism cost or efficiency, we exhibit a regime where cost becomes irrelevant for survival, and link this observation to generic properties of high-dimensional geometry.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.

PubMed

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-04-08

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

PubMed Central

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-01-01

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves. PMID:24711719

Strongly Correlated Metal Built from Sachdev-Ye-Kitaev Models

NASA Astrophysics Data System (ADS)

Song, Xue-Yang; Jian, Chao-Ming; Balents, Leon

2017-11-01

Prominent systems like the high-Tc cuprates and heavy fermions display intriguing features going beyond the quasiparticle description. The Sachdev-Ye-Kitaev (SYK) model describes a (0 +1 )D quantum cluster with random all-to-all four-fermion interactions among N fermion modes which becomes exactly solvable as N →∞ , exhibiting a zero-dimensional non-Fermi-liquid with emergent conformal symmetry and complete absence of quasiparticles. Here we study a lattice of complex-fermion SYK dots with random intersite quadratic hopping. Combining the imaginary time path integral with real time path integral formulation, we obtain a heavy Fermi liquid to incoherent metal crossover in full detail, including thermodynamics, low temperature Landau quasiparticle interactions, and both electrical and thermal conductivity at all scales. We find linear in temperature resistivity in the incoherent regime, and a Lorentz ratio L ≡(κ ρ /T ) varies between two universal values as a function of temperature. Our work exemplifies an analytically controlled study of a strongly correlated metal.

A generalized linear integrate-and-fire neural model produces diverse spiking behaviors.

PubMed

Mihalaş, Stefan; Niebur, Ernst

2009-03-01

For simulations of neural networks, there is a trade-off between the size of the network that can be simulated and the complexity of the model used for individual neurons. In this study, we describe a generalization of the leaky integrate-and-fire model that produces a wide variety of spiking behaviors while still being analytically solvable between firings. For different parameter values, the model produces spiking or bursting, tonic, phasic or adapting responses, depolarizing or hyperpolarizing after potentials and so forth. The model consists of a diagonalizable set of linear differential equations describing the time evolution of membrane potential, a variable threshold, and an arbitrary number of firing-induced currents. Each of these variables is modified by an update rule when the potential reaches threshold. The variables used are intuitive and have biological significance. The model's rich behavior does not come from the differential equations, which are linear, but rather from complex update rules. This single-neuron model can be implemented using algorithms similar to the standard integrate-and-fire model. It is a natural match with event-driven algorithms for which the firing times are obtained as a solution of a polynomial equation.

Partial Wave Dispersion Relations: Application to Electron-Atom Scattering

NASA Technical Reports Server (NTRS)

Temkin, A.; Drachman, Richard J.

1999-01-01

In this Letter we propose the use of partial wave dispersion relations (DR's) as the way of solving the long-standing problem of correctly incorporating exchange in a valid DR for electron-atom scattering. In particular a method is given for effectively calculating the contribution of the discontinuity and/or poles of the partial wave amplitude which occur in the negative E plane. The method is successfully tested in three cases: (i) the analytically solvable exponential potential, (ii) the Hartree potential, and (iii) the S-wave exchange approximation for electron-hydrogen scattering.

Solvability of the electrocardiology inverse problem for a moving dipole.

PubMed

Tolkachev, V; Bershadsky, B; Nemirko, A

1993-01-01

New formulations of the direct and inverse problems for the moving dipole are offered. It has been suggested to limit the study by a small area on the chest surface. This lowers the role of the medium inhomogeneity. When formulating the direct problem, irregular components are considered. The algorithm of simultaneous determination of the dipole and regular noise parameters has been described and analytically investigated. It is shown that temporal overdetermination of the equations offers a single solution of the inverse problem for the four leads.

The Dirac-Moshinsky oscillator coupled to an external field and its connection to quantum optics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Torres, Juan Mauricio; Sadurni, Emerson; Seligman, Thomas H.

2010-12-23

The Dirac-Moshinsky oscillator is an elegant example of an exactly solvable quantum relativistic model that under certain circumstances can be mapped onto the Jaynes-Cummings model in quantum optics. In this work we show, how to do this in detail. Then we extend it by considering its coupling with an external (isospin) field and find the conditions that maintain solvability. We use this extended system to explore entanglement in relativistic systems and then identify its quantum optical analog: two different atoms interacting with an electromagnetic mode. We show different aspects of entanglement which gain relevance in this last system, which canmore » be used to emulate the former.« less

A Generalized Linear Integrate-and-Fire Neural Model Produces Diverse Spiking Behaviors

PubMed Central

Mihalaş, Ştefan; Niebur, Ernst

2010-01-01

For simulations of neural networks, there is a trade-off between the size of the network that can be simulated and the complexity of the model used for individual neurons. In this study, we describe a generalization of the leaky integrate-and-fire model that produces a wide variety of spiking behaviors while still being analytically solvable between firings. For different parameter values, the model produces spiking or bursting, tonic, phasic or adapting responses, depolarizing or hyperpolarizing after potentials and so forth. The model consists of a diagonalizable set of linear differential equations describing the time evolution of membrane potential, a variable threshold, and an arbitrary number of firing-induced currents. Each of these variables is modified by an update rule when the potential reaches threshold. The variables used are intuitive and have biological significance. The model’s rich behavior does not come from the differential equations, which are linear, but rather from complex update rules. This single-neuron model can be implemented using algorithms similar to the standard integrate-and-fire model. It is a natural match with event-driven algorithms for which the firing times are obtained as a solution of a polynomial equation. PMID:18928368

Theoretical studies on a new pattern of laser-driven systems: towards elucidation of direct photo-injection in dye-sensitized solar cells

NASA Astrophysics Data System (ADS)

Mishima, Kenji; Yamashita, Koichi

2011-03-01

We theoretically and numerically investigated a new type of analytically solvable laser-driven systems inspired by electron-injection dynamics in dye-sensitized solar cells. The simple analytical expressions were found to be useful for understanding the difference between dye excitation and direct photo-injection occurring between dye molecule and semiconductor nanoparticles. More importantly, we propose a method for discriminating experimentally dye excitation and direct photo-injection by using time-dependent fluorescence. We found that dye excitation shows no significant quantum beat whereas the direct photo-injection shows a significant quantum beat. This work was supported by Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST) ``Development of Organic Photovoltaics toward a Low-Carbon Society,'' Cabinet Office, Japan.

Effective equilibrium states in mixtures of active particles driven by colored noise

NASA Astrophysics Data System (ADS)

Wittmann, René; Brader, J. M.; Sharma, A.; Marconi, U. Marini Bettolo

2018-01-01

We consider the steady-state behavior of pairs of active particles having different persistence times and diffusivities. To this purpose we employ the active Ornstein-Uhlenbeck model, where the particles are driven by colored noises with exponential correlation functions whose intensities and correlation times vary from species to species. By extending Fox's theory to many components, we derive by functional calculus an approximate Fokker-Planck equation for the configurational distribution function of the system. After illustrating the predicted distribution in the solvable case of two particles interacting via a harmonic potential, we consider systems of particles repelling through inverse power-law potentials. We compare the analytic predictions to computer simulations for such soft-repulsive interactions in one dimension and show that at linear order in the persistence times the theory is satisfactory. This work provides the toolbox to qualitatively describe many-body phenomena, such as demixing and depletion, by means of effective pair potentials.

The second Eshelby problem and its solvability

NASA Astrophysics Data System (ADS)

Zou, Wen-Nan; Zheng, Quan-Shui

2012-10-01

It is still a challenge to clarify the dependence of overall elastic properties of heterogeneous materials on the microstructures of non-elliposodal inhomogeneities (cracks, pores, foreign particles). From the theory of elasticity, the formulation of the perturbance elastic fields, coming from a non-ellipsoidal inhomogeneity embedded in an infinitely extended material with remote constant loading, inevitably involve one or more integral equations. Up to now, due to the mathematical difficulty, there is almost no explicit analytical solution obtained except for the ellipsoidal inhomogeneity. In this paper, we point out the impossibility to transform this inhomogeneity problem into a conventional Eshelby problem by the equivalent inclusion method even if the eigenstrain is chosen to be non-uniform. We also build up an equivalent model, called the second Eshelby problem, to investigate the perturbance stress. It is probably a better template to make use of the profound methods and results of conventional Eshelby problems of non-ellipsoidal inclusions.

Relative frequencies of constrained events in stochastic processes: An analytical approach.

PubMed

Rusconi, S; Akhmatskaya, E; Sokolovski, D; Ballard, N; de la Cal, J C

2015-10-01

The stochastic simulation algorithm (SSA) and the corresponding Monte Carlo (MC) method are among the most common approaches for studying stochastic processes. They relies on knowledge of interevent probability density functions (PDFs) and on information about dependencies between all possible events. Analytical representations of a PDF are difficult to specify in advance, in many real life applications. Knowing the shapes of PDFs, and using experimental data, different optimization schemes can be applied in order to evaluate probability density functions and, therefore, the properties of the studied system. Such methods, however, are computationally demanding, and often not feasible. We show that, in the case where experimentally accessed properties are directly related to the frequencies of events involved, it may be possible to replace the heavy Monte Carlo core of optimization schemes with an analytical solution. Such a replacement not only provides a more accurate estimation of the properties of the process, but also reduces the simulation time by a factor of order of the sample size (at least ≈10(4)). The proposed analytical approach is valid for any choice of PDF. The accuracy, computational efficiency, and advantages of the method over MC procedures are demonstrated in the exactly solvable case and in the evaluation of branching fractions in controlled radical polymerization (CRP) of acrylic monomers. This polymerization can be modeled by a constrained stochastic process. Constrained systems are quite common, and this makes the method useful for various applications.

Saddles and dynamics in a solvable mean-field model

NASA Astrophysics Data System (ADS)

Angelani, L.; Ruocco, G.; Zamponi, F.

2003-05-01

We use the saddle-approach, recently introduced in the numerical investigation of simple model liquids, in the analysis of a mean-field solvable system. The investigated system is the k-trigonometric model, a k-body interaction mean field system, that generalizes the trigonometric model introduced by Madan and Keyes [J. Chem. Phys. 98, 3342 (1993)] and that has been recently introduced to investigate the relationship between thermodynamics and topology of the configuration space. We find a close relationship between the properties of saddles (stationary points of the potential energy surface) visited by the system and the dynamics. In particular the temperature dependence of saddle order follows that of the diffusivity, both having an Arrhenius behavior at low temperature and a similar shape in the whole temperature range. Our results confirm the general usefulness of the saddle-approach in the interpretation of dynamical processes taking place in interacting systems.

Fluid Intelligence and Cognitive Reflection in a Strategic Environment: Evidence from Dominance-Solvable Games

PubMed Central

Hanaki, Nobuyuki; Jacquemet, Nicolas; Luchini, Stéphane; Zylbersztejn, Adam

2016-01-01

Dominance solvability is one of the most straightforward solution concepts in game theory. It is based on two principles: dominance (according to which players always use their dominant strategy) and iterated dominance (according to which players always act as if others apply the principle of dominance). However, existing experimental evidence questions the empirical accuracy of dominance solvability. In this study, we study the relationships between the key facets of dominance solvability and two cognitive skills, cognitive reflection, and fluid intelligence. We provide evidence that the behaviors in accordance with dominance and one-step iterated dominance are both predicted by one's fluid intelligence rather than cognitive reflection. Individual cognitive skills, however, only explain a small fraction of the observed failure of dominance solvability. The accuracy of theoretical predictions on strategic decision making thus not only depends on individual cognitive characteristics, but also, perhaps more importantly, on the decision making environment itself. PMID:27559324

Solving three-body-breakup problems with outgoing-flux asymptotic conditions

NASA Astrophysics Data System (ADS)

Randazzo, J. M.; Buezas, F.; Frapiccini, A. L.; Colavecchia, F. D.; Gasaneo, G.

2011-11-01

An analytically solvable three-body collision system (s wave) model is used to test two different theoretical methods. The first one is a configuration interaction expansion of the scattering wave function using a basis set of Generalized Sturmian Functions (GSF) with purely outgoing flux (CISF), introduced recently in A. L. Frapicinni, J. M. Randazzo, G. Gasaneo, and F. D. Colavecchia [J. Phys. B: At. Mol. Opt. Phys.JPAPEH0953-407510.1088/0953-4075/43/10/101001 43, 101001 (2010)]. The second one is a finite element method (FEM) calculation performed with a commercial code. Both methods are employed to analyze different ways of modeling the asymptotic behavior of the wave function in finite computational domains. The asymptotes can be simulated very accurately by choosing hyperspherical or rectangular contours with the FEM software. In contrast, the CISF method can be defined both in an infinite domain or within a confined region in space. We found that the hyperspherical (rectangular) FEM calculation and the infinite domain (confined) CISF evaluation are equivalent. Finally, we apply these models to the Temkin-Poet approach of hydrogen ionization.

Competition between Chaotic and Nonchaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model.

PubMed

Chen, Xin; Fan, Ruihua; Chen, Yiming; Zhai, Hui; Zhang, Pengfei

2017-11-17

The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study non-Fermi liquid properties, holographic duality, and maximally chaotic behavior. In this work, we consider a generalization of the SYK model that contains two SYK models with a different number of Majorana modes coupled by quadratic terms. This model is also solvable, and the solution shows a zero-temperature quantum phase transition between two non-Fermi liquid chaotic phases. This phase transition is driven by tuning the ratio of two mode numbers, and a nonchaotic Fermi liquid sits at the critical point with an equal number of modes. At a finite temperature, the Fermi liquid phase expands to a finite regime. More intriguingly, a different non-Fermi liquid phase emerges at a finite temperature. We characterize the phase diagram in terms of the spectral function, the Lyapunov exponent, and the entropy. Our results illustrate a concrete example of the quantum phase transition and critical behavior between two non-Fermi liquid phases.

Hypergeometric type operators and their supersymmetric partners

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cotfas, Nicolae; Cotfas, Liviu Adrian

2011-05-15

The generalization of the factorization method performed by Mielnik [J. Math. Phys. 25, 3387 (1984)] opened new ways to generate exactly solvable potentials in quantum mechanics. We present an application of Mielnik's method to hypergeometric type operators. It is based on some solvable Riccati equations and leads to a unitary description of the quantum systems exactly solvable in terms of orthogonal polynomials or associated special functions.

R matrices of three-state Hamiltonians solvable by coordinate Bethe ansatz

NASA Astrophysics Data System (ADS)

Fonseca, T.; Frappat, L.; Ragoucy, E.

2015-01-01

We review some of the strategies that can be implemented to infer an R-matrix from the knowledge of its Hamiltonian. We apply them to the classification achieved in Crampé, Frappat, and Ragoucy, J. Phys. A 46, 405001 (2013), on three state U(1)-invariant Hamiltonians solvable by coordinate Bethe ansatz, focusing on models for which the S-matrix is not trivial. For the 19-vertex solutions, we recover the R-matrices of the well-known Zamolodchikov-Fateev and Izergin-Korepin models. We point out that the generalized Bariev Hamiltonian is related to both main and special branches studied by Martins in Nucl. Phys. B 874, 243 (2013), that we prove to generate the same Hamiltonian. The 19-vertex SpR model still resists to the analysis, although we are able to state some no-go theorems on its R-matrix. For 17-vertex Hamiltonians, we produce a new R-matrix.

Exactly solvable model of transitional nuclei based on dual algebraic structure for the three level pairing model in the framework of sdg interacting boson model

NASA Astrophysics Data System (ADS)

Jafarizadeh, M. A.; Ranjbar, Z.; Fouladi, N.; Ghapanvari, M.

2018-01-01

In this paper, a successful algebraic method based on the dual algebraic structure for three level pairing model in the framework of sdg IBM is proposed for transitional nuclei which show transitional behavior from spherical to gamma-unstable quantum shape phase transition. In this method complicated sdg Hamiltonian, which is a three level pairing Hamiltonian is determined easily via the exactly solvable method. This description provides a better interpretation of some observables such as BE (4) in nuclei which exhibits the necessity of inclusion of g boson in the sd IBM, while BE (4) cannot be explained in the sd boson model. Some observables such as Energy levels, BE (2), BE (4), the two neutron separation energies signature splitting of the γ-vibrational band and expectation values of the g-boson number operator are calculated and examined for 46 104 - 110Pd isotopes.

Exact mode volume and Purcell factor of open optical systems

NASA Astrophysics Data System (ADS)

Muljarov, E. A.; Langbein, W.

2016-12-01

The Purcell factor quantifies the change of the radiative decay of a dipole in an electromagnetic environment relative to free space. Designing this factor is at the heart of photonics technology, striving to develop ever smaller or less lossy optical resonators. The Purcell factor can be expressed using the electromagnetic eigenmodes of the resonators, introducing the notion of a mode volume for each mode. This approach allows an analytic treatment, reducing the Purcell factor and other observables to sums over eigenmode resonances. Calculating the mode volumes requires a correct normalization of the modes. We introduce an exact normalization of modes, not relying on perfectly matched layers. We present an analytic theory of the Purcell effect based on this exact mode normalization and the resulting effective mode volume. We use a homogeneous dielectric sphere in vacuum, which is analytically solvable, to exemplify these findings. We furthermore verify the applicability of the normalization to numerically determined modes of a finite dielectric cylinder.

A second-order 3D electromagnetics algorithm for curved interfaces between anisotropic dielectrics on a Yee mesh

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bauer, Carl A., E-mail: bauerca@colorado.ed; Werner, Gregory R.; Cary, John R.

A new frequency-domain electromagnetics algorithm is developed for simulating curved interfaces between anisotropic dielectrics embedded in a Yee mesh with second-order error in resonant frequencies. The algorithm is systematically derived using the finite integration formulation of Maxwell's equations on the Yee mesh. Second-order convergence of the error in resonant frequencies is achieved by guaranteeing first-order error on dielectric boundaries and second-order error in bulk (possibly anisotropic) regions. Convergence studies, conducted for an analytically solvable problem and for a photonic crystal of ellipsoids with anisotropic dielectric constant, both show second-order convergence of frequency error; the convergence is sufficiently smooth that Richardsonmore » extrapolation yields roughly third-order convergence. The convergence of electric fields near the dielectric interface for the analytic problem is also presented.« less

Analysis of fast boundary-integral approximations for modeling electrostatic contributions of molecular binding

PubMed Central

Kreienkamp, Amelia B.; Liu, Lucy Y.; Minkara, Mona S.; Knepley, Matthew G.; Bardhan, Jaydeep P.; Radhakrishnan, Mala L.

2013-01-01

We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins—a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue interactions in protein–protein binding, using the widely studied model system of trypsin and bovine pancreatic trypsin inhibitor (BPTI). Finding that the BIBEE/I model performs surprisingly less well in this task than simpler BIBEE models, we seek to explain this behavior in terms of the models’ differing spectral approximations of the exact boundary-integral operator. Calculations of analytically solvable systems (spheres and tri-axial ellipsoids) suggest two possibilities for improvement. The first is a modified BIBEE/I approach that captures the asymptotic eigenvalue limit correctly, and the second involves the dipole and quadrupole modes for ellipsoidal approximations of protein geometries. Our analysis suggests that fast, rigorous approximate models derived from reduced-basis approximation of boundary-integral equations might reach unprecedented accuracy, if the dipole and quadrupole modes can be captured quickly for general shapes. PMID:24466561

An exactly solvable, spatial model of mutation accumulation in cancer

NASA Astrophysics Data System (ADS)

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

2016-12-01

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

A Watched Ocean World Never Boils: Inspecting the Geochemical Impact on Ocean Worlds from Their Thermal Evolution

NASA Astrophysics Data System (ADS)

Spiers, E. M.; Schmidt, B. E.

2018-05-01

I aim to acquire better understanding of coupled thermal evolution and geochemical fluxes of an ocean world through a box model. A box model divides the system into plainer elements with realistically-solvable, dynamic equations.

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

NASA Astrophysics Data System (ADS)

Kuznetsov, Alexander M.; Medvedev, Igor G.

2006-05-01

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

Exact Solution of a Two-Species Quantum Dimer Model for Pseudogap Metals

NASA Astrophysics Data System (ADS)

Feldmeier, Johannes; Huber, Sebastian; Punk, Matthias

2018-05-01

We present an exact ground state solution of a quantum dimer model introduced by Punk, Allais, and Sachdev [Quantum dimer model for the pseudogap metal, Proc. Natl. Acad. Sci. U.S.A. 112, 9552 (2015)., 10.1073/pnas.1512206112], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-Tc cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit.

Two charges on plane in a magnetic field I. “Quasi-equal” charges and neutral quantum system at rest cases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Escobar-Ruiz, M.A., E-mail: mauricio.escobar@nucleares.unam.mx; Turbiner, A.V., E-mail: turbiner@nucleares.unam.mx

Low-lying bound states for the problem of two Coulomb charges of finite masses on a plane subject to a constant magnetic field B perpendicular to the plane are considered. Major emphasis is given to two systems: two charges with the equal charge-to-mass ratio (quasi-equal charges) and neutral systems with concrete results for the hydrogen atom and two electrons (quantum dot). It is shown that for these two cases, when a neutral system is at rest (the center-of-mass momentum is zero), some outstanding properties occur: in double polar coordinates in CMS (R,ϕ) and relative (ρ,φ) coordinate systems (i) the eigenfunctions aremore » factorizable, all factors except for ρ-dependent are found analytically, they have definite relative angular momentum, (ii) dynamics in ρ-direction is the same for both systems being described by a funnel-type potential; (iii) at some discrete values of dimensionless magnetic fields b≤1 the system becomes quasi-exactly-solvable and a finite number of eigenfunctions in ρ are polynomials. The variational method is employed. Trial functions are based on combining for the phase of a wavefunction (a) the WKB expansion at large distances, (b) the perturbation theory at small distances (c) with a form of the known analytically (quasi-exactly-solvable) eigenfunctions. Such a form of trial function appears as a compact uniform approximation for lowest eigenfunctions. For the lowest states with relative magnetic quantum numbers s=0,1,2 this approximation gives not less than 7 s.d., 8 s.d., 9 s.d., respectively, for the total energy E(B) for magnetic fields 0.049a.u.« less

Probing topological order with Rényi entropy

NASA Astrophysics Data System (ADS)

Halász, Gábor B.; Hamma, Alioscia

2012-12-01

We present an analytical study of the quantum phase transition between the topologically ordered toric-code-model ground state and the disordered spin-polarized state. The phase transition is induced by applying an external magnetic field, and the variation in topological order is detected via two nonlocal quantities: the Wilson loop and the topological Rényi entropy of order 2. By exploiting an equivalence with the transverse-field Ising model and considering two different variants of the problem, we investigate the field dependence of these quantities by means of an exact treatment in the exactly solvable variant and complementary perturbation theories around the limits of zero and infinite fields in both variants. We find strong evidence that the phase transition point between topological order and disorder is marked by a discontinuity in the topological Rényi entropy and that the two phases around the phase transition point are characterized by its different constant values. Our results therefore indicate that the topological Rényi entropy is a proper topological invariant: its allowed values are discrete and can be used to distinguish between different phases of matter.

New strings for old Veneziano amplitudes. II. Group-theoretic treatment

NASA Astrophysics Data System (ADS)

Kholodenko, A. L.

2006-09-01

In this part of our four parts work we use theory of polynomial invariants of finite pseudo-reflection groups in order to reconstruct both the Veneziano and Veneziano-like (tachyon-free) amplitudes and the generating function reproducing these amplitudes. We demonstrate that such generating function and amplitudes associated with it can be recovered with help of finite dimensional exactly solvableN=2 supersymmetric quantum mechanical model known earlier from works of Witten, Stone and others. Using the Lefschetz isomorphism theorem we replace traditional supersymmetric calculations by the group-theoretic thus solving the Veneziano model exactly using standard methods of representation theory. Mathematical correctness of our arguments relies on important theorems by Shepard and Todd, Serre and Solomon proven respectively in the early 50s and 60s and documented in the monograph by Bourbaki. Based on these theorems, we explain why the developed formalism leaves all known results of conformal field theories unchanged. We also explain why these theorems impose stringent requirements connecting analytical properties of scattering amplitudes with symmetries of space-time in which such amplitudes act.

On the global well-posedness of BV weak solutions to the Kuramoto-Sakaguchi equation

NASA Astrophysics Data System (ADS)

Amadori, Debora; Ha, Seung-Yeal; Park, Jinyeong

2017-01-01

The Kuramoto model is a prototype phase model describing the synchronous behavior of weakly coupled limit-cycle oscillators. When the number of oscillators is sufficiently large, the dynamics of Kuramoto ensemble can be effectively approximated by the corresponding mean-field equation, namely "the Kuramoto-Sakaguchi (KS) equation". This KS equation is a kind of scalar conservation law with a nonlocal flux function due to the mean-field interactions among oscillators. In this paper, we provide a unique global solvability of bounded variation (BV) weak solutions to the kinetic KS equation for identical oscillators using the method of front-tracking in hyperbolic conservation laws. Moreover, we also show that our BV weak solutions satisfy local-in-time L1-stability with respect to BV-initial data. For the ensemble of identical Kuramoto oscillators, we explicitly construct an exponentially growing BV weak solution generated from BV perturbation of incoherent state for any positive coupling strength. This implies the nonlinear instability of incoherent state in a positive coupling strength regime. We provide several numerical examples and compare them with our analytical results.

Quantum dynamical framework for Brownian heat engines

NASA Astrophysics Data System (ADS)

Agarwal, G. S.; Chaturvedi, S.

2013-07-01

We present a self-contained formalism modeled after the Brownian motion of a quantum harmonic oscillator for describing the performance of microscopic Brownian heat engines such as Carnot, Stirling, and Otto engines. Our theory, besides reproducing the standard thermodynamics results in the steady state, enables us to study the role dissipation plays in determining the efficiency of Brownian heat engines under actual laboratory conditions. In particular, we analyze in detail the dynamics associated with decoupling a system in equilibrium with one bath and recoupling it to another bath and obtain exact analytical results, which are shown to have significant ramifications on the efficiencies of engines involving such a step. We also develop a simple yet powerful technique for computing corrections to the steady state results arising from finite operation time and use it to arrive at the thermodynamic complementarity relations for various operating conditions and also to compute the efficiencies of the three engines cited above at maximum power. Some of the methods and exactly solvable models presented here are interesting in their own right and could find useful applications in other contexts as well.

Non-polynomial extensions of solvable potentials à la Abraham-Moses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Odake, Satoru; Sasaki, Ryu; Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan

2013-10-15

Abraham-Moses transformations, besides Darboux transformations, are well-known procedures to generate extensions of solvable potentials in one-dimensional quantum mechanics. Here we present the explicit forms of infinitely many seed solutions for adding eigenstates at arbitrary real energy through the Abraham-Moses transformations for typical solvable potentials, e.g., the radial oscillator, the Darboux-Pöschl-Teller, and some others. These seed solutions are simple generalisations of the virtual state wavefunctions, which are obtained from the eigenfunctions by discrete symmetries of the potentials. The virtual state wavefunctions have been an essential ingredient for constructing multi-indexed Laguerre and Jacobi polynomials through multiple Darboux-Crum transformations. In contrast to themore » Darboux transformations, the virtual state wavefunctions generate non-polynomial extensions of solvable potentials through the Abraham-Moses transformations.« less

Interaction between mean flow and turbulence in two dimensions

PubMed Central

2016-01-01

This short note is written to call attention to an analytic approach to the interaction of developed turbulence with mean flows of simple geometry (jets and vortices). It is instructive to compare cases in two and three dimensions and see why the former are solvable and the latter are not (yet). We present the analytical solutions for two-dimensional mean flows generated by an inverse turbulent cascade on a sphere and in planar domains of different aspect ratios. These solutions are obtained in the limit of small friction when the flow is strong while turbulence can be considered weak and treated perturbatively. I then discuss when these simple solutions can be realized and when more complicated flows may appear instead. The next step of describing turbulence statistics inside a flow and directions of possible future progress are briefly discussed at the end. PMID:27493579

Thermo-solutal and kinetic modes of stable dendritic growth with different symmetries of crystalline anisotropy in the presence of convection

NASA Astrophysics Data System (ADS)

Alexandrov, Dmitri V.; Galenko, Peter K.; Toropova, Lyubov V.

2018-01-01

Motivated by important applications in materials science and geophysics, we consider the steady-state growth of anisotropic needle-like dendrites in undercooled binary mixtures with a forced convective flow. We analyse the stable mode of dendritic evolution in the case of small anisotropies of growth kinetics and surface energy for arbitrary Péclet numbers and n-fold symmetry of dendritic crystals. On the basis of solvability and stability theories, we formulate a selection criterion giving a stable combination between dendrite tip diameter and tip velocity. A set of nonlinear equations consisting of the solvability criterion and undercooling balance is solved analytically for the tip velocity V and tip diameter ρ of dendrites with n-fold symmetry in the absence of convective flow. The case of convective heat and mass transfer mechanisms in a binary mixture occurring as a result of intensive flows in the liquid phase is detailed. A selection criterion that describes such solidification conditions is derived. The theory under consideration comprises previously considered theoretical approaches and results as limiting cases. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.

Effect of the SOS response on the mean fitness of unicellular populations: a quasispecies approach.

PubMed

Kama, Amit; Tannenbaum, Emmanuel

2010-11-30

The goal of this paper is to develop a mathematical model that analyzes the selective advantage of the SOS response in unicellular organisms. To this end, this paper develops a quasispecies model that incorporates the SOS response. We consider a unicellular, asexually replicating population of organisms, whose genomes consist of a single, double-stranded DNA molecule, i.e. one chromosome. We assume that repair of post-replication mismatched base-pairs occurs with probability , and that the SOS response is triggered when the total number of mismatched base-pairs is at least . We further assume that the per-mismatch SOS elimination rate is characterized by a first-order rate constant . For a single fitness peak landscape where the master genome can sustain up to mismatches and remain viable, this model is analytically solvable in the limit of infinite sequence length. The results, which are confirmed by stochastic simulations, indicate that the SOS response does indeed confer a fitness advantage to a population, provided that it is only activated when DNA damage is so extensive that a cell will die if it does not attempt to repair its DNA.

Asymptotic Normalization Coefficients in a Potential Model Involving Forbidden States

NASA Astrophysics Data System (ADS)

Blokhintsev, L. D.; Savin, D. A.

2018-03-01

It is shown that values obtained for asymptotic normalization coefficients by means of a potential fitted to experimental data on elastic scattering depend substantially on the presence and the number n of possible forbidden states in the fitted potential. The present analysis was performed within exactly solvable potential models for various nuclear systems and various potentials without and with allowance for Coulomb interaction. Various methods for changing the number n that are based on the use of various versions of the change in the parameters of the potential model were studied. A compact analytic expression for the asymptotic normalization coefficients was derived for the case of the Hulthén potential. Specifically, the d + α and α + 12C systems, which are of importance for astrophysics, were examined. It was concluded that an incorrect choice of n could lead to a substantial errors in determining the asymptotic normalization coefficients. From the results of our calculations, it also follows that, for systems with a low binding energy and, as a consequence, with a large value of the Coulomb parameter, the inclusion of the Coulomb interaction may radically change the asymptotic normalization coefficients, increasing them sharply.

Eigenmode analysis of a high-gain free-electron laser based on a transverse gradient undulator

DOE PAGES

Baxevanis, Panagiotis; Huang, Zhirong; Ruth, Ronald; ...

2015-01-27

Here, the use of a transverse gradient undulator (TGU) is viewed as an attractive option for free-electron lasers (FELs) driven by beams with a large energy spread. By suitably dispersing the electron beam and tilting the undulator poles, the energy spread effect can be substantially mitigated. However, adding the dispersion typically leads to electron beams with large aspect ratios. As a result, the presence of higher-order modes in the FEL radiation can become significant. To investigate this effect, we study the eigenmode properties of a TGU-based, high-gain FEL, using both an analytically-solvable model and a variational technique. Our analysis, whichmore » includes the fundamental and the higher-order FEL eigenmodes, can provide an estimate of the mode content for the output radiation. This formalism also enables us to study the trade-off between FEL gain and transverse coherence. Numerical results are presented for a representative soft X-ray, TGU FEL example.« less

Eigenmode analysis of a high-gain free-electron laser based on a transverse gradient undulator

NASA Astrophysics Data System (ADS)

Baxevanis, Panagiotis; Huang, Zhirong; Ruth, Ronald; Schroeder, Carl B.

2015-01-01

The use of a transverse gradient undulator (TGU) is viewed as an attractive option for free-electron lasers (FELs) driven by beams with a large energy spread. By suitably dispersing the electron beam and tilting the undulator poles, the energy spread effect can be substantially mitigated. However, adding the dispersion typically leads to electron beams with large aspect ratios. As a result, the presence of higher-order modes in the FEL radiation can become significant. To investigate this effect, we study the eigenmode properties of a TGU-based, high-gain FEL, using both an analytically-solvable model and a variational technique. Our analysis, which includes the fundamental and the higher-order FEL eigenmodes, can provide an estimate of the mode content for the output radiation. This formalism also enables us to study the trade-off between FEL gain and transverse coherence. Numerical results are presented for a representative soft X-ray, TGU FEL example.

Accelerated and Airy-Bloch oscillations

NASA Astrophysics Data System (ADS)

Longhi, Stefano

2016-09-01

A quantum particle subjected to a constant force undergoes an accelerated motion following a parabolic path, which differs from the classical motion just because of wave packet spreading (quantum diffusion). However, when a periodic potential is added (such as in a crystal) the particle undergoes Bragg scattering and an oscillatory (rather than accelerated) motion is found, corresponding to the famous Bloch oscillations (BOs). Here, we introduce an exactly-solvable quantum Hamiltonian model, corresponding to a generalized Wannier-Stark Hamiltonian Ĥ, in which a quantum particle shows an intermediate dynamical behavior, namely an oscillatory motion superimposed to an accelerated one. Such a novel dynamical behavior is referred to as accelerated BOs. Analytical expressions of the spectrum, improper eigenfunctions and propagator of the generalized Wannier-Stark Hamiltonian Ĥ are derived. Finally, it is shown that acceleration and quantum diffusion in the generalized Wannier-Stark Hamiltonian are prevented for Airy wave packets, which undergo a periodic breathing dynamics that can be referred to as Airy-Bloch oscillations.

A new approach to the Schrödinger equation with rational potentials

NASA Astrophysics Data System (ADS)

Dong, Ming-de; Chu, Jue-Hui

1984-04-01

A new analytic theory is established for the Schrödinger equation with a rational potential, including a complete classification of the regular eigenfunctions into three different types, an exact method of obtaining wavefunctions, an explicit formulation of the spectral equation (3 x 3 determinant) etc. All representations are exhibited in a unifying way via function-theoretic methods and therefore given in explicit form, in contrast to the prevailing discussion appealing to perturbation or variation methods or continued-fraction techniques. The irregular eigenfunctions at infinity can be obtained analogously and will be discussed separately as another solvable case for singular potentials.

Managing Inflections in Life and Career: Tale from a Physicist

NASA Astrophysics Data System (ADS)

Bhattacharya, Santanu

2010-03-01

By training, a physicist possesses one of the rarest qualities ever imparted in an educational degree program, namely, the ability to take on complex problems, divide them into ``solvable'' parts, derive solutions and put them back as insightful outputs. Dr Bhattacharya, CEO of Salorix, a research, analytics and consulting firm, explains how he has used these skills learned at the graduate school to build a career as a scientist, management consultant and entrepreneur. He will also speak about how the real-life skillsets of understanding and dealing with ``Inflections'', self discovery and introspection can be a great tool for managing one's life and career progression.

High-spin level structure and Ground-state phase transition in the odd-mass 103-109Rh isotopes in the framework of exactly solvable sdg interacting boson-fermion model

NASA Astrophysics Data System (ADS)

Ghapanvari, M.; Ghorashi, A. H.; Ranjbar, Z.; Jafarizadeh, M. A.

2018-03-01

In this article, the negative-parity states in the odd-mass 103 - 109Rh isotopes in terms of the sd and sdg interacting-boson fermion models were studied. The transitional interacting boson-fermion model Hamiltonians in sd and sdg-IBFM versions based on affine SU (1 , 1) Lie Algebra were employed to describe the evolution from the spherical to deformed gamma unstable shapes along with the chain of Rh isotopes. In this method, sdg-IBFM Hamiltonian, which is a three level pairing Hamiltonian was determined easily via the exactly solvable method. Some observables of the shape phase transitions such as energy levels, the two neutron separation energies, signature splitting of the γ-vibrational band, the α-decay and double β--decay energies were calculated and examined for these isotopes. The present calculation correctly reproduces the spherical to gamma-soft phase transition in the Rh isotopes. Some comparisons were made with sd-IBFM.

Modeling cometary photopolarimetric characteristics with Sh-matrix method

NASA Astrophysics Data System (ADS)

Kolokolova, L.; Petrov, D.

2017-12-01

Cometary dust is dominated by particles of complex shape and structure, which are often considered as fractal aggregates. Rigorous modeling of light scattering by such particles, even using parallelized codes and NASA supercomputer resources, is very computer time and memory consuming. We are presenting a new approach to modeling cometary dust that is based on the Sh-matrix technique (e.g., Petrov et al., JQSRT, 112, 2012). This method is based on the T-matrix technique (e.g., Mishchenko et al., JQSRT, 55, 1996) and was developed after it had been found that the shape-dependent factors could be separated from the size- and refractive-index-dependent factors and presented as a shape matrix, or Sh-matrix. Size and refractive index dependences are incorporated through analytical operations on the Sh-matrix to produce the elements of T-matrix. Sh-matrix method keeps all advantages of the T-matrix method, including analytical averaging over particle orientation. Moreover, the surface integrals describing the Sh-matrix elements themselves can be solvable analytically for particles of any shape. This makes Sh-matrix approach an effective technique to simulate light scattering by particles of complex shape and surface structure. In this paper, we present cometary dust as an ensemble of Gaussian random particles. The shape of these particles is described by a log-normal distribution of their radius length and direction (Muinonen, EMP, 72, 1996). Changing one of the parameters of this distribution, the correlation angle, from 0 to 90 deg., we can model a variety of particles from spheres to particles of a random complex shape. We survey the angular and spectral dependencies of intensity and polarization resulted from light scattering by such particles, studying how they depend on the particle shape, size, and composition (including porous particles to simulate aggregates) to find the best fit to the cometary observations.

Z/sub n/ Baxter model: Critical behavior

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tracy, C.A.

1986-07-01

The Z/sub n/ Baxter Model is an exactly solvable lattice model in the special case of the Belavin parametrization. We calculate the critical behavior of Prob/sub n/ (q = w/sup k/) using techniques developed in number theory in the study of the congruence properties of p(m), the number of unrestricted partitions of an integer m.

Revisiting Unemployment in Intermediate Macroeconomics: A New Approach for Teaching Diamond-Mortensen-Pissarides

ERIC Educational Resources Information Center

Bhattacharya, Arghya; Jackson, Paul; Jenkins, Brian C.

2018-01-01

The authors present a version of the Diamond-Mortensen-Pissarides model of unemployment that is accessible to undergraduates and preserve the dynamic structure of the original model. The model is solvable in closed form using basic algebra and admits a graphical representation useful for illustrating a variety of comparative statics. They show how…

Emery-Kivelson solution of the two-channel Kondo problem

NASA Astrophysics Data System (ADS)

Sengupta, Anirvan M.; Georges, Antoine

1994-04-01

We consider the two-channel Kondo model in the Emery-Kivelson approach, and calculate the total susceptibility enhancement due to the impurity χimp=χ-χbulk. We find that χimp exactly vanishes at the solvable point, in a completely analogous way to the singular part of the specific heat Cimp. A perturbative calculation around the solvable point yields the generic behavior χimp~log(1/T), Cimp~T logT and the known universal value of the Wilson ratio RW=8/3. From this calculation, the Kondo temperature can be identified and is found to behave as the inverse square of the perturbation parameter. The small-field, zero-temperature behavior χimp~log(1/h) is also recovered.

Quantifying uncertainty in climate change science through empirical information theory.

PubMed

Majda, Andrew J; Gershgorin, Boris

2010-08-24

Quantifying the uncertainty for the present climate and the predictions of climate change in the suite of imperfect Atmosphere Ocean Science (AOS) computer models is a central issue in climate change science. Here, a systematic approach to these issues with firm mathematical underpinning is developed through empirical information theory. An information metric to quantify AOS model errors in the climate is proposed here which incorporates both coarse-grained mean model errors as well as covariance ratios in a transformation invariant fashion. The subtle behavior of model errors with this information metric is quantified in an instructive statistically exactly solvable test model with direct relevance to climate change science including the prototype behavior of tracer gases such as CO(2). Formulas for identifying the most sensitive climate change directions using statistics of the present climate or an AOS model approximation are developed here; these formulas just involve finding the eigenvector associated with the largest eigenvalue of a quadratic form computed through suitable unperturbed climate statistics. These climate change concepts are illustrated on a statistically exactly solvable one-dimensional stochastic model with relevance for low frequency variability of the atmosphere. Viable algorithms for implementation of these concepts are discussed throughout the paper.

How animals move along? Exactly solvable model of superdiffusive spread resulting from animal's decision making.

PubMed

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.

Dynamically enriched topological orders in driven two-dimensional systems

NASA Astrophysics Data System (ADS)

Potter, Andrew C.; Morimoto, Takahiro

2017-04-01

Time-periodic driving of a quantum system can enable new dynamical topological phases of matter that could not exist in thermal equilibrium. We investigate two related classes of dynamical topological phenomena in 2D systems: Floquet symmetry-protected topological phases (FSPTs) and Floquet enriched topological orders (FETs). By constructing solvable lattice models for a complete set of 2D bosonic FSPT phases, we show that bosonic FSPTs can be understood as topological pumps which deposit loops of 1D SPT chains onto the boundary during each driving cycle, which protects a nontrivial edge state by dynamically tuning the edge to a self-dual point poised between the 1D SPT and trivial phases of the edge. By coupling these FSPT models to dynamical gauge fields, we construct solvable models of FET orders in which anyon excitations are dynamically transmuted into topologically distinct anyon types during each driving period. These bosonic FSPT and gauged FSPT models are classified by group cohomology methods. In addition, we also construct examples of "beyond cohomology" FET orders, which can be viewed as topological pumps of 1D topological chains formed of emergent anyonic quasiparticles.

Decoherence at constant excitation

NASA Astrophysics Data System (ADS)

Torres, J. M.; Sadurní, E.; Seligman, T. H.

2012-02-01

We present a simple exactly solvable extension of the Jaynes-Cummings model by adding dissipation. This is done such that the total number of excitations is conserved. The Liouville operator in the resulting master equation can be reduced to blocks of 4×4 matrices.

Two particle model for studying the effects of space-charge force on strong head-tail instabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chin, Yong Ho; Chao, Alexander Wu; Blaskiewicz, Michael M.

In this paper, we present a new two particle model for studying the strong head-tail instabilities in the presence of the space-charge force. It is a simple expansion of the well-known two particle model for strong head-tail instability and is still analytically solvable. No chromaticity effect is included. It leads to a formula for the growth rate as a function of the two dimensionless parameters: the space-charge tune shift parameter (normalized by the synchrotron tune) and the wakefield strength, Upsilon. The three-dimensional contour plot of the growth rate as a function of those two dimensionless parameters reveals stopband structures. Manymore » simulation results generally indicate that a strong head-tail instability can be damped by a weak space-charge force, but the beam becomes unstable again when the space-charge force is further increased. The new two particle model indicates a similar behavior. In weak space-charge regions, additional tune shifts by the space-charge force dissolve the mode coupling. As the space-charge force is increased, they conversely restore the mode coupling, but then a further increase of the space-charge force decouples the modes again. Lastly, this mode coupling/decoupling behavior creates the stopband structures.« less

Two particle model for studying the effects of space-charge force on strong head-tail instabilities

DOE PAGES

Chin, Yong Ho; Chao, Alexander Wu; Blaskiewicz, Michael M.

2016-01-19

In this paper, we present a new two particle model for studying the strong head-tail instabilities in the presence of the space-charge force. It is a simple expansion of the well-known two particle model for strong head-tail instability and is still analytically solvable. No chromaticity effect is included. It leads to a formula for the growth rate as a function of the two dimensionless parameters: the space-charge tune shift parameter (normalized by the synchrotron tune) and the wakefield strength, Upsilon. The three-dimensional contour plot of the growth rate as a function of those two dimensionless parameters reveals stopband structures. Manymore » simulation results generally indicate that a strong head-tail instability can be damped by a weak space-charge force, but the beam becomes unstable again when the space-charge force is further increased. The new two particle model indicates a similar behavior. In weak space-charge regions, additional tune shifts by the space-charge force dissolve the mode coupling. As the space-charge force is increased, they conversely restore the mode coupling, but then a further increase of the space-charge force decouples the modes again. Lastly, this mode coupling/decoupling behavior creates the stopband structures.« less

The solvability of quantum k-pair network in a measurement-based way.

PubMed

Li, Jing; Xu, Gang; Chen, Xiu-Bo; Qu, Zhiguo; Niu, Xin-Xin; Yang, Yi-Xian

2017-12-01

Network coding is an effective means to enhance the communication efficiency. The characterization of network solvability is one of the most important topic in this field. However, for general network, the solvability conditions are still a challenge. In this paper, we consider the solvability of general quantum k-pair network in measurement-based framework. For the first time, a detailed account of measurement-based quantum network coding(MB-QNC) is specified systematically. Differing from existing coding schemes, single qubit measurements on a pre-shared graph state are the only allowed coding operations. Since no control operations are concluded, it makes MB-QNC schemes more feasible. Further, the sufficient conditions formulating by eigenvalue equations and stabilizer matrix are presented, which build an unambiguous relation among the solvability and the general network. And this result can also analyze the feasibility of sharing k EPR pairs task in large-scale networks. Finally, in the presence of noise, we analyze the advantage of MB-QNC in contrast to gate-based way. By an instance network [Formula: see text], we show that MB-QNC allows higher error thresholds. Specially, for X error, the error threshold is about 30% higher than 10% in gate-based way. In addition, the specific expressions of fidelity subject to some constraint conditions are given.

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 publishing your work in Journal of Physics A: Mathematical and General may be found at www.iop.org/Journals/jphysa. bullet Contributions to the Special Issue should if possible be submitted electronically by web upload at {www.iop.org/Journals/jphysa or by e-mail to jphysa@iop.org, quoting `JPhysA Special Issue-Quantum Mechanics: Solvable Models'. Submissions should ideally be in standard LaTeX form; we are, however, able to accept most formats including Microsoft Word. Please see the web site for further information on electronic submissions. bullet Authors unable to submit electronically may send hard copy contributions to: Publishing Administrators, Journal of Physics A, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK, enclosing the electronic code on floppy disk if available and quoting `JPhysA Special Issue-Quantum Mechanics: Solvable Models'. bullet All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. This special issue will be published in the paper and online version of the journal. The corresponding author of each contribution will receive a complimentary copy of the issue. G Dell'Antonio, P Exner and V Geyler Guest Editors

M1 distributions for 163Dy and 157Gd in the SUBFsdg(3) and SUBFsd(3) × 1g limits of pn-sdgIBFM

NASA Astrophysics Data System (ADS)

Devi, Y. D.; Kota, V. K. B.

1996-02-01

The SU sdgBF(3) limit of pn-sdgIBFM, which was developed earlier, is applied with success in analyzing the recently observed M1 data in the 163Dy nucleus. As new experiments are being planned for 157Gd nucleus and that 156Gd is known to be a good SU sd(3)×1g nucleus, in the second part of the paper a formalism for M1 distributions in the SU sdBF(3)×1g limit is developed. In both these analytically solvable limiting situations, predictions are made for M1 distributions in the 157Gd nucleus.

The electrobrachistochrone

NASA Astrophysics Data System (ADS)

Lipscombe, Trevor C.; Mungan, Carl E.

2018-05-01

The brachistochrone problem consists of finding the track of shortest travel time between given initial and final points for a particle sliding frictionlessly along it under the influence of a given external force field. Solvable variations of the standard example of a uniform gravitational field would be suitable for homework and computer projects by undergraduate physics students studying intermediate mechanics and electromagnetism. An electrobrachistochrone problem is here proposed, in which a charged particle moves along a frictionless track under the influence of its electrostatic force of attraction to an image charge in a grounded conducting plane below the track. The path of least time is found to be a foreshortened cycloid and its properties are investigated analytically and graphically.

Nonlocal Symmetries, Consistent Riccati Expansion, and Analytical Solutions of the Variant Boussinesq System

NASA Astrophysics Data System (ADS)

Feng, Lian-Li; Tian, Shou-Fu; Zhang, Tian-Tian; Zhou, Jun

2017-07-01

Under investigation in this paper is the variant Boussinesq system, which describes the propagation of surface long wave towards two directions in a certain deep trough. With the help of the truncated Painlevé expansion, we construct its nonlocal symmetry, Bäcklund transformation, and Schwarzian form, respectively. The nonlocal symmetries can be localised to provide the corresponding nonlocal group, and finite symmetry transformations and similarity reductions are computed. Furthermore, we verify that the variant Boussinesq system is solvable via the consistent Riccati expansion (CRE). By considering the consistent tan-function expansion (CTE), which is a special form of CRE, the interaction solutions between soliton and cnoidal periodic wave are explicitly studied.

Supercurrent survival under a Rosen-Zener quench of hard-core bosons.

PubMed

Klich, I; Lannert, C; Refael, G

2007-11-16

We study the survival of supercurrents in a system of impenetrable bosons on a lattice, subject to a quantum quench from its critical superfluid phase to an insulating phase. We show that the evolution of the current when the quench follows a Rosen-Zener profile is exactly solvable. This allows us to analyze a quench of arbitrary rate, from a sudden destruction of the superfluid to a slow opening of a gap. The decay and oscillations of the current are analytically derived and studied numerically along with the momentum distribution after the quench. In the case of small supercurrent boosts nu, we find that the current surviving at long times is proportional to nu3.

Solvable two-dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime

NASA Astrophysics Data System (ADS)

Fring, Andreas; Frith, Thomas

2018-06-01

We provide exact analytical solutions for a two-dimensional explicitly time-dependent non-Hermitian quantum system. While the time-independent variant of the model studied is in the broken PT-symmetric phase for the entire range of the model parameters, and has therefore a partially complex energy eigenspectrum, its time-dependent version has real energy expectation values at all times. In our solution procedure we compare the two equivalent approaches of directly solving the time-dependent Dyson equation with one employing the Lewis–Riesenfeld method of invariants. We conclude that the latter approach simplifies the solution procedure due to the fact that the invariants of the non-Hermitian and Hermitian system are related to each other in a pseudo-Hermitian fashion, which in turn does not hold for their corresponding time-dependent Hamiltonians. Thus constructing invariants and subsequently using the pseudo-Hermiticity relation between them allows to compute the Dyson map and to solve the Dyson equation indirectly. In this way one can bypass to solve nonlinear differential equations, such as the dissipative Ermakov–Pinney equation emerging in our and many other systems.

The paradoxical zero reflection at zero energy

NASA Astrophysics Data System (ADS)

Ahmed, Zafar; Sharma, Vibhu; Sharma, Mayank; Singhal, Ankush; Kaiwart, Rahul; Priyadarshini, Pallavi

2017-03-01

Usually, the reflection probability R(E) of a particle of zero energy incident on a potential which converges to zero asymptotically is found to be 1: R(0)=1. But earlier, a paradoxical phenomenon of zero reflection at zero energy (R(0)=0) has been revealed as a threshold anomaly. Extending the concept of half-bound state (HBS) of 3D, here we show that in 1D when a symmetric (asymmetric) attractive potential well possesses a zero-energy HBS, R(0)=0 (R(0)\\ll 1). This can happen only at some critical values q c of an effective parameter q of the potential well in the limit E\\to {0}+. We demonstrate this critical phenomenon in two simple analytically solvable models: square and exponential wells. However, in numerical calculations, even for these two models R(0)=0 is observed only as extrapolation to zero energy from low energies, close to a precise critical value q c. By numerical investigation of a variety of potential wells, we conclude that for a given potential well (symmetric or asymmetric), we can adjust the effective parameter q to have a low reflection at a low energy.

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.

Exactly and quasi-exactly solvable 'discrete' quantum mechanics.

PubMed

Sasaki, Ryu

2011-03-28

A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.

On a local solvability and stability of the inverse transmission eigenvalue problem

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia; Buterin, Sergey

2017-11-01

We prove a local solvability and stability of the inverse transmission eigenvalue problem posed by McLaughlin and Polyakov (1994 J. Diff. Equ. 107 351-82). In particular, this result establishes the minimality of the data used therein. The proof is constructive.

Immune networks: multitasking capabilities near saturation

NASA Astrophysics Data System (ADS)

Agliari, E.; Annibale, A.; Barra, A.; Coolen, A. C. C.; Tantari, D.

2013-10-01

Pattern-diluted associative networks were recently introduced as models for the immune system, with nodes representing T-lymphocytes and stored patterns representing signalling protocols between T- and B-lymphocytes. It was shown earlier that in the regime of extreme pattern dilution, a system with NT T-lymphocytes can manage a number N_B={ {O}}(N_T^\\delta ) of B-lymphocytes simultaneously, with δ < 1. Here we study this model in the extensive load regime NB = αNT, with a high degree of pattern dilution, in agreement with immunological findings. We use graph theory and statistical mechanical analysis based on replica methods to show that in the finite-connectivity regime, where each T-lymphocyte interacts with a finite number of B-lymphocytes as NT → ∞, the T-lymphocytes can coordinate effective immune responses to an extensive number of distinct antigen invasions in parallel. As α increases, the system eventually undergoes a second order transition to a phase with clonal cross-talk interference, where the system’s performance degrades gracefully. Mathematically, the model is equivalent to a spin system on a finitely connected graph with many short loops, so one would expect the available analytical methods, which all assume locally tree-like graphs, to fail. Yet it turns out to be solvable. Our results are supported by numerical simulations.

Explicitly solvable complex Chebyshev approximation problems related to sine polynomials

NASA Technical Reports Server (NTRS)

Freund, Roland

1989-01-01

Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.

Dispatching power system for preventive and corrective voltage collapse problem in a deregulated power system

NASA Astrophysics Data System (ADS)

Alemadi, Nasser Ahmed

Deregulation has brought opportunities for increasing efficiency of production and delivery and reduced costs to customers. Deregulation has also bought great challenges to provide the reliability and security customers have come to expect and demand from the electrical delivery system. One of the challenges in the deregulated power system is voltage instability. Voltage instability has become the principal constraint on power system operation for many utilities. Voltage instability is a unique problem because it can produce an uncontrollable, cascading instability that results in blackout for a large region or an entire country. In this work we define a system of advanced analytical methods and tools for secure and efficient operation of the power system in the deregulated environment. The work consists of two modules; (a) contingency selection module and (b) a Security Constrained Optimization module. The contingency selection module to be used for voltage instability is the Voltage Stability Security Assessment and Diagnosis (VSSAD). VSSAD shows that each voltage control area and its reactive reserve basin describe a subsystem or agent that has a unique voltage instability problem. VSSAD identifies each such agent. VS SAD is to assess proximity to voltage instability for each agent and rank voltage instability agents for each contingency simulated. Contingency selection and ranking for each agent is also performed. Diagnosis of where, why, when, and what can be done to cure voltage instability for each equipment outage and transaction change combination that has no load flow solution is also performed. A security constrained optimization module developed solves a minimum control solvability problem. A minimum control solvability problem obtains the reactive reserves through action of voltage control devices that VSSAD determines are needed in each agent to obtain solution of the load flow. VSSAD makes a physically impossible recommendation of adding reactive generation capability to specific generators to allow a load flow solution to be obtained. The minimum control solvability problem can also obtain solution of the load flow without curtailing transactions that shed load and generation as recommended by VSSAD. A minimum control solvability problem will be implemented as a corrective control, that will achieve the above objectives by using minimum control changes. The control includes; (1) voltage setpoint on generator bus voltage terminals; (2) under load tap changer tap positions and switchable shunt capacitors; and (3) active generation at generator buses. The minimum control solvability problem uses the VSSAD recommendation to obtain the feasible stable starting point but completely eliminates the impossible or onerous recommendation made by VSSAD. This thesis reviews the capabilities of Voltage Stability Security Assessment and Diagnosis and how it can be used to implement a contingency selection module for the Open Access System Dispatch (OASYDIS). The OASYDIS will also use the corrective control computed by Security Constrained Dispatch. The corrective control would be computed off line and stored for each contingency that produces voltage instability. The control is triggered and implemented to correct the voltage instability in the agent experiencing voltage instability only after the equipment outage or operating changes predicted to produce voltage instability have occurred. The advantages and the requirements to implement the corrective control are also discussed.

Analytical theory of mesoscopic Bose-Einstein condensation in an ideal gas

NASA Astrophysics Data System (ADS)

Kocharovsky, Vitaly V.; Kocharovsky, Vladimir V.

2010-03-01

We find the universal structure and scaling of the Bose-Einstein condensation (BEC) statistics and thermodynamics (Gibbs free energy, average energy, heat capacity) for a mesoscopic canonical-ensemble ideal gas in a trap with an arbitrary number of atoms, any volume, and any temperature, including the whole critical region. We identify a universal constraint-cutoff mechanism that makes BEC fluctuations strongly non-Gaussian and is responsible for all unusual critical phenomena of the BEC phase transition in the ideal gas. The main result is an analytical solution to the problem of critical phenomena. It is derived by, first, calculating analytically the universal probability distribution of the noncondensate occupation, or a Landau function, and then using it for the analytical calculation of the universal functions for the particular physical quantities via the exact formulas which express the constraint-cutoff mechanism. We find asymptotics of that analytical solution as well as its simple analytical approximations which describe the universal structure of the critical region in terms of the parabolic cylinder or confluent hypergeometric functions. The obtained results for the order parameter, all higher-order moments of BEC fluctuations, and thermodynamic quantities perfectly match the known asymptotics outside the critical region for both low and high temperature limits. We suggest two- and three-level trap models of BEC and find their exact solutions in terms of the cutoff negative binomial distribution (which tends to the cutoff gamma distribution in the continuous limit) and the confluent hypergeometric distribution, respectively. Also, we present an exactly solvable cutoff Gaussian model of BEC in a degenerate interacting gas. All these exact solutions confirm the universality and constraint-cutoff origin of the strongly non-Gaussian BEC statistics. We introduce a regular refinement scheme for the condensate statistics approximations on the basis of the infrared universality of higher-order cumulants and the method of superposition and show how to model BEC statistics in the actual traps. In particular, we find that the three-level trap model with matching the first four or five cumulants is enough to yield remarkably accurate results for all interesting quantities in the whole critical region. We derive an exact multinomial expansion for the noncondensate occupation probability distribution and find its high-temperature asymptotics (Poisson distribution) and corrections to it. Finally, we demonstrate that the critical exponents and a few known terms of the Taylor expansion of the universal functions, which were calculated previously from fitting the finite-size simulations within the phenomenological renormalization-group theory, can be easily obtained from the presented full analytical solutions for the mesoscopic BEC as certain approximations in the close vicinity of the critical point.

Intuition and deliberation: two systems for strategizing in the brain.

PubMed

Kuo, Wen-Jui; Sjöström, Tomas; Chen, Yu-Ping; Wang, Yen-Hsiang; Huang, Chen-Ying

2009-04-24

Dual-process theories distinguish between intuition (fast and emotional) and reasoning (slow and controlled) as a basis for human decision-making. We contrast dominance-solvable games, which can be solved by step-by-step deliberative reasoning, with pure coordination games, which must be solved intuitively. Using functional magnetic resonance imaging, we found that the middle frontal gyrus, the inferior parietal lobule, and the precuneus were more active in dominance-solvable games than in coordination games. The insula and anterior cingulate cortex showed the opposite pattern. Moreover, precuneus activity correlates positively with how "effortful" a dominance-solvable game is, whereas insula activity correlates positively with how "effortless" a coordination game is.

Electroosmotic flow in capillary channels filled with nonconstant viscosity electrolytes: exact solution of the Navier-Stokes equation.

PubMed

Otevrel, Marek; Klepárník, Karel

2002-10-01

The partial differential equation describing unsteady velocity profile of electroosmotic flow (EOF) in a cylindrical capillary filled with a nonconstant viscosity electrolyte was derived. Analytical solution, based on the general Navier-Stokes equation, was found for constant viscosity electrolytes using the separation of variables (Fourier method). For the case of a nonconstant viscosity electrolyte, the steady-state velocity profile was calculated assuming that the viscosity decreases exponentially in the direction from the wall to the capillary center. Since the respective equations with nonconstant viscosity term are not solvable in general, the method of continuous binding conditions was used to solve this problem. In this method, an arbitrary viscosity profile can be modeled. The theoretical conclusions show that the relaxation times at which an EOF approaches the steady state are too short to have an impact on a separation process in any real systems. A viscous layer at the wall affects EOF significantly, if it is thicker than the Debye length of the electric double layer. The presented description of the EOF dynamics is applicable to any microfluidic systems.

Ergodic properties of spiking neuronal networks with delayed interactions

NASA Astrophysics Data System (ADS)

Palmigiano, Agostina; Wolf, Fred

The dynamical stability of neuronal networks, and the possibility of chaotic dynamics in the brain pose profound questions to the mechanisms underlying perception. Here we advance on the tractability of large neuronal networks of exactly solvable neuronal models with delayed pulse-coupled interactions. Pulse coupled delayed systems with an infinite dimensional phase space can be studied in equivalent systems of fixed and finite degrees of freedom by introducing a delayer variable for each neuron. A Jacobian of the equivalent system can be analytically obtained, and numerically evaluated. We find that depending on the action potential onset rapidness and the level of heterogeneities, the asynchronous irregular regime characteristic of balanced state networks loses stability with increasing delays to either a slow synchronous irregular or a fast synchronous irregular state. In networks of neurons with slow action potential onset, the transition to collective oscillations leads to an increase of the exponential rate of divergence of nearby trajectories and of the entropy production rate of the chaotic dynamics. The attractor dimension, instead of increasing linearly with increasing delay as reported in many other studies, decreases until eventually the network reaches full synchrony

The Crystalline Dynamics of Spiral-Shaped Curves

NASA Astrophysics Data System (ADS)

Dudziński, Marcin; Górka, Przemysław

2015-07-01

We study the motion of spiral-shaped polygonal curves by crystalline curvature. We describe this dynamics by the corresponding infinitely dimensional system of ordinary differential equations and show that the considered model is uniquely solvable. Banach's Contraction Mapping Theorem and the Bellman-Gronwall inequality are the main tools applied in our proof.

Some Fundamental Issues of Mathematical Simulation in Biology

NASA Astrophysics Data System (ADS)

Razzhevaikin, V. N.

2018-02-01

Some directions of simulation in biology leading to original formulations of mathematical problems are overviewed. Two of them are discussed in detail: the correct solvability of first-order linear equations with unbounded coefficients and the construction of a reaction-diffusion equation with nonlinear diffusion for a model of genetic wave propagation.

Can I cut the Gordian tnok? The impact of pronounceability, actual solvability, and length on intuitive problem assessments of anagrams.

PubMed

Topolinski, Sascha; Bakhtiari, Giti; Erle, Thorsten M

2016-01-01

When assessing a problem, many cues can be used to predict solvability and solving effort. Some of these cues, however, can be misleading. The present approach shows that a feature of a problem that is actually related to solving difficulty is used as a cue for solving ease when assessing the problem in the first place. For anagrams, it is an established effect that easy-to-pronounce anagrams (e.g., NOGAL) take more time to being solved than hard-to-pronounce anagrams (e.g., HNWEI). However, when assessing an anagram in the first place, individuals use the feature of pronounceability to predict solving ease, because pronounceability is an instantiation of the general mechanism of processing fluency. Participants (total N=536) received short and long anagrams and nonanagrams and judged solvability and solving ease intuitively without actually solving the items. Easy-to-pronounce letter strings were more frequently judged as being solvable than hard-to-pronounce letters strings (Experiment 1), and were estimated to require less effort (Experiments 2, 4-7) and time to be solved (Experiment 3). This effect was robust for short and long items, anagrams and nonanagrams, and presentation timings from 4 down to 0.5s, and affected novices and experts alike. Spontaneous solutions did not mediate this effect. Participants were sensitive to actual solvability even for long anagrams (6-11 letters long) presented only for 500 ms. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

Schematic baryon models, their tight binding description and their microwave realization

NASA Astrophysics Data System (ADS)

Sadurní, E.; Franco-Villafañe, J. A.; Kuhl, U.; Mortessagne, F.; Seligman, T. H.

2013-12-01

A schematic model for baryon excitations is presented in terms of a symmetric Dirac gyroscope, a relativistic model solvable in closed form, that reduces to a rotor in the non-relativistic limit. The model is then mapped on a nearest neighbour tight binding model. In its simplest one-dimensional form this model yields a finite equidistant spectrum. This is experimentally implemented as a chain of dielectric resonators under conditions where their coupling is evanescent and a good agreement with the prediction is achieved.

Markov-switching multifractal models as another class of random-energy-like models in one-dimensional space

NASA Astrophysics Data System (ADS)

Saakian, David B.

2012-03-01

We map the Markov-switching multifractal model (MSM) onto the random energy model (REM). The MSM is, like the REM, an exactly solvable model in one-dimensional space with nontrivial correlation functions. According to our results, four different statistical physics phases are possible in random walks with multifractal behavior. We also introduce the continuous branching version of the model, calculate the moments, and prove multiscaling behavior. Different phases have different multiscaling properties.

Multi-phase-field method for surface tension induced elasticity

NASA Astrophysics Data System (ADS)

Schiedung, Raphael; Steinbach, Ingo; Varnik, Fathollah

2018-01-01

A method, based on the multi-phase-field framework, is proposed that adequately accounts for the effects of a coupling between surface free energy and elastic deformation in solids. The method is validated via a number of analytically solvable problems. In addition to stress states at mechanical equilibrium in complex geometries, the underlying multi-phase-field framework naturally allows us to account for the influence of surface energy induced stresses on phase transformation kinetics. This issue, which is of fundamental importance on the nanoscale, is demonstrated in the limit of fast diffusion for a solid sphere, which melts due to the well-known Gibbs-Thompson effect. This melting process is slowed down when coupled to surface energy induced elastic deformation.

Exactly solvable random graph ensemble with extensively many short cycles

NASA Astrophysics Data System (ADS)

Aguirre López, Fabián; Barucca, Paolo; Fekom, Mathilde; Coolen, Anthony C. C.

2018-02-01

We introduce and analyse ensembles of 2-regular random graphs with a tuneable distribution of short cycles. The phenomenology of these graphs depends critically on the scaling of the ensembles’ control parameters relative to the number of nodes. A phase diagram is presented, showing a second order phase transition from a connected to a disconnected phase. We study both the canonical formulation, where the size is large but fixed, and the grand canonical formulation, where the size is sampled from a discrete distribution, and show their equivalence in the thermodynamical limit. We also compute analytically the spectral density, which consists of a discrete set of isolated eigenvalues, representing short cycles, and a continuous part, representing cycles of diverging size.

SoftWAXS: a computational tool for modeling wide-angle X-ray solution scattering from biomolecules.

PubMed

Bardhan, Jaydeep; Park, Sanghyun; Makowski, Lee

2009-10-01

This paper describes a computational approach to estimating wide-angle X-ray solution scattering (WAXS) from proteins, which has been implemented in a computer program called SoftWAXS. The accuracy and efficiency of SoftWAXS are analyzed for analytically solvable model problems as well as for proteins. Key features of the approach include a numerical procedure for performing the required spherical averaging and explicit representation of the solute-solvent boundary and the surface of the hydration layer. These features allow the Fourier transform of the excluded volume and hydration layer to be computed directly and with high accuracy. This approach will allow future investigation of different treatments of the electron density in the hydration shell. Numerical results illustrate the differences between this approach to modeling the excluded volume and a widely used model that treats the excluded-volume function as a sum of Gaussians representing the individual atomic excluded volumes. Comparison of the results obtained here with those from explicit-solvent molecular dynamics clarifies shortcomings inherent to the representation of solvent as a time-averaged electron-density profile. In addition, an assessment is made of how the calculated scattering patterns depend on input parameters such as the solute-atom radii, the width of the hydration shell and the hydration-layer contrast. These results suggest that obtaining predictive calculations of high-resolution WAXS patterns may require sophisticated treatments of solvent.

Integrable discrete PT symmetric model.

PubMed

Ablowitz, Mark J; Musslimani, Ziad H

2014-09-01

An exactly solvable discrete PT invariant nonlinear Schrödinger-like model is introduced. It is an integrable Hamiltonian system that exhibits a nontrivial nonlinear PT symmetry. A discrete one-soliton solution is constructed using a left-right Riemann-Hilbert formulation. It is shown that this pure soliton exhibits unique features such as power oscillations and singularity formation. The proposed model can be viewed as a discretization of a recently obtained integrable nonlocal nonlinear Schrödinger equation.

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

NASA Astrophysics Data System (ADS)

Sadurní, E.; Torres, J. M.; Seligman, T. H.

2010-07-01

The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of a solution is given by recasting the known solution of the Dirac oscillator into matrix form; there one notes that a block-diagonal form arises in a Hamiltonian formulation. The blocks are two dimensional. Choosing couplings that do not affect the block structure, these blow up the 2 × 2 matrices to 4 × 4 matrices, thus conserving solvability. The result can be cast again in covariant form. By way of an example we apply this exact solution to calculate the evolution of entanglement.

A Solvable Self-Similar Model of the Sausage Instability in a Resistive Z-Pinch

DTIC Science & Technology

1989-09-20

Ithaca, NY 14853 Dr. V. Nardi Dr. John C. Riordan Stevens Institute of Technology Physics International Co. Hoboken, NJ 07803 2700 Merced Street Dr...92122 Dr. Rick B. Spielman Dr. Frank C. Young Sandia National Laboratories Naval Research Laboratory P.O. Box 5800 Code 4770.1 Albuquerque, NM 87115

Simulating Conditions of Learned Helplessness: The Effects of Interventions and Attributions.

ERIC Educational Resources Information Center

Donovan, Wilberta L.; Leavitt, Lewis A.

1985-01-01

Using a version of the "learned helplessness" paradigm, assesses mothers' performance on a solvable task following pretreatments that involved exposure to an infant cry but that differed in the mothers' ability to exert control over termination of the cry. Proposes that learned helplessness models are relevant to the study of…

Absence of a charge diffusion pole at finite energies in an exactly solvable interacting flat-band model in d dimensions

NASA Astrophysics Data System (ADS)

Phillips, Philip W.; Setty, Chandan; Zhang, Shuyi

2018-05-01

Motivated by recent bounds for charge diffusion in critical matter, we investigate the following question: What sets the scale for the velocity for diffusing degrees of freedom in a scale-invariant system? To make our statements precise, we analyze the diffusion pole in an exactly solvable model for a Mott transition in the presence of a long-range interaction term. To achieve scale invariance, we limit our discussion to the flat-band regime. We find in this limit that the diffusion pole, which would normally obtain at finite energy, is pushed to zero energy, resulting in a vanishing of the diffusion constant. This occurs even in the presence of interactions in certain limits, indicating the robustness of this result to the inclusion of a scale in the problem. Consequently, scale invariance precludes any reasonable definition of the diffusion constant. Nonetheless, we do find that a scale can be defined, albeit irrelevant to diffusion, which is the product of the squared band velocity and the density of states.

An (almost) solvable model for bacterial pattern formation

NASA Astrophysics Data System (ADS)

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

2007-10-01

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

Informations in Models of Evolutionary Dynamics

NASA Astrophysics Data System (ADS)

Rivoire, Olivier

2016-03-01

Biological organisms adapt to changes by processing informations from different sources, most notably from their ancestors and from their environment. We review an approach to quantify these informations by analyzing mathematical models of evolutionary dynamics and show how explicit results are obtained for a solvable subclass of these models. In several limits, the results coincide with those obtained in studies of information processing for communication, gambling or thermodynamics. In the most general case, however, information processing by biological populations shows unique features that motivate the analysis of specific models.

Hydrodynamics at the smallest scales: a solvability criterion for Navier-Stokes equations in high dimensions.

PubMed

Viswanathan, T M; Viswanathan, G M

2011-01-28

Strong global solvability is difficult to prove for high-dimensional hydrodynamic systems because of the complex interplay between nonlinearity and scale invariance. We define the Ladyzhenskaya-Lions exponent α(L)(n)=(2+n)/4 for Navier-Stokes equations with dissipation -(-Δ)(α) in R(n), for all n≥2. We review the proof of strong global solvability when α≥α(L)(n), given smooth initial data. If the corresponding Euler equations for n>2 were to allow uncontrolled growth of the enstrophy (1/2)∥∇u∥(L²)(2), then no globally controlled coercive quantity is currently known to exist that can regularize solutions of the Navier-Stokes equations for α<α(L)(n). The energy is critical under scale transformations only for α=α(L)(n).

On solvability of boundary value problems for hyperbolic fourth-order equations with nonlocal boundary conditions of integral type

NASA Astrophysics Data System (ADS)

Popov, Nikolay S.

2017-11-01

Solvability of some initial-boundary value problems for linear hyperbolic equations of the fourth order is studied. A condition on the lateral boundary in these problems relates the values of a solution or the conormal derivative of a solution to the values of some integral operator applied to a solution. Nonlocal boundary-value problems for one-dimensional hyperbolic second-order equations with integral conditions on the lateral boundary were considered in the articles by A.I. Kozhanov. Higher-dimensional hyperbolic equations of higher order with integral conditions on the lateral boundary were not studied earlier. The existence and uniqueness theorems of regular solutions are proven. The method of regularization and the method of continuation in a parameter are employed to establish solvability.

A one-dimensional statistical mechanics model for nucleosome positioning on genomic DNA.

PubMed

Tesoro, S; Ali, I; Morozov, A N; Sulaiman, N; Marenduzzo, D

2016-02-12

The first level of folding of DNA in eukaryotes is provided by the so-called '10 nm chromatin fibre', where DNA wraps around histone proteins (∼10 nm in size) to form nucleosomes, which go on to create a zig-zagging bead-on-a-string structure. In this work we present a one-dimensional statistical mechanics model to study nucleosome positioning within one such 10 nm fibre. We focus on the case of genomic sheep DNA, and we start from effective potentials valid at infinite dilution and determined from high-resolution in vitro salt dialysis experiments. We study positioning within a polynucleosome chain, and compare the results for genomic DNA to that obtained in the simplest case of homogeneous DNA, where the problem can be mapped to a Tonks gas. First, we consider the simple, analytically solvable, case where nucleosomes are assumed to be point-like. Then, we perform numerical simulations to gauge the effect of their finite size on the nucleosomal distribution probabilities. Finally we compare nucleosome distributions and simulated nuclease digestion patterns for the two cases (homogeneous and sheep DNA), thereby providing testable predictions of the effect of sequence on experimentally observable quantities in experiments on polynucleosome chromatin fibres reconstituted in vitro.

Phase transitions in community detection: A solvable toy model

NASA Astrophysics Data System (ADS)

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

2014-05-01

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

Spatially dependent diffusion coefficient as a model for pH sensitive microgel particles in microchannels

PubMed Central

Pieprzyk, S.; Heyes, D. M.; Brańka, A. C.

2016-01-01

Solute transport and intermixing in microfluidic devices is strongly dependent on diffusional processes. Brownian Dynamics simulations of pressure-driven flow of model microgel particles in microchannels have been carried out to explore these processes and the factors that influence them. The effects of a pH-field that induces a spatial dependence of particle size and consequently the self-diffusion coefficient and system thermodynamic state were focused on. Simulations were carried out in 1D to represent some of the cross flow dependencies, and in 2D and 3D to include the effects of flow and particle concentration, with typical stripe-like diffusion coefficient spatial variations. In 1D, the mean square displacement and particle displacement probability distribution function agreed well with an analytically solvable model consisting of infinitely repulsive walls and a discontinuous pH-profile in the middle of the channel. Skew category Brownian motion and non-Gaussian dynamics were observed, which follows from correlations of step lengths in the system, and can be considered to be an example of so-called “diffusing diffusivity.” In Poiseuille flow simulations, the particles accumulated in regions of larger diffusivity and the largest particle concentration throughput was found when this region was in the middle of the channel. The trends in the calculated cross-channel diffusional behavior were found to be very similar in 2D and 3D. PMID:27795750

An Exact Solvable Model of Rocket Dynamics in Atmosphere

ERIC Educational Resources Information Center

Rodrigues, H.; Pinho, M. O.; Portes, D., Jr.; Santiago, A.

2009-01-01

In basic physics courses at undergraduate level, the dynamics of self-propelled bodies is presented as an example of momentum conservation law applied to systems with time-varying mass. However, is often studied the simple situation of free motion or the motion under the action of a constant gravitational field. In this work, we investigate the…

Exact analytic solution of position-dependent mass Schrödinger equation

NASA Astrophysics Data System (ADS)

Rajbongshi, Hangshadhar

2018-03-01

Exact analytic solution of position-dependent mass Schrödinger equation is generated by using extended transformation, a method of mapping a known system into a new system equipped with energy eigenvalues and corresponding wave functions. First order transformation is performed on D-dimensional radial Schrödinger equation with constant mass by taking trigonometric Pöschl-Teller potential as known system. The exactly solvable potentials with position-dependent mass generated for different choices of mass functions through first order transformation are also taken as known systems in the second order transformation performed on D-dimensional radial position-dependent mass Schrödinger equation. The solutions are fitted for "Zhu and Kroemer" ordering of ambiguity. All the wave functions corresponding to nonzero energy eigenvalues are normalizable. The new findings are that the normalizability condition of the wave functions remains independent of mass functions, and some of the generated potentials show a family relationship among themselves where power law potentials also get related to non-power law potentials and vice versa through the transformation.

Perturbation theory for arbitrary coupling strength?

NASA Astrophysics Data System (ADS)

Mahapatra, Bimal P.; Pradhan, Noubihary

2018-03-01

We present a new formulation of perturbation theory for quantum systems, designated here as: “mean field perturbation theory” (MFPT), which is free from power-series-expansion in any physical parameter, including the coupling strength. Its application is thereby extended to deal with interactions of arbitrary strength and to compute system-properties having non-analytic dependence on the coupling, thus overcoming the primary limitations of the “standard formulation of perturbation theory” (SFPT). MFPT is defined by developing perturbation about a chosen input Hamiltonian, which is exactly solvable but which acquires the nonlinearity and the analytic structure (in the coupling strength) of the original interaction through a self-consistent, feedback mechanism. We demonstrate Borel-summability of MFPT for the case of the quartic- and sextic-anharmonic oscillators and the quartic double-well oscillator (QDWO) by obtaining uniformly accurate results for the ground state of the above systems for arbitrary physical values of the coupling strength. The results obtained for the QDWO may be of particular significance since “renormalon”-free, unambiguous results are achieved for its spectrum in contrast to the well-known failure of SFPT in this case.

Thermo-solutal growth of an anisotropic dendrite with six-fold symmetry

NASA Astrophysics Data System (ADS)

Alexandrov, D. V.; Galenko, P. K.

2018-03-01

A stable growth of dendritic crystal with the six-fold crystalline anisotropy is analyzed in a binary nonisothermal mixture. A selection criterion representing a relationship between the dendrite tip velocity and its tip diameter is derived on the basis of morphological stability analysis and solvability theory. A complete set of nonlinear equations, consisting of the selection criterion and undercooling balance condition, which determines implicit dependencies of the dendrite tip velocity and tip diameter as functions of the total undercooling, is formulated. Exact analytical solutions of these nonlinear equations are found in a parametric form. Asymptotic solutions describing the crystal growth at small Péclet numbers are determined. Theoretical predictions are compared with experimental data obtained for ice dendrites growing in binary water-ethylenglycol solutions as well as in pure water.

Shortcuts to adiabaticity. Suppression of pair production in driven Dirac dynamics

DOE PAGES

Deffner, Sebastian

2015-12-21

By achieving effectively adiabatic dynamics in finite time, we have found that it is our ubiquitous goal in virtually all areas of modern physics. So-called shortcuts to adiabaticity refer to a set of methods and techniques that allow us to produce in a short time the same final state that would result from an adiabatic, infinitely slow process. In this paper we generalize one of these methods—the fast-forward technique—to driven Dirac dynamics. We find that our main result shortcuts to adiabaticity for the (1+1)-dimensional Dirac equation are facilitated by a combination of both scalar and pseudoscalar potentials. Our findings aremore » illustrated for two analytically solvable examples, namely charged particles driven in spatially homogeneous and linear vector fields.« less

Plasma equilibrium with fast ion orbit width, pressure anisotropy, and toroidal flow effects

DOE PAGES

Gorelenkov, Nikolai N.; Zakharov, Leonid E.

2018-04-27

Here, we formulate the problem of tokamak plasma equilibrium including the toroidal flow and fast ion (or energetic particle, EP) pressure anisotropy and the finite drift orbit width (FOW) effects. The problem is formulated via the standard Grad-Shafranov equation (GShE) amended by the solvability condition which imposes physical constraints on allowed spacial dependencies of the anisotropic pressure. The GShE problem employs the pressure coupling scheme and includes the dominant diagonal terms and non-diagonal corrections to the standard pressure tensor. The anisotropic tensor elements are obtained via the distribution function represented in the factorized form via the constants of motion. Consideredmore » effects on the plasma equilibrium are estimated analytically, if possible, to understand their importance for GShE tokamak plasma problem.« less

Characterization and solvability of quasipolynomial symplectic mappings

NASA Astrophysics Data System (ADS)

Hernández-Bermejo, Benito; Brenig, Léon

2004-02-01

Quasipolynomial (or QP) mappings constitute a wide generalization of the well-known Lotka-Volterra mappings, of importance in different fields such as population dynamics, physics, chemistry or economy. In addition, QP mappings are a natural discrete-time analogue of the continuous QP systems, which have been extensively used in different pure and applied domains. After presenting the basic definitions and properties of QP mappings in a previous paper [1], the purpose of this work is to focus on their characterization by considering the existence of symplectic QP mappings. In what follows such QP symplectic maps are completely characterized. Moreover, use of the QP formalism can be made in order to demonstrate that all QP symplectic mappings have an analytical solution that is explicitly and generally constructed. Examples are given.

Plasma equilibrium with fast ion orbit width, pressure anisotropy, and toroidal flow effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorelenkov, Nikolai N.; Zakharov, Leonid E.

Here, we formulate the problem of tokamak plasma equilibrium including the toroidal flow and fast ion (or energetic particle, EP) pressure anisotropy and the finite drift orbit width (FOW) effects. The problem is formulated via the standard Grad-Shafranov equation (GShE) amended by the solvability condition which imposes physical constraints on allowed spacial dependencies of the anisotropic pressure. The GShE problem employs the pressure coupling scheme and includes the dominant diagonal terms and non-diagonal corrections to the standard pressure tensor. The anisotropic tensor elements are obtained via the distribution function represented in the factorized form via the constants of motion. Consideredmore » effects on the plasma equilibrium are estimated analytically, if possible, to understand their importance for GShE tokamak plasma problem.« less

Analytical Solution for Interface Flow to a Sink With an Upconed Saline Water Lens: Strack's Regimes Revisited

NASA Astrophysics Data System (ADS)

Kacimov, A. R.; Obnosov, Y. V.

2018-01-01

A study is made of a steady, two-dimensional groundwater flow with a horizontal well (drain), which pumps out freshwater from an aquifer sandwiched between a horizontal bedrock and ponded soil surface, and containing a lens-shaped static volume of a heavier saline water (DNAPL-dense nonaqueous phase liquid) as a free surface. For flow toward a line sink, an explicit analytical solution is obtained by a conformal mapping of the hexagon in the complex potential plane onto a reference plane and the Keldysh-Sedov integral representation of a mixed boundary-value problem for a complex physical coordinate. The interface is found as a function of the pumping rate, the well locus, the ratio of liquid densities, and the hydraulic heads at the soil surface and in the well. The shape with two inflexion points and fronts varies from a small-thickness bedrock-spread pancake to a critical curvilinear triangle, which cusps toward the sink. The problem is mathematically solvable in a relatively narrow band of geometric and hydraulic parameters. A similar analytic solution for a static heavy bubble confined by a closed-curve interface (no contact with the bedrock) is outlined as an illustration of the method to solve a mixed boundary-value problem.

Algorithmics - Is There Hope for a Unified Theory?

NASA Astrophysics Data System (ADS)

Hromkovič, Juraj

Computer science was born with the formal definition of the notion of an algorithm. This definition provides clear limits of automatization, separating problems into algorithmically solvable problems and algorithmically unsolvable ones. The second big bang of computer science was the development of the concept of computational complexity. People recognized that problems that do not admit efficient algorithms are not solvable in practice. The search for a reasonable, clear and robust definition of the class of practically solvable algorithmic tasks started with the notion of the class {P} and of {NP}-completeness. In spite of the fact that this robust concept is still fundamental for judging the hardness of computational problems, a variety of approaches was developed for solving instances of {NP}-hard problems in many applications. Our 40-years short attempt to fix the fuzzy border between the practically solvable problems and the practically unsolvable ones partially reminds of the never-ending search for the definition of "life" in biology or for the definitions of matter and energy in physics. Can the search for the formal notion of "practical solvability" also become a never-ending story or is there hope for getting a well-accepted, robust definition of it? Hopefully, it is not surprising that we are not able to answer this question in this invited talk. But to deal with this question is of crucial importance, because only due to enormous effort scientists get a better and better feeling of what the fundamental notions of science like life and energy mean. In the flow of numerous technical results, we must not forget the fact that most of the essential revolutionary contributions to science were done by defining new concepts and notions.

On the physical Hilbert space of loop quantum cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noui, Karim; Perez, Alejandro; Vandersloot, Kevin

2005-02-15

In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a cosmological constant, the model is exactly solvable and we show explicitly that the physical Hilbert space is separable, consisting of a single physical state. We extend the model to the Lorentzian sector and discuss important implications for standard loop quantum cosmology.

Speeding up N-body simulations of modified gravity: chameleon screening models

NASA Astrophysics Data System (ADS)

Bose, Sownak; Li, Baojiu; Barreira, Alexandre; He, Jian-hua; Hellwing, Wojciech A.; Koyama, Kazuya; Llinares, Claudio; Zhao, Gong-Bo

2017-02-01

We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f(R) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f(R) simulations. For example, a test simulation with 5123 particles in a box of size 512 Mpc/h is now 5 times faster than before, while a Millennium-resolution simulation for f(R) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.

Absorption dynamics and delay time in complex potentials

NASA Astrophysics Data System (ADS)

Villavicencio, Jorge; Romo, Roberto; Hernández-Maldonado, Alberto

2018-05-01

The dynamics of absorption is analyzed by using an exactly solvable model that deals with an analytical solution to Schrödinger’s equation for cutoff initial plane waves incident on a complex absorbing potential. A dynamical absorption coefficient which allows us to explore the dynamical loss of particles from the transient to the stationary regime is derived. We find that the absorption process is characterized by the emission of a series of damped periodic pulses in time domain, associated with damped Rabi-type oscillations with a characteristic frequency, ω = (E + ε)/ℏ, where E is the energy of the incident waves and ‑ε is energy of the quasidiscrete state of the system induced by the absorptive part of the Hamiltonian; the width γ of this resonance governs the amplitude of the pulses. The resemblance of the time-dependent absorption coefficient with a real decay process is discussed, in particular the transition from exponential to nonexponential regimes, a well-known feature of quantum decay. We have also analyzed the effect of the absorptive part of the potential on the dynamical delay time, which behaves differently from the one observed in attractive real delta potentials, exhibiting two regimes: time advance and time delay.

Hydrostatic equilibrium of stars without electroneutrality constraint

NASA Astrophysics Data System (ADS)

Krivoruchenko, M. I.; Nadyozhin, D. K.; Yudin, A. V.

2018-04-01

The general solution of hydrostatic equilibrium equations for a two-component fluid of ions and electrons without a local electroneutrality constraint is found in the framework of Newtonian gravity theory. In agreement with the Poincaré theorem on analyticity and in the context of Dyson's argument, the general solution is demonstrated to possess a fixed (essential) singularity in the gravitational constant G at G =0 . The regular component of the general solution can be determined by perturbation theory in G starting from a locally neutral solution. The nonperturbative component obtained using the method of Wentzel, Kramers and Brillouin is exponentially small in the inner layers of the star and grows rapidly in the outward direction. Near the surface of the star, both components are comparable in magnitude, and their nonlinear interplay determines the properties of an electro- or ionosphere. The stellar charge varies within the limits of -0.1 to 150 C per solar mass. The properties of electro- and ionospheres are exponentially sensitive to variations of the fluid densities in the central regions of the star. The general solutions of two exactly solvable stellar models without a local electroneutrality constraint are also presented.

Z/sub n/ Baxter model: symmetries and the Belavin parametrization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richey, M.P.; Tracy, C.A.

1986-02-01

The Z/sub n/ Baxter model is an exactly solvable lattice model in the special case of the Belavin parametrization. For this parametrization the authors calculate the partition function in an antiferromagnetic region and the order parameter in a ferromagnetic region. They find that the order parameter is expressible in terms of a modular function of level n which for n=2 is the Onsager-Yang-Baxter result. In addition they determine the symmetry group of the finite lattice partition function for the general Z/sub n/ Baxter model.

Attenuation Factors for B(E2) in the Microscopic Description of Multiphonon States ---A Simple Model Analysis---

NASA Astrophysics Data System (ADS)

Matsuyanagi, K.

1982-05-01

With an exactly solvable O(4) model of Piepenbring, Silvestre-Brac and Szymanski, we demonstrate that the attenuation factor for the B(E2) values, derived by the lowest-order approximation of the multiphonon method, takes excellent care of the kinematical anharmonicity effects, if multiphonon states are defined in the intrinsic subspace orthogonal to the pairing rotation. It is also shown that the other attenuation effect characterizing the interacting boson model is not a dominant effect in the model analysed here.

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

PubMed

Mandal, Dibyendu; Jarzynski, Christopher

2012-07-17

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

T\\overline{T} -deformations, AdS/CFT and correlation functions

NASA Astrophysics Data System (ADS)

Giribet, Gaston

2018-02-01

A solvable irrelevant deformation of AdS3/CFT2 correspondence leading to a theory with Hagedorn spectrum at high energy has been recently proposed. It consists of a single trace deformation of the boundary theory, which is inspired by the recent work on solvable T\\overline{T} deformations of two-dimensional CFTs. Thought of as a worldsheet σ-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS3 in the IR and a linear dilaton vacuum of little string theory in the UV. The insertion of the operator that realizes the deformation in the correlation functions produces a logarithmic divergence, leading to the renormalization of the primary operators, which thus acquire an anomalous dimension. We compute this anomalous dimension explicitly, and this provides us with a direct way of determining the spectrum of the theory. We discuss this and other features of the correlation functions in presence of the deformation.

Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method

NASA Astrophysics Data System (ADS)

Alekseev, G.; Tokhtina, A.; Soboleva, O.

2017-10-01

Two approaches (direct design and inverse design methods) for solving problems of designing devices providing invisibility of material bodies of detection using different physical fields - electromagnetic, acoustic and static are discussed. The second method is applied for solving problems of designing cloaking devices for the 3D stationary thermal scattering model. Based on this method the design problems under study are reduced to respective control problems. The material parameters (radial and tangential heat conductivities) of the inhomogeneous anisotropic medium filling the thermal cloak and the density of auxiliary heat sources play the role of controls. A unique solvability of direct thermal scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and numerical algorithms for solving particular thermal cloaking problem are proposed.

Degeneracy of energy levels of pseudo-Gaussian oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iacob, Theodor-Felix; Iacob, Felix, E-mail: felix@physics.uvt.ro; Lute, Marina

2015-12-07

We study the main features of the isotropic radial pseudo-Gaussian oscillators spectral properties. This study is made upon the energy levels degeneracy with respect to orbital angular momentum quantum number. In a previous work [6] we have shown that the pseudo-Gaussian oscillators belong to the class of quasi-exactly solvable models and an exact solution has been found.

Solvable model for chimera states of coupled oscillators.

PubMed

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

2008-08-22

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

Diagonalization of transfer matrix of supersymmetry U{sub q}(sl-caret(M+1|N+1)) chain with a boundary

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kojima, Takeo

2013-04-15

We study the supersymmetry U{sub q}(sl-caret(M+1|N+1)) analogue of the supersymmetric t-J model with a boundary. Our approach is based on the algebraic analysis method of solvable lattice models. We diagonalize the commuting transfer matrix by using the bosonizations of the vertex operators associated with the quantum affine supersymmetry U{sub q}(sl-caret(M+1|N+1)).

3-D Printing as a Tool to Investigate the Effects of Changes in Rock Microstructures on Permeability

NASA Astrophysics Data System (ADS)

Head, D. A.; Vanorio, T.

2016-12-01

Rocks are naturally heterogeneous; two rock samples with identical bulk properties can vary widely in microstructure. Understanding the evolutionary trends of rock properties requires the ability to connect time-lapse measurements of properties at different scales: the macro- scale used in the laboratory and field analyses capturing the bulk scale changes and the micro- scale used in imaging and digital techniques capturing the changes to the pore space. However, measuring those properties at different scales is very challenging, and sometimes impossible. The advent of modern 3D printing has provided an unprecedented opportunity to link those scales by combining the strengths of digital and experimental rock physics. To determine the feasibility of this technique we characterized the resolution capabilities of two different 3D printers. To calibrate our digital models with our printed models, we created a sample with an analytically solvable permeability. This allowed us to directly compare analytic calculation, numerical simulation, and laboratory measurement of permeability of the exact same sample. Next we took a CT-scanned model of a natural carbonate pore space, then iteratively digitally manipulated, 3D printed, and measured the flow properties in the laboratory. This approach allowed us to access multiple scales digitally and experimentally, to test hypotheses about how changes in rock microstructure due to compaction and dissolution affect bulk transport properties, and to connect laboratory measurements of porosity and permeability to quantities that are traditionally impossible to measure in the laboratory such as changes in surface area and tortuosity. As 3D printing technology continues to advance, we expect this technique to contribute to our ability to characterize the properties of remote and/or delicate samples as well as to test the impact of microstructural alteration on bulk physical properties in the lab in a highly consistent, repeatable manner.

Qiang-Dong proper quantization rule and its applications to exactly solvable quantum systems

NASA Astrophysics Data System (ADS)

Serrano, F. A.; Gu, Xiao-Yan; Dong, Shi-Hai

2010-08-01

We propose proper quantization rule, ∫x_Ax_B k(x)dx-∫x0Ax0Bk0(x)dx=nπ, where k(x )=√2M[E -V(x)] /ℏ. The xA and xB are two turning points determined by E =V(x), and n is the number of the nodes of wave function ψ(x ). We carry out the exact solutions of solvable quantum systems by this rule and find that the energy spectra of solvable systems can be determined only from its ground state energy. The previous complicated and tedious integral calculations involved in exact quantization rule are greatly simplified. The beauty and simplicity of the rule come from its meaning—whenever the number of the nodes of ϕ(x ) or the number of the nodes of the wave function ψ(x ) increases by 1, the momentum integral ∫xAxBk(x )dx will increase by π. We apply this proper quantization rule to carry out solvable quantum systems such as the one-dimensional harmonic oscillator, the Morse potential and its generalization, the Hulthén potential, the Scarf II potential, the asymmetric trigonometric Rosen-Morse potential, the Pöschl-Teller type potentials, the Rosen-Morse potential, the Eckart potential, the harmonic oscillator in three dimensions, the hydrogen atom, and the Manning-Rosen potential in D dimensions.

Dynamical Scaling and Phase Coexistence in Topologically Constrained DNA Melting.

PubMed

Fosado, Y A G; Michieletto, D; Marenduzzo, D

2017-09-15

There is a long-standing experimental observation that the melting of topologically constrained DNA, such as circular closed plasmids, is less abrupt than that of linear molecules. This finding points to an important role of topology in the physics of DNA denaturation, which is, however, poorly understood. Here, we shed light on this issue by combining large-scale Brownian dynamics simulations with an analytically solvable phenomenological Landau mean field theory. We find that the competition between melting and supercoiling leads to phase coexistence of denatured and intact phases at the single-molecule level. This coexistence occurs in a wide temperature range, thereby accounting for the broadening of the transition. Finally, our simulations show an intriguing topology-dependent scaling law governing the growth of denaturation bubbles in supercoiled plasmids, which can be understood within the proposed mean field theory.

Optimal control problem for linear fractional-order systems, described by equations with Hadamard-type derivative

NASA Astrophysics Data System (ADS)

Postnov, Sergey

2017-11-01

Two kinds of optimal control problem are investigated for linear time-invariant fractional-order systems with lumped parameters which dynamics described by equations with Hadamard-type derivative: the problem of control with minimal norm and the problem of control with minimal time at given restriction on control norm. The problem setting with nonlocal initial conditions studied. Admissible controls allowed to be the p-integrable functions (p > 1) at half-interval. The optimal control problem studied by moment method. The correctness and solvability conditions for the corresponding moment problem are derived. For several special cases the optimal control problems stated are solved analytically. Some analogies pointed for results obtained with the results which are known for integer-order systems and fractional-order systems describing by equations with Caputo- and Riemann-Liouville-type derivatives.

Random graph models of social networks.

PubMed

Newman, M E J; Watts, D J; Strogatz, S H

2002-02-19

We describe some new exactly solvable models of the structure of social networks, based on random graphs with arbitrary degree distributions. We give models both for simple unipartite networks, such as acquaintance networks, and bipartite networks, such as affiliation networks. We compare the predictions of our models to data for a number of real-world social networks and find that in some cases, the models are in remarkable agreement with the data, whereas in others the agreement is poorer, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph.

A model of the normal and null states of pulsars

NASA Astrophysics Data System (ADS)

Jones, P. B.

1981-12-01

A solvable three-dimensional polar cap model of pair creation and charged particle acceleration has been derived. There are no free parameters of significance apart from the polar surface magnetic flux density. The parameter determining the acceleration potential difference has been obtained by calculation of elementary nuclear and electromagnetic processes. Solutions of the model exist for both normal and null states of a pulsar, and the instability in the normal state leading to the normal to null transition has been identified. The predicted necessary condition for the transition is entirely consistent with observation.

A model of the normal and null states of pulsars

NASA Astrophysics Data System (ADS)

Jones, P. B.

A solvable three dimensional polar cap model of pair creation and charged particle acceleration is derived. There are no free parameters of significance apart from the polar surface magnetic flux density. The parameter CO determining the acceleration potential difference was obtained by calculation of elementary nuclear and electromagnetic processes. Solutions of the model exist for both normal and null states of a pulsar, and the instability in the normal state leading to the normal to null transition is identified. The predicted necessary condition for the transition is entirely consistent with observation.

Nonparametric method for failures detection and localization in the actuating subsystem of aircraft control system

NASA Astrophysics Data System (ADS)

Karpenko, S. S.; Zybin, E. Yu; Kosyanchuk, V. V.

2018-02-01

In this paper we design a nonparametric method for failures detection and localization in the aircraft control system that uses the measurements of the control signals and the aircraft states only. It doesn’t require a priori information of the aircraft model parameters, training or statistical calculations, and is based on algebraic solvability conditions for the aircraft model identification problem. This makes it possible to significantly increase the efficiency of detection and localization problem solution by completely eliminating errors, associated with aircraft model uncertainties.

Few-Photon Model of the Optical Emission of Semiconductor Quantum Dots

NASA Astrophysics Data System (ADS)

Richter, Marten; Carmele, Alexander; Sitek, Anna; Knorr, Andreas

2009-08-01

The Jaynes-Cummings model provides a well established theoretical framework for single electron two level systems in a radiation field. Similar exactly solvable models for semiconductor light emitters such as quantum dots dominated by many particle interactions are not known. We access these systems by a generalized cluster expansion, the photon-probability cluster expansion: a reliable approach for few-photon dynamics in many body electron systems. As a first application, we discuss vacuum Rabi oscillations and show that their amplitude determines the number of electrons in the quantum dot.

Solvable multistate model of Landau-Zener transitions in cavity QED

DOE PAGES

Sinitsyn, Nikolai; Li, Fuxiang

2016-06-29

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

Quantum morphogenesis: A variation on Thom's catastrophe theory

NASA Astrophysics Data System (ADS)

Aerts, Dirk; Czachor, Marek; Gabora, Liane; Kuna, Maciej; Posiewnik, Andrzej; Pykacz, Jarosław; Syty, Monika

2003-05-01

Noncommutative propositions are characteristic of both quantum and nonquantum (sociological, biological, and psychological) situations. In a Hilbert space model, states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment, their dynamics is nonlinear. Nonlinear evolutions of density matrices lead to the phenomenon of morphogenesis that may occur in noncommutative systems. Several explicit exactly solvable models are presented, including “birth and death of an organism” and “development of complementary properties.”

Spatiotemporal correlation buildup after an interaction quench in the Luttinger model

NASA Astrophysics Data System (ADS)

Abeling, Nils O.; Kehrein, Stefan

We study the evolution of density-density correlations at different times and distances in the exactly solvable Luttinger model after a sudden quench from the ground state. We discuss the difference between correlations and susceptibilities, and how these results can be interpreted from the point of view of Lieb-Robinson bounds. For the correlation functions we specifically show that pre-quench entanglement in the ground state leads to algebraically decaying long distance tails outside the light cone.

Aspects of the inverse problem for the Toda chain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kozlowski, K. K., E-mail: karol.kozlowski@u-bourgogne.fr

We generalize Babelon's approach to equations in dual variables so as to be able to treat new types of operators which we build out of the sub-constituents of the model's monodromy matrix. Further, we also apply Sklyanin's recent monodromy matrix identities so as to obtain equations in dual variables for yet other operators. The schemes discussed in this paper appear to be universal and thus, in principle, applicable to many models solvable through the quantum separation of variables.

Dynamical Friedel oscillations of a Fermi sea

NASA Astrophysics Data System (ADS)

Zhang, J. M.; Liu, Y.

2018-02-01

We study the scenario of quenching an interaction-free Fermi sea on a one-dimensional lattice ring by suddenly changing the potential of a site. From the point-of-view of the conventional Friedel oscillation, which is a static or equilibrium problem, it is of interest what temporal and spatial oscillations the local sudden quench will induce. Numerically, the primary observation is that for a generic site, the local particle density switches between two plateaus periodically in time. Making use of the proximity of the realistic model to an exactly solvable model and employing the Abel regularization to assign a definite value to a divergent series, we obtain an analytical formula for the heights of the plateaus, which turns out to be very accurate for sites not too close to the quench site. The unexpect relevance and the incredible accuracy of the Abel regularization are yet to be understood. Eventually, when the contribution of the defect mode is also taken into account, the plateaus for those sites close to or on the quench site can also be accurately predicted. We have also studied the infinite lattice case. In this case, ensuing the quench, the out-going wave fronts leave behind a stable density oscillation pattern. Because of some interesting single-particle property, this dynamically generated Friedel oscillation differs from its conventional static counterpart only by the defect mode.

Orbital currents in a generalized Hubbard ladder

NASA Astrophysics Data System (ADS)

Fjaerestad, John O.

2004-03-01

We study a phase with orbital currents (d-density wave (DDW)/staggered flux phase) in a generalized Hubbard model on the two-leg ladder at zero temperature. Bosonization and perturbative renormalization-group calculations are used to identify a parameter region with long-range DDW order in the weakly interacting half-filled ladder. Finite-size density-matrix renormalization-group (DMRG) studies of ladders with up to 200 rungs, for rational hole dopings δ and intermediate-strength interactions, find that currents remain large in the doped DDW phase, with no evidence of decay.^1,2,3 Motivated by these results, we consider an effective bosonization description of the doped DDW phase in which quantum fluctuations in the total charge mode are neglected.^3 This leads to an analytically solvable Frenkel-Kontorova-like model which predicts that the staggered rung current and the rung electron density show periodic spatial oscillations with wavelengths 2/δ and 1/δ, respectively, with the density minima located at the zeros (domain walls) of the staggered rung current, in good agreement with the DMRG results. We comment on the question of the nature of the asymptotic current correlations in the doped DDW phase. ^1U. Schollwöck, S. Chakravarty, J. O. Fjaerestad, J. B. Marston, and M. Troyer, Phys. Rev. Lett. 90, 186401 (2003). ^2M. Troyer, invited talk at this meeting. ^3J. O. Fjaerestad, J. B. Marston, and U. Schollwöck, unpublished.

Exactly Solvable Multidimensional Nonlinear Equations and Inverse Scattering,

DTIC Science & Technology

1986-12-01

time dimension. Here the prototype euQation is 1 the Kadomtsev - Petviashvili (K-P) equation : .0 6u , x , x - )3,:’u ,’ which is the cop,patliil ity...AD-R193 274 EXACTLY SOLVABLE MULTIDIMENSIONAL NONLINEAR EQUATIONS L/1 AND INVERSE SCATTERING(U) CLARKSON UNIV POTSDAM MY A J MBLOUITZ DEC 86 NSOSI4...ecuations by associating thnm with appropriate compatible linear equations , -ne of which is identified as a Scattering prooD,, ne others(s) serves to

Quantum glassiness in strongly correlated clean systems: an example of topological overprotection.

PubMed

Chamon, Claudio

2005-02-04

This Letter presents solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three-dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, (1) have no quenched disorder, (2) have solely local interactions, (3) have an exactly solvable spectrum, (4) have topologically ordered ground states, and (5) have slow dynamical relaxation rates akin to those of strong structural glasses.

Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection

NASA Astrophysics Data System (ADS)

Chamon, Claudio

2005-01-01

This Letter presents solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three-dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, (1)have no quenched disorder, (2)have solely local interactions, (3)have an exactly solvable spectrum, (4)have topologically ordered ground states, and (5)have slow dynamical relaxation rates akin to those of strong structural glasses.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bose, Sownak; Li, Baojiu; He, Jian-hua

We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f ( R ) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergencemore » rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f ( R ) simulations. For example, a test simulation with 512{sup 3} particles in a box of size 512 Mpc/ h is now 5 times faster than before, while a Millennium-resolution simulation for f ( R ) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.« less

Perturbatively deformed defects in Pöschl-Teller-driven scenarios for quantum mechanics

NASA Astrophysics Data System (ADS)

Bernardini, Alex E.; da Rocha, Roldão

2016-07-01

Pöschl-Teller-driven solutions for quantum mechanical fluctuations are triggered off by single scalar field theories obtained through a systematic perturbative procedure for generating deformed defects. The analytical properties concerning the quantum fluctuations in one-dimension, zero-mode states, first- and second-excited states, and energy density profiles are all obtained from deformed topological and non-topological structures supported by real scalar fields. Results are firstly derived from an integrated λϕ4 theory, with corresponding generalizations applied to starting λχ4 and sine-Gordon theories. By focusing our calculations on structures supported by the λϕ4 theory, the outcome of our study suggests an exact quantitative correspondence to Pöschl-Teller-driven systems. Embedded into the perturbative quantum mechanics framework, such a correspondence turns into a helpful tool for computing excited states and continuous mode solutions, as well as their associated energy spectrum, for quantum fluctuations of perturbatively deformed structures. Perturbative deformations create distinct physical scenarios in the context of exactly solvable quantum systems and may also work as an analytical support for describing novel braneworld universes embedded into a 5-dimensional gravity bulk.

Parametric symmetries in exactly solvable real and PT symmetric complex potentials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yadav, Rajesh Kumar, E-mail: rajeshastrophysics@gmail.com; Khare, Avinash, E-mail: khare@physics.unipune.ac.in; Bagchi, Bijan, E-mail: bbagchi123@gmail.com

In this paper, we discuss the parametric symmetries in different exactly solvable systems characterized by real or complex PT symmetric potentials. We focus our attention on the conventional potentials such as the generalized Pöschl Teller (GPT), Scarf-I, and PT symmetric Scarf-II which are invariant under certain parametric transformations. The resulting set of potentials is shown to yield a completely different behavior of the bound state solutions. Further, the supersymmetric partner potentials acquire different forms under such parametric transformations leading to new sets of exactly solvable real and PT symmetric complex potentials. These potentials are also observed to be shape invariantmore » (SI) in nature. We subsequently take up a study of the newly discovered rationally extended SI potentials, corresponding to the above mentioned conventional potentials, whose bound state solutions are associated with the exceptional orthogonal polynomials (EOPs). We discuss the transformations of the corresponding Casimir operator employing the properties of the so(2, 1) algebra.« less

The Lp Robin problem for Laplace equations in Lipschitz and (semi-)convex domains

NASA Astrophysics Data System (ADS)

Yang, Sibei; Yang, Dachun; Yuan, Wen

2018-01-01

Let n ≥ 3 and Ω be a bounded Lipschitz domain in Rn. Assume that p ∈ (2 , ∞) and the function b ∈L∞ (∂ Ω) is non-negative, where ∂Ω denotes the boundary of Ω. Denote by ν the outward unit normal to ∂Ω. In this article, the authors give two necessary and sufficient conditions for the unique solvability of the Robin problem for the Laplace equation Δu = 0 in Ω with boundary data ∂ u / ∂ ν + bu = f ∈Lp (∂ Ω), respectively, in terms of a weak reverse Hölder inequality with exponent p or the unique solvability of the Robin problem with boundary data in some weighted L2 (∂ Ω) space. As applications, the authors obtain the unique solvability of the Robin problem for the Laplace equation in the bounded (semi-)convex domain Ω with boundary data in (weighted) Lp (∂ Ω) for any given p ∈ (1 , ∞).

Quantum models with energy-dependent potentials solvable in terms of exceptional orthogonal polynomials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schulze-Halberg, Axel, E-mail: axgeschu@iun.edu; Department of Physics, Indiana University Northwest, 3400 Broadway, Gary IN 46408; Roy, Pinaki, E-mail: pinaki@isical.ac.in

We construct energy-dependent potentials for which the Schrödinger equations admit solutions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations of exceptional Hermite, Jacobi and Laguerre polynomials. We present several examples of boundary-value problems with energy-dependent potentials that admit a discrete spectrum and the corresponding normalizable solutions in closed form.

On boundary fusion and functional relations in the Baxterized affine Hecke algebra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Babichenko, A., E-mail: babichen@weizmann.ac.il; Regelskis, V., E-mail: v.regelskis@surrey.ac.uk

2014-04-15

We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain models. We show that these operators lead to a family of commuting transfer matrices of Sklyanin type. We derive fusion type functional relations for these operators for two families of representations.

INFORMS Section on Location Analysis Dissertation Award Submission

DOE Office of Scientific and Technical Information (OSTI.GOV)

Waddell, Lucas

This research effort can be summarized by two main thrusts, each of which has a chapter of the dissertation dedicated to it. First, I pose a novel polyhedral approach for identifying polynomially solvable in- stances of the QAP based on an application of the reformulation-linearization technique (RLT), a general procedure for constructing mixed 0-1 linear reformulations of 0-1 pro- grams. The feasible region to the continuous relaxation of the level-1 RLT form is a polytope having a highly specialized structure. Every binary solution to the QAP is associated with an extreme point of this polytope, and the objective function valuemore » is preserved at each such point. However, there exist extreme points that do not correspond to binary solutions. The key insight is a previously unnoticed and unexpected relationship between the polyhedral structure of the continuous relaxation of the level-1 RLT representation and various classes of readily solvable instances. Specifically, we show that a variety of apparently unrelated solvable cases of the QAP can all be categorized in the following sense: each such case has an objective function which ensures that an optimal solution to the continuous relaxation of the level-1 RLT form occurs at a binary extreme point. Interestingly, there exist instances that are solvable by the level-1 RLT form which do not satisfy the conditions of these cases, so that the level-1 form theoretically identifies a richer family of solvable instances. Second, I focus on instances of the QAP known in the literature as linearizable. An instance of the QAP is defined to be linearizable if and only if the problem can be equivalently written as a linear assignment problem that preserves the objective function value at all feasible solutions. I provide an entirely new polyheral-based perspective on the concept of linearizable by showing that an instance of the QAP is linearizable if and only if a relaxed version of the continuous relaxation of the level-1 RLT form is bounded. We also shows that the level-1 RLT form can identify a richer family of solvable instances than those deemed linearizable by demonstrating that the continuous relaxation of the level-1 RLT form can have an optimal binary solution for instances that are not linearizable. As a byproduct, I use this theoretical framework to explicity, in closed form, characterize the dimensions of the level-1 RLT form and various other problem relaxations.« less

Scalar and vector Keldysh models in the time domain

NASA Astrophysics Data System (ADS)

Kiselev, M. N.; Kikoin, K. A.

2009-04-01

The exactly solvable Keldysh model of disordered electron system in a random scattering field with extremely long correlation length is converted to the time-dependent model with extremely long relaxation. The dynamical problem is solved for the ensemble of two-level systems (TLS) with fluctuating well depths having the discrete Z 2 symmetry. It is shown also that the symmetric TLS with fluctuating barrier transparency may be described in terms of the vector Keldysh model with dime-dependent random planar rotations in xy plane having continuous SO(2) symmetry. Application of this model to description of dynamic fluctuations in quantum dots and optical lattices is discussed.

A meshless approach to thermomechanics of DC casting of aluminium billets

NASA Astrophysics Data System (ADS)

Mavrič, B.; Šarler, B.

2016-03-01

The ability to model thermomechanics in DC casting is important due to the technological challenges caused by physical phenomena such as different ingot distortions, cracking, hot tearing and residual stress. Many thermomechanical models already exist and usually take into account three contributions: elastic, thermal expansion, and viscoplastic to model the mushy zone. These models are, in a vast majority, solved by the finite element method. In the present work the elastic model that accounts for linear thermal expansion is considered. The method used for solving the model is of a novel meshless type and extends our previous meshless attempts in solving fluid mechanics problems. The solution to the problem is constructed using collocation on the overlapping subdomains, which are composed of computational nodes. Multiquadric radial basis functions, augmented by monomials, are used for the displacement interpolation. The interpolation is constructed in such a manner that it readily satisfies the boundary conditions. The discretization results in construction of a global square sparse matrix representing the system of linear equations for the displacement field. The developed method has many advantages. The system of equations can be easily constructed and efficiently solved. There is no need to perform expensive meshing of the domain and the formulation of the method is similar in two and three dimensions. Since no meshing is required, the nodes can easily be added or removed, which allows for efficient adaption of the node arrangement density. The order of convergence, estimated through an analytically solvable test, can be adjusted through the number of interpolation nodes in the subdomain, with 6 nodes being enough for the second order convergence. Simulations of axisymmetric mechanical problems, associated with low frequency electromagnetic DC casting are presented.

A Mixed-Integer Linear Programming Problem which is Efficiently Solvable.

DTIC Science & Technology

1987-10-01

INTEGER LINEAR PROGRAMMING PROBLEM WHICH IS EFFICIENTLY SOLVABLE 12. PERSONAL AUTHOR(S) Leiserson, Charles, and Saxe, James B. 13a. TYPE OF REPORT j13b TIME...ger prongramn rg versions or the problem is not ac’hievable in genieral for sparse inistancves of’ P rolem(r Mi. Th le remrai nder or thris paper is...rClazes c:oIh edge (i,I*) by comlpli urg +- rnirr(z 3, ,x + a,j). A sirnI) le analysis (11 vto Nei [131 indicates why whe Iellinan-Ford algorithm works

Classical analogous of quantum cosmological perfect fluid models

NASA Astrophysics Data System (ADS)

Batista, A. B.; Fabris, J. C.; Gonçalves, S. V. B.; Tossa, J.

2001-05-01

Quantization in the minisuperspace of a gravity system coupled to a perfect fluid, leads to a solvable model which implies singularity free solutions through the construction of a superposition of the wavefunctions. We show that such models are equivalent to a classical system where, besides the perfect fluid, a repulsive fluid with an equation of state pQ= ρQ is present. This leads to speculate on the true nature of this quantization procedure. A perturbative analysis of the classical system reveals the condition for the stability of the classical system in terms of the existence of an anti-gravity phase.

Exactly Solvable Models for Topological Phases of Matter

NASA Astrophysics Data System (ADS)

Tarantino, Nicolas Alessandro

Topological systems are characterized by some collection of features which remain unchanged under deformations of the Hamiltonian which leave the band gap open. The earliest examples of these were free fermion systems, allowing us to study the band structure to determine if a candidate material supports topological features. However, we can also ask the reversed question, i.e. Given a band gap, what topological features can be engineered? This classification problem proved to have numerous answers depending on which extra assumptions we allow, producing many candidate phases. While free fermion topological features could be classified by their band structures (culminating in the 10-fold way), strongly interacting systems defied this approach, and so classification outstripped the construction of even the most elementary Hamiltonians, leaving us with a number of phases which could exist, but do not have a single strongly interacting representative. The purpose of this thesis is to resolve this in certain cases by constructing commuting projector models (CPM), a class of exactly solvable models, for two types of topological phases, known as symmetry enriched topological (SET) order and fermionic symmetry protected topological (SPT) phases respectively. After introducing the background and history of commuting projector models, we will move on to the details of how these Hamiltonians are built. In the first case, we construct a CPM for a SET, showing how to encode the necessary group cohomology data into a lattice model. In the second, we construct a CPM for a fermionic SPT, and find that we must include a combinatorial representation of a spin structure to make the model consistent. While these two projects were independent, they are linked thematically by a technique known as decoration, where extra data is encoded onto simple models to generate exotic phases.

The element level time domain (ELTD) method for the analysis of nano-optical systems: I. Nondispersive media

NASA Astrophysics Data System (ADS)

Fallahi, Arya; Oswald, Benedikt; Leidenberger, Patrick

2012-04-01

We study a 3-dimensional, dual-field, fully explicit method for the solution of Maxwell's equations in the time domain on unstructured, tetrahedral grids. The algorithm uses the element level time domain (ELTD) discretization of the electric and magnetic vector wave equations. In particular, the suitability of the method for the numerical analysis of nanometer structured systems in the optical region of the electromagnetic spectrum is investigated. The details of the theory and its implementation as a computer code are introduced and its convergence behavior as well as conditions for stable time domain integration is examined. Here, we restrict ourselves to non-dispersive dielectric material properties since dielectric dispersion will be treated in a subsequent paper. Analytically solvable problems are analyzed in order to benchmark the method. Eventually, a dielectric microlens is considered to demonstrate the potential of the method. A flexible method of 2nd order accuracy is obtained that is applicable to a wide range of nano-optical configurations and can be a serious competitor to more conventional finite difference time domain schemes which operate only on hexahedral grids. The ELTD scheme can resolve geometries with a wide span of characteristic length scales and with the appropriate level of detail, using small tetrahedra where delicate, physically relevant details must be modeled.

The hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gadella, M.; Kuru, Ş.; Negro, J., E-mail: jnegro@fta.uva.es

We study the scattering produced by a one dimensional hyperbolic step potential, which is exactly solvable and shows an unusual interest because of its asymmetric character. The analytic continuation of the scattering matrix in the momentum representation has a branch cut and an infinite number of simple poles on the negative imaginary axis which are related with the so called anti-bound states. This model does not show resonances. Using the wave functions of the anti-bound states, we obtain supersymmetric (SUSY) partners which are the series of Rosen–Morse II potentials. We have computed the Wigner reflection and transmission time delays formore » the hyperbolic step and such SUSY partners. Our results show that the more bound states a partner Hamiltonian has the smaller is the time delay. We also have evaluated time delays for the hyperbolic step potential in the classical case and have obtained striking similitudes with the quantum case. - Highlights: • The scattering matrix of hyperbolic step potential is studied. • The scattering matrix has a branch cut and an infinite number of poles. • The poles are associated to anti-bound states. • Susy partners using antibound states are computed. • Wigner time delays for the hyperbolic step and partner potentials are compared.« less

Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension

NASA Astrophysics Data System (ADS)

Jaschke, Daniel; Wall, Michael L.; Carr, Lincoln D.

2018-04-01

Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States (MPSs), have attracted interest from different fields of quantum physics ranging from solid state systems to quantum simulators and quantum computing. Our open source MPS code provides the community with a toolset to analyze the statics and dynamics of one-dimensional quantum systems. Here, we present our open source library, Open Source Matrix Product States (OSMPS), of MPS methods implemented in Python and Fortran2003. The library includes tools for ground state calculation and excited states via the variational ansatz. We also support ground states for infinite systems with translational invariance. Dynamics are simulated with different algorithms, including three algorithms with support for long-range interactions. Convenient features include built-in support for fermionic systems and number conservation with rotational U(1) and discrete Z2 symmetries for finite systems, as well as data parallelism with MPI. We explain the principles and techniques used in this library along with examples of how to efficiently use the general interfaces to analyze the Ising and Bose-Hubbard models. This description includes the preparation of simulations as well as dispatching and post-processing of them.

Entropic manifestations of topological order in three dimensions

NASA Astrophysics Data System (ADS)

Bullivant, Alex; Pachos, Jiannis K.

2016-03-01

We evaluate the entanglement entropy of exactly solvable Hamiltonians corresponding to general families of three-dimensional topological models. We show that the modification to the entropic area law due to three-dimensional topological properties is richer than the two-dimensional case. In addition to the reduction of the entropy caused by a nonzero vacuum expectation value of contractible loop operators, a topological invariant emerges that increases the entropy if the model consists of nontrivially braiding anyons. As a result the three-dimensional topological entanglement entropy provides only partial information about the two entropic topological invariants.

Monte Carlo simulation of a dynamical fermion problem: The light q sup 2 q sup 2 system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grondin, G.

1991-01-01

We present results from a Guided Random Walk Monte Carlo simulation of the light q{sup 2}{bar q}{sup 2} system in a Coulomb-plus-linear quark potential model using an Intel iPSC/860 hypercube. A solvable model problem is first considered, after which we study the full q{sup 2}{bar q}{sup 2} system in (J,I) = (2,2) and (2,0) sectors. We find evidence for no bound states below the vector-vector threshold in these systems. 17 refs., 6 figs.

Gauged BPS baby Skyrmions with quantized magnetic flux

NASA Astrophysics Data System (ADS)

Adam, C.; Wereszczynski, A.

2017-06-01

A new type of gauged BPS baby Skyrme model is presented, where the derivative term is just the Schroers current (i.e., gauge invariant and conserved version of the topological current) squared. This class of models has a topological bound saturated for solutions of the pertinent Bogomolnyi equations supplemented by a so-called superpotential equation. In contrast to the gauged BPS baby Skyrme models considered previously, the superpotential equation is linear and, hence, completely solvable. Furthermore, the magnetic flux is quantized in units of 2 π , which allows, in principle, to define this theory on a compact manifold without boundary, unlike all gauged baby Skyrme models considered so far.

Solute transport with multisegment, equilibrium-controlled, classical reactions: Problem solvability and feed forward method's applicability for complex segments of at most binary participants

USGS Publications Warehouse

Rubin, Jacob

1992-01-01

The feed forward (FF) method derives efficient operational equations for simulating transport of reacting solutes. It has been shown to be applicable in the presence of networks with any number of homogeneous and/or heterogeneous, classical reaction segments that consist of three, at most binary participants. Using a sequential (network type after network type) exploration approach and, independently, theoretical explanations, it is demonstrated for networks with classical reaction segments containing more than three, at most binary participants that if any one of such networks leads to a solvable transport problem then the FF method is applicable. Ways of helping to avoid networks that produce problem insolvability are developed and demonstrated. A previously suggested algebraic, matrix rank procedure has been adapted and augmented to serve as the main, easy-to-apply solvability test for already postulated networks. Four network conditions that often generate insolvability have been identified and studied. Their early detection during network formulation may help to avoid postulation of insolvable networks.

Development of kinks in car-following models

NASA Astrophysics Data System (ADS)

Kurtze, Douglas A.

2017-03-01

Many car-following models of traffic flow admit the possibility of absolute stability, a situation in which uniform traffic flow at any spacing is linearly stable. Near the threshold of absolute stability, these models can often be reduced to a modified Korteweg-deVries (mKdV) equation plus small corrections. The hyperbolic-tangent "kink" solutions of the mKdV equation are usually of particular interest, as they represent transition zones between regions of different traffic spacings. Solvability analysis is believed to show that only a single member of the one-parameter family of kink solutions is preserved by the correction terms, and this is interpreted as a kind of selection. We show, however, that the usual solvability calculation rests on an unstated, unjustified assumption, and that without this assumption it merely gives a first-order correction to the relation between the traffic spacings far behind and far ahead of the kink, rather than any kind of "selection" criterion for the family of kink solutions. On the other hand, we display a two-parameter family of traveling wave solutions of the mKdV equation, which describe regions of one traffic spacing embedded in traffic of a different spacing; this family includes the kink solutions as a limiting case. We carry out a multiple-time-scales calculation and find conditions under which the inclusions decay, conditions that lead to a selected inclusion, and conditions for which the inclusion evolves into a pair of kinks.

Weighted Lq-estimates for stationary Stokes system with partially BMO coefficients

NASA Astrophysics Data System (ADS)

Dong, Hongjie; Kim, Doyoon

2018-04-01

We prove the unique solvability of solutions in Sobolev spaces to the stationary Stokes system on a bounded Reifenberg flat domain when the coefficients are partially BMO functions, i.e., locally they are merely measurable in one direction and have small mean oscillations in the other directions. Using this result, we establish the unique solvability in Muckenhoupt type weighted Sobolev spaces for the system with partially BMO coefficients on a Reifenberg flat domain. We also present weighted a priori Lq-estimates for the system when the domain is the whole Euclidean space or a half space.

Complete Firing-Rate Response of Neurons with Complex Intrinsic Dynamics

PubMed Central

Puelma Touzel, Maximilian; Wolf, Fred

2015-01-01

The response of a neuronal population over a space of inputs depends on the intrinsic properties of its constituent neurons. Two main modes of single neuron dynamics–integration and resonance–have been distinguished. While resonator cell types exist in a variety of brain areas, few models incorporate this feature and fewer have investigated its effects. To understand better how a resonator’s frequency preference emerges from its intrinsic dynamics and contributes to its local area’s population firing rate dynamics, we analyze the dynamic gain of an analytically solvable two-degree of freedom neuron model. In the Fokker-Planck approach, the dynamic gain is intractable. The alternative Gauss-Rice approach lifts the resetting of the voltage after a spike. This allows us to derive a complete expression for the dynamic gain of a resonator neuron model in terms of a cascade of filters on the input. We find six distinct response types and use them to fully characterize the routes to resonance across all values of the relevant timescales. We find that resonance arises primarily due to slow adaptation with an intrinsic frequency acting to sharpen and adjust the location of the resonant peak. We determine the parameter regions for the existence of an intrinsic frequency and for subthreshold and spiking resonance, finding all possible intersections of the three. The expressions and analysis presented here provide an account of how intrinsic neuron dynamics shape dynamic population response properties and can facilitate the construction of an exact theory of correlations and stability of population activity in networks containing populations of resonator neurons. PMID:26720924

Symmetry Enriched Topological Phases and Their Edge Theories

NASA Astrophysics Data System (ADS)

Heinrich, Christopher

In this thesis we investigate topological phases of matter that have a global, unbroken symmetry group--also known as symmetry enriched topological (SET) phases. We address three questions about these phases: (1) how can we build exactly solvable models that realize them? (2) how can we determine if their edge theories can be gapped without breaking the symmetry? and (3) how do we understand the phenomenon of decoupled charge and neutral modes which occurs in certain fractional quantum Hall states? More specifically, we address the first question by constructing exactly solvable models for a wide class of symmetry enriched topological (SET) phases, which we call symmetry-enriched string nets. The construction applies to 2D bosonic SET phases with finite unitary onsite symmetry group G, and we conjecture that our models realize every phase in this class that can be described by a commuting projector Hamiltonian. As an example, we present a model for a phase with the same anyon excitations as the toric code and with a Z2 symmetry which exchanges the e and m type anyons. We further illustrate our construction with a number of additional examples. For the second question, we focus on the edge theories of 2D SET phases with Z2 symmetry. The central problem we seek to solve is to determine which edge theories can be gapped without breaking the symmetry. Previous attempts to answer this question in special cases relied on constructing perturbations of a particular type to gap the edge. This method proves the edge can be gapped when the appropriate perturbations can be found, but is inconclusive if they cannot be found. We build on this previous work by deriving a necessary and sufficient algebraic condition for when the edge can be gapped. Our results apply to Z2 symmetry protected topological phases as well as Abelian Z2 SET phases. Finally, in the fourth chapter, we describe solvable models that capture how impurity scattering in certain fractional quantum Hall edges can give rise to a neutral mode--i.e. an edge mode that does not carry electric charge. These models consist of two counter-propagating chiral Luttinger liquids together with a collection of discrete impurity scatterers. Our main result is an exact solution of these models in the limit of infinitely strong impurity scattering. From this solution, we explicitly derive the existence of a neutral mode and we determine all of its microscopic properties including its velocity. We also study the stability of the neutral mode and show that it survives at finite but sufficiently strong scattering. Our results are applicable to a family of Abelian fractional quantum Hall states of which the nu = 2/3 state is the most prominent example.

Exact wave functions of two-electron quantum rings.

PubMed

Loos, Pierre-François; Gill, Peter M W

2012-02-24

We demonstrate that the Schrödinger equation for two electrons on a ring, which is the usual paradigm to model quantum rings, is solvable in closed form for particular values of the radius. We show that both polynomial and irrational solutions can be found for any value of the angular momentum and that the singlet and triplet manifolds, which are degenerate, have distinct geometric phases. We also study the nodal structure associated with these two-electron states.

Quantum Darwinism for mixed-state environment

NASA Astrophysics Data System (ADS)

Quan, Haitao; Zwolak, Michael; Zurek, Wojciech

2009-03-01

We exam quantum darwinism when a system is in the presence of a mixed environment, and we find a general relation between the mutual information for the mixed-state environment and the change of the entropy of the fraction of the environment. We then look at a particular solvable model, and we numerically exam the time evolution of the ``mutual information" for large environment. Finally we discuss about the exact expressions for all entropies and the mutual information at special time.

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

NASA Astrophysics Data System (ADS)

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

2014-02-01

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

Quantum mechanics and hidden superconformal symmetry

NASA Astrophysics Data System (ADS)

Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.

2017-12-01

Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp (1 |2 ) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp (1 |2 ) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantum mechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models—both oscillator and particlelike—realize all possible unitary irreducible representations of osp (1 |2 ).

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

PubMed

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

2014-02-07

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

Star-triangle and star-star relations in statistical mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baxter, R.J.

1997-01-20

The homogeneous three-layer Zamolodchikov model is equivalent to a four-state model on the checkerboard lattice which closely resembles the four-state critical Potts model, but with some of its Boltzmann weights negated. Here the author shows that it satisfies a star-to-reverse-star (or simply star-star) relation, even though they know of no star-triangle relation for this model. For any nearest-neighbor checkerboard model, they show that this star-star relation is sufficient to ensure that the decimated model (where half the spins have been summed over) satisfies a twisted Yang-Baxter relation. This ensures that the transfer matrices of the original model commute in pairs,more » which is an adequate condition for solvability.« less

Deformed quantum double realization of the toric code and beyond

NASA Astrophysics Data System (ADS)

Padmanabhan, Pramod; Ibieta-Jimenez, Juan Pablo; Bernabe Ferreira, Miguel Jorge; Teotonio-Sobrinho, Paulo

2016-09-01

Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase and destroying the exact solvability of the quantum double model. We modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase, thus nullifying the effect of the perturbation. The algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra. The Abelian cases are shown to be in the quantum double phase whereas the non-Abelian phases are shown to be in a modified phase of the corresponding quantum double phase. These are illustrated with the groups Zn and S3. The quantum phases are determined by studying the excitations of these systems namely their fusion rules and the statistics. We then go further to construct a transfer matrix which contains the other Z2 phase namely the double semion phase. More generally for other discrete groups these transfer matrices contain the twisted quantum double models. These transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories. These parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice. As in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties.

Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system modeling coral fertilization

NASA Astrophysics Data System (ADS)

Espejo, Elio; Winkler, Michael

2018-04-01

The interplay of chemotaxis, convection and reaction terms is studied in the particular framework of a refined model for coral broadcast spawning, consisting of three equations describing the population densities of unfertilized sperms and eggs and the concentration of a chemical released by the latter, coupled to the incompressible Navier-Stokes equations. Under mild assumptions on the initial data, global existence of classical solutions to an associated initial-boundary value problem in bounded planar domains is established. Moreover, all these solutions are shown to approach a spatially homogeneous equilibrium in the large time limit.

Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

DOE PAGES

Smith, J. C.; Pribram-Jones, A.; Burke, K.

2016-06-14

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.

Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, J. C.; Pribram-Jones, A.; Burke, K.

Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.

Asymptotic behaviour of two-point functions in multi-species models

NASA Astrophysics Data System (ADS)

Kozlowski, Karol K.; Ragoucy, Eric

2016-05-01

We extract the long-distance asymptotic behaviour of two-point correlation functions in massless quantum integrable models containing multi-species excitations. For such a purpose, we extend to these models the method of a large-distance regime re-summation of the form factor expansion of correlation functions. The key feature of our analysis is a technical hypothesis on the large-volume behaviour of the form factors of local operators in such models. We check the validity of this hypothesis on the example of the SU (3)-invariant XXX magnet by means of the determinant representations for the form factors of local operators in this model. Our approach confirms the structure of the critical exponents obtained previously for numerous models solvable by the nested Bethe Ansatz.

Evolutionary Oseen Model for Generalized Newtonian Fluid with Multivalued Nonmonotone Friction Law

NASA Astrophysics Data System (ADS)

Migórski, Stanisław; Dudek, Sylwia

2018-03-01

The paper deals with the non-stationary Oseen system of equations for the generalized Newtonian incompressible fluid with multivalued and nonmonotone frictional slip boundary conditions. First, we provide a result on existence of a unique solution to an abstract evolutionary inclusion involving the Clarke subdifferential term for a nonconvex function. We employ a method based on a surjectivity theorem for multivalued L-pseudomonotone operators. Then, we exploit the abstract result to prove the weak unique solvability of the Oseen system.

Microcanonical Szilárd engines beyond the quasistatic regime

NASA Astrophysics Data System (ADS)

Acconcia, Thiago V.; Bonança, Marcus V. S.

2017-12-01

We discuss the possibility of extracting energy from a single thermal bath using microcanonical Szilárd engines operating in finite time. This extends previous works on the topic which are restricted to the quasistatic regime. The feedback protocol is implemented based on linear response predictions of the excess work. It is claimed that the underlying mechanism leading to energy extraction does not violate Liouville's theorem and preserves ergodicity throughout the cycle. We illustrate our results with several examples including an exactly solvable model.

Microcanonical Szilárd engines beyond the quasistatic regime.

PubMed

Acconcia, Thiago V; Bonança, Marcus V S

2017-12-01

We discuss the possibility of extracting energy from a single thermal bath using microcanonical Szilárd engines operating in finite time. This extends previous works on the topic which are restricted to the quasistatic regime. The feedback protocol is implemented based on linear response predictions of the excess work. It is claimed that the underlying mechanism leading to energy extraction does not violate Liouville's theorem and preserves ergodicity throughout the cycle. We illustrate our results with several examples including an exactly solvable model.

Models in Insurance: Paradigms, Puzzles, Communications and Revolutions.

DTIC Science & Technology

1980-06-01

80.7] G. Buoro, G. Pavesi and G. Zucchiatti, "Osservazioni sul Sistema di Calcolo del Margine di Solvabiliti," 71-80. [80.8] J. Calcanis and A...Vegas, "Un Ensayo sobre la Concepci6n Sistema aplicada a la Empresa de Seguros," 443-462. [80.41] K. H. Wolff, "Zur numerischen Berechnung der... Teoria della Credibilit&," Giornale dell’ Istituto degli Attuari, 27, 219-231 (1964). (D51 N. De Pril, "The Efficiency of a Bonus-Malus System," AB, 10

Logic integer programming models for signaling networks.

PubMed

Haus, Utz-Uwe; Niermann, Kathrin; Truemper, Klaus; Weismantel, Robert

2009-05-01

We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this, we use the two different mathematical tools of Propositional Logic and Integer Programming. The power of discrete mathematics for handling qualitative as well as quantitative data has so far not been exploited in molecular biology, which is mostly driven by experimental research, relying on first-order or statistical models. The arising logic statements and integer programs are analyzed and can be solved with standard software. For a restricted class of problems the logic models reduce to a polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic model enables enumeration of possible time resolutions in poly-logarithmic time. Computational experiments are included.

A New Framework for Analysis of Coevolutionary Systems-Directed Graph Representation and Random Walks.

PubMed

Chong, Siang Yew; Tiňo, Peter; He, Jun; Yao, Xin

2017-11-20

Studying coevolutionary systems in the context of simplified models (i.e., games with pairwise interactions between coevolving solutions modeled as self plays) remains an open challenge since the rich underlying structures associated with pairwise-comparison-based fitness measures are often not taken fully into account. Although cyclic dynamics have been demonstrated in several contexts (such as intransitivity in coevolutionary problems), there is no complete characterization of cycle structures and their effects on coevolutionary search. We develop a new framework to address this issue. At the core of our approach is the directed graph (digraph) representation of coevolutionary problems that fully captures structures in the relations between candidate solutions. Coevolutionary processes are modeled as a specific type of Markov chains-random walks on digraphs. Using this framework, we show that coevolutionary problems admit a qualitative characterization: a coevolutionary problem is either solvable (there is a subset of solutions that dominates the remaining candidate solutions) or not. This has an implication on coevolutionary search. We further develop our framework that provides the means to construct quantitative tools for analysis of coevolutionary processes and demonstrate their applications through case studies. We show that coevolution of solvable problems corresponds to an absorbing Markov chain for which we can compute the expected hitting time of the absorbing class. Otherwise, coevolution will cycle indefinitely and the quantity of interest will be the limiting invariant distribution of the Markov chain. We also provide an index for characterizing complexity in coevolutionary problems and show how they can be generated in a controlled manner.

Successive phase transitions and kink solutions in Φ⁸, Φ¹⁰, and Φ¹² field theories

DOE PAGES

Khare, Avinash; Christov, Ivan C.; Saxena, Avadh

2014-08-27

We obtain exact solutions for kinks in Φ⁸, Φ¹⁰, and Φ¹² field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically-decaying tails and also asymmetric cases with mixed exponential-algebraic tail decay, unlike the lower-order Φ⁴ and Φ⁶ theories. Additionally, we construct distinct kinks withmore » equal energies in all three field theories considered, and we show the co-existence of up to three distinct kinks (for a Φ¹² potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the Φ¹⁰ field theory, which is a quasi-exactly solvable (QES) model akin to Φ⁶, we are also able to obtain three analytical solutions for the classical free energy as well as the probability distribution function in the thermodynamic limit.« less

Entropic anomaly and maximal efficiency of microscopic heat engines.

PubMed

Bo, Stefano; Celani, Antonio

2013-05-01

The efficiency of microscopic heat engines in a thermally heterogenous environment is considered. We show that-as a consequence of the recently discovered entropic anomaly-quasistatic engines, whose efficiency is maximal in a fluid at uniform temperature, have in fact vanishing efficiency in the presence of temperature gradients. For slow cycles the efficiency falls off as the inverse of the period. The maximum efficiency is reached at a finite value of the cycle period that is inversely proportional to the square root of the gradient intensity. The relative loss in maximal efficiency with respect to the thermally homogeneous case grows as the square root of the gradient. As an illustration of these general results, we construct an explicit, analytically solvable example of a Carnot stochastic engine. In this thought experiment, a Brownian particle is confined by a harmonic trap and immersed in a fluid with a linear temperature profile. This example may serve as a template for the design of real experiments in which the effect of the entropic anomaly can be measured.

Singular Hopf bifurcation in a differential equation with large state-dependent delay

PubMed Central

Kozyreff, G.; Erneux, T.

2014-01-01

We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawtooth oscillations. The dependence of the delay on the solution can be either linear or nonlinear, with at least quadratic dependence. In the former case, an asymptotic connection is made with the Rayleigh oscillator. In the latter, van der Pol’s equation is derived for the small-amplitude oscillations. SDD differential equations are currently the subject of intense research in order to establish or amend general theorems valid for constant-delay differential equation, but explicit analytical construction of solutions are rare. This paper illustrates the use of singular perturbation techniques and the unusual way in which solvability conditions can arise for SDD problems with large delays. PMID:24511255

Singular Hopf bifurcation in a differential equation with large state-dependent delay.

PubMed

Kozyreff, G; Erneux, T

2014-02-08

We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawtooth oscillations. The dependence of the delay on the solution can be either linear or nonlinear, with at least quadratic dependence. In the former case, an asymptotic connection is made with the Rayleigh oscillator. In the latter, van der Pol's equation is derived for the small-amplitude oscillations. SDD differential equations are currently the subject of intense research in order to establish or amend general theorems valid for constant-delay differential equation, but explicit analytical construction of solutions are rare. This paper illustrates the use of singular perturbation techniques and the unusual way in which solvability conditions can arise for SDD problems with large delays.

Quality of herbal medicines: challenges and solutions.

PubMed

Zhang, Junhua; Wider, Barbara; Shang, Hongcai; Li, Xuemei; Ernst, Edzard

2012-01-01

The popularity of herbal medicines has risen worldwide. This increase in usage renders safety issues important. Many adverse events of herbal medicines can be attributed to the poor quality of the raw materials or the finished products. Different types of herbal medicines are associated with different problems. Quality issues of herbal medicines can be classified into two categories: external and internal. In this review, external issues including contamination (e.g. toxic metals, pesticides residues and microbes), adulteration and misidentification are detailed. Complexity and non-uniformity of the ingredients in herbal medicines are the internal issues affecting the quality of herbal medicines. Solutions to the raised problems are discussed. The rigorous implementation of Good Agricultural and Collection Practices (GACP) and Good Manufacturing Practices (GMP) would undoubtedly reduce the risk of external issues. Through the use of modern analytical methods and pharmaceutical techniques, previously unsolved internal issues have become solvable. Standard herbal products can be manufactured from the standard herbal extracts. Copyright © 2011 Elsevier Ltd. All rights reserved.

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

NASA Astrophysics Data System (ADS)

Wu, Sheng-Jhih; Chu, Moody T.

2017-08-01

An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.

Segmentation in cohesive systems constrained by elastic environments

NASA Astrophysics Data System (ADS)

Novak, I.; Truskinovsky, L.

2017-04-01

The complexity of fracture-induced segmentation in elastically constrained cohesive (fragile) systems originates from the presence of competing interactions. The role of discreteness in such phenomena is of interest in a variety of fields, from hierarchical self-assembly to developmental morphogenesis. In this paper, we study the analytically solvable example of segmentation in a breakable mass-spring chain elastically linked to a deformable lattice structure. We explicitly construct the complete set of local minima of the energy in this prototypical problem and identify among them the states corresponding to the global energy minima. We show that, even in the continuum limit, the dependence of the segmentation topology on the stretching/pre-stress parameter in this problem takes the form of a devil's type staircase. The peculiar nature of this staircase, characterized by locking in rational microstructures, is of particular importance for biological applications, where its structure may serve as an explanation of the robustness of stress-driven segmentation. This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

Gegenbauer-solvable quantum chain model

NASA Astrophysics Data System (ADS)

Znojil, Miloslav

2010-11-01

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

Lack of consensus in social systems

NASA Astrophysics Data System (ADS)

Benczik, I. J.; Benczik, S. Z.; Schmittmann, B.; Zia, R. K. P.

2008-05-01

We propose an exactly solvable model for the dynamics of voters in a two-party system. The opinion formation process is modeled on a random network of agents. The dynamical nature of interpersonal relations is also reflected in the model, as the connections in the network evolve with the dynamics of the voters. In the infinite time limit, an exact solution predicts the emergence of consensus, for arbitrary initial conditions. However, before consensus is reached, two different metastable states can persist for exponentially long times. One state reflects a perfect balancing of opinions, the other reflects a completely static situation. An estimate of the associated lifetimes suggests that lack of consensus is typical for large systems.

Selective Transient Cooling by Impulse Perturbations in a Simple Toy Model

NASA Astrophysics Data System (ADS)

Fabrizio, Michele

2018-06-01

We show in a simple exactly solvable toy model that a properly designed impulse perturbation can transiently cool down low-energy degrees of freedom at the expense of high-energy ones that heat up. The model consists of two infinite-range quantum Ising models: one, the high-energy sector, with a transverse field much bigger than the other, the low-energy sector. The finite-duration perturbation is a spin exchange that couples the two Ising models with an oscillating coupling strength. We find a cooling of the low-energy sector that is optimized by the oscillation frequency in resonance with the spin exchange excitation. After the perturbation is turned off, the Ising model with a low transverse field can even develop a spontaneous symmetry breaking despite being initially above the critical temperature.

Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations

NASA Astrophysics Data System (ADS)

He, Wei

2015-02-01

The Gauge/Bethe correspondence relates Omega-deformed N = 2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory with an adjoint matter, or with 4 fundamental matters, the potential of corresponding quantum model is the elliptic function. If the mass of matter takes special value then the potential is an elliptic solution of KdV hierarchy. We show that the deformed prepotential of gauge theory can be obtained from the average densities of conserved charges of the classical KdV solution, the UV gauge coupling dependence is assembled into the Eisenstein series. The gauge theory with adjoint mass is taken as the example.

CTE Solvability, Exact Solutions and Nonlocal Symmetries of the Sharma-Tasso-Olver Equation

NASA Astrophysics Data System (ADS)

Pu, Huan; Jia, Man

2015-12-01

In this letter, we prove that the STO equation is CTE solvable and obtain the exact solutions of solitons fission and fusion. We also provide the nonlocal symmetries of the STO equation related to CTE. The nonlocal symmetries are localized by prolonging the related enlarged system. Supported by National Natural Science Foundation of China under Grant Nos. 11205092, 11175092 and 11435005, Ningbo Natural Science Foundation under Grant Nos. 2015A610159 and 2012A610178 and by the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No. xkzw11502. And the authors were sponsored by K. C. Wong Magna Fund in Ningbo University

Coherent population transfer in multi-level Allen-Eberly models

NASA Astrophysics Data System (ADS)

Li, Wei; Cen, Li-Xiang

2018-04-01

We investigate the solvability of multi-level extensions of the Allen-Eberly model and the population transfer yielded by the corresponding dynamical evolution. We demonstrate that, under a matching condition of the frequency, the driven two-level system and its multi-level extensions possess a stationary-state solution in a canonical representation associated with a unitary transformation. As a consequence, we show that the resulting protocol is able to realize complete population transfer in a nonadiabatic manner. Moreover, we explore the imperfect pulsing process with truncation and display that the nonadiabatic effect in the evolution can lead to suppression to the cutoff error of the protocol.

The continuum fusion theory of signal detection applied to a bi-modal fusion problem

NASA Astrophysics Data System (ADS)

Schaum, A.

2011-05-01

A new formalism has been developed that produces detection algorithms for model-based problems, in which one or more parameter values is unknown. Continuum Fusion can be used to generate different flavors of algorithm for any composite hypothesis testing problem. The methodology is defined by a fusion logic that can be translated into max/min conditions. Here it is applied to a simple sensor fusion model, but one for which the generalized likelihood ratio test is intractable. By contrast, a fusion-based response to the same problem can be devised that is solvable in closed form and represents a good approximation to the GLR test.

Mapping quorum sensing onto neural networks to understand collective decision making in heterogeneous microbial communities

NASA Astrophysics Data System (ADS)

Yusufaly, Tahir I.; Boedicker, James Q.

2017-08-01

Microbial communities frequently communicate via quorum sensing (QS), where cells produce, secrete, and respond to a threshold level of an autoinducer (AI) molecule, thereby modulating gene expression. However, the biology of QS remains incompletely understood in heterogeneous communities, where variant bacterial strains possess distinct QS systems that produce chemically unique AIs. AI molecules bind to ‘cognate’ receptors, but also to ‘non-cognate’ receptors found in other strains, resulting in inter-strain crosstalk. Understanding these interactions is a prerequisite for deciphering the consequences of crosstalk in real ecosystems, where multiple AIs are regularly present in the same environment. As a step towards this goal, we map crosstalk in a heterogeneous community of variant QS strains onto an artificial neural network model. This formulation allows us to systematically analyze how crosstalk regulates the community’s capacity for flexible decision making, as quantified by the Boltzmann entropy of all QS gene expression states of the system. In a mean-field limit of complete cross-inhibition between variant strains, the model is exactly solvable, allowing for an analytical formula for the number of variants that maximize capacity as a function of signal kinetics and activation parameters. An analysis of previous experimental results on the Staphylococcus aureus two-component Agr system indicates that the observed combination of variant numbers, gene expression rates and threshold concentrations lies near this critical regime of parameter space where capacity peaks. The results are suggestive of a potential evolutionary driving force for diversification in certain QS systems.

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

PubMed

Kinjo, Ken; Uchibe, Eiji; Doya, Kenji

2013-01-01

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

Phase diagram and quench dynamics of the cluster-XY spin chain

NASA Astrophysics Data System (ADS)

Montes, Sebastián; Hamma, Alioscia

2012-08-01

We study the complete phase space and the quench dynamics of an exactly solvable spin chain, the cluster-XY model. In this chain, the cluster term and the XY couplings compete to give a rich phase diagram. The phase diagram is studied by means of the quantum geometric tensor. We study the time evolution of the system after a critical quantum quench using the Loschmidt echo. The structure of the revivals after critical quantum quenches presents a nontrivial behavior depending on the phase of the initial state and the critical point.

Andreev bound states. Some quasiclassical reflections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Y., E-mail: yiriolin@illinois.edu; Leggett, A. J.

2014-12-15

We discuss a very simple and essentially exactly solvable model problem which illustrates some nice features of Andreev bound states, namely, the trapping of a single Bogoliubov quasiparticle in a neutral s-wave BCS superfluid by a wide and shallow Zeeman trap. In the quasiclassical limit, the ground state is a doublet with a splitting which is proportional to the exponentially small amplitude for “normal” reflection by the edges of the trap. We comment briefly on a prima facie paradox concerning the continuity equation and conjecture a resolution to it.

An optimization method for the problems of thermal cloaking of material bodies

NASA Astrophysics Data System (ADS)

Alekseev, G. V.; Levin, V. A.

2016-11-01

Inverse heat-transfer problems related to constructing special thermal devices such as cloaking shells, thermal-illusion or thermal-camouflage devices, and heat-flux concentrators are studied. The heatdiffusion equation with a variable heat-conductivity coefficient is used as the initial heat-transfer model. An optimization method is used to reduce the above inverse problems to the respective control problem. The solvability of the above control problem is proved, an optimality system that describes necessary extremum conditions is derived, and a numerical algorithm for solving the control problem is proposed.

Diffusion approximation of the radiative-conductive heat transfer model with Fresnel matching conditions

NASA Astrophysics Data System (ADS)

Chebotarev, Alexander Yu.; Grenkin, Gleb V.; Kovtanyuk, Andrey E.; Botkin, Nikolai D.; Hoffmann, Karl-Heinz

2018-04-01

The paper is concerned with a problem of diffraction type. The study starts with equations of complex (radiative and conductive) heat transfer in a multicomponent domain with Fresnel matching conditions at the interfaces. Applying the diffusion, P1, approximation yields a pair of coupled nonlinear PDEs describing the radiation intensity and temperature for each component of the domain. Matching conditions for these PDEs, imposed at the interfaces between the domain components, are derived. The unique solvability of the obtained problem is proven, and numerical experiments are conducted.

Andreev bound states. Some quasiclassical reflections

NASA Astrophysics Data System (ADS)

Lin, Y.; Leggett, A. J.

2014-12-01

We discuss a very simple and essentially exactly solvable model problem which illustrates some nice features of Andreev bound states, namely, the trapping of a single Bogoliubov quasiparticle in a neutral s-wave BCS superfluid by a wide and shallow Zeeman trap. In the quasiclassical limit, the ground state is a doublet with a splitting which is proportional to the exponentially small amplitude for "normal" reflection by the edges of the trap. We comment briefly on a prima facie paradox concerning the continuity equation and conjecture a resolution to it.

Renormalization of Extended QCD2

NASA Astrophysics Data System (ADS)

Fukaya, Hidenori; Yamamura, Ryo

2015-10-01

Extended QCD (XQCD), proposed by Kaplan [D. B. Kaplan, arXiv:1306.5818], is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low-energy hadronic models. We analyze the renormalization group flow of 2D (X)QCD, which is solvable in the limit of a large number of colors N_c, to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low-energy region.

Phase diagram and quench dynamics of the cluster-XY spin chain.

PubMed

Montes, Sebastián; Hamma, Alioscia

2012-08-01

We study the complete phase space and the quench dynamics of an exactly solvable spin chain, the cluster-XY model. In this chain, the cluster term and the XY couplings compete to give a rich phase diagram. The phase diagram is studied by means of the quantum geometric tensor. We study the time evolution of the system after a critical quantum quench using the Loschmidt echo. The structure of the revivals after critical quantum quenches presents a nontrivial behavior depending on the phase of the initial state and the critical point.

Production of a sterile species via active-sterile mixing: An exactly solvable model

NASA Astrophysics Data System (ADS)

Boyanovsky, D.

2007-11-01

The production of a sterile species via active-sterile mixing in a thermal medium is studied in an exactly solvable model. The exact time evolution of the sterile distribution function is determined by the dispersion relations and damping rates Γ1,2 for the quasiparticle modes. These depend on γ˜=Γaa/2ΔE, with Γaa the interaction rate of the active species in absence of mixing and ΔE the oscillation frequency in the medium without damping. γ˜≪1, γ˜≫1 describe the weak and strong damping limits, respectively. For γ˜≪1, Γ1=Γaacos⁡2θm; Γ2=Γaasin⁡2θm where θm is the mixing angle in the medium and the sterile distribution function does not obey a simple rate equation. For γ˜≫1, Γ1=Γaa and Γ2=Γaasin⁡22θm/4γ˜2, is the sterile production rate. In this regime sterile production is suppressed and the oscillation frequency vanishes at an Mikheyev-Smirnov-Wolfenstein (MSW) resonance, with a breakdown of adiabaticity. These are consequences of quantum Zeno suppression. For active neutrinos with standard model interactions the strong damping limit is only available near an MSW resonance if sin⁡2θ≪αw with θ the vacuum mixing angle. The full set of quantum kinetic equations for sterile production for arbitrary γ˜ are obtained from the quantum master equation. Cosmological resonant sterile neutrino production is quantum Zeno suppressed relieving potential uncertainties associated with the QCD phase transition.

Differential geometric treewidth estimation in adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Wang, Chi; Jonckheere, Edmond; Brun, Todd

2016-10-01

The D-Wave adiabatic quantum computing platform is designed to solve a particular class of problems—the Quadratic Unconstrained Binary Optimization (QUBO) problems. Due to the particular "Chimera" physical architecture of the D-Wave chip, the logical problem graph at hand needs an extra process called minor embedding in order to be solvable on the D-Wave architecture. The latter problem is itself NP-hard. In this paper, we propose a novel polynomial-time approximation to the closely related treewidth based on the differential geometric concept of Ollivier-Ricci curvature. The latter runs in polynomial time and thus could significantly reduce the overall complexity of determining whether a QUBO problem is minor embeddable, and thus solvable on the D-Wave architecture.

Quantum glassiness in clean strongly correlated systems: an example of topological overprotection

NASA Astrophysics Data System (ADS)

Chamon, Claudio

2005-03-01

Describing matter at near absolute zero temperature requires understanding a system's quantum ground state and the low energy excitations around it, the quasiparticles, which are thermally populated by the system's contact to a heat bath. However, this paradigm breaks down if thermal equilibration is obstructed. I present solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, 1) have no quenched disorder, 2) have solely local interactions, 3) have an exactly solvable spectrum, 4) have topologically ordered ground states, and 5) have slow dynamical relaxation rates akin to those of strong structural glasses.

Extended Islands of Tractability for Parsimony Haplotyping

NASA Astrophysics Data System (ADS)

Fleischer, Rudolf; Guo, Jiong; Niedermeier, Rolf; Uhlmann, Johannes; Wang, Yihui; Weller, Mathias; Wu, Xi

Parsimony haplotyping is the problem of finding a smallest size set of haplotypes that can explain a given set of genotypes. The problem is NP-hard, and many heuristic and approximation algorithms as well as polynomial-time solvable special cases have been discovered. We propose improved fixed-parameter tractability results with respect to the parameter "size of the target haplotype set" k by presenting an O *(k 4k )-time algorithm. This also applies to the practically important constrained case, where we can only use haplotypes from a given set. Furthermore, we show that the problem becomes polynomial-time solvable if the given set of genotypes is complete, i.e., contains all possible genotypes that can be explained by the set of haplotypes.

Evolutionary Games with Randomly Changing Payoff Matrices

NASA Astrophysics Data System (ADS)

Yakushkina, Tatiana; Saakian, David B.; Bratus, Alexander; Hu, Chin-Kun

2015-06-01

Evolutionary games are used in various fields stretching from economics to biology. In most of these games a constant payoff matrix is assumed, although some works also consider dynamic payoff matrices. In this article we assume a possibility of switching the system between two regimes with different sets of payoff matrices. Potentially such a model can qualitatively describe the development of bacterial or cancer cells with a mutator gene present. A finite population evolutionary game is studied. The model describes the simplest version of annealed disorder in the payoff matrix and is exactly solvable at the large population limit. We analyze the dynamics of the model, and derive the equations for both the maximum and the variance of the distribution using the Hamilton-Jacobi equation formalism.

Designing Kitaev Spin Liquids in Metal-Organic Frameworks

NASA Astrophysics Data System (ADS)

Yamada, Masahiko G.; Fujita, Hiroyuki; Oshikawa, Masaki

2017-08-01

Kitaev's honeycomb lattice spin model is a remarkable exactly solvable model, which has a particular type of spin liquid (Kitaev spin liquid) as the ground state. Although its possible realization in iridates and α -RuCl3 has been vigorously discussed recently, these materials have substantial non-Kitaev direct exchange interactions and do not have a spin liquid ground state. We propose metal-organic frameworks (MOFs) with Ru3 + (or Os3 + ), forming the honeycomb lattice as promising candidates for a more ideal realization of Kitaev-type spin models, where the direct exchange interaction is strongly suppressed. The great flexibility of MOFs allows generalization to other three-dimensional lattices for the potential realization of a variety of spin liquids, such as a Weyl spin liquid.

Scalar products of Bethe vectors in models with {\\mathfrak{gl}}(2| 1) symmetry 1. Super-analog of Reshetikhin formula

NASA Astrophysics Data System (ADS)

Hutsalyuk, A.; Liashyk, A.; Pakuliak, S. Z.; Ragoucy, E.; Slavnov, N. A.

2016-11-01

We study the scalar products of Bethe vectors in integrable models solvable by the nested algebraic Bethe ansatz and possessing {gl}(2| 1) symmetry. Using explicit formulas of the monodromy matrix entries’ multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions of the Bethe parameters. It can be used for the analysis of scalar products involving on-shell Bethe vectors. As a by-product, we obtain a determinant representation for the scalar products of generic Bethe vectors in integrable models with {gl}(1| 1) symmetry. Dedicated to the memory of Petr Petrovich Kulish.

Corrected Mean-Field Model for Random Sequential Adsorption on Random Geometric Graphs

NASA Astrophysics Data System (ADS)

Dhara, Souvik; van Leeuwaarden, Johan S. H.; Mukherjee, Debankur

2018-03-01

A notorious problem in mathematics and physics is to create a solvable model for random sequential adsorption of non-overlapping congruent spheres in the d-dimensional Euclidean space with d≥ 2 . Spheres arrive sequentially at uniformly chosen locations in space and are accepted only when there is no overlap with previously deposited spheres. Due to spatial correlations, characterizing the fraction of accepted spheres remains largely intractable. We study this fraction by taking a novel approach that compares random sequential adsorption in Euclidean space to the nearest-neighbor blocking on a sequence of clustered random graphs. This random network model can be thought of as a corrected mean-field model for the interaction graph between the attempted spheres. Using functional limit theorems, we characterize the fraction of accepted spheres and its fluctuations.

Solvable Hydrodynamics of Quantum Integrable Systems

NASA Astrophysics Data System (ADS)

Bulchandani, Vir B.; Vasseur, Romain; Karrasch, Christoph; Moore, Joel E.

2017-12-01

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudomomenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudomomentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.

Generalised Central Limit Theorems for Growth Rate Distribution of Complex Systems

NASA Astrophysics Data System (ADS)

Takayasu, Misako; Watanabe, Hayafumi; Takayasu, Hideki

2014-04-01

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety of fields can be derived from this basic physical model. Statistical data of growth rates for about 1 million business firms are analysed as a real-world example of randomly growing systems. Not only are the scaling relations consistent with the theoretical solution, but the entire functional form of the growth rate distribution is fitted with a theoretical distribution that has a power-law tail.

Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing

NASA Astrophysics Data System (ADS)

Durang, Xavier; Henkel, Malte

2017-12-01

Motivated by an analogy with the spherical model of a ferromagnet, the three Arcetri models are defined. They present new universality classes, either for the growth of interfaces, or else for lattice gases. They are distinct from the common Edwards-Wilkinson and Kardar-Parisi-Zhang universality classes. Their non-equilibrium evolution can be studied by the exact computation of their two-time correlators and responses. In both interpretations, the first model has a critical point in any dimension and shows simple ageing at and below criticality. The exact universal exponents are found. The second and third model are solved at zero temperature, in one dimension, where both show logarithmic sub-ageing, of which several distinct types are identified. Physically, the second model describes a lattice gas and the third model describes interface growth. A clear physical picture on the subsequent time and length scales of the sub-ageing process emerges.

Z3 topological order in the face-centered-cubic quantum plaquette model

NASA Astrophysics Data System (ADS)

Devakul, Trithep

2018-04-01

We examine the topological order in the resonating singlet valence plaquette (RSVP) phase of the hard-core quantum plaquette model (QPM) on the face centered cubic (FCC) lattice. To do this, we construct a Rohksar-Kivelson type Hamiltonian of local plaquette resonances. This model is shown to exhibit a Z3 topological order, which we show by identifying a Z3 topological constant (which leads to a 33-fold topological ground state degeneracy on the 3-torus) and topological pointlike charge and looplike magnetic excitations which obey Z3 statistics. We also consider an exactly solvable generalization of this model, which makes the geometrical origin of the Z3 order explicitly clear. For other models and lattices, such generalizations produce a wide variety of topological phases, some of which are novel fracton phases.

Dolan Grady relations and noncommutative quasi-exactly solvable systems

NASA Astrophysics Data System (ADS)

Klishevich, Sergey M.; Plyushchay, Mikhail S.

2003-11-01

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the {\\mathfrak{su}}(2) and {\\mathfrak{sl}}(2,{\\bb {R}}) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.

Effects of methylphenidate on the persistence of ADHD boys following failure experiences.

PubMed

Milich, R; Carlson, C L; Pelham, W E; Licht, B G

1991-10-01

We examined the effects of methylphenidate on the task persistence of 21 boys with attention-deficit hyperactivity disorder (ADHD), after they had been exposed to both solvable and insolvable problems. The boys attempted to solve 10 different find-a-word puzzles on each of 4 days, involving the crossing of medication (placebo vs. 0.3 mg/kg) and prior task difficulty (solvable vs. insolvable). The results revealed that medication prevented the decrement in performance following the insolvable problems that was evident with the placebo days. In addition, on medication compared with placebo, the boys were more likely to make external attributions for failure and internal attributions for success. The results are discussed in terms of the impact of medication on ADHD boys' performance as mediated by cognitive-motivational state mechanisms.

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium.

PubMed

Netz, Roland R

2018-05-14

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium parameter α from experimental spectral response and fluctuation data.

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium

NASA Astrophysics Data System (ADS)

Netz, Roland R.

2018-05-01

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium parameter α from experimental spectral response and fluctuation data.

Semidefinite Relaxation-Based Optimization of Multiple-Input Wireless Power Transfer Systems

NASA Astrophysics Data System (ADS)

Lang, Hans-Dieter; Sarris, Costas D.

2017-11-01

An optimization procedure for multi-transmitter (MISO) wireless power transfer (WPT) systems based on tight semidefinite relaxation (SDR) is presented. This method ensures physical realizability of MISO WPT systems designed via convex optimization -- a robust, semi-analytical and intuitive route to optimizing such systems. To that end, the nonconvex constraints requiring that power is fed into rather than drawn from the system via all transmitter ports are incorporated in a convex semidefinite relaxation, which is efficiently and reliably solvable by dedicated algorithms. A test of the solution then confirms that this modified problem is equivalent (tight relaxation) to the original (nonconvex) one and that the true global optimum has been found. This is a clear advantage over global optimization methods (e.g. genetic algorithms), where convergence to the true global optimum cannot be ensured or tested. Discussions of numerical results yielded by both the closed-form expressions and the refined technique illustrate the importance and practicability of the new method. It, is shown that this technique offers a rigorous optimization framework for a broad range of current and emerging WPT applications.

Contextualising eating problems in individual diet counselling.

PubMed

Kristensen, Søren T; Køster, Allan

2014-05-01

Health professionals consider diet to be a vital component in managing weight, chronic diseases and the overall promotion of health. This article takes the position that the complexity and contextual nature of individual eating problems needs to be addressed in a more systematic and nuanced way than is usually the case in diet counselling, motivational interviewing and health coaching. We suggest the use of narrative practice as a critical and context-sensitive counselling approach to eating problems. Principles of externalisation and co-researching are combined within a counselling framework that employs logistic, social and discursive eating problems as analytic categories. Using cases from a health clinic situated at the Metropolitan University College in Copenhagen, we show that even if the structural conditions associated with eating problems may not be solvable through individual counselling sessions, exploration of the complex structures of food and eating with the client can provide agency by helping them navigate within the context of the problem. We also exemplify why a reflexive and critical approach to the way health is perceived by clients should be an integrated part of diet counselling.

A boundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in two dimensions.

PubMed

Yang, S A

2002-10-01

This paper presents an effective solution method for predicting acoustic radiation and scattering fields in two dimensions. The difficulty of the fictitious characteristic frequency is overcome by incorporating an auxiliary interior surface that satisfies certain boundary condition into the body surface. This process gives rise to a set of uniquely solvable boundary integral equations. Distributing monopoles with unknown strengths over the body and interior surfaces yields the simple source formulation. The modified boundary integral equations are further transformed to ordinary ones that contain nonsingular kernels only. This implementation allows direct application of standard quadrature formulas over the entire integration domain; that is, the collocation points are exactly the positions at which the integration points are located. Selecting the interior surface is an easy task. Moreover, only a few corresponding interior nodal points are sufficient for the computation. Numerical calculations consist of the acoustic radiation and scattering by acoustically hard elliptic and rectangular cylinders. Comparisons with analytical solutions are made. Numerical results demonstrate the efficiency and accuracy of the current solution method.

Segmentation in cohesive systems constrained by elastic environments

PubMed Central

Novak, I.

2017-01-01

The complexity of fracture-induced segmentation in elastically constrained cohesive (fragile) systems originates from the presence of competing interactions. The role of discreteness in such phenomena is of interest in a variety of fields, from hierarchical self-assembly to developmental morphogenesis. In this paper, we study the analytically solvable example of segmentation in a breakable mass–spring chain elastically linked to a deformable lattice structure. We explicitly construct the complete set of local minima of the energy in this prototypical problem and identify among them the states corresponding to the global energy minima. We show that, even in the continuum limit, the dependence of the segmentation topology on the stretching/pre-stress parameter in this problem takes the form of a devil's type staircase. The peculiar nature of this staircase, characterized by locking in rational microstructures, is of particular importance for biological applications, where its structure may serve as an explanation of the robustness of stress-driven segmentation. This article is part of the themed issue ‘Patterning through instabilities in complex media: theory and applications.’ PMID:28373383

Liquid to liquid extraction and liquid chromatography-tandem mass spectrometry determination of hainanmycin in feed.

PubMed

Wang, Ze Ping; Shen, Jian Zhong; Linhardt, Robert J; Jiang, Hui; Cheng, Lin Li

2017-03-01

Hainanmycin is a new veterinary polyether antibiotic and has few sensitive analytical method in present days. In this study, a liquid chromatography-tandem mass spectrometry (LC-MS/MS) relying on multiple reaction monitoring (MRM) detection was developed for analysis of hainanmycin in animal feed. Feed samples were extracted with ethyl acetate and purified by two steps of liquid-liquid extraction (LLE) to get rid of water solvable matrix and lipids one by one. The final simple was analyzed by LC-MS/MS. The LC mobile phase was composed of 0.1% aqueous formic acid and 0.1% formic acidified acetonitrile by gradient elution. Average recoveries ranged from 74.22% to 87.85%, as determined by spiking with 2.0 (LOQ) ∼2500μgkg -1 of hainanmycin. The inter-day and intra-day coefficient of variation was 9.21% to 11.77% and 7.67% to 13.49%, respectively. The limit of detection (LOD) and the limit of quantitation (LOQ) were 0.36μgkg -1 and 2.0μgkg -1 , respectively. Copyright © 2016. Published by Elsevier B.V.

Selected mode of dendritic growth with n-fold symmetry in the presence of a forced flow

NASA Astrophysics Data System (ADS)

Alexandrov, D. V.; Galenko, P. K.

2017-07-01

The effect of n-fold crystal symmetry is investigated for a two-dimensional stable dendritic growth in the presence of a forced convective flow. We consider dendritic growth in a one-component undercooled liquid. The theory is developed for the parabolic solid-liquid surface of dendrite growing at arbitrary growth Péclet numbers keeping in mind small anisotropies of surface energy and growth kinetics. The selection criterion determining the stable growth velocity of the dendritic tip and its stable tip diameter is found on the basis of solvability analysis. The obtained criterion includes previously developed theories of thermally and kinetically controlled dendritic growth with convection for the case of four-fold crystal symmetry. The obtained nonlinear system of equations (representing the selection criterion and undercooling balance) for the determination of dendrite tip velocity and dendrite tip diameter is analytically solved in a parametric form. These exact solutions clearly demonstrate a transition between thermally and kinetically controlled growth regimes. In addition, we show that the dendrites with larger crystal symmetry grow faster than those with smaller symmetry.

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

PubMed

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.

Critical energy flux and mass in solvable theories of 2D dilaton gravity

NASA Astrophysics Data System (ADS)

Fabbri, A.; Navarro-Salas, J.

1998-10-01

In this paper we address the issue of determining the semiclassical threshold for black hole formation in the context of a one-parameter family of theories which continuously interpolates between the RST and BPP models. We find that the results depend significantly on the initial static configuration of the spacetime geometry before the influx of matter is turned on. In some cases there is a critical energy density, given by the Hawking rate of evaporation, as well as a critical mass mcr (eventually vanishing). In others there is neither mcr nor a critical flux.

Geometric Hitting Set for Segments of Few Orientations

DOE PAGES

Fekete, Sandor P.; Huang, Kan; Mitchell, Joseph S. B.; ...

2016-01-13

Here we study several natural instances of the geometric hitting set problem for input consisting of sets of line segments (and rays, lines) having a small number of distinct slopes. These problems model path monitoring (e.g., on road networks) using the fewest sensors (the \\hitting points"). We give approximation algorithms for cases including (i) lines of 3 slopes in the plane, (ii) vertical lines and horizontal segments, (iii) pairs of horizontal/vertical segments. Lastly, we give hardness and hardness of approximation results for these problems. We prove that the hitting set problem for vertical lines and horizontal rays is polynomially solvable.

Application of Finite Element Modeling Methods in Magnetic Resonance Imaging-Based Research and Clinical Management

NASA Astrophysics Data System (ADS)

Fwu, Peter Tramyeon

The medical image is very complex by its nature. Modeling built upon the medical image is challenging due to the lack of analytical solution. Finite element method (FEM) is a numerical technique which can be used to solve the partial differential equations. It utilized the transformation from a continuous domain into solvable discrete sub-domains. In three-dimensional space, FEM has the capability dealing with complicated structure and heterogeneous interior. That makes FEM an ideal tool to approach the medical-image based modeling problems. In this study, I will address the three modeling in (1) photon transport inside the human breast by implanting the radiative transfer equation to simulate the diffuse optical spectroscopy imaging (DOSI) in order to measurement the percent density (PD), which has been proven as a cancer risk factor in mammography. Our goal is to use MRI as the ground truth to optimize the DOSI scanning protocol to get a consistent measurement of PD. Our result shows DOSI measurement is position and depth dependent and proper scanning scheme and body configuration are needed; (2) heat flow in the prostate by implementing the Penne's bioheat equation to evaluate the cooling performance of regional hypothermia during the robot assisted radical prostatectomy for the individual patient in order to achieve the optimal cooling setting. Four factors are taken into account during the simulation: blood abundance, artery perfusion, cooling balloon temperature, and the anatomical distance. The result shows that blood abundance, prostate size, and anatomical distance are significant factors to the equilibrium temperature of neurovascular bundle; (3) shape analysis in hippocampus by using the radial distance mapping, and two registration methods to find the correlation between sub-regional change to the age and cognition performance, which might not reveal in the volumetric analysis. The result gives a fundamental knowledge of normal distribution in young preadolescent children who may be compared to children with, or at risk of, neurological diseases for early diagnosis.

Self-optimized construction of transition rate matrices from accelerated atomistic simulations with Bayesian uncertainty quantification

NASA Astrophysics Data System (ADS)

Swinburne, Thomas D.; Perez, Danny

2018-05-01

A massively parallel method to build large transition rate matrices from temperature-accelerated molecular dynamics trajectories is presented. Bayesian Markov model analysis is used to estimate the expected residence time in the known state space, providing crucial uncertainty quantification for higher-scale simulation schemes such as kinetic Monte Carlo or cluster dynamics. The estimators are additionally used to optimize where exploration is performed and the degree of temperature acceleration on the fly, giving an autonomous, optimal procedure to explore the state space of complex systems. The method is tested against exactly solvable models and used to explore the dynamics of C15 interstitial defects in iron. Our uncertainty quantification scheme allows for accurate modeling of the evolution of these defects over timescales of several seconds.

Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators.

PubMed

Hong, Hyunsuk; Strogatz, Steven H

2011-02-04

We consider a generalization of the Kuramoto model in which the oscillators are coupled to the mean field with random signs. Oscillators with positive coupling are "conformists"; they are attracted to the mean field and tend to synchronize with it. Oscillators with negative coupling are "contrarians"; they are repelled by the mean field and prefer a phase diametrically opposed to it. The model is simple and exactly solvable, yet some of its behavior is surprising. Along with the stationary states one might have expected (a desynchronized state, and a partially-synchronized state, with conformists and contrarians locked in antiphase), it also displays a traveling wave, in which the mean field oscillates at a frequency different from the population's mean natural frequency.

Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

Strategic analysis for safeguards systems: a feasibility study. Volume 2. Appendix

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goldman, A J

1984-12-01

This appendix provides detailed information regarding game theory (strategic analysis) and its potential role in safeguards to supplement the main body of this report. In particualr, it includes an extensive, though not comprehensive review of literature on game theory and on other topics that relate to the formulation of a game-theoretic model (e.g. the payoff functions). The appendix describes the basic form and components of game theory models, and the solvability of various models. It then discusses three basic issues related to the use of strategic analysis in material accounting: (1) its understandability; (2) its viability in regulatory settings; andmore » (3) difficulties in the use of mixed strategies. Each of the components of a game theoretic model are then discussed and related to the present context.« less

Topological Sachdev-Ye-Kitaev model

NASA Astrophysics Data System (ADS)

Zhang, Pengfei; Zhai, Hui

2018-05-01

In this Rapid Communication, we construct a large-N exactly solvable model to study the interplay between interaction and topology, by connecting the Sachdev-Ye-Kitaev (SYK) model with constant hopping. The hopping forms a band structure that can exhibit both topologically trivial and nontrivial phases. Starting from a topologically trivial insulator with zero Hall conductance, we show that the interaction can drive a phase transition to a topologically nontrivial insulator with quantized nonzero Hall conductance, and a single gapless Dirac fermion emerges when the interaction is fine tuned to the critical point. The finite temperature effect is also considered, and we show that the topological phase with a stronger interaction is less stable against temperature. Our model provides a concrete example to illustrate the interacting topological phases and phase transitions, and can shed light on similar problems in physical systems.

Collective Traffic-like Movement of Ants on a Trail: Dynamical Phases and Phase Transitions

NASA Astrophysics Data System (ADS)

Kunwar, Ambarish; John, Alexander; Nishinari, Katsuhiro; Schadschneider, Andreas; Chowdhury, Debashish

2004-11-01

The traffic-like collective movement of ants on a trail can be described by a stochastic cellular automaton model. We have earlier investigated its unusual flow-density relation by using various mean field approximations and computer simulations. In this paper, we study the model following an alternative approach based on the analogy with the zero range process, which is one of the few known exactly solvable stochastic dynamical models. We show that our theory can quantitatively account for the unusual non-monotonic dependence of the average speed of the ants on their density for finite lattices with periodic boundary conditions. Moreover, we argue that the model exhibits a continuous phase transition at the critial density only in a limiting case. Furthermore, we investigate the phase diagram of the model by replacing the periodic boundary conditions by open boundary conditions.

Quantum vertex model for reversible classical computing.

PubMed

Chamon, C; Mucciolo, E R; Ruckenstein, A E; Yang, Z-C

2017-05-12

Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model that exhibits no bulk classical thermodynamic phase transition, independent of the computational circuit. Within our approach the solution of the computation is encoded in the ground state of the vertex model and its complexity is reflected in the dynamics of the relaxation of the system to its ground state. We use thermal annealing with and without 'learning' to explore typical computational problems. We also construct a mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating an approach to reversible classical computation based on state-of-the-art implementations of quantum annealing.

Dissociative recombination by frame transformation to Siegert pseudostates: A comparison with a numerically solvable model

NASA Astrophysics Data System (ADS)

Hvizdoš, Dávid; Váňa, Martin; Houfek, Karel; Greene, Chris H.; Rescigno, Thomas N.; McCurdy, C. William; Čurík, Roman

2018-02-01

We present a simple two-dimensional model of the indirect dissociative recombination process. The model has one electronic and one nuclear degree of freedom and it can be solved to high precision, without making any physically motivated approximations, by employing the exterior complex scaling method together with the finite-elements method and discrete variable representation. The approach is applied to solve a model for dissociative recombination of H2 + in the singlet ungerade channels, and the results serve as a benchmark to test validity of several physical approximations commonly used in the computational modeling of dissociative recombination for real molecular targets. The second, approximate, set of calculations employs a combination of multichannel quantum defect theory and frame transformation into a basis of Siegert pseudostates. The cross sections computed with the two methods are compared in detail for collision energies from 0 to 2 eV.

Quantum vertex model for reversible classical computing

NASA Astrophysics Data System (ADS)

Chamon, C.; Mucciolo, E. R.; Ruckenstein, A. E.; Yang, Z.-C.

2017-05-01

Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model that exhibits no bulk classical thermodynamic phase transition, independent of the computational circuit. Within our approach the solution of the computation is encoded in the ground state of the vertex model and its complexity is reflected in the dynamics of the relaxation of the system to its ground state. We use thermal annealing with and without `learning' to explore typical computational problems. We also construct a mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating an approach to reversible classical computation based on state-of-the-art implementations of quantum annealing.

Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets

NASA Astrophysics Data System (ADS)

Yuzbashyan, Emil A.

2018-05-01

We solve the non-stationary Schrödinger equation for several time-dependent Hamiltonians, such as the BCS Hamiltonian with an interaction strength inversely proportional to time, periodically driven BCS and linearly driven inhomogeneous Dicke models as well as various multi-level Landau-Zener tunneling models. The latter are Demkov-Osherov, bow-tie, and generalized bow-tie models. We show that these Landau-Zener problems and their certain interacting many-body generalizations map to Gaudin magnets in a magnetic field. Moreover, we demonstrate that the time-dependent Schrödinger equation for the above models has a similar structure and is integrable with a similar technique as Knizhnik-Zamolodchikov equations. We also discuss applications of our results to the problem of molecular production in an atomic Fermi gas swept through a Feshbach resonance and to the evaluation of the Landau-Zener transition probabilities.

Repelling Point Bosons

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGuire, J. B.

2011-12-01

There is a body of conventional wisdom that holds that a solvable quantum problem, by virtue of its solvability, is pathological and thus irrelevant. It has been difficult to refute this view owing to the paucity of theoretical constructs and experimental results. Recent experiments involving equivalent ions trapped in a spatial conformation of extreme anisotropic confinement (longitudinal extension tens, hundreds or even thousands of times transverse extension) have modified the view of relevancy, and it is now possible to consider systems previously thought pathological, in particular point Bosons that repel in one dimension. It has been difficult for the experimentalistsmore » to utilize existing theory, mainly due to long-standing theoretical misunderstanding of the relevance of the permutation group, in particular the non-commutativity of translations (periodicity) and transpositions (permutation). This misunderstanding is most easily rectified in the case of repelling Bosons.« less

On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

NASA Astrophysics Data System (ADS)

Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad

2017-01-01

In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.

A new numerical approach for uniquely solvable exterior Riemann-Hilbert problem on region with corners

NASA Astrophysics Data System (ADS)

Zamzamir, Zamzana; Murid, Ali H. M.; Ismail, Munira

2014-06-01

Numerical solution for uniquely solvable exterior Riemann-Hilbert problem on region with corners at offcorner points has been explored by discretizing the related integral equation using Picard iteration method without any modifications to the left-hand side (LHS) and right-hand side (RHS) of the integral equation. Numerical errors for all iterations are converge to the required solution. However, for certain problems, it gives lower accuracy. Hence, this paper presents a new numerical approach for the problem by treating the generalized Neumann kernel at LHS and the function at RHS of the integral equation. Due to the existence of the corner points, Gaussian quadrature is employed which avoids the corner points during numerical integration. Numerical example on a test region is presented to demonstrate the effectiveness of this formulation.

Models and materials for generalized Kitaev magnetism

NASA Astrophysics Data System (ADS)

Winter, Stephen M.; Tsirlin, Alexander A.; Daghofer, Maria; van den Brink, Jeroen; Singh, Yogesh; Gegenwart, Philipp; Valentí, Roser

2017-12-01

The exactly solvable Kitaev model on the honeycomb lattice has recently received enormous attention linked to the hope of achieving novel spin-liquid states with fractionalized Majorana-like excitations. In this review, we analyze the mechanism proposed by Jackeli and Khaliullin to identify Kitaev materials based on spin-orbital dependent bond interactions and provide a comprehensive overview of its implications in real materials. We set the focus on experimental results and current theoretical understanding of planar honeycomb systems (Na2IrO3, α-Li2IrO3, and α-RuCl3), three-dimensional Kitaev materials (β- and γ-Li2IrO3), and other potential candidates, completing the review with the list of open questions awaiting new insights.

Shape selection criterion for cellular array during constrained growth of binary alloys - Need for low gravity experiment

NASA Technical Reports Server (NTRS)

Tewari, Surendra N.; Trivedi, Rohit

1991-01-01

Development of steady-state periodic cellular array is one of the critical problems in the study of nonlinear pattern formation during directional solidification of binary alloys. The criterion which establishes the values of cell tip radius and spacing under given growth condition is not known. Theoretical models, such as marginal stability and microscopic solvability, have been developed for purely diffusive regime. However, the experimental conditions where cellular structures are stable are precisely the ones where the convection effects are predominant. Thus, the critical data for meaningful evaluation of cellular array growth models can only be obtained by partial directional solidification and quenching experiments carried out in the low gravity environment of space.

{\\ {PT}}-symmetric models in curved manifolds

NASA Astrophysics Data System (ADS)

Krejčiřík, David; Siegl, Petr

2010-12-01

We consider the Laplace-Beltrami operator in tubular neighborhoods of curves on two-dimensional Riemannian manifolds, subject to non-Hermitian parity and time preserving boundary conditions. We are interested in the interplay between the geometry and spectrum. After introducing a suitable Hilbert space framework in the general situation, which enables us to realize the Laplace-Beltrami operator as an m-sectorial operator, we focus on solvable models defined on manifolds of constant curvature. In some situations, notably for non-Hermitian Robin-type boundary conditions, we are able to prove either the reality of the spectrum or the existence of complex conjugate pairs of eigenvalues, and establish similarity of the non-Hermitian m-sectorial operators to normal or self-adjoint operators. The study is illustrated by numerical computations.

Mean-Field-Game Model for Botnet Defense in Cyber-Security

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolokoltsov, V. N., E-mail: v.kolokoltsov@warwick.ac.uk; Bensoussan, A.

We initiate the analysis of the response of computer owners to various offers of defence systems against a cyber-hacker (for instance, a botnet attack), as a stochastic game of a large number of interacting agents. We introduce a simple mean-field game that models their behavior. It takes into account both the random process of the propagation of the infection (controlled by the botner herder) and the decision making process of customers. Its stationary version turns out to be exactly solvable (but not at all trivial) under an additional natural assumption that the execution time of the decisions of the customersmore » (say, switch on or out the defence system) is much faster that the infection rates.« less

Analysis of passive scalar advection in parallel shear flows: Sorting of modes at intermediate time scales

NASA Astrophysics Data System (ADS)

Camassa, Roberto; McLaughlin, Richard M.; Viotti, Claudio

2010-11-01

The time evolution of a passive scalar advected by parallel shear flows is studied for a class of rapidly varying initial data. Such situations are of practical importance in a wide range of applications from microfluidics to geophysics. In these contexts, it is well-known that the long-time evolution of the tracer concentration is governed by Taylor's asymptotic theory of dispersion. In contrast, we focus here on the evolution of the tracer at intermediate time scales. We show how intermediate regimes can be identified before Taylor's, and in particular, how the Taylor regime can be delayed indefinitely by properly manufactured initial data. A complete characterization of the sorting of these time scales and their associated spatial structures is presented. These analytical predictions are compared with highly resolved numerical simulations. Specifically, this comparison is carried out for the case of periodic variations in the streamwise direction on the short scale with envelope modulations on the long scales, and show how this structure can lead to "anomalously" diffusive transients in the evolution of the scalar onto the ultimate regime governed by Taylor dispersion. Mathematically, the occurrence of these transients can be viewed as a competition in the asymptotic dominance between large Péclet (Pe) numbers and the long/short scale aspect ratios (LVel/LTracer≡k), two independent nondimensional parameters of the problem. We provide analytical predictions of the associated time scales by a modal analysis of the eigenvalue problem arising in the separation of variables of the governing advection-diffusion equation. The anomalous time scale in the asymptotic limit of large k Pe is derived for the short scale periodic structure of the scalar's initial data, for both exactly solvable cases and in general with WKBJ analysis. In particular, the exactly solvable sawtooth flow is especially important in that it provides a short cut to the exact solution to the eigenvalue problem for the physically relevant vanishing Neumann boundary conditions in linear-shear channel flow. We show that the life of the corresponding modes at large Pe for this case is shorter than the ones arising from shear free zones in the fluid's interior. A WKBJ study of the latter modes provides a longer intermediate time evolution. This part of the analysis is technical, as the corresponding spectrum is dominated by asymptotically coalescing turning points in the limit of large Pe numbers. When large scale initial data components are present, the transient regime of the WKBJ (anomalous) modes evolves into one governed by Taylor dispersion. This is studied by a regular perturbation expansion of the spectrum in the small wavenumber regimes.

History-Dependent Problems with Applications to Contact Models for Elastic Beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bartosz, Krzysztof; Kalita, Piotr; Migórski, Stanisław

We prove an existence and uniqueness result for a class of subdifferential inclusions which involve a history-dependent operator. Then we specialize this result in the study of a class of history-dependent hemivariational inequalities. Problems of such kind arise in a large number of mathematical models which describe quasistatic processes of contact. To provide an example we consider an elastic beam in contact with a reactive obstacle. The contact is modeled with a new and nonstandard condition which involves both the subdifferential of a nonconvex and nonsmooth function and a Volterra-type integral term. We derive a variational formulation of the problemmore » which is in the form of a history-dependent hemivariational inequality for the displacement field. Then, we use our abstract result to prove its unique weak solvability. Finally, we consider a numerical approximation of the model, solve effectively the approximate problems and provide numerical simulations.« less

Phase separation in an exactly solvable model binary solution with three-body interactions and intermolecular bonding.

PubMed

Lungu, Radu P; Huckaby, Dale A; Buzatu, Florin D

2006-02-01

A model is presented in which the bonds of a honeycomb lattice are covered by rodlike molecules of types AA and BB, molecular ends near a common site having both three-body interactions and orientation-dependent bonding between two A molecular ends and between an A and a B molecular end. Phase diagrams corresponding to the separation into AA-rich and BB-rich phases are calculated exactly. Depending on the relative strengths of the interactions, one of several qualitatively different types of phase diagrams can result, including diagrams containing phenomena such as a double critical point or two separate asymmetric closed loops. The model is essentially a limiting case of a previously considered ternary solution model, and it is equivalent to a two-component system of interacting A and B molecules on the sites of a kagomé lattice.

A Temperature-Dependent Phase-Field Model for Phase Separation and Damage

NASA Astrophysics Data System (ADS)

Heinemann, Christian; Kraus, Christiane; Rocca, Elisabetta; Rossi, Riccarda

2017-07-01

In this paper we study a model for phase separation and damage in thermoviscoelastic materials. The main novelty of the paper consists in the fact that, in contrast with previous works in the literature concerning phase separation and damage processes in elastic media, in our model we encompass thermal processes, nonlinearly coupled with the damage, concentration and displacement evolutions. More particularly, we prove the existence of "entropic weak solutions", resorting to a solvability concept first introduced in Feireisl (Comput Math Appl 53:461-490, 2007) in the framework of Fourier-Navier-Stokes systems and then recently employed in Feireisl et al. (Math Methods Appl Sci 32:1345-1369, 2009) and Rocca and Rossi (Math Models Methods Appl Sci 24:1265-1341, 2014) for the study of PDE systems for phase transition and damage. Our global-in-time existence result is obtained by passing to the limit in a carefully devised time-discretization scheme.

Cellular automaton model for molecular traffic jams

NASA Astrophysics Data System (ADS)

Belitsky, V.; Schütz, G. M.

2011-07-01

We consider the time evolution of an exactly solvable cellular automaton with random initial conditions both in the large-scale hydrodynamic limit and on the microscopic level. This model is a version of the totally asymmetric simple exclusion process with sublattice parallel update and thus may serve as a model for studying traffic jams in systems of self-driven particles. We study the emergence of shocks from the microscopic dynamics of the model. In particular, we introduce shock measures whose time evolution we can compute explicitly, both in the thermodynamic limit and for open boundaries where a boundary-induced phase transition driven by the motion of a shock occurs. The motion of the shock, which results from the collective dynamics of the exclusion particles, is a random walk with an internal degree of freedom that determines the jump direction. This type of hopping dynamics is reminiscent of some transport phenomena in biological systems.

Classification of three-state Hamiltonians solvable by the coordinate Bethe ansatz

NASA Astrophysics Data System (ADS)

Crampé, N.; Frappat, L.; Ragoucy, E.

2013-10-01

We classify ‘all’ Hamiltonians with rank 1 symmetry and nearest-neighbour interactions, acting on a periodic three-state spin chain, and solvable through (generalization of) the coordinate Bethe ansatz (CBA). In this way we obtain four multi-parametric extensions of the known 19-vertex Hamiltonians (such as Zamolodchikov-Fateev, Izergin-Korepin and Bariev Hamiltonians). Apart from the 19-vertex Hamiltonians, there exist 17-vertex and 14-vertex Hamiltonians that cannot be viewed as subcases of the 19-vertex ones. In the case of 17-vertex Hamiltonians, we get a generalization of the genus 5 special branch found by Martins, plus three new ones. We also get two 14-vertex Hamiltonians. We solve all these Hamiltonians using CBA, and provide their spectrum, eigenfunctions and Bethe equations. Special attention is given to provide the specifications of our multi-parametric Hamiltonians that give back known Hamiltonians.

Experimentally-induced learned helplessness in adolescents with type 1 diabetes.

PubMed

McLaughlin, Elizabeth; Lefaivre, Marie-josée; Cummings, Elizabeth

2010-05-01

To determine whether adolescents with type 1 diabetes are more at risk for learned helplessness than their healthy peers. Twenty-three adolescents with diabetes and 25 controls completed a solvable or unsolvable concept formation task. All completed pre- and post-task performance and attribution ratings, and later completed an anagram-solving task to determine if perceived helplessness on the first task would negatively impact performance on the second. Participants in the unsolvable condition solved fewer anagrams; those with diabetes did not show weaker performance than controls. Participants in the solvable condition (diabetes and controls) showed an increase in internal attributions from before the concept formation task to after. In the unsolvable condition, only participants with diabetes made more external attributions for their failure. Contrary to the only other controlled study to use this paradigm in youth with chronic illness, adolescents with diabetes were not more susceptible to learned helplessness.

Macroscopic behavior and fluctuation-dissipation response of stochastic ecohydrological systems

NASA Astrophysics Data System (ADS)

Porporato, A. M.

2017-12-01

The coupled dynamics of water, carbon and nutrient cycles in ecohydrological systems is forced by unpredictable and intermittent hydroclimatic fluctuations at different time scales. While modeling and long-term prediction of these complex interactions often requires a probabilistic approach, the resulting stochastic equations however are only solvable in special cases. To obtain information on the behavior of the system one typically has to resort to approximation methods. Here we discuss macroscopic equations for the averages and fluctuation-dissipation estimates for the general correlations between the forcing and the ecohydrological response for the soil moisture-plant biomass interaction and the problem of primary salinization and nitrogen retention in soils.

A Class of time-fractional hemivariational inequalities with application to frictional contact problem

NASA Astrophysics Data System (ADS)

Zeng, Shengda; Migórski, Stanisław

2018-03-01

In this paper a class of elliptic hemivariational inequalities involving the time-fractional order integral operator is investigated. Exploiting the Rothe method and using the surjectivity of multivalued pseudomonotone operators, a result on existence of solution to the problem is established. Then, this abstract result is applied to provide a theorem on the weak solvability of a fractional viscoelastic contact problem. The process is quasistatic and the constitutive relation is modeled with the fractional Kelvin-Voigt law. The friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals. The variational formulation of this problem leads to a fractional hemivariational inequality.

Soliton cellular automaton associated with Dn(1)-crystal B2,s

NASA Astrophysics Data System (ADS)

Misra, Kailash C.; Wilson, Evan A.

2013-04-01

A solvable vertex model in ferromagnetic regime gives rise to a soliton cellular automaton which is a discrete dynamical system in which site variables take on values in a finite set. We study the scattering of a class of soliton cellular automata associated with the U_q(D_n^{(1)})-perfect crystal B2, s. We calculate the combinatorial R matrix for all elements of B2, s ⊗ B2, 1. In particular, we show that the scattering rule for our soliton cellular automaton can be identified with the combinatorial R matrix for U_q(A_1^{(1)}) oplus U_q(D_{n-2}^{(1)})-crystals.

Exactly solvable Schrödinger equation with double-well potential for hydrogen bond

NASA Astrophysics Data System (ADS)

Sitnitsky, A. E.

2017-05-01

We construct a double-well potential for which the Schrödinger equation can be exactly solved via reducing to the confluent Heun's one. Thus the wave function is expressed via the confluent Heun's function. The latter is tabulated in Maple so that the obtained solution is easily treated. The potential is infinite at the boundaries of the final interval that makes it to be highly suitable for modeling hydrogen bonds (both ordinary and low-barrier ones). We exemplify theoretical results by detailed treating the hydrogen bond in KHCO3 and show their good agreement with literature experimental data.

Chiral symmetry breaking in a semilocalized magnetic field

NASA Astrophysics Data System (ADS)

Cao, Gaoqing

2018-03-01

In this work, we explore the pattern of chiral symmetry breaking and restoration in a solvable magnetic field configuration within the Nambu-Jona-Lasinio model. The special semilocalized static magnetic field can roughly mimic the realistic situation in peripheral heavy ion collisions; thus, the study is important for the dynamical evolution of quark matter. We find that the magnetic-field-dependent contribution from discrete spectra usually dominates over the contribution from continuum spectra and chiral symmetry breaking is locally catalyzed by both the magnitude and scale of the magnetic field. The study is finally extended to the case with finite temperature or chemical potential.

Time dependence of correlation functions following a quantum quench.

PubMed

Calabrese, Pasquale; Cardy, John

2006-04-07

We show that the time dependence of correlation functions in an extended quantum system in d dimensions, which is prepared in the ground state of some Hamiltonian and then evolves without dissipation according to some other Hamiltonian, may be extracted using methods of boundary critical phenomena in d + 1 dimensions. For d = 1 particularly powerful results are available using conformal field theory. These are checked against those available from solvable models. They may be explained in terms of a picture, valid more generally, whereby quasiparticles, entangled over regions of the order of the correlation length in the initial state, then propagate classically through the system.

Energy spectra of vibron and cluster models in molecular and nuclear systems

NASA Astrophysics Data System (ADS)

Jalili Majarshin, A.; Sabri, H.; Jafarizadeh, M. A.

2018-03-01

The relation of the algebraic cluster model, i.e., of the vibron model and its extension, to the collective structure, is discussed. In the first section of the paper, we study the energy spectra of vibron model, for diatomic molecule then we derive the rotation-vibration spectrum of 2α, 3α and 4α configuration in the low-lying spectrum of 8Be, 12C and 16O nuclei. All vibrational and rotational states with ground and excited A, E and F states appear to have been observed, moreover the transitional descriptions of the vibron model and α-cluster model were considered by using an infinite-dimensional algebraic method based on the affine \\widehat{SU(1,1)} Lie algebra. The calculated energy spectra are compared with experimental data. Applications to the rotation-vibration spectrum for the diatomic molecule and many-body nuclear clusters indicate that there are solvable models and they can be approximated very well using the transitional theory.

Treatment of charge singularities in implicit solvent models.

PubMed

Geng, Weihua; Yu, Sining; Wei, Guowei

2007-09-21

This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green's function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2 A for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.

Treatment of charge singularities in implicit solvent models

NASA Astrophysics Data System (ADS)

Geng, Weihua; Yu, Sining; Wei, Guowei

2007-09-01

This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green's function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2Å for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.

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

PubMed Central

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

1990-01-01

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

Development of guidelines for the definition of the relavant information content in data classes

NASA Technical Reports Server (NTRS)

Schmitt, E.

1973-01-01

The problem of experiment design is defined as an information system consisting of information source, measurement unit, environmental disturbances, data handling and storage, and the mathematical analysis and usage of data. Based on today's concept of effective computability, general guidelines for the definition of the relevant information content in data classes are derived. The lack of a universally applicable information theory and corresponding mathematical or system structure is restricting the solvable problem classes to a small set. It is expected that a new relativity theory of information, generally described by a universal algebra of relations will lead to new mathematical models and system structures capable of modeling any well defined practical problem isomorphic to an equivalence relation at any corresponding level of abstractness.

Nonclassical Kinetics of Clonal yet Heterogeneous Enzymes.

PubMed

Park, Seong Jun; Song, Sanggeun; Jeong, In-Chun; Koh, Hye Ran; Kim, Ji-Hyun; Sung, Jaeyoung

2017-07-06

Enzyme-to-enzyme variation in the catalytic rate is ubiquitous among single enzymes created from the same genetic information, which persists over the lifetimes of living cells. Despite advances in single-enzyme technologies, the lack of an enzyme reaction model accounting for the heterogeneous activity of single enzymes has hindered a quantitative understanding of the nonclassical stochastic outcome of single enzyme systems. Here we present a new statistical kinetics and exactly solvable models for clonal yet heterogeneous enzymes with possibly nonergodic state dynamics and state-dependent reactivity, which enable a quantitative understanding of modern single-enzyme experimental results for the mean and fluctuation in the number of product molecules created by single enzymes. We also propose a new experimental measure of the heterogeneity and nonergodicity for a system of enzymes.

An Exactly Solvable Spin Chain Related to Hahn Polynomials

NASA Astrophysics Data System (ADS)

Stoilova, Neli I.; van der Jeugt, Joris

2011-03-01

We study a linear spin chain which was originally introduced by Shi et al. [Phys. Rev. A 71 (2005), 032309, 5 pages], for which the coupling strength contains a parameter α and depends on the parity of the chain site. Extending the model by a second parameter β, it is shown that the single fermion eigenstates of the Hamiltonian can be computed in explicit form. The components of these eigenvectors turn out to be Hahn polynomials with parameters (α,β) and (α+1,β-1). The construction of the eigenvectors relies on two new difference equations for Hahn polynomials. The explicit knowledge of the eigenstates leads to a closed form expression for the correlation function of the spin chain. We also discuss some aspects of a q-extension of this model.

Nonequilibrium Chromosome Looping via Molecular Slip Links

NASA Astrophysics Data System (ADS)

Brackley, C. A.; Johnson, J.; Michieletto, D.; Morozov, A. N.; Nicodemi, M.; Cook, P. R.; Marenduzzo, D.

2017-09-01

We propose a model for the formation of chromatin loops based on the diffusive sliding of molecular slip links. These mimic the behavior of molecules like cohesin, which, along with the CTCF protein, stabilize loops which contribute to organizing the genome. By combining 3D Brownian dynamics simulations and 1D exactly solvable nonequilibrium models, we show that diffusive sliding is sufficient to account for the strong bias in favor of convergent CTCF-mediated chromosome loops observed experimentally. We also find that the diffusive motion of multiple slip links along chromatin is rectified by an intriguing ratchet effect that arises if slip links bind to the chromatin at a preferred "loading site." This emergent collective behavior favors the extrusion of loops which are much larger than the ones formed by single slip links.

Global strong solutions to the one-dimensional heat-conductive model for planar non-resistive magnetohydrodynamics with large data

NASA Astrophysics Data System (ADS)

Li, Yang

2018-06-01

In this paper, we consider the initial-boundary value problem to the one-dimensional compressible heat-conductive model for planar non-resistive magnetohydrodynamics. By making full use of the effective viscous flux and an analogue, together with the structure of the equations, global existence and uniqueness of strong solutions are obtained on condition that the initial density is bounded below away from vacuum and the heat conductivity coefficient κ satisfies the growth condition κ _1(1+θ^{α })≤ κ (θ)≤ κ _2(1+θ^{α }),\\quad { for some }0< α < ∞, with κ _1,κ _2 being positive constants. Moreover, global solvability of strong solutions is shown with the initial vacuum. The results are obtained without any smallness restriction to the initial data.

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

NASA Astrophysics Data System (ADS)

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

2015-06-01

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

Character expansion methods for matrix models of dually weighted graphs

NASA Astrophysics Data System (ADS)

Kazakov, Vladimir A.; Staudacher, Matthias; Wynter, Thomas

1996-04-01

We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally due to Itzykson and Di Francesco, and then demonstrate how to take the large N limit of this expansion. The relationship to the usual matrix model resolvent is elucidated. Our methods give as a by-product an extremely simple derivation of the Migdal integral equation describing the large N limit of the Itzykson-Zuber formula. We illustrate and check our methods by analysing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphys possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating the equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problems of phase transitions from random to flat lattices. January 1995

a Framework for Voxel-Based Global Scale Modeling of Urban Environments

NASA Astrophysics Data System (ADS)

Gehrung, Joachim; Hebel, Marcus; Arens, Michael; Stilla, Uwe

2016-10-01

The generation of 3D city models is a very active field of research. Modeling environments as point clouds may be fast, but has disadvantages. These are easily solvable by using volumetric representations, especially when considering selective data acquisition, change detection and fast changing environments. Therefore, this paper proposes a framework for the volumetric modeling and visualization of large scale urban environments. Beside an architecture and the right mix of algorithms for the task, two compression strategies for volumetric models as well as a data quality based approach for the import of range measurements are proposed. The capabilities of the framework are shown on a mobile laser scanning dataset of the Technical University of Munich. Furthermore the loss of the compression techniques is evaluated and their memory consumption is compared to that of raw point clouds. The presented results show that generation, storage and real-time rendering of even large urban models are feasible, even with off-the-shelf hardware.

The Role of Proof in Comprehending and Teaching Elementary Linear Algebra.

ERIC Educational Resources Information Center

Uhlig, Frank

2002-01-01

Describes how elementary linear algebra can be taught successfully while introducing students to the concept and practice of mathematical proof. Suggests exploring the concept of solvability of linear systems first via the row echelon form (REF). (Author/KHR)

Geometric rectification for nanoscale vibrational energy harvesting

NASA Astrophysics Data System (ADS)

Bustos-Marún, Raúl A.

2018-02-01

In this work, we present a mechanism that, based on quantum-mechanical principles, allows one to recover kinetic energy at the nanoscale. Our premise is that very small mechanical excitations, such as those arising from sound waves propagating through a nanoscale system or similar phenomena, can be quite generally converted into useful electrical work by applying the same principles behind conventional adiabatic quantum pumping. The proposal is potentially useful for nanoscale vibrational energy harvesting where it can have several advantages. The most important one is that it avoids the use of classical rectification mechanisms as it is based on what we call geometric rectification. We show that this geometric rectification results from applying appropriate but quite general initial conditions to damped harmonic systems coupled to electronic reservoirs. We analyze an analytically solvable example consisting of a wire suspended over permanent charges where we find the condition for maximizing the pumped charge. We also studied the effects of coupling the system to a capacitor including the effect of current-induced forces and analyzing the steady-state voltage of operation. Finally, we show how quantum effects can be used to boost the performance of the proposed device.

WPS mediation: An approach to process geospatial data on different computing backends

NASA Astrophysics Data System (ADS)

Giuliani, Gregory; Nativi, Stefano; Lehmann, Anthony; Ray, Nicolas

2012-10-01

The OGC Web Processing Service (WPS) specification allows generating information by processing distributed geospatial data made available through Spatial Data Infrastructures (SDIs). However, current SDIs have limited analytical capacities and various problems emerge when trying to use them in data and computing-intensive domains such as environmental sciences. These problems are usually not or only partially solvable using single computing resources. Therefore, the Geographic Information (GI) community is trying to benefit from the superior storage and computing capabilities offered by distributed computing (e.g., Grids, Clouds) related methods and technologies. Currently, there is no commonly agreed approach to grid-enable WPS. No implementation allows one to seamlessly execute a geoprocessing calculation following user requirements on different computing backends, ranging from a stand-alone GIS server up to computer clusters and large Grid infrastructures. Considering this issue, this paper presents a proof of concept by mediating different geospatial and Grid software packages, and by proposing an extension of WPS specification through two optional parameters. The applicability of this approach will be demonstrated using a Normalized Difference Vegetation Index (NDVI) mediated WPS process, highlighting benefits, and issues that need to be further investigated to improve performances.

Perturbative stability of SFT-based cosmological models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Galli, Federico; Koshelev, Alexey S., E-mail: fgalli@tena4.vub.ac.be, E-mail: alexey.koshelev@vub.ac.be

2011-05-01

We review the appearance of multiple scalar fields in linearized SFT based cosmological models with a single non-local scalar field. Some of these local fields are canonical real scalar fields and some are complex fields with unusual coupling. These systems only admit numerical or approximate analysis. We introduce a modified potential for multiple scalar fields that makes the system exactly solvable in the cosmological context of Friedmann equations and at the same time preserves the asymptotic behavior expected from SFT. The main part of the paper consists of the analysis of inhomogeneous cosmological perturbations in this system. We show numericallymore » that perturbations corresponding to the new type of complex fields always vanish. As an example of application of this model we consider an explicit construction of the phantom divide crossing and prove the perturbative stability of this process at the linear order. The issue of ghosts and ways to resolve it are briefly discussed.« less

Trading strategies for distribution company with stochastic distributed energy resources

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Chunyu; Wang, Qi; Wang, Jianhui

2016-09-01

This paper proposes a methodology to address the trading strategies of a proactive distribution company (PDISCO) engaged in the transmission-level (TL) markets. A one-leader multi-follower bilevel model is presented to formulate the gaming framework between the PDISCO and markets. The lower-level (LL) problems include the TL day-ahead market and scenario-based real-time markets, respectively with the objectives of maximizing social welfare and minimizing operation cost. The upper-level (UL) problem is to maximize the PDISCO’s profit across these markets. The PDISCO’s strategic offers/bids interactively influence the outcomes of each market. Since the LL problems are linear and convex, while the UL problemmore » is non-linear and non-convex, an equivalent primal–dual approach is used to reformulate this bilevel model to a solvable mathematical program with equilibrium constraints (MPEC). The effectiveness of the proposed model is verified by case studies.« less

Simulations of thermodynamics and kinetics on rough energy landscapes with milestoning.

PubMed

Bello-Rivas, Juan M; Elber, Ron

2016-03-05

We investigated by computational means the kinetics and stationary behavior of stochastic dynamics on an ensemble of rough two-dimensional energy landscapes. There are no obvious separations of temporal scales in these systems, which constitute a simple model for the behavior of glasses and some biomaterials. Even though there are significant computational challenges present in these systems due to the large number of metastable states, the Milestoning method is able to compute their kinetic and thermodynamic properties exactly. We observe two clearly distinguished regimes in the overall kinetics: one in which diffusive behavior dominates and another that follows an Arrhenius law (despite the absence of a dominant barrier). We compare our results with those obtained with an exactly-solvable one-dimensional model, and with the results from the rough one-dimensional energy model introduced by Zwanzig. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Ising Criticality of the Clock Model from Density of States Obtained by the Replica Exchange-Wang-Landau Method

NASA Astrophysics Data System (ADS)

Cadilhe, Antonio

2018-04-01

We performed extensive simulations, using the Replica Exchange-Wang-Landau method, of the clock model for orders 3 and 4 on a square lattice, where critical behaviors are expected to belong to the Ising universality class. Though order 2 represents the Ising model, thus, being exactly solvable in two-dimensions, we still provide such results for comparison to the other two orders. Results for various energy related quantities such as the mean energy per spin, specific heat, as well as logarithm scaling of the peak of the specific heat are presented and shown to follow Ising behavior. Additionally, we also present results related to magnetic quantities, such as the magnetization, magnetic susceptibility, and corresponding scaling behavior of the peak of the magnetic susceptibility. Again, our results show scaling in conformity to Ising critical behavior.

Excitation basis for (3+1)d topological phases

NASA Astrophysics Data System (ADS)

Delcamp, Clement

2017-12-01

We consider an exactly solvable model in 3+1 dimensions, based on a finite group, which is a natural generalization of Kitaev's quantum double model. The corresponding lattice Hamiltonian yields excitations located at torus-boundaries. By cutting open the three-torus, we obtain a manifold bounded by two tori which supports states satisfying a higher-dimensional version of Ocneanu's tube algebra. This defines an algebraic structure extending the Drinfel'd double. Its irreducible representations, labeled by two fluxes and one charge, characterize the torus-excitations. The tensor product of such representations is introduced in order to construct a basis for (3+1)d gauge models which relies upon the fusion of the defect excitations. This basis is defined on manifolds of the form Σ × S_1 , with Σ a two-dimensional Riemann surface. As such, our construction is closely related to dimensional reduction from (3+1)d to (2+1)d topological orders.

Physics of the Kitaev Model: Fractionalization, Dynamic Correlations, and Material Connections

NASA Astrophysics Data System (ADS)

Hermanns, M.; Kimchi, I.; Knolle, J.

2018-03-01

Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples - they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li)2IrO3 iridates and RuCl3. In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.

A Nonlinear Elasticity Model of Macromolecular Conformational Change Induced by Electrostatic Forces

PubMed Central

Zhou, Y. C.; Holst, Michael; McCammon, J. Andrew

2008-01-01

In this paper we propose a nonlinear elasticity model of macromolecular conformational change (deformation) induced by electrostatic forces generated by an implicit solvation model. The Poisson-Boltzmann equation for the electrostatic potential is analyzed in a domain varying with the elastic deformation of molecules, and a new continuous model of the electrostatic forces is developed to ensure solvability of the nonlinear elasticity equations. We derive the estimates of electrostatic forces corresponding to four types of perturbations to an electrostatic potential field, and establish the existance of an equilibrium configuration using a fixed-point argument, under the assumption that the change in the ionic strength and charges due to the additional molecules causing the deformation are sufficiently small. The results are valid for elastic models with arbitrarily complex dielectric interfaces and cavities, and can be generalized to large elastic deformation caused by high ionic strength, large charges, and strong external fields by using continuation methods. PMID:19461946

Administration Planning for Tomorrow.

ERIC Educational Resources Information Center

Murray, Albert

After defining administrative planning and outlining deficits and gains of the past 20 years in American schooling, this address underlines the necessity for educational restructuring. Specifically, educational leaders need to: (1) gather data determining the status quo and suggest incremental improvements; (2) address new solvable challenges and…

Solvable Quantum Macroscopic Motions and Decoherence Mechanisms in Quantum Mechanics on Nonstandard Space

NASA Technical Reports Server (NTRS)

Kobayashi, Tsunehiro

1996-01-01

Quantum macroscopic motions are investigated in the scheme consisting of N-number of harmonic oscillators in terms of ultra-power representations of nonstandard analysis. Decoherence is derived from the large internal degrees of freedom of macroscopic matters.

Local and nonlocal order parameters in the Kitaev chain

NASA Astrophysics Data System (ADS)

Chitov, Gennady Y.

2018-02-01

We have calculated order parameters for the phases of the Kitaev chain with interaction and dimerization at a special symmetric point applying the Jordan-Wigner and other duality transformations. We use string order parameters (SOPs) defined via the correlation functions of the Majorana string operators. The SOPs are mapped onto the local order parameters of some dual Hamiltonians and easily calculated. We have shown that the phase diagram of the interacting dimerized chain comprises the phases with the conventional local order as well as the phases with nonlocal SOPs. From the results for the critical indices, we infer the two-dimensional Ising universality class of criticality at the particular symmetry point where the model is exactly solvable.

Analysis of a Two-Dimensional Thermal Cloaking Problem on the Basis of Optimization

NASA Astrophysics Data System (ADS)

Alekseev, G. V.

2018-04-01

For a two-dimensional model of thermal scattering, inverse problems arising in the development of tools for cloaking material bodies on the basis of a mixed thermal cloaking strategy are considered. By applying the optimization approach, these problems are reduced to optimization ones in which the role of controls is played by variable parameters of the medium occupying the cloaking shell and by the heat flux through a boundary segment of the basic domain. The solvability of the direct and optimization problems is proved, and an optimality system is derived. Based on its analysis, sufficient conditions on the input data are established that ensure the uniqueness and stability of optimal solutions.

Probing quantum frustrated systems via factorization of the ground state.

PubMed

Giampaolo, Salvatore M; Adesso, Gerardo; Illuminati, Fabrizio

2010-05-21

The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling transitions determines the range of applicability of mean-field descriptions in biological and physical problems such as stochastic gene expression and the stability of long-period modulated structures.

Dynamic history-dependent variational-hemivariational inequalities with applications to contact mechanics

NASA Astrophysics Data System (ADS)

Migórski, Stanislaw; Ogorzaly, Justyna

2017-02-01

In the paper we deliver a new existence and uniqueness result for a class of abstract nonlinear variational-hemivariational inequalities which are governed by two operators depending on the history of the solution, and include two nondifferentiable functionals, a convex and a nonconvex one. Then, we consider an initial boundary value problem which describes a model of evolution of a viscoelastic body in contact with a foundation. The contact process is assumed to be dynamic, and the friction is described by subdifferential boundary conditions. Both the constitutive law and the contact condition involve memory operators. As an application of the abstract theory, we provide a result on the unique weak solvability of the contact problem.

Liouvillian propagators, Riccati equation and differential Galois theory

NASA Astrophysics Data System (ADS)

Acosta-Humánez, Primitivo; Suazo, Erwin

2013-11-01

In this paper a Galoisian approach to building propagators through Riccati equations is presented. The main result corresponds to the relationship between the Galois integrability of the linear Schrödinger equation and the virtual solvability of the differential Galois group of its associated characteristic equation. As the main application of this approach we solve Ince’s differential equation through the Hamiltonian algebrization procedure and the Kovacic algorithm to find the propagator for a generalized harmonic oscillator. This propagator has applications which describe the process of degenerate parametric amplification in quantum optics and light propagation in a nonlinear anisotropic waveguide. Toy models of propagators inspired by integrable Riccati equations and integrable characteristic equations are also presented.

Microscopic boson approach to nuclear collective motion

NASA Astrophysics Data System (ADS)

Kuchta, R.

1989-10-01

A quantum mechanical approach to the maximally decoupled nuclear collective motion is proposed. The essential idea is to transcribe the original shell-model hamiltonian in terms of boson operators, then to isolate the collective one-boson eigenstates of the mapped hamiltonian and to perform a canonical transformation which eliminates (up to the two-body terms) the coupling between the collective and noncollective bosons. Unphysical states arising due to the violation of the Pauli principle in the boson space are identified and removed within a suitable approximation. The method is applied to study the low-lying collective states of nuclei which are successfully described by the exactly solvable multi-level pairing hamiltonian (Sn, Ni, Pb).

The origin of nulls mode changes and timing noise in pulsars

NASA Astrophysics Data System (ADS)

Jones, P. B.

A solvable polar cap model obtained previously has normal states which may be associated with radio emission and null states. The solutions cannot be time-independent; the neutron star surface temperature T and mean surface nuclear charge Z are both functions of time. The normal and null states, and the transitions between them, form closed cycles in the T-Z plane. Normal-null transitions can occur inside a fraction of the area on the neutron star surface intersected by open magnetic flux lines. The fraction increases with pulsar period and becomes unity when the pulsar nears extinction. Frequency noise, mode changes, and pulse nulls have a common explanation in the transitions.

The origin of nulls, mode changes and timing noise in pulsars

NASA Astrophysics Data System (ADS)

Jones, P. B.

1982-09-01

A solvable polar cap model obtained previously has normal states which may be associated with radio emission, and null states. The solutions cannot be time-independent; the neutron star surface temperature T and mean surface nuclear charge Z are both functions of time. The normal and null states and the transitions between them, form closed cycles in the T-Z plane. Normal-null transitions can occur inside a fraction of the area of the neutron star surface intersected by open magnetic flux lines. The fraction increases with pulsar period and becomes unity when the pulsar nears extinction. Frequency noise, mode changes and pulse nulls have a common explanation in the transitions.

Summing Feynman graphs by Monte Carlo: Planar ϕ3-theory and dynamically triangulated random surfaces

NASA Astrophysics Data System (ADS)

Boulatov, D. V.; Kazakov, V. A.

1988-12-01

New combinatorial identities are suggested relating the ratio of (n - 1)th and nth orders of (planar) perturbation expansion for any quantity to some average over the ensemble of all planar graphs of the nth order. These identities are used for Monte Carlo calculation of critical exponents γstr (string susceptibility) in planar ϕ3-theory and in the dynamically triangulated random surface (DTRS) model near the convergence circle for various dimensions. In the solvable case D = 1 the exact critical properties of the theory are reproduced numerically. After August 3, 1988 the address will be: Cybernetics Council, Academy of Science, ul. Vavilova 40, 117333 Moscow, USSR.

Production of Entanglement Entropy by Decoherence

NASA Astrophysics Data System (ADS)

Merkli, M.; Berman, G. P.; Sayre, R. T.; Wang, X.; Nesterov, A. I.

We examine the dynamics of entanglement entropy of all parts in an open system consisting of a two-level dimer interacting with an environment of oscillators. The dimer-environment interaction is almost energy conserving. We find the precise link between decoherence and production of entanglement entropy. We show that not all environment oscillators carry significant entanglement entropy and we identify the oscillator frequency regions which contribute to the production of entanglement entropy. For energy conserving dimer-environment interactions the models are explicitly solvable and our results hold for all dimer-environment coupling strengths. We carry out a mathematically rigorous perturbation theory around the energy conserving situation in the presence of small non-energy conserving interactions.

Charge transfer excitations from exact and approximate ensemble Kohn-Sham theory

NASA Astrophysics Data System (ADS)

Gould, Tim; Kronik, Leeor; Pittalis, Stefano

2018-05-01

By studying the lowest excitations of an exactly solvable one-dimensional soft-Coulomb molecular model, we show that components of Kohn-Sham ensembles can be used to describe charge transfer processes. Furthermore, we compute the approximate excitation energies obtained by using the exact ensemble densities in the recently formulated ensemble Hartree-exchange theory [T. Gould and S. Pittalis, Phys. Rev. Lett. 119, 243001 (2017)]. Remarkably, our results show that triplet excitations are accurately reproduced across a dissociation curve in all cases tested, even in systems where ground state energies are poor due to strong static correlations. Singlet excitations exhibit larger deviations from exact results but are still reproduced semi-quantitatively.

Quantum Discord Preservation for Two Quantum-Correlated Qubits in Two Independent Reserviors

NASA Astrophysics Data System (ADS)

Xu, Lan

2018-03-01

We investigate the dynamics of quantum discord using an exactly solvable model where two qubits coupled to independent thermal environments. The quantum discord is employed as a non-classical correlation quantifier. By studying the quantum discord of a class of initial states, we find discord remains preserve for a finite time. The effects of the temperature, initial-state parameter, system-reservoir coupling constant and temperature difference parameter of the two independent reserviors are also investigated. We discover that the quantum nature loses faster in high temperature, however, one can extend the time of quantum nature by choosing smaller system-reservoir coupling constant, larger certain initial-state parameter and larger temperature difference parameter.

Solution of the determinantal assignment problem using the Grassmann matrices

NASA Astrophysics Data System (ADS)

Karcanias, Nicos; Leventides, John

2016-02-01

The paper provides a direct solution to the determinantal assignment problem (DAP) which unifies all frequency assignment problems of the linear control theory. The current approach is based on the solvability of the exterior equation ? where ? is an n -dimensional vector space over ? which is an integral part of the solution of DAP. New criteria for existence of solution and their computation based on the properties of structured matrices are referred to as Grassmann matrices. The solvability of this exterior equation is referred to as decomposability of ?, and it is in turn characterised by the set of quadratic Plücker relations (QPRs) describing the Grassmann variety of the corresponding projective space. Alternative new tests for decomposability of the multi-vector ? are given in terms of the rank properties of the Grassmann matrix, ? of the vector ?, which is constructed by the coordinates of ?. It is shown that the exterior equation is solvable (? is decomposable), if and only if ? where ?; the solution space for a decomposable ?, is the space ?. This provides an alternative linear algebra characterisation of the decomposability problem and of the Grassmann variety to that defined by the QPRs. Further properties of the Grassmann matrices are explored by defining the Hodge-Grassmann matrix as the dual of the Grassmann matrix. The connections of the Hodge-Grassmann matrix to the solution of exterior equations are examined, and an alternative new characterisation of decomposability is given in terms of the dimension of its image space. The framework based on the Grassmann matrices provides the means for the development of a new computational method for the solutions of the exact DAP (when such solutions exist), as well as computing approximate solutions, when exact solutions do not exist.

Thermodynamically Constrained Averaging Theory (TCAT) Two-Phase Flow Model: Derivation, Closure, and Simulation Results

NASA Astrophysics Data System (ADS)

Weigand, T. M.; Miller, C. T.; Dye, A. L.; Gray, W. G.; McClure, J. E.; Rybak, I.

2015-12-01

The thermodynamically constrained averaging theory (TCAT) has been usedto formulate general classes of porous medium models, including newmodels for two-fluid-phase flow. The TCAT approach provides advantagesthat include a firm connection between the microscale, or pore scale,and the macroscale; a thermodynamically consistent basis; explicitinclusion of factors such as interfacial areas, contact angles,interfacial tension, and curvatures; and dynamics of interface movementand relaxation to an equilibrium state. In order to render the TCATmodel solvable, certain closure relations are needed to relate fluidpressure, interfacial areas, curvatures, and relaxation rates. In thiswork, we formulate and solve a TCAT-based two-fluid-phase flow model. We detail the formulation of the model, which is a specific instancefrom a hierarchy of two-fluid-phase flow models that emerge from thetheory. We show the closure problem that must be solved. Using recentresults from high-resolution microscale simulations, we advance a set ofclosure relations that produce a closed model. Lastly, we solve the model using a locally conservative numerical scheme and compare the TCAT model to the traditional model.

Magnetic and magnetocaloric properties of the exactly solvable mixed-spin Ising model on a decorated triangular lattice in a magnetic field

NASA Astrophysics Data System (ADS)

Gálisová, Lucia; Strečka, Jozef

2018-05-01

The ground state, zero-temperature magnetization process, critical behaviour and isothermal entropy change of the mixed-spin Ising model on a decorated triangular lattice in a magnetic field are exactly studied after performing the generalized decoration-iteration mapping transformation. It is shown that both the inverse and conventional magnetocaloric effect can be found near the absolute zero temperature. The former phenomenon can be found in a vicinity of the discontinuous phase transitions and their crossing points, while the latter one occurs in some paramagnetic phases due to a spin frustration to be present at zero magnetic field. The inverse magnetocaloric effect can also be detected slightly above continuous phase transitions following the power-law dependence | - ΔSisomin | ∝hn, where n depends basically on the ground-state spin ordering.

Path Integral Computation of Quantum Free Energy Differences Due to Alchemical Transformations Involving Mass and Potential.

PubMed

Pérez, Alejandro; von Lilienfeld, O Anatole

2011-08-09

Thermodynamic integration, perturbation theory, and λ-dynamics methods were applied to path integral molecular dynamics calculations to investigate free energy differences due to "alchemical" transformations. Several estimators were formulated to compute free energy differences in solvable model systems undergoing changes in mass and/or potential. Linear and nonlinear alchemical interpolations were used for the thermodynamic integration. We find improved convergence for the virial estimators, as well as for the thermodynamic integration over nonlinear interpolation paths. Numerical results for the perturbative treatment of changes in mass and electric field strength in model systems are presented. We used thermodynamic integration in ab initio path integral molecular dynamics to compute the quantum free energy difference of the isotope transformation in the Zundel cation. The performance of different free energy methods is discussed.

Majorana fermion surface code for universal quantum computation

DOE PAGES

Vijay, Sagar; Hsieh, Timothy H.; Fu, Liang

2015-12-10

In this study, we introduce an exactly solvable model of interacting Majorana fermions realizing Z 2 topological order with a Z 2 fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid-state systems, including topological insulators, nanowires, or two-dimensional electron gases, proximitized by s-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physicalmore » ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.« less

Interplay between cost and benefits triggers nontrivial vaccination uptake

NASA Astrophysics Data System (ADS)

Steinegger, Benjamin; Cardillo, Alessio; Rios, Paolo De Los; Gómez-Gardeñes, Jesús; Arenas, Alex

2018-03-01

The containment of epidemic spreading is a major challenge in science. Vaccination, whenever available, is the best way to prevent the spreading, because it eventually immunizes individuals. However, vaccines are not perfect, and total immunization is not guaranteed. Imperfect immunization has driven the emergence of antivaccine movements that totally alter the predictions about the epidemic incidence. Here, we propose a mathematically solvable mean-field vaccination model to mimic the spontaneous adoption of vaccines against influenzalike diseases and the expected epidemic incidence. The results are in agreement with extensive Monte Carlo simulations of the epidemics and vaccination coevolutionary processes. Interestingly, the results reveal a nonmonotonic behavior on the vaccination coverage that increases with the imperfection of the vaccine and after decreases. This apparent counterintuitive behavior is analyzed and understood from stability principles of the proposed mathematical model.

Single-machine group scheduling problems with deteriorating and learning effect

NASA Astrophysics Data System (ADS)

Xingong, Zhang; Yong, Wang; Shikun, Bai

2016-07-01

The concepts of deteriorating jobs and learning effects have been individually studied in many scheduling problems. However, most studies considering the deteriorating and learning effects ignore the fact that production efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known as 'group technology' in the literature. In this paper, a new group scheduling model with deteriorating and learning effects is proposed, where learning effect depends not only on job position, but also on the position of the corresponding job group; deteriorating effect depends on its starting time of the job. This paper shows that the makespan and the total completion time problems remain polynomial optimal solvable under the proposed model. In addition, a polynomial optimal solution is also presented to minimise the maximum lateness problem under certain agreeable restriction.

Role of initial state and final quench temperature on aging properties in phase-ordering kinetics.

PubMed

Corberi, Federico; Villavicencio-Sanchez, Rodrigo

2016-05-01

We study numerically the two-dimensional Ising model with nonconserved dynamics quenched from an initial equilibrium state at the temperature T_{i}≥T_{c} to a final temperature T_{f} below the critical one. By considering processes initiating both from a disordered state at infinite temperature T_{i}=∞ and from the critical configurations at T_{i}=T_{c} and spanning the range of final temperatures T_{f}∈[0,T_{c}[ we elucidate the role played by T_{i} and T_{f} on the aging properties and, in particular, on the behavior of the autocorrelation C and of the integrated response function χ. Our results show that for any choice of T_{f}, while the autocorrelation function exponent λ_{C} takes a markedly different value for T_{i}=∞ [λ_{C}(T_{i}=∞)≃5/4] or T_{i}=T_{c} [λ_{C}(T_{i}=T_{c})≃1/8] the response function exponents are unchanged. Supported by the outcome of the analytical solution of the solvable spherical model we interpret this fact as due to the different contributions provided to autocorrelation and response by the large-scale properties of the system. As changing T_{f} is considered, although this is expected to play no role in the large-scale and long-time properties of the system, we show important effects on the quantitative behavior of χ. In particular, data for quenches to T_{f}=0 are consistent with a value of the response function exponent λ_{χ}=1/2λ_{C}(T_{i}=∞)=5/8 different from the one [λ_{χ}∈(0.5-0.56)] found in a wealth of previous numerical determinations in quenches to finite final temperatures. This is interpreted as due to important preasymptotic corrections associated to T_{f}>0.

What One Physicist Has to Offer

NASA Astrophysics Data System (ADS)

Ross, Marc

2004-05-01

I was a particle theorist. In the early 1970s I began to analyze energy and its use in society. My theme is: What can physicists offer on a societal issue like energy? I have four topics: 1) Traffic safety and vehicle mass. The measurements are the record of some 40,000 deaths per year, vehicle characterizations and registrations. The statistical record is good, but information is lacking on physical processes in serious crashes. Our insight: while driver behavior is critical to safety, so is vehicle quality and design. Although one cannot definitively separate the injury impacts associated with momentum transfer from those due to intrusion, mass as such is not critical to safety. 2) Prospects for improving the energy efficiency of industrial processes. Our "measurements" were planning documents and interviews enabling us to analyze which "energy projects" were undertaken and which not. Insight: capital for projects was not allocated according to textbook economics; instead it was rationed. 3) Energy use by cars. Based on dynamometer studies motivated by the 1990 Clean Air Act Amendments, we created models of energy consumption that enable evaluation of modifications such as adopting a small engine while supplementing its capability for power. Insight: Vehicles could be designed to use much less fuel; but the gain for society is offset by low interest by new-car-buyers and manufacturers. 4) The effectiveness of automotive emissions controls. In addition to laboratory studies, we had surveys in "non-attainment" areas. Insight: Controls installed by original manufacturers are more robust and effective than repairs. Of the four, this is the one success for society. Conclusions: There are fascinating and solvable analytical challenges everywhere you look. But applications are hampered by the lack of a heritage and the close coupling between theorists and experimenters we know in physics.

Self-similar dynamics of air film entrained by a solid disk in confined space: A simple prototype of topological transitions

NASA Astrophysics Data System (ADS)

Nakazato, Hana; Yamagishi, Yuki; Okumura, Ko

2018-05-01

In hydrodynamic topological transitions, one mass of fluid breaks into two or two merge into one. For example, in honey-drop formation when honey is dripping from a spoon, honey is extended to separate into two masses as the liquid neck bridging them thins down to the micron scale. At the moment when the topology changes due to the breakup, physical observables such as surface curvature locally diverge. Such singular dynamics has widely attracted physicists, revealing universality in self-similar dynamics, which shares much in common with critical phenomena in thermodynamics. Many experimental examples have been found, including an electric spout and vibration-induced jet eruption. However, only a few cases have been physically understood on the basis of equations that govern the singular dynamics and even in such a case the physical understanding is mathematically complicated, inevitably involving delicate numerical calculations. Here we study the breakup of air film entrained by a solid disk into viscous liquid in a confined space, which leads to formation, thinning, and breakup of the neck of air. As a result, we unexpectedly find that equations governing the neck dynamics can be solved analytically by virtue of two remarkable experimental features: Only a single length scale linearly dependent on time remains near the singularity and two universal scaling functions describing the singular neck shape and velocity field are both analytic. The present solvable case would be essential for a better understanding of the singular dynamics and will help reveal the physics of unresolved examples intimately related to daily-life phenomena and diverse practical applications.

A possible generalization of the harmonic oscillator potential

NASA Technical Reports Server (NTRS)

Levai, Geza

1995-01-01

A four-parameter potential is analyzed, which contains the three-dimensional harmonic oscillator as a special case. This potential is exactly solvable and retains several characteristics of the harmonic oscillator, and also of the Coulomb problem. The possibility of similar generalizations of other potentials is also pointed out.

Arithmetic Word-Problem-Solving in Huntington's Disease

ERIC Educational Resources Information Center

Allain, P.; Verny, C.; Aubin, G.; Pinon, K.; Bonneau, D.; Dubas, F.; Gall, D.L.

2005-01-01

The purpose of this study was to examine executive functioning in patients with Huntington's disease using an arithmetic word-problem-solving task including eight solvable problems of increasing complexity and four aberrant problems. Ten patients with Huntington's disease and 12 normal control subjects matched by age and education were tested.…

Laplace Boundary-Value Problem in Paraboloidal Coordinates

ERIC Educational Resources Information Center

Duggen, L.; Willatzen, M.; Voon, L. C. Lew Yan

2012-01-01

This paper illustrates both a problem in mathematical physics, whereby the method of separation of variables, while applicable, leads to three ordinary differential equations that remain fully coupled via two separation constants and a five-term recurrence relation for series solutions, and an exactly solvable problem in electrostatics, as a…

Project on National Security Reform: Vision Working Group Report and Scenarios

DTIC Science & Technology

2010-07-01

from radiation produced by harmless, everyday substances such as bananas , cat litter, glass, and concrete.40 The DHS began installing first...solvable. The skills are potentially there, but the incentives and then the funding to make them emerge 234 and flower across the whole of the U.S

Statistical properties of fluctuations of time series representing appearances of words in nationwide blog data and their applications: An example of modeling fluctuation scalings of nonstationary time series.

PubMed

Watanabe, Hayafumi; Sano, Yukie; Takayasu, Hideki; Takayasu, Misako

2016-11-01

To elucidate the nontrivial empirical statistical properties of fluctuations of a typical nonsteady time series representing the appearance of words in blogs, we investigated approximately 3×10^{9} Japanese blog articles over a period of six years and analyze some corresponding mathematical models. First, we introduce a solvable nonsteady extension of the random diffusion model, which can be deduced by modeling the behavior of heterogeneous random bloggers. Next, we deduce theoretical expressions for both the temporal and ensemble fluctuation scalings of this model, and demonstrate that these expressions can reproduce all empirical scalings over eight orders of magnitude. Furthermore, we show that the model can reproduce other statistical properties of time series representing the appearance of words in blogs, such as functional forms of the probability density and correlations in the total number of blogs. As an application, we quantify the abnormality of special nationwide events by measuring the fluctuation scalings of 1771 basic adjectives.

Yang-Baxter algebras, integrable theories and Bethe Ansatz

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Vega, H.J.

1990-03-10

This paper presents the Yang-Baxter algebras (YBA) in a general framework stressing their power to exactly solve the lattice models associated to them. The algebraic Behe Ansatz is developed as an eigenvector construction based on the YBA. The six-vertex model solution is given explicitly. The generalization of YB algebras to face language is considered. The algebraic BA for the SOS model of Andrews, Baxter and Forrester is described using these face YB algebras. It is explained how these lattice models yield both solvable massive QFT and conformal models in appropriated scaling (continuous) limits within the lattice light-cone approach. This approachmore » permit to define and solve rigorously massive QFT as an appropriate continuum limit of gapless vertex models. The deep links between the YBA and Lie algebras are analyzed including the quantum groups that underlay the trigonometric/hyperbolic YBA. Braid and quantum groups are derived from trigonometric/hyperbolic YBA in the limit of infinite spectral parameter. To conclude, some recent developments in the domain of integrable theories are summarized.« less

Floating potential in electronegative plasmas for non-zero ion temperatures

NASA Astrophysics Data System (ADS)

Regodón, Guillermo Fernando; Fernández Palop, José Ignacio; Tejero-del-Caz, Antonio; Díaz-Cabrera, Juan Manuel; Carmona-Cabezas, Rafael; Ballesteros, Jerónimo

2018-02-01

The floating potential of a Langmuir probe immersed in an electronegative plasma is studied theoretically under the assumption of radial positive ion fluid movement for non-zero positive ion temperature: both cylindrical and spherical geometries are studied. The model is solvable exactly. The special characteristics of the electronegative pre-sheath are found and the influence of the stratified electronegative pre-sheath is shown to be very small in practical applications. It is suggested that the use of the floating potential in the measurement of negative ions population density is convenient, in view of the numerical results obtained. The differences between the two radial geometries, which become very important for small probe radii of the order of magnitude of the Debye length, are studied.

Localization of massless Dirac particles via spatial modulations of the Fermi velocity

NASA Astrophysics Data System (ADS)

Downing, C. A.; Portnoi, M. E.

2017-08-01

The electrons found in Dirac materials are notorious for being difficult to manipulate due to the Klein phenomenon and absence of backscattering. Here we investigate how spatial modulations of the Fermi velocity in two-dimensional Dirac materials can give rise to localization effects, with either full (zero-dimensional) confinement or partial (one-dimensional) confinement possible depending on the geometry of the velocity modulation. We present several exactly solvable models illustrating the nature of the bound states which arise, revealing how the gradient of the Fermi velocity is crucial for determining fundamental properties of the bound states such as the zero-point energy. We discuss the implications for guiding electronic waves in few-mode waveguides formed by Fermi velocity modulation.

Amplitudes on plane waves from ambitwistor strings

NASA Astrophysics Data System (ADS)

Adamo, Tim; Casali, Eduardo; Mason, Lionel; Nekovar, Stefan

2017-11-01

In marked contrast to conventional string theory, ambitwistor strings remain solvable worldsheet theories when coupled to curved background fields. We use this fact to consider the quantization of ambitwistor strings on plane wave metric and plane wave gauge field backgrounds. In each case, the worldsheet model is anomaly free as a consequence of the background satisfying the field equations. We derive vertex operators (in both fixed and descended picture numbers) for gravitons and gluons on these backgrounds from the worldsheet CFT, and study the 3-point functions of these vertex operators on the Riemann sphere. These worldsheet correlation functions reproduce the known results for 3-point scattering amplitudes of gravitons and gluons in gravitational and gauge theoretic plane wave backgrounds, respectively.

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

NASA Astrophysics Data System (ADS)

Hilbert, Stefan; Dunkel, Jörn

2006-07-01

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

Radical chiral Floquet phases in a periodically driven Kitaev model and beyond

NASA Astrophysics Data System (ADS)

Po, Hoi Chun; Fidkowski, Lukasz; Vishwanath, Ashvin; Potter, Andrew C.

2017-12-01

We theoretically discover a family of nonequilibrium fractional topological phases in which time-periodic driving of a 2D system produces excitations with fractional statistics, and produces chiral quantum channels that propagate a quantized fractional number of qubits along the sample edge during each driving period. These phases share some common features with fractional quantum Hall states, but are sharply distinct dynamical phenomena. Unlike the integer-valued invariant characterizing the equilibrium quantum Hall conductance, these phases are characterized by a dynamical topological invariant that is a square root of a rational number, inspiring the label: radical chiral Floquet phases. We construct solvable models of driven and interacting spin systems with these properties, and identify an unusual bulk-boundary correspondence between the chiral edge dynamics and bulk "anyon time-crystal" order characterized by dynamical transmutation of electric-charge into magnetic-flux excitations in the bulk.

The equal load-sharing model of cascade failures in power grids

NASA Astrophysics Data System (ADS)

Scala, Antonio; De Sanctis Lucentini, Pier Giorgio

2016-11-01

Electric power-systems are one of the most important critical infrastructures. In recent years, they have been exposed to extreme stress due to the increasing power demand, the introduction of distributed renewable energy sources, and the development of extensive interconnections. We investigate the phenomenon of abrupt breakdown of an electric power-system under two scenarios: load growth (mimicking the ever-increasing customer demand) and power fluctuations (mimicking the effects of renewable sources). Our results indicate that increasing the system size causes breakdowns to become more abrupt; in fact, mapping the system to a solvable statistical-physics model indicates the occurrence of a first order transition in the large size limit. Such an enhancement for the systemic risk failures (black-outs) with increasing network size is an effect that should be considered in the current projects aiming to integrate national power-grids into ;super-grids;.

An extension of the Bardeen-Cooper-Schrieffer model of superconductivity

NASA Astrophysics Data System (ADS)

Maćkowiak, J.; Tarasewicz, P.

An extension of the BCS Hamiltonian of HBCS, the form H= HBCS+ W+ V, where W=∑ kγknk+ nk-, V=-| Λ| -1∑ k, k‧ gk, k‧ bk* b- k* b- k‧ bk‧ , nkσ = akσ * akσ , bk= ak+ ak- and akσ *, akσ are fermion creation and annihilation operators, is investigated. It is shown that H represents a solvable mean-field model in the thermodynamic limit. H exhibits a 2nd-order phase transition if W is sufficiently strongly attractive and the low-temperature phase, characterized by two order parameters, contains two condensates: a condensate of BCS-type fermion pairs and a condensate of fermion quadruples with momenta and spins ( p, σ) equal {( p, σ),(- p, σ), ( p,- σ), (- p,- σ)}. If γk<0, a pseudogap is present in the excitation spectrum in the normal phase.

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

NASA Astrophysics Data System (ADS)

Lu, Yanrong; Liao, Fucheng; Deng, Jiamei; Liu, Huiyang

2017-09-01

This paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation.

Simulation of Two-Phase Flow Based on a Thermodynamically Constrained Averaging Theory Flow Model

NASA Astrophysics Data System (ADS)

Weigand, T. M.; Dye, A. L.; McClure, J. E.; Farthing, M. W.; Gray, W. G.; Miller, C. T.

2014-12-01

The thermodynamically constrained averaging theory (TCAT) has been used to formulate general classes of porous medium models, including new models for two-fluid-phase flow. The TCAT approach provides advantages that include a firm connection between the microscale, or pore scale, and the macroscale; a thermodynamically consistent basis; explicit inclusion of factors such as interfacial areas, contact angles, interfacial tension, and curvatures; and dynamics of interface movement and relaxation to an equilibrium state. In order to render the TCAT model solvable, certain closure relations are needed to relate fluid pressure, interfacial areas, curvatures, and relaxation rates. In this work, we formulate and solve a TCAT-based two-fluid-phase flow model. We detail the formulation of the model, which is a specific instance from a hierarchy of two-fluid-phase flow models that emerge from the theory. We show the closure problem that must be solved. Using recent results from high-resolution microscale simulations, we advance a set of closure relations that produce a closed model. Lastly, we use locally conservative spatial discretization and higher order temporal discretization methods to approximate the solution to this new model and compare the solution to the traditional model.

Environment and initial state engineered dynamics of quantum and classical correlations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Cheng-Zhi, E-mail: czczwang@outlook.com; Li, Chun-Xian; Guo, Yu

Based on an open exactly solvable system coupled to an environment with nontrivial spectral density, we connect the features of quantum and classical correlations with some features of the environment, initial states of the system, and the presence of initial system–environment correlations. Some interesting features not revealed before are observed by changing the structure of environment, the initial states of system, and the presence of initial system–environment correlations. The main results are as follows. (1) Quantum correlations exhibit temporary freezing and permanent freezing even at high temperature of the environment, for which the necessary and sufficient conditions are given bymore » three propositions. (2) Quantum correlations display a transition from temporary freezing to permanent freezing by changing the structure of environment. (3) Quantum correlations can be enhanced all the time, for which the condition is put forward. (4) The one-to-one dependency relationship between all kinds of dynamic behaviors of quantum correlations and the initial states of the system as well as environment structure is established. (5) In the presence of initial system–environment correlations, quantum correlations under local environment exhibit temporary multi-freezing phenomenon. While under global environment they oscillate, revive, and damp, an explanation for which is given. - Highlights: • Various interesting behaviors of quantum and classical correlations are observed in an open exactly solvable model. • The important effects of the bath structure on quantum and classical correlations are revealed. • The one-to-one correspondence between the type of dynamical behavior of quantum discord and the initial state is given. • Quantum correlations are given in the presence of initial qubits–bath correlations.« less

Dissipation in adiabatic quantum computers: lessons from an exactly solvable model

NASA Astrophysics Data System (ADS)

Keck, Maximilian; Montangero, Simone; Santoro, Giuseppe E.; Fazio, Rosario; Rossini, Davide

2017-11-01

We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the interplay between nonadiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (the average value of the Hamiltonian) as a measure of the deviation from reaching the final target ground state. We compute the excess energy in a variety of different situations, where the nature of the bath and the Hamiltonian is modified. We find robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the nonadiabatic effects and the dissipative processes. We compare these results with the matrix-product-operator simulations of an Ising system and show that the phenomenology we found also applies for this more realistic case.

Quantum Quench of the Sachdev-Ye-Kitaev Model

NASA Astrophysics Data System (ADS)

Steinberg, Julia; Eberlein, Andreas; Sachdev, Subir

The Sachdev-Ye-Kitaev model is a single site model containing N flavors of fermions with random infinite range interactions. It is exactly solvable in the large N limit and has an emergent reparameterization symmetry in time at low temperatures and strong coupling. This leads to many interesting properties such as locally critical behavior in correlation functions and the saturation of the chaos bound proposed .We start with the generalized Sachdev-Ye-Kitaev with quadratic and quartic interactions. This Hamiltonian has the form of a 0+1d Fermi liquid and contains long-lived quasiparticles at all values of the quadratic coupling. We quench the system into a locally critical state without quasiparticles by turning off the quadratic coupling at some initial time. We numerically study the spectral function at intermediate and long times and determine the timescale in which the system loses memory of the quasiparticles. J.S. is supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE1144152.

A Cartoon in One Dimension of the Hydrogen Molecular Ion

ERIC Educational Resources Information Center

Dutta, Sourav; Ganguly, Shreemoyee; Dutta-Roy, Binayak

2008-01-01

To illustrate the basic methodology involved in the quantum mechanics of molecules, a one-dimensional caricature of the hydrogen molecular ion (H[superscript +][subscript 2]) is presented, which is exactly solvable, in the Born-Oppenheimer approximation, in terms of elementary functions. The purpose of the exercise is to elucidate in a simple…

Grand Challenges and Great Potential in Foreign Language Teaching and Learning

ERIC Educational Resources Information Center

Hlas, Anne Cummings

2018-01-01

This article argues for the field of foreign languages to begin to identify and define our Grand Challenges, which are difficult yet solvable problems facing our field. Seeking answers to these challenges can provide new opportunities for collaboration and can spur new directions and innovation within language learning and teaching. Researchable…

New Potentials for Old: The Darboux Transformation in Quantum Mechanics

ERIC Educational Resources Information Center

Williams, Brian Wesley; Celius, Tevye C.

2008-01-01

The Darboux transformation in quantum mechanics is reviewed at a basic level. Examples of how this transformation leads to exactly solvable potentials related to the "particle in a box" and the harmonic oscillator are shown in detail. The connection between the Darboux transformation and some modern operator based approaches to quantum mechanics…

Some Schools of Architecture Could Use a Good Architect

ERIC Educational Resources Information Center

Fisher, Thomas

2008-01-01

Like the proverbial shoemaker's child who goes barefoot, many architecture students learn the best practices of their discipline in some of the worst buildings on their campuses. The problems with the newest architecture-school buildings, says the writer, are both similar and solvable. In a new book, teams of architecture faculty members and…

Estimation for bilinear stochastic systems

NASA Technical Reports Server (NTRS)

Willsky, A. S.; Marcus, S. I.

1974-01-01

Three techniques for the solution of bilinear estimation problems are presented. First, finite dimensional optimal nonlinear estimators are presented for certain bilinear systems evolving on solvable and nilpotent lie groups. Then the use of harmonic analysis for estimation problems evolving on spheres and other compact manifolds is investigated. Finally, an approximate estimation technique utilizing cumulants is discussed.

Helping Minority Students Graduate from College--A Comprehensive Approach. ERIC Digest.

ERIC Educational Resources Information Center

Richardson, Richard C., Jr.; de los Santos, Alfredo G., Jr.

Blacks, Hispanics, and American Indians remain less likely to graduate from college than other Americans. This persistent and serious problem is solvable if concerned institutions use a comprehensive approach, implementing 10 principles in order to successfully remove race and ethnicity as factors in college completion. The principles listed are…

Solvability and Regularity for an Elliptic System Prescribing the Curl, Divergence, and Partial Trace of a Vector Field on Sobolev-Class Domains

NASA Astrophysics Data System (ADS)

Cheng, C. H. Arthur; Shkoller, Steve

2017-09-01

We provide a self-contained proof of the solvability and regularity of a Hodge-type elliptic system, wherein the divergence and curl of a vector field u are prescribed in an open, bounded, Sobolev-class domain {Ω \\subseteq R^n}, and either the normal component {{u} \\cdot {N}} or the tangential components of the vector field {{u} × {N}} are prescribed on the boundary {partial Ω}. For {k > n/2}, we prove that u is in the Sobolev space {H^k+1(Ω)} if {Ω} is an {H^k+1}-domain, and the divergence, curl, and either the normal or tangential trace of u has sufficient regularity. The proof is based on a regularity theory for vector elliptic equations set on Sobolev-class domains and with Sobolev-class coefficients, and with a rather general set of Dirichlet and Neumann boundary conditions. The resulting regularity theory for the vector u is fundamental in the analysis of free-boundary and moving interface problems in fluid dynamics.

Generic dynamical phase transition in one-dimensional bulk-driven lattice gases with exclusion

NASA Astrophysics Data System (ADS)

Lazarescu, Alexandre

2017-06-01

Dynamical phase transitions are crucial features of the fluctuations of statistical systems, corresponding to boundaries between qualitatively different mechanisms of maintaining unlikely values of dynamical observables over long periods of time. They manifest themselves in the form of non-analyticities in the large deviation function of those observables. In this paper, we look at bulk-driven exclusion processes with open boundaries. It is known that the standard asymmetric simple exclusion process exhibits a dynamical phase transition in the large deviations of the current of particles flowing through it. That phase transition has been described thanks to specific calculation methods relying on the model being exactly solvable, but more general methods have also been used to describe the extreme large deviations of that current, far from the phase transition. We extend those methods to a large class of models based on the ASEP, where we add arbitrary spatial inhomogeneities in the rates and short-range potentials between the particles. We show that, as for the regular ASEP, the large deviation function of the current scales differently with the size of the system if one considers very high or very low currents, pointing to the existence of a dynamical phase transition between those two regimes: high current large deviations are extensive in the system size, and the typical states associated to them are Coulomb gases, which are highly correlated; low current large deviations do not depend on the system size, and the typical states associated to them are anti-shocks, consistently with a hydrodynamic behaviour. Finally, we illustrate our results numerically on a simple example, and we interpret the transition in terms of the current pushing beyond its maximal hydrodynamic value, as well as relate it to the appearance of Tracy-Widom distributions in the relaxation statistics of such models. , which features invited work from the best early-career researchers working within the scope of J. Phys. A. This project is part of the Journal of Physics series’ 50th anniversary celebrations in 2017. Alexandre Lazarescu was selected by the Editorial Board of J. Phys. A as an Emerging Talent.

On-Line Algorithms and Reverse Mathematics

NASA Astrophysics Data System (ADS)

Harris, Seth

In this thesis, we classify the reverse-mathematical strength of sequential problems. If we are given a problem P of the form ∀X(alpha(X) → ∃Zbeta(X,Z)) then the corresponding sequential problem, SeqP, asserts the existence of infinitely many solutions to P: ∀X(∀nalpha(Xn) → ∃Z∀nbeta(X n,Zn)). P is typically provable in RCA0 if all objects involved are finite. SeqP, however, is only guaranteed to be provable in ACA0. In this thesis we exactly characterize which sequential problems are equivalent to RCA0, WKL0, or ACA0.. We say that a problem P is solvable by an on-line algorithm if P can be solved according to a two-player game, played by Alice and Bob, in which Bob has a winning strategy. Bob wins the game if Alice's sequence of plays 〈a0, ..., ak〉 and Bob's sequence of responses 〈 b0, ..., bk〉 constitute a solution to P. Formally, an on-line algorithm A is a function that inputs an admissible sequence of plays 〈a 0, b0, ..., aj〉 and outputs a new play bj for Bob. (This differs from the typical definition of "algorithm", though quite often a concrete set of instructions can be easily deduced from A.). We show that SeqP is provable in RCA0 precisely when P is solvable by an on-line algorithm. Schmerl proved this result specifically for the graph coloring problem; we generalize Schmerl's result to any problem that is on-line solvable. To prove our separation, we introduce a principle called Predictk(r) that is equivalent to -WKL0 for standard k, r.. We show that WKL0 is sufficient to prove SeqP precisely when P has a solvable closed kernel. This means that a solution exists, and each initial segment of this solution is a solution to the corresponding initial segment of the problem. (Certain bounding conditions are necessary as well.) If no such solution exists, then SeqP is equivalent to ACA0 over RCA 0 + ISigma02; RCA0 alone suffices if only sequences of standard length are considered. We use different techniques from Schmerl to prove this separation, and in the process we improve some of Schmerl's results on Grundy colorings. In Chapter 4 we analyze a variety of applications, classifying their sequential forms by reverse-mathematical strength. This builds upon similar work by Dorais and Hirst and Mummert. We consider combinatorial applications such as matching problems and Dilworth's theorems, and we also consider classic algorithms such as the task scheduling and paging problems. Tables summarizing our findings can be found at the end of Chapter 4.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ko, L.F.

Calculations for the two-point correlation functions in the scaling limit for two statistical models are presented. In Part I, the Ising model with a linear defect is studied for T < T/sub c/ and T > T/sub c/. The transfer matrix method of Onsager and Kaufman is used. The energy-density correlation is given by functions related to the modified Bessel functions. The dispersion expansion for the spin-spin correlation functions are derived. The dominant behavior for large separations at T not equal to T/sub c/ is extracted. It is shown that these expansions lead to systems of Fredholm integral equations. Inmore » Part II, the electric correlation function of the eight-vertex model for T < T/sub c/ is studied. The eight vertex model decouples to two independent Ising models when the four spin coupling vanishes. To first order in the four-spin coupling, the electric correlation function is related to a three-point function of the Ising model. This relation is systematically investigated and the full dispersion expansion (to first order in four-spin coupling) is obtained. The results is a new kind of structure which, unlike those of many solvable models, is apparently not expressible in terms of linear integral equations.« less

Bidirectional holographic codes and sub-AdS locality

NASA Astrophysics Data System (ADS)

Yang, Zhao; Hayden, Patrick; Qi, Xiaoliang

Tensor networks implementing quantum error correcting codes have recently been used as toy models of the holographic duality which explicitly realize some of the more puzzling features of the AdS/CFT correspondence. These models reproduce the Ryu-Takayanagi entropy formula for boundary intervals, and allow bulk operators to be mapped to the boundary in a redundant fashion. These exactly solvable, explicit models have provided valuable insight but nonetheless suffer from many deficiencies, some of which we attempt to address in this talk. We propose a new class of tensor network models that subsume the earlier advances and, in addition, incorporate additional features of holographic duality, including: (1) a holographic interpretation of all boundary states, not just those in a ''code'' subspace, (2) a set of bulk states playing the role of ''classical geometries'' which reproduce the Ryu-Takayanagi formula for boundary intervals, (3) a bulk gauge symmetry analogous to diffeomorphism invariance in gravitational theories, (4) emergent bulk locality for sufficiently sparse excitations, and the ability to describe geometry at sub-AdS resolutions or even flat space. David and Lucile Packard Foundation.

Bidirectional holographic codes and sub-AdS locality

NASA Astrophysics Data System (ADS)

Yang, Zhao; Hayden, Patrick; Qi, Xiao-Liang

2016-01-01

Tensor networks implementing quantum error correcting codes have recently been used to construct toy models of holographic duality explicitly realizing some of the more puzzling features of the AdS/CFT correspondence. These models reproduce the Ryu-Takayanagi entropy formula for boundary intervals, and allow bulk operators to be mapped to the boundary in a redundant fashion. These exactly solvable, explicit models have provided valuable insight but nonetheless suffer from many deficiencies, some of which we attempt to address in this article. We propose a new class of tensor network models that subsume the earlier advances and, in addition, incorporate additional features of holographic duality, including: (1) a holographic interpretation of all boundary states, not just those in a "code" subspace, (2) a set of bulk states playing the role of "classical geometries" which reproduce the Ryu-Takayanagi formula for boundary intervals, (3) a bulk gauge symmetry analogous to diffeomorphism invariance in gravitational theories, (4) emergent bulk locality for sufficiently sparse excitations, and (5) the ability to describe geometry at sub-AdS resolutions or even flat space.

Dual measurement self-sensing technique of NiTi actuators for use in robust control

NASA Astrophysics Data System (ADS)

Gurley, Austin; Lambert, Tyler Ross; Beale, David; Broughton, Royall

2017-10-01

Using a shape memory alloy actuator as both an actuator and a sensor provides huge benefits in cost reduction and miniaturization of robotic devices. Despite much effort, reliable and robust self-sensing (using the actuator as a position sensor) had not been achieved for general temperature, loading, hysteresis path, and fatigue conditions. Prior research has sought to model the intricacies of the electrical resistivity changes within the NiTi material. However, for the models to be solvable, nearly every previous technique only models the actuator within very specific boundary conditions. Here, we measure both the voltage across the entire NiTi wire and of a fixed-length segment of it; these dual measurements allow direct calculation of the actuator length without a material model. We review previous self-sensing literature, illustrate the mechanism design that makes the new technique possible, and use the dual measurement technique to determine the length of a single straight wire actuator under controlled conditions. This robust measurement can be used for feedback control in unknown ambient and loading conditions.

Eye Movements in Strategic Choice

PubMed Central

Gächter, Simon; Noguchi, Takao; Mullett, Timothy L.

2015-01-01

Abstract In risky and other multiattribute choices, the process of choosing is well described by random walk or drift diffusion models in which evidence is accumulated over time to threshold. In strategic choices, level‐k and cognitive hierarchy models have been offered as accounts of the choice process, in which people simulate the choice processes of their opponents or partners. We recorded the eye movements in 2 × 2 symmetric games including dominance‐solvable games like prisoner's dilemma and asymmetric coordination games like stag hunt and hawk–dove. The evidence was most consistent with the accumulation of payoff differences over time: we found longer duration choices with more fixations when payoffs differences were more finely balanced, an emerging bias to gaze more at the payoffs for the action ultimately chosen, and that a simple count of transitions between payoffs—whether or not the comparison is strategically informative—was strongly associated with the final choice. The accumulator models do account for these strategic choice process measures, but the level‐k and cognitive hierarchy models do not. © 2015 The Authors. Journal of Behavioral Decision Making published by John Wiley & Sons Ltd. PMID:27513881

Metallic quantum critical points with finite BCS couplings

NASA Astrophysics Data System (ADS)

Raghu, Srinivas

The problem of superconductivity near quantum critical points (QCPs) remains a central topic of modern condensed matter physics. In such systems, there is a competition between the enhanced pairing tendency due to the presence of long-range attractive interactions near criticality, and the suppression of superconductivity due to the destruction of Landau quasiparticles. I will describe some recent work that addresses these competing effects in the context of a solvable model of a metallic quantum critical point. I will show that the two effects - namely the enhanced pairing and the destruction of Landau quasiparticles - can offset one another, resulting in stable ''naked'' quantum critical points without superconductivity. However, the resulting quantum critical metal exhibits strong superconducting fluctuations on all length scales. Reference: S.R., Gonzalo Torroba, and Huajia Wang, arXiv1507.06652, PRB(2015).

Changing Horses in Midstream: The Dangers of Unplanned Head Transitions

ERIC Educational Resources Information Center

Quinby, Lee

2015-01-01

Quick leadership transitions may succeed in other industries, but they don't usually work in the "business of relationships" we call school. Boards that respond to a solvable problem by firing the head may believe that action is necessary and good for the school. In truth, these abrupt changes almost always hurt schools, with devastating…

A Versatile Technique for Solving Quintic Equations

ERIC Educational Resources Information Center

Kulkarni, Raghavendra G.

2006-01-01

In this paper we present a versatile technique to solve several types of solvable quintic equations. In the technique described here, the given quintic is first converted to a sextic equation by adding a root, and the resulting sextic equation is decomposed into two cubic polynomials as factors in a novel fashion. The resultant cubic equations are…

Characteristics of Problem Posing of Grade 9 Students on Geometric Tasks

ERIC Educational Resources Information Center

Chua, Puay Huat; Wong, Khoon Yoong

2012-01-01

This is an exploratory study into the individual problem-posing characteristics of 480 Grade 9 Singapore students who were novice problem posers working on two geometric tasks. The students were asked to pose a problem for their friends to solve. Analyses of solvable posed problems were based on the problem type, problem information, solution type…

Hungry Kids: The Solvable Crisis

ERIC Educational Resources Information Center

Felling, Christy

2013-01-01

The numbers speak for themselves in terms of the crisis of hunger among kids in the United States: More than 16 million children--one in five--live in households that struggle to put food on the table. Nearly half of all food stamp recipients are children. But, argues Felling, the battle against childhood hunger can be won; the United States has…

Solvability of a Nonlinear Integral Equation in Dynamical String Theory

NASA Astrophysics Data System (ADS)

Khachatryan, A. Kh.; Khachatryan, Kh. A.

2018-04-01

We investigate an integral equation of the convolution type with a cubic nonlinearity on the entire real line. This equation has a direct application in open-string field theory and in p-adic string theory and describes nonlocal interactions. We prove that there exists a one-parameter family of bounded monotonic solutions and calculate the limits of solutions constructed at infinity.

Generalizability Theory Research on Developing a Scoring Rubric to Assess Primary School Students' Problem Posing Skills

ERIC Educational Resources Information Center

Cankoy, Osman; Özder, Hasan

2017-01-01

The aim of this study is to develop a scoring rubric to assess primary school students' problem posing skills. The rubric including five dimensions namely solvability, reasonability, mathematical structure, context and language was used. The raters scored the students' problem posing skills both with and without the scoring rubric to test the…

Regularity for Fully Nonlinear Elliptic Equations with Oblique Boundary Conditions

NASA Astrophysics Data System (ADS)

Li, Dongsheng; Zhang, Kai

2018-06-01

In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions. In particular, we derive the pointwise C α, C 1,α and C 2,α regularity. As byproducts, we also prove the A-B-P maximum principle, Harnack inequality, uniqueness and solvability of the equations.

Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

NASA Astrophysics Data System (ADS)

Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.

2018-04-01

We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.

Solvability of a fourth-order boundary value problem with periodic boundary conditions II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gupta, Chaitan P.

1991-01-01

Lemore » t f : [ 0 , 1 ] × R 4 → R be a function satisfying Caratheodory's conditions and e ( x ) ∈ L 1 [ 0 , 1 ] . This paper is concerned with the solvability of the fourth-order fully quasilinear boundary value problem d 4 u d x 4 + f ( x , u ( x ) , u ′ ( x ) , u ″ ( x ) , u ‴ ( x ) ) = e ( x ) ,    0 < x < 1 , with u ( 0 ) − u ( 1 ) = u ′ ( 0 ) − u ′ ( 1 ) = u ″ ( 0 ) - u ″ ( 1 ) = u ‴ ( 0 ) - u ‴ ( 1 ) = 0 . This problem was studied earlier by the author in the special case when f was of the form f ( x , u ( x ) ) , i.e., independent of u ′ ( x ) , u ″ ( x ) , u ‴ ( x ) . It turns out that the earlier methods do not apply in this general case. The conditions need to be related to both of the linear eigenvalue problems d 4 u d x 4 = λ 4 u and d 4 u d x 4 = − λ 2 d 2 u d x 2 with periodic boundary conditions.« less

Exactly solvable field theories of closed strings

NASA Astrophysics Data System (ADS)

Brézin, E.; Kazakov, V. A.

1990-02-01

Field theories of closed strings are shown to be exactly solvable for a central charge of matter fields c=1-6/m(m+1),m=1,2, 3, .... The two-point function χ(λ,N), in which λ is the cosmological constant and N-1 is the string coupling constant, obeys a scaling law χ(λ,N=N-(m+1/2)C((λc-λ)Nm/(m+1/2)) in the limit in which N-1 goes to zero and λ goes to a critical value λc we have determined the universal non-linear differential equation satisfied by the function C. From this equation it is found that a phase transition takes place for some finite value of the scaling parameter (λc-λ)Nm/(m+1/2); this transition is a ``condensation of handles'' on the world sheet, characterized by a divergence of the averaged genus of the world sheets. The cases m=2,3 are elaborated in more details, and the case m=1, which corresponds to the embedding of a bosonic string in -2 dimensions, is reduced to explicit quadratures. Permanent address: Cybernetics Council and Academy of Sciences, ul. Vavilova 40, SU-117 333 Moscow, USSR.

Limitations of demand- and pressure-driven modeling for large deficient networks

NASA Astrophysics Data System (ADS)

Braun, Mathias; Piller, Olivier; Deuerlein, Jochen; Mortazavi, Iraj

2017-10-01

The calculation of hydraulic state variables for a network is an important task in managing the distribution of potable water. Over the years the mathematical modeling process has been improved by numerous researchers for utilization in new computer applications and the more realistic modeling of water distribution networks. But, in spite of these continuous advances, there are still a number of physical phenomena that may not be tackled correctly by current models. This paper will take a closer look at the two modeling paradigms given by demand- and pressure-driven modeling. The basic equations are introduced and parallels are drawn with the optimization formulations from electrical engineering. These formulations guarantee the existence and uniqueness of the solution. One of the central questions of the French and German research project ResiWater is the investigation of the network resilience in the case of extreme events or disasters. Under such extraordinary conditions where models are pushed beyond their limits, we talk about deficient network models. Examples of deficient networks are given by highly regulated flow, leakage or pipe bursts and cases where pressure falls below the vapor pressure of water. These examples will be presented and analyzed on the solvability and physical correctness of the solution with respect to demand- and pressure-driven models.

On determinant representations of scalar products and form factors in the SoV approach: the XXX case

NASA Astrophysics Data System (ADS)

Kitanine, N.; Maillet, J. M.; Niccoli, G.; Terras, V.

2016-03-01

In the present article we study the form factors of quantum integrable lattice models solvable by the separation of variables (SoVs) method. It was recently shown that these models admit universal determinant representations for the scalar products of the so-called separate states (a class which includes in particular all the eigenstates of the transfer matrix). These results permit to obtain simple expressions for the matrix elements of local operators (form factors). However, these representations have been obtained up to now only for the completely inhomogeneous versions of the lattice models considered. In this article we give a simple algebraic procedure to rewrite the scalar products (and hence the form factors) for the SoV related models as Izergin or Slavnov type determinants. This new form leads to simple expressions for the form factors in the homogeneous and thermodynamic limits. To make the presentation of our method clear, we have chosen to explain it first for the simple case of the XXX Heisenberg chain with anti-periodic boundary conditions. We would nevertheless like to stress that the approach presented in this article applies as well to a wide range of models solved in the SoV framework.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ortiz, Gerardo, E-mail: ortizg@indiana.edu; Cobanera, Emilio

We investigate Majorana modes of number-conserving fermionic superfluids from both basic physics principles, and concrete models perspectives. After reviewing a criterion for establishing topological superfluidity in interacting systems, based on many-body fermionic parity switches, we reveal the emergence of zero-energy modes anticommuting with fermionic parity. Those many-body Majorana modes are constructed as coherent superpositions of states with different number of fermions. While realization of Majorana modes beyond mean field is plausible, we show that the challenge to quantum-control them is compounded by particle-conservation, and more realistic protocols will have to balance engineering needs with astringent constraints coming from superselection rules.more » Majorana modes in number-conserving systems are the result of a peculiar interplay between quantum statistics, fermionic parity, and an unusual form of spontaneous symmetry breaking. We test these ideas on the Richardson–Gaudin–Kitaev chain, a number-conserving model solvable by way of the algebraic Bethe ansatz, and equivalent in mean field to a long-range Kitaev chain.« less

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

NASA Astrophysics Data System (ADS)

Chew, Aaron; Essin, Andrew; Alicea, Jason

The Sachdev-Ye-Kitaev (SYK) model describes a large collection of Majorana fermions coupled via random, `all-to-all' four-fermion interactions. This model enjoys broad interdisciplinary interest because it provides a solvable realization of holography in 0+1 dimensions, exhibits unusual spectral and thermodynamic properties, and shares deep connections to chaos and black holes. We propose a solid-state implementation of the SYK Hamiltonian that employs quantum dots coupled to arrays of topological superconductors hosting Majorana end-states. All-to-all four-Majorana couplings are mediated by interactions in the dot, while the randomness originates from disorder in the hoppings between the Majorana modes and dot levels. Using perturbation theory and explicit numerics, we study the properties of the dot-wire array system under various experimental conditions. Interestingly, our setup not only allows exploration of SYK physics, but also provides a controlled testbed for interaction effects on the topological classification of fermionic phases. Supported by the National Science Foundation (DMR-1341822), Institute for Quantum Information and Matter, and Walter Burke Institute at Caltech. AC gratefully acknowledges support from the Dominic Orr Fellowship.

Discontinuous finite volume element discretization for coupled flow-transport problems arising in models of sedimentation

NASA Astrophysics Data System (ADS)

Bürger, Raimund; Kumar, Sarvesh; Ruiz-Baier, Ricardo

2015-10-01

The sedimentation-consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.

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.

Multipeak low-temperature behavior of specific heat capacity in frustrated magnetic systems: An exact theoretical analysis

NASA Astrophysics Data System (ADS)

Jurčišinová, E.; Jurčišin, M.

2018-05-01

We investigate in detail the process of formation of the multipeak low-temperature structure in the behavior of the specific heat capacity in frustrated magnetic systems in the framework of the exactly solvable antiferromagnetic spin-1 /2 Ising model with the multisite interaction in the presence of the external magnetic field on the kagome-like Husimi lattice. The behavior of the entropy of the model is studied and exact values of the residual entropies of all ground states are found. It is shown that the multipeak structure in the behavior of the specific heat capacity is related to the formation of the multilevel hierarchical ordering in the system of all ground states of the model. Direct relation between the maximal number of peaks in the specific heat capacity behavior and the number of independent interactions in studied frustrated magnetic system is identified. The mechanism of the formation of the multipeak structure in the specific heat capacity is described and studied in detail, and it is generalized to frustrated magnetic systems with arbitrary numbers of independent interactions.

Two charges on a plane in a magnetic field: hidden algebra, (particular) integrability, polynomial eigenfunctions

NASA Astrophysics Data System (ADS)

Turbiner, A. V.; Escobar-Ruiz, M. A.

2013-07-01

The quantum mechanics of two Coulomb charges on a plane (e1, m1) and (e2, m2) subject to a constant magnetic field B perpendicular to the plane is considered. Four integrals of motion are explicitly indicated. It is shown that for two physically important particular cases, namely that of two particles of equal Larmor frequencies, {e_c} \\propto \\frac{e_1}{m_1}-\\frac{e_2}{m_2}=0 (e.g. two electrons) and one of a neutral system (e.g. the electron-positron pair, hydrogen atom) at rest (the center-of-mass momentum is zero) some outstanding properties occur. They are the most visible in double polar coordinates in CMS (R, ϕ) and relative (ρ, φ) coordinate systems: (i) eigenfunctions are factorizable, all factors except one with the explicit ρ-dependence are found analytically, they have definite relative angular momentum, (ii) dynamics in the ρ-direction is the same for both systems, it corresponds to a funnel-type potential and it has hidden sl(2) algebra, at some discrete values of dimensionless magnetic fields b ⩽ 1, (iii) particular integral(s) occur, (iv) the hidden sl(2) algebra emerges in finite-dimensional representation, thus, the system becomes quasi-exactly-solvable and (v) a finite number of polynomial eigenfunctions in ρ appear. Nine families of eigenfunctions are presented explicitly.

Accurate Estimation of Solvation Free Energy Using Polynomial Fitting Techniques

PubMed Central

Shyu, Conrad; Ytreberg, F. Marty

2010-01-01

This report details an approach to improve the accuracy of free energy difference estimates using thermodynamic integration data (slope of the free energy with respect to the switching variable λ) and its application to calculating solvation free energy. The central idea is to utilize polynomial fitting schemes to approximate the thermodynamic integration data to improve the accuracy of the free energy difference estimates. Previously, we introduced the use of polynomial regression technique to fit thermodynamic integration data (Shyu and Ytreberg, J Comput Chem 30: 2297–2304, 2009). In this report we introduce polynomial and spline interpolation techniques. Two systems with analytically solvable relative free energies are used to test the accuracy of the interpolation approach. We also use both interpolation and regression methods to determine a small molecule solvation free energy. Our simulations show that, using such polynomial techniques and non-equidistant λ values, the solvation free energy can be estimated with high accuracy without using soft-core scaling and separate simulations for Lennard-Jones and partial charges. The results from our study suggest these polynomial techniques, especially with use of non-equidistant λ values, improve the accuracy for ΔF estimates without demanding additional simulations. We also provide general guidelines for use of polynomial fitting to estimate free energy. To allow researchers to immediately utilize these methods, free software and documentation is provided via http://www.phys.uidaho.edu/ytreberg/software. PMID:20623657

Topological dynamics of gyroscopic and Floquet lattices from Newton's laws

NASA Astrophysics Data System (ADS)

Lee, Ching Hua; Li, Guangjie; Jin, Guliuxin; Liu, Yuhan; Zhang, Xiao

2018-02-01

Despite intense interest in realizing topological phases across a variety of electronic, photonic, and mechanical platforms, the detailed microscopic origin of topological behavior often remains elusive. To bridge this conceptual gap, we show how hallmarks of topological modes—boundary localization and chirality—emerge from Newton's laws in mechanical topological systems. We first construct a gyroscopic lattice with analytically solvable edge modes, and show how the Lorentz and spring restoring forces conspire to support very robust "dangling bond" boundary modes. The chirality and locality of these modes intuitively emerges from microscopic balancing of restoring forces and cyclotron tendencies. Next, we introduce the highlight of this work, an experimentally realistic mechanical nonequilibrium (Floquet) Chern lattice driven by ac electromagnets. Through appropriate synchronization of the ac driving protocol, the Floquet lattice is "pushed around" by a rotating potential analogous to an object washed ashore by water waves. Besides hosting "dangling bond" chiral modes analogous to the gyroscopic boundary modes, our Floquet Chern lattice also supports peculiar half-period chiral modes with no static analog, i.e., analogs of anomalous Floquet Chern insulators edge modes. With key parameters controlled electronically, our setup has the advantage of being dynamically tunable for applications involving arbitrary Floquet modulations. The physical intuition gleaned from our two prototypical topological systems is applicable not just to arbitrarily complicated mechanical systems, but also photonic and electrical topological setups.

Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.

PubMed

Gosset, David; Terhal, Barbara M; Vershynina, Anna

2015-04-10

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

There aren't Non-Standard Solutions for the Braid Group Representations of the QYBE Associated with 10-D Representations of SU(4)

NASA Technical Reports Server (NTRS)

Yijun, Huang; Guochen, Yu; Hong, Sun

1996-01-01

It is well known that the quantum Yang-Baxter equations (QYBE) play an important role in various theoretical and mathematical physics, such as completely integrable system in (1 + 1)-dimensions, exactly solvable models in statistical mechanics, the quantum inverse scattering method and the conformal field theories in 2-dimensions. Recently, much remarkable progress has been made in constructing the solutions of the QYBE associated with the representations of lie algebras. It is shown that for some cases except the standard solutions, there also exist new solutions, but the others have not non-standard solutions. In this paper by employing the weight conservation and the diagrammatic techniques we show that the solution associated with the 10-D representations of SU (4) are standard alone.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Curchod, Basile F. E.; Agostini, Federica, E-mail: agostini@mpi-halle.mpg.de; Gross, E. K. U.

Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region. In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface—the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrastmore » to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics one of the exact nuclear probability densities.« less

On the matrix Fourier filtering problem for a class of models of nonlinear optical systems with a feedback

NASA Astrophysics Data System (ADS)

Razgulin, A. V.; Sazonova, S. V.

2017-09-01

A novel statement of the Fourier filtering problem based on the use of matrix Fourier filters instead of conventional multiplier filters is considered. The basic properties of the matrix Fourier filtering for the filters in the Hilbert-Schmidt class are established. It is proved that the solutions with a finite energy to the periodic initial boundary value problem for the quasi-linear functional differential diffusion equation with the matrix Fourier filtering Lipschitz continuously depend on the filter. The problem of optimal matrix Fourier filtering is formulated, and its solvability for various classes of matrix Fourier filters is proved. It is proved that the objective functional is differentiable with respect to the matrix Fourier filter, and the convergence of a version of the gradient projection method is also proved.

Universal Adiabatic Quantum Computation via the Space-Time Circuit-to-Hamiltonian Construction

NASA Astrophysics Data System (ADS)

Gosset, David; Terhal, Barbara M.; Vershynina, Anna

2015-04-01

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic X X Z chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q -deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

Quantum Quench Dynamics

NASA Astrophysics Data System (ADS)

Mitra, Aditi

2018-03-01

Quench dynamics is an active area of study encompassing condensed matter physics and quantum information, with applications to cold-atomic gases and pump-probe spectroscopy of materials. Recent theoretical progress in studying quantum quenches is reviewed. Quenches in interacting one-dimensional systems as well as systems in higher spatial dimensions are covered. The appearance of nontrivial steady states following a quench in exactly solvable models is discussed, and the stability of these states to perturbations is described. Proper conserving approximations needed to capture the onset of thermalization at long times are outlined. The appearance of universal scaling for quenches near critical points and the role of the renormalization group in capturing the transient regime are reviewed. Finally, the effect of quenches near critical points on the dynamics of entanglement entropy and entanglement statistics is discussed. The extraction of critical exponents from the entanglement statistics is outlined.

Solution Methods for Certain Evolution Equations

NASA Astrophysics Data System (ADS)

Vega-Guzman, Jose Manuel

Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.

Computer calculation of Witten's 3-manifold invariant

NASA Astrophysics Data System (ADS)

Freed, Daniel S.; Gompf, Robert E.

1991-10-01

Witten's 2+1 dimensional Chern-Simons theory is exactly solvable. We compute the partition function, a topological invariant of 3-manifolds, on generalized Seifert spaces. Thus we test the path integral using the theory of 3-manifolds. In particular, we compare the exact solution with the asymptotic formula predicted by perturbation theory. We conclude that this path integral works as advertised and gives an effective topological invariant.

The Complexity of Developing Properly Trained Education Professionals for African American Children: Exploring an African Indigenous Socialization Process

ERIC Educational Resources Information Center

Shockley, Kmt G.

2011-01-01

African centered educationists view the problems that Black children are facing in schools as a part of the disenfranchisement and disorganization of the Black community at large. In that vein, they do not believe that the problems which Black children are experiencing in America's public (and many private) schools are solvable by taking them out…

The business plan: an AR perspective.

PubMed

Hajny, Tom

2008-01-01

It is important to periodically reassess the environment and what we need to accomplish in the near-term (or mid- or long term). Our skills, insights, knowledge, and talents grow yearly and maybe, just maybe, problems that we thought were intractable are, indeed, solvable. Play with the idea of Mission Statement, Objectives, and Keys to Success to stir up your neurons to execute a plan of excellence.

Dynamic output feedback control of a flexible air-breathing hypersonic vehicle via T-S fuzzy approach

NASA Astrophysics Data System (ADS)

Hu, Xiaoxiang; Wu, Ligang; Hu, Changhua; Wang, Zhaoqiang; Gao, Huijun

2014-08-01

By utilising Takagi-Sugeno (T-S) fuzzy set approach, this paper addresses the robust H∞ dynamic output feedback control for the non-linear longitudinal model of flexible air-breathing hypersonic vehicles (FAHVs). The flight control of FAHVs is highly challenging due to the unique dynamic characteristics, and the intricate couplings between the engine and fight dynamics and external disturbance. Because of the dynamics' enormous complexity, currently, only the longitudinal dynamics models of FAHVs have been used for controller design. In this work, T-S fuzzy modelling technique is utilised to approach the non-linear dynamics of FAHVs, then a fuzzy model is developed for the output tracking problem of FAHVs. The fuzzy model contains parameter uncertainties and disturbance, which can approach the non-linear dynamics of FAHVs more exactly. The flexible models of FAHVs are difficult to measure because of the complex dynamics and the strong couplings, thus a full-order dynamic output feedback controller is designed for the fuzzy model. A robust H∞ controller is designed for the obtained closed-loop system. By utilising the Lyapunov functional approach, sufficient solvability conditions for such controllers are established in terms of linear matrix inequalities. Finally, the effectiveness of the proposed T-S fuzzy dynamic output feedback control method is demonstrated by numerical simulations.

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

PubMed

Fouxon, Itzhak; Holzner, Markus

2016-08-01

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

Hidden Symmetries in String Theory

NASA Astrophysics Data System (ADS)

Chervonyi, Iurii

In this thesis we study hidden symmetries within the framework of string theory. Symmetries play a very important role in physics: they lead to drastic simplifications, which allow one to compute various physical quantities without relying on perturbative techniques. There are two kinds of hidden symmetries investigated in this work: the first type is associated with dynamics of quantum fields and the second type is related to integrability of strings on various backgrounds. Integrability is a remarkable property of some theories that allows one to determine all dynamical properties of the system using purely analytical methods. The goals of this thesis are twofold: extension of hidden symmetries known in General Relativity to stringy backgrounds in higher dimensions and construction of new integrable string theories. In the context of the first goal we study hidden symmetries of stringy backgrounds, with and without supersymmetry. For supersymmetric geometries produced by D-branes we identify the backgrounds with solvable equations for geodesics, which can potentially give rise to integrable string theories. Relaxing the requirement of supersymmetry, we also study charged black holes in higher dimensions and identify their hidden symmetries encoded in so-called Killing(-Yano) tensors. We construct the explicit form of the Killing(-Yano) tensors for the charged rotating black hole in arbitrary number of dimensions, study behavior of such tensors under string dualities, and use the analysis of hidden symmetries to explain why exact solutions for black rings (black holes with non-spherical event horizons) in more than five dimensions remain elusive. As a byproduct we identify the standard parameterization of AdSp x Sq backgrounds with elliptic coordinates on a flat base. The second goal of this work is construction of new integrable string theories by applying continuous deformations of known examples. We use the recent developments called (generalized) lambda-deformation to construct new integrable backgrounds depending on several continuous parameters and study analytical properties of the such deformations.

A border-ownership model based on computational electromagnetism.

PubMed

Zainal, Zaem Arif; Satoh, Shunji

2018-03-01

The mathematical relation between a vector electric field and its corresponding scalar potential field is useful to formulate computational problems of lower/middle-order visual processing, specifically related to the assignment of borders to the side of the object: so-called border ownership (BO). BO coding is a key process for extracting the objects from the background, allowing one to organize a cluttered scene. We propose that the problem is solvable simultaneously by application of a theorem of electromagnetism, i.e., "conservative vector fields have zero rotation, or "curl." We hypothesize that (i) the BO signal is definable as a vector electric field with arrowheads pointing to the inner side of perceived objects, and (ii) its corresponding scalar field carries information related to perceived order in depth of occluding/occluded objects. A simple model was developed based on this computational theory. Model results qualitatively agree with object-side selectivity of BO-coding neurons, and with perceptions of object order. The model update rule can be reproduced as a plausible neural network that presents new interpretations of existing physiological results. Results of this study also suggest that T-junction detectors are unnecessary to calculate depth order. Copyright © 2017 Elsevier Ltd. All rights reserved.

Exactly solvable model of the two-dimensional electrical double layer.

PubMed

Samaj, L; Bajnok, Z

2005-12-01

We consider equilibrium statistical mechanics of a simplified model for the ideal conductor electrode in an interface contact with a classical semi-infinite electrolyte, modeled by the two-dimensional Coulomb gas of pointlike unit charges in the stability-against-collapse regime of reduced inverse temperatures 0< or = beta < 2. If there is a potential difference between the bulk interior of the electrolyte and the grounded electrode, the electrolyte region close to the electrode (known as the electrical double layer) carries some nonzero surface charge density. The model is mappable onto an integrable semi-infinite sine-Gordon theory with Dirichlet boundary conditions. The exact form-factor and boundary state information gained from the mapping provide asymptotic forms of the charge and number density profiles of electrolyte particles at large distances from the interface. The result for the asymptotic behavior of the induced electric potential, related to the charge density via the Poisson equation, confirms the validity of the concept of renormalized charge and the corresponding saturation hypothesis. It is documented on the nonperturbative result for the asymptotic density profile at a strictly nonzero beta that the Debye-Hückel beta-->0 limit is a delicate issue.

Extremely Rare Interbreeding Events Can Explain Neanderthal DNA in Living Humans

PubMed Central

Neves, Armando G. M.; Serva, Maurizio

2012-01-01

Considering the recent experimental discovery of Green et al that present-day non-Africans have 1 to of their nuclear DNA of Neanderthal origin, we propose here a model which is able to quantify the genetic interbreeding between two subpopulations with equal fitness, living in the same geographic region. The model consists of a solvable system of deterministic ordinary differential equations containing as a stochastic ingredient a realization of the neutral Wright-Fisher process. By simulating the stochastic part of the model we are able to apply it to the interbreeding ofthe African ancestors of Eurasians and Middle Eastern Neanderthal subpopulations and estimate the only parameter of the model, which is the number of individuals per generation exchanged between subpopulations. Our results indicate that the amount of Neanderthal DNA in living non-Africans can be explained with maximum probability by the exchange of a single pair of individuals between the subpopulations at each 77 generations, but larger exchange frequencies are also allowed with sizeable probability. The results are compatible with a long coexistence time of 130,000 years, a total interbreeding population of order individuals, and with all living humans being descendants of Africans both for mitochondrial DNA and Y chromosome. PMID:23112810

Adiabatic cooling processes in frustrated magnetic systems with pyrochlore structure

NASA Astrophysics Data System (ADS)

Jurčišinová, E.; Jurčišin, M.

2017-11-01

We investigate in detail the process of adiabatic cooling in the framework of the exactly solvable antiferromagnetic spin-1/2 Ising model in the presence of the external magnetic field on an approximate lattice with pyrochlore structure. The behavior of the entropy of the model is studied and exact values of the residual entropies of all ground states are found. The temperature variation of the system under adiabatic (de)magnetization is investigated and the central role of the macroscopically degenerated ground states in cooling processes is explicitly demonstrated. It is shown that the model parameter space of the studied geometrically frustrated system is divided into five disjunct regions with qualitatively different processes of the adiabatic cooling. The effectiveness of the adiabatic (de)magnetization cooling in the studied model is compared to the corresponding processes in paramagnetic salts. It is shown that the processes of the adiabatic cooling in the antiferromagnetic frustrated systems are much more effective especially in nonzero external magnetic fields. It means that the frustrated magnetic materials with pyrochlore structure can be considered as very promising refrigerants mainly in the situations with nonzero final values of the magnetic field.

Adiabatic cooling processes in frustrated magnetic systems with pyrochlore structure.

PubMed

Jurčišinová, E; Jurčišin, M

2017-11-01

We investigate in detail the process of adiabatic cooling in the framework of the exactly solvable antiferromagnetic spin-1/2 Ising model in the presence of the external magnetic field on an approximate lattice with pyrochlore structure. The behavior of the entropy of the model is studied and exact values of the residual entropies of all ground states are found. The temperature variation of the system under adiabatic (de)magnetization is investigated and the central role of the macroscopically degenerated ground states in cooling processes is explicitly demonstrated. It is shown that the model parameter space of the studied geometrically frustrated system is divided into five disjunct regions with qualitatively different processes of the adiabatic cooling. The effectiveness of the adiabatic (de)magnetization cooling in the studied model is compared to the corresponding processes in paramagnetic salts. It is shown that the processes of the adiabatic cooling in the antiferromagnetic frustrated systems are much more effective especially in nonzero external magnetic fields. It means that the frustrated magnetic materials with pyrochlore structure can be considered as very promising refrigerants mainly in the situations with nonzero final values of the magnetic field.

An attempt at the computer-aided management of HIV infection

NASA Astrophysics Data System (ADS)

Ida, A.; Oharu, Y.; Sankey, O.

2007-07-01

The immune system is a complex and diverse system in the human body and HIV virus disrupts and destroys it through extremely complicated but surprisingly logical process. The purpose of this paper is to make an attempt to present a method for the computer-aided management of HIV infection process by means of a mathematical model describing the dynamics of the host pathogen interaction with HIV-1. Treatments for the AIDS disease must be changed to more efficient ones in accordance with the disease progression and the status of the immune system. The level of progression and the status are represented by parameters which are governed by our mathematical model. It is then exhibited that our model is numerically stable and uniquely solvable. With this knowledge, our mathematical model for HIV disease progression is formulated and physiological interpretations are provided. The results of our numerical simulations are visualized, and it is seen that our results agree with medical aspects from the point of view of antiretroviral therapy. It is then expected that our approach will take to address practical clinical issues and will be applied to the computer-aided management of antiretroviral therapies.

Ocean and coastal data management

USGS Publications Warehouse

de La Beaujardière, Jeff; Beegle-Krause, C; Bermudez, Luis; Hankin, Steven C.; Hazard, Lisa; Howlett, Eoin; Le, Steven; Proctor, Roger; Signell, Richard P.; Snowden, Derrick P.; Thomas, Julie

2010-01-01

We introduce data management concepts, including what we mean by "data" and its "management," sources of data, interoperability, and data geometry. We then discuss various components of a data management system. Finally, we summarize some existing ocean and coastal data management efforts. We make specific recommendations throughout the paper. We are generally optimistic that ocean and coastal data management is an interesting and solvable challenge that will provide great benefit to society.

Reverse engineering of integrated circuits

DOEpatents

Chisholm, Gregory H.; Eckmann, Steven T.; Lain, Christopher M.; Veroff, Robert L.

2003-01-01

Software and a method therein to analyze circuits. The software comprises several tools, each of which perform particular functions in the Reverse Engineering process. The analyst, through a standard interface, directs each tool to the portion of the task to which it is most well suited, rendering previously intractable problems solvable. The tools are generally used iteratively to produce a successively more abstract picture of a circuit, about which incomplete a priori knowledge exists.

Optimal Control of Evolution Mixed Variational Inclusions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alduncin, Gonzalo, E-mail: alduncin@geofisica.unam.mx

2013-12-15

Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.

DOE Office of Scientific and Technical Information (OSTI.GOV)

He, Yang; Xiao, Jianyuan; Zhang, Ruili

Hamiltonian time integrators for the Vlasov-Maxwell equations are developed by a Hamiltonian splitting technique. The Hamiltonian functional is split into five parts, which produces five exactly solvable subsystems. Each subsystem is a Hamiltonian system equipped with the Morrison-Marsden-Weinstein Poisson bracket. Compositions of the exact solutions provide Poisson structure preserving/Hamiltonian methods of arbitrary high order for the Vlasov-Maxwell equations. They are then accurate and conservative over a long time because of the Poisson-preserving nature.

Global solvability and asymptotic behavior of a free boundary problem for the one-dimensional viscous radiative and reactive gas

NASA Astrophysics Data System (ADS)

Jiang, Jie; Zheng, Songmu

2012-12-01

In this paper, we study a Neumann and free boundary problem for the one-dimensional viscous radiative and reactive gas. We prove that under rather general assumptions on the heat conductivity κ, for any arbitrary large smooth initial data, the problem admits a unique global classical solution. Our global existence results improve those results by Umehara and Tani ["Global solution to the one-dimensional equations for a self-gravitating viscous radiative and reactive gas," J. Differ. Equations 234(2), 439-463 (2007), 10.1016/j.jde.2006.09.023; Umehara and Tani "Global solvability of the free-boundary problem for one-dimensional motion of a self-gravitating viscous radiative and reactive gas," Proc. Jpn. Acad., Ser. A: Math. Sci. 84(7), 123-128 (2008)], 10.3792/pjaa.84.123 and by Qin, Hu, and Wang ["Global smooth solutions for the compressible viscous and heat-conductive gas," Q. Appl. Math. 69(3), 509-528 (2011)]., 10.1090/S0033-569X-2011-01218-0 Moreover, we analyze the asymptotic behavior of the global solutions to our problem, and we prove that the global solution will converge to an equilibrium as time goes to infinity. This is the result obtained for this problem in the literature for the first time.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ballesteros, Ángel, E-mail: angelb@ubu.es; Enciso, Alberto, E-mail: aenciso@icmat.es; Herranz, Francisco J., E-mail: fjherranz@ubu.es

In this paper we quantize the N-dimensional classical Hamiltonian system H=(|q|)/(2(η+|q|)) p{sup 2}−k/(η+|q|) , that can be regarded as a deformation of the Coulomb problem with coupling constant k, that it is smoothly recovered in the limit η→0. Moreover, the kinetic energy term in H is just the one corresponding to an N-dimensional Taub–NUT space, a fact that makes this system relevant from a geometric viewpoint. Since the Hamiltonian H is known to be maximally superintegrable, we propose a quantization prescription that preserves such superintegrability in the quantum mechanical setting. We show that, to this end, one must choose asmore » the kinetic part of the Hamiltonian the conformal Laplacian of the underlying Riemannian manifold, which combines the usual Laplace–Beltrami operator on the Taub–NUT manifold and a multiple of its scalar curvature. As a consequence, we obtain a novel exactly solvable deformation of the quantum Coulomb problem, whose spectrum is computed in closed form for positive values of η and k, and showing that the well-known maximal degeneracy of the flat system is preserved in the deformed case. Several interesting algebraic and physical features of this new exactly solvable quantum system are analyzed, and the quantization problem for negative values of η and/or k is also sketched.« less

Stakeholder perspectives on decision-analytic modeling frameworks to assess genetic services policy.

PubMed

Guzauskas, Gregory F; Garrison, Louis P; Stock, Jacquie; Au, Sylvia; Doyle, Debra Lochner; Veenstra, David L

2013-01-01

Genetic services policymakers and insurers often make coverage decisions in the absence of complete evidence of clinical utility and under budget constraints. We evaluated genetic services stakeholder opinions on the potential usefulness of decision-analytic modeling to inform coverage decisions, and asked them to identify genetic tests for decision-analytic modeling studies. We presented an overview of decision-analytic modeling to members of the Western States Genetic Services Collaborative Reimbursement Work Group and state Medicaid representatives and conducted directed content analysis and an anonymous survey to gauge their attitudes toward decision-analytic modeling. Participants also identified and prioritized genetic services for prospective decision-analytic evaluation. Participants expressed dissatisfaction with current processes for evaluating insurance coverage of genetic services. Some participants expressed uncertainty about their comprehension of decision-analytic modeling techniques. All stakeholders reported openness to using decision-analytic modeling for genetic services assessments. Participants were most interested in application of decision-analytic concepts to multiple-disorder testing platforms, such as next-generation sequencing and chromosomal microarray. Decision-analytic modeling approaches may provide a useful decision tool to genetic services stakeholders and Medicaid decision-makers.

Pressure in an exactly solvable model of active fluid

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

Highly macroscopically degenerated single-point ground states as source of specific heat capacity anomalies in magnetic frustrated systems

NASA Astrophysics Data System (ADS)

Jurčišinová, E.; Jurčišin, M.

2018-04-01

Anomalies of the specific heat capacity are investigated in the framework of the exactly solvable antiferromagnetic spin- 1 / 2 Ising model in the external magnetic field on the geometrically frustrated tetrahedron recursive lattice. It is shown that the Schottky-type anomaly in the behavior of the specific heat capacity is related to the existence of unique highly macroscopically degenerated single-point ground states which are formed on the borders between neighboring plateau-like ground states. It is also shown that the very existence of these single-point ground states with large residual entropies predicts the appearance of another anomaly in the behavior of the specific heat capacity for low temperatures, namely, the field-induced double-peak structure, which exists, and should be observed experimentally, along with the Schottky-type anomaly in various frustrated magnetic system.

Mutual information and spontaneous symmetry breaking

NASA Astrophysics Data System (ADS)

Hamma, A.; Giampaolo, S. M.; Illuminati, F.

2016-01-01

We show that the metastable, symmetry-breaking ground states of quantum many-body Hamiltonians have vanishing quantum mutual information between macroscopically separated regions and are thus the most classical ones among all possible quantum ground states. This statement is obvious only when the symmetry-breaking ground states are simple product states, e.g., at the factorization point. On the other hand, symmetry-breaking states are in general entangled along the entire ordered phase, and to show that they actually feature the least macroscopic correlations compared to their symmetric superpositions is highly nontrivial. We prove this result in general, by considering the quantum mutual information based on the two-Rényi entanglement entropy and using a locality result stemming from quasiadiabatic continuation. Moreover, in the paradigmatic case of the exactly solvable one-dimensional quantum X Y model, we further verify the general result by considering also the quantum mutual information based on the von Neumann entanglement entropy.

Classification and properties of quantum spin liquids on the hyperhoneycomb lattice

NASA Astrophysics Data System (ADS)

Huang, Biao; Choi, Wonjune; Kim, Yong Baek; Lu, Yuan-Ming

2018-05-01

The family of "Kitaev materials" provides an ideal platform to study quantum spin liquids and their neighboring magnetic orders. Motivated by the possibility of a quantum spin liquid ground state in pressurized hyperhoneycomb iridate β -Li2IrO3 , we systematically classify and study symmetric quantum spin liquids on the hyperhoneycomb lattice, using the Abrikosov-fermion representation. Among the 176 symmetric U (1 ) spin liquids (and 160 Z2 spin liquids), we identify eight "root" U (1 ) spin liquids in proximity to the ground state of the solvable Kitave model on the hyperhonecyomb lattice. These eight states are promising candidates for possible U (1 ) spin liquid ground states in pressurized β -Li2IrO3 . We further discuss physical properties of these eight U (1 ) spin liquid candidates, and show that they all support nodal-line-shaped spinon Fermi surfaces.

Non-perturbative String Theory from Water Waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iyer, Ramakrishnan; Johnson, Clifford V.; /Southern California U.

2012-06-14

We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of which were conjectured to be the type IIA and IIB string theoriesmore » coupled to (4, 4k ? 2) superconformal minimal models of type (A, D). Our present paper shows that these new theories have smooth non-perturbative extensions. We also find evidence for putative new string theories that were not apparent in the perturbative analysis.« less

Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations

NASA Astrophysics Data System (ADS)

Ashida, Yuto; Ueda, Masahito

2018-05-01

The ability to measure single quanta allows the complete characterization of small quantum systems known as full-counting statistics. Quantum gas microscopy enables one to observe many-body systems at the single-atom precision. We extend the idea of full-counting statistics to nonequilibrium open many-particle dynamics and apply it to discuss the quench dynamics. By way of illustration, we consider an exactly solvable model to demonstrate the emergence of unique phenomena such as nonlocal and chiral propagation of correlations, leading to a concomitant oscillatory entanglement growth. We find that correlations can propagate beyond the conventional maximal speed, known as the Lieb-Robinson bound, at the cost of probabilistic nature of quantum measurement. These features become most prominent at the real-to-complex spectrum transition point of an underlying parity-time-symmetric effective non-Hermitian Hamiltonian. A possible experimental situation with quantum gas microscopy is discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marquette, Ian, E-mail: i.marquette@uq.edu.au; Quesne, Christiane, E-mail: cquesne@ulb.ac.be

The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent P{sub IV}, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed X{sub m{sub 1,m{sub 2,…,m{sub k}}}} Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite andmore » Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.« less

Two-time correlation function of an open quantum system in contact with a Gaussian reservoir

NASA Astrophysics Data System (ADS)

Ban, Masashi; Kitajima, Sachiko; Shibata, Fumiaki

2018-05-01

An exact formula of a two-time correlation function is derived for an open quantum system which interacts with a Gaussian thermal reservoir. It is provided in terms of functional derivative with respect to fictitious fields. A perturbative expansion and its diagrammatic representation are developed, where the small expansion parameter is related to a correlation time of the Gaussian thermal reservoir. The two-time correlation function of the lowest order is equivalent to that calculated by means of the quantum regression theorem. The result clearly shows that the violation of the quantum regression theorem is caused by a finiteness of the reservoir correlation time. By making use of an exactly solvable model consisting of a two-level system and a set of harmonic oscillators, it is shown that the two-time correlation function up to the first order is a good approximation to the exact one.

Abruptness of Cascade Failures in Power Grids

NASA Astrophysics Data System (ADS)

Pahwa, Sakshi; Scoglio, Caterina; Scala, Antonio

2014-01-01

Electric power-systems are one of the most important critical infrastructures. In recent years, they have been exposed to extreme stress due to the increasing demand, the introduction of distributed renewable energy sources, and the development of extensive interconnections. We investigate the phenomenon of abrupt breakdown of an electric power-system under two scenarios: load growth (mimicking the ever-increasing customer demand) and power fluctuations (mimicking the effects of renewable sources). Our results on real, realistic and synthetic networks indicate that increasing the system size causes breakdowns to become more abrupt; in fact, mapping the system to a solvable statistical-physics model indicates the occurrence of a first order transition in the large size limit. Such an enhancement for the systemic risk failures (black-outs) with increasing network size is an effect that should be considered in the current projects aiming to integrate national power-grids into ``super-grids''.

Abruptness of cascade failures in power grids.

PubMed

Pahwa, Sakshi; Scoglio, Caterina; Scala, Antonio

2014-01-15

Electric power-systems are one of the most important critical infrastructures. In recent years, they have been exposed to extreme stress due to the increasing demand, the introduction of distributed renewable energy sources, and the development of extensive interconnections. We investigate the phenomenon of abrupt breakdown of an electric power-system under two scenarios: load growth (mimicking the ever-increasing customer demand) and power fluctuations (mimicking the effects of renewable sources). Our results on real, realistic and synthetic networks indicate that increasing the system size causes breakdowns to become more abrupt; in fact, mapping the system to a solvable statistical-physics model indicates the occurrence of a first order transition in the large size limit. Such an enhancement for the systemic risk failures (black-outs) with increasing network size is an effect that should be considered in the current projects aiming to integrate national power-grids into "super-grids".

Integrability in dipole-deformed \\boldsymbol{N=4} super Yang-Mills

NASA Astrophysics Data System (ADS)

Guica, Monica; Levkovich Maslyuk, Fedor; Zarembo, Konstantin

2017-09-01

We study the null dipole deformation of N=4 super Yang-Mills theory, which is an example of a potentially solvable ‘dipole CFT’: a theory that is non-local along a null direction, has non-relativistic conformal invariance along the remaining ones, and is holographically dual to a Schrödinger space-time. We initiate the field-theoretical study of the spectrum in this model by using integrability inherited from the parent theory. The dipole deformation corresponds to a nondiagonal Drinfeld-Reshetikhin twist in the spin chain picture, which renders the traditional Bethe ansatz inapplicable from the very beginning. We use instead the Baxter equation supplemented with nontrivial asymptotics, which gives the full 1-loop spectrum in the sl(2) sector. We show that anomalous dimensions of long gauge theory operators perfectly match the string theory prediction, providing a quantitative test of Schrödinger holography. Dedicated to the memory of Petr Petrovich Kulish.

Abruptness of Cascade Failures in Power Grids

PubMed Central

Pahwa, Sakshi; Scoglio, Caterina; Scala, Antonio

2014-01-01

Electric power-systems are one of the most important critical infrastructures. In recent years, they have been exposed to extreme stress due to the increasing demand, the introduction of distributed renewable energy sources, and the development of extensive interconnections. We investigate the phenomenon of abrupt breakdown of an electric power-system under two scenarios: load growth (mimicking the ever-increasing customer demand) and power fluctuations (mimicking the effects of renewable sources). Our results on real, realistic and synthetic networks indicate that increasing the system size causes breakdowns to become more abrupt; in fact, mapping the system to a solvable statistical-physics model indicates the occurrence of a first order transition in the large size limit. Such an enhancement for the systemic risk failures (black-outs) with increasing network size is an effect that should be considered in the current projects aiming to integrate national power-grids into “super-grids”. PMID:24424239

Band structure of an electron in a kind of periodic potentials with singularities

NASA Astrophysics Data System (ADS)

Hai, Kuo; Yu, Ning; Jia, Jiangping

2018-06-01

Noninteracting electrons in some crystals may experience periodic potentials with singularities and the governing Schrödinger equation cannot be defined at the singular points. The band structure of a single electron in such a one-dimensional crystal has been calculated by using an equivalent integral form of the Schrödinger equation. Both the perturbed and exact solutions are constructed respectively for the cases of a general singular weak-periodic system and its an exactly solvable version, Kronig-Penney model. Any one of them leads to a special band structure of the energy-dependent parameter, which results in an effective correction to the previous energy-band structure and gives a new explanation for forming the band structure. The used method and obtained results could be a valuable aid in the study of energy bands in solid-state physics, and the new explanation may trigger investigation to different physical mechanism of electron band structures.

Emergent dynamics of Cucker-Smale particles under the effects of random communication and incompressible fluids

NASA Astrophysics Data System (ADS)

Ha, Seung-Yeal; Xiao, Qinghua; Zhang, Xiongtao

2018-04-01

We study the dynamics of infinitely many Cucker-Smale (C-S) flocking particles under the interplay of random communication and incompressible fluids. For the dynamics of an ensemble of flocking particles, we use the kinetic Cucker-Smale-Fokker-Planck (CS-FP) equation with a degenerate diffusion, whereas for the fluid component, we use the incompressible Navier-Stokes (N-S) equations. These two subsystems are coupled via the drag force. For this coupled model, we present the global existence of weak and strong solutions in Rd (d = 2 , 3). Under the extra regularity assumptions of the initial data, the unique solvability of strong solutions is also established in R2. In a large coupling regime and periodic spatial domain T2 : =R2 /Z2, we show that the velocities of C-S particles and fluids are asymptotically aligned to two constant velocities which may be different.

An Absolute Phase Space for the Physicality of Matter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valentine, John S.

2010-12-22

We define an abstract and absolute phase space (''APS'') for sub-quantum intrinsic wave states, in three axes, each mapping directly to a duality having fundamental ontological basis. Many aspects of quantum physics emerge from the interaction algebra and a model deduced from principles of 'unique solvability' and 'identifiable entity', and we reconstruct previously abstract fundamental principles and phenomena from these new foundations. The physical model defines bosons as virtual continuous waves pairs in the APS, and fermions as real self-quantizing snapshots of those waves when simple conditions are met. The abstraction and physical model define a template for the constitutionmore » of all fermions, a template for all the standard fundamental bosons and their local interactions, in a common framework and compactified phase space for all forms of real matter and virtual vacuum energy, and a distinct algebra for observables and unobservables. To illustrate our scheme's potential, we provide examples of slit experiment variations (where the model finds theoretical basis for interference only occurring between two final sources), QCD (where we may model most attributes known to QCD, and a new view on entanglement), and we suggest approaches for other varied applications. We believe this is a viable candidate for further exploration as a foundational proposition for physics.« less

Statistically Qualified Neuro-Analytic system and Method for Process Monitoring

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vilim, Richard B.; Garcia, Humberto E.; Chen, Frederick W.

1998-11-04

An apparatus and method for monitoring a process involves development and application of a statistically qualified neuro-analytic (SQNA) model to accurately and reliably identify process change. The development of the SQNA model is accomplished in two steps: deterministic model adaption and stochastic model adaptation. Deterministic model adaption involves formulating an analytic model of the process representing known process characteristics,augmenting the analytic model with a neural network that captures unknown process characteristics, and training the resulting neuro-analytic model by adjusting the neural network weights according to a unique scaled equation emor minimization technique. Stochastic model adaptation involves qualifying any remaining uncertaintymore » in the trained neuro-analytic model by formulating a likelihood function, given an error propagation equation, for computing the probability that the neuro-analytic model generates measured process output. Preferably, the developed SQNA model is validated using known sequential probability ratio tests and applied to the process as an on-line monitoring system.« less

Cure Monitoring Techniques for Adhesive Bonding Techniques.

DTIC Science & Technology

1980-11-01

l TABLE OF CONTIW Section Pase I INTRODUCTION 1. Program Overviev 1 2. Smary 2 II MONITORING SYSTEM IMPROVEMENTS 3 1. Development of a...encountered in the electronics/signal/ computer interfaces, although solvable, have slowed progress and starting a bondline monitoring program to do a...AIWAL/MLBC) as Project Engineer. The program manager is Mr. C. A. May. The principal investigator is Dr. A. Wereta, Jr., assisted by Mass. W. G. Caple, J

Representation of solution for fully nonlocal diffusion equations with deviation time variable

NASA Astrophysics Data System (ADS)

Drin, I. I.; Drin, S. S.; Drin, Ya. M.

2018-01-01

We prove the solvability of the Cauchy problem for a nonlocal heat equation which is of fractional order both in space and time. The representation formula for classical solutions for time- and space- fractional partial differential operator Dat + a2 (-Δ) γ/2 (0 <= α <= 1, γ ɛ (0, 2]) and deviation time variable is given in terms of the Fox H-function, using the step by step method.

A hierarchy of generalized Jaulent-Miodek equations and their explicit solutions

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Guan, Liang; Xue, Bo

A hierarchy of generalized Jaulent-Miodek (JM) equations related to a new spectral problem with energy-dependent potentials is proposed. Depending on the Lax matrix and elliptic variables, the generalized JM hierarchy is decomposed into two systems of solvable ordinary differential equations. Explicit theta function representations of the meromorphic function and the Baker-Akhiezer function are constructed, the solutions of the hierarchy are obtained based on the theory of algebraic curves.

Boundedness and almost Periodicity in Time of Solutions of Evolutionary Variational Inequalities

NASA Astrophysics Data System (ADS)

Pankov, A. A.

1983-04-01

In this paper existence theorems are obtained for the solutions of abstract parabolic variational inequalities, which are bounded with respect to time (in the Stepanov and L^\\infty norms). The regularity and almost periodicity properties of such solutions are studied. Theorems are also established concerning their solvability in spaces of Besicovitch almost periodic functions. The majority of the results are obtained without any compactness assumptions. Bibliography: 30 titles.

Distribution of joint local and total size and of extension for avalanches in the Brownian force model

NASA Astrophysics Data System (ADS)

Delorme, Mathieu; Le Doussal, Pierre; Wiese, Kay Jörg

2016-05-01

The Brownian force model is a mean-field model for local velocities during avalanches in elastic interfaces of internal space dimension d , driven in a random medium. It is exactly solvable via a nonlinear differential equation. We study avalanches following a kick, i.e., a step in the driving force. We first recall the calculation of the distributions of the global size (total swept area) and of the local jump size for an arbitrary kick amplitude. We extend this calculation to the joint density of local and global sizes within a single avalanche in the limit of an infinitesimal kick. When the interface is driven by a single point, we find new exponents τ0=5 /3 and τ =7 /4 , depending on whether the force or the displacement is imposed. We show that the extension of a "single avalanche" along one internal direction (i.e., the total length in d =1 ) is finite, and we calculate its distribution following either a local or a global kick. In all cases, it exhibits a divergence P (ℓ ) ˜ℓ-3 at small ℓ . Most of our results are tested in a numerical simulation in dimension d =1 .

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

NASA Astrophysics Data System (ADS)

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

2009-10-01

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

TRIBUTE: Brian G Wybourne: Innovator

NASA Astrophysics Data System (ADS)

Louck, James D.

2006-03-01

This volume encloses the Proceedings of the Eighth Summer School on Theoretical Physics under the banner title Symmetry and Structural Properties of Condensed Matter (SSPCM 2005). The School, organised by Rzeszów University of Technology, Poland, together with Laboratory of Physical Foundation of Information Processing, Poland (LFPPI), was held between 31 August and 7 September 2005 in Myczkowce. The main goal of the whole series of biannual SSPCM schools (since 1990) is promotion of advanced mathematical methods within condensed matter physics, directed towards its symmetry and structural properties. This SSPCM 05 School focused on the following three main subjects: decoherence and quantum computers; the role of combinatorics in classification of solutions for exactly solvable models; geometric aspects in nanophysics. The Proceedings are divided into three parts accordingly, but particular topics can overlap between main subjects, and be related to problems pursued in previous SSPCM schools. In this way, the present school is concentrated on various aspects of theory and technology of quantum informatics, with the inclusion of exactly solvable models of statistical physics of condensed matter in low dimensions, as some natural theoretical prototypes of a quantum computer. The last SSPCM 05 was devoted to the memory of Professor Brian G Wybourne, a great Inspirer, inestimable Patron and Lecturer of the whole series of these schools. The School gathered together more than 50 participants, both advanced researchers in physics and mathematics, as well as their young collaborators and students, representing altogether 10 countries from all over the world. The Organising Committee would like to express their gratitude to all members of the International Advisory Committee for their opinions and support and to all invited lecturers and contributors for their talks and preparation of their manuscripts. Special thanks are addressed to all participants and everyone who attended for creating such a stimulating and friendly atmosphere during our meeting, and for several valuable discussions. We thank all chairmen for their polite but efficient leading of sessions. Many thanks are due to the referees who improved significantly the quality of papers presented in this volume. The organisers address special thanks to The Nicholas C. Metropolis Mathematics Foundation (USA) for a substantial initiating support, and to the Polish State Committee for Scientific Research. The hospitality of the whole team of the hotel 'Energetyk' Myczkowce is also appreciated.

Bidirectional plant canopy reflection models derived from the radiation transfer equation

NASA Technical Reports Server (NTRS)

Beeth, D. R.

1975-01-01

A collection of bidirectional canopy reflection models was obtained from the solution of the radiation transfer equation for a horizontally homogeneous canopy. A phase function is derived for a collection of bidirectionally reflecting and transmitting planar elements characterized geometrically by slope and azimuth density functions. Two approaches to solving the radiation transfer equation for the canopy are presented. One approach factors the radiation transfer equation into a solvable set of three first-order linear differential equations by assuming that the radiation field within the canopy can be initially approximated by three components: uniformly diffuse downwelling, uniformly diffuse upwelling, and attenuated specular. The solution to these equations, which can be iterated to any degree of accuracy, was used to obtain overall canopy reflection from the formal solution to the radiation transfer equation. A programable solution to canopy overall bidirectional reflection is given for this approach. The special example of Lambertian leaves with constant leaf bidirectional reflection and scattering functions is considered, and a programmable solution for this example is given. The other approach to solving the radiation transfer equation, a generalized Chandrasekhar technique, is presented in the appendix.

Analogue Hawking radiation in an exactly solvable model of BEC

NASA Astrophysics Data System (ADS)

Parola, Alberto; Tettamanti, Manuele; Cacciatori, Sergio L.

2017-09-01

Hawking radiation, the spontaneous emission of thermal photons from an event horizon, is one of the most intriguing and elusive predictions of field theory in curved spacetimes. A formally analogue phenomenon occurs at the supersonic transition of a fluid: in this respect, ultracold gases stand out among the most promising systems but the theoretical modelling of this effect has always been carried out in semiclassical approximation, borrowing part of the analysis from the gravitational analogy. Here we discuss the exact solution of a one-dimensional Bose gas flowing against an obstacle, showing that spontaneous phonon emission (the analogue of Hawking radiation) is predicted without reference to the gravitational analogy. Long after the creation of the obstacle, the fluid settles into a stationary state displaying the emission of sound waves (phonons) in the upstream direction. A careful analysis shows that a precise correspondence between this phenomenon and the spontaneous emission of radiation from an event horizon requires additional conditions to be met in future experiments aimed at identifying the occurrence of the Hawking-like mechanism in Bose-Einstein condensates.

Pseudothermalization in driven-dissipative non-Markovian open quantum systems

NASA Astrophysics Data System (ADS)

Lebreuilly, José; Chiocchetta, Alessio; Carusotto, Iacopo

2018-03-01

We investigate a pseudothermalization effect, where an open quantum system coupled to a nonequilibrated environment consisting of several non-Markovian reservoirs presents an emergent thermal behavior. This thermal behavior is visible at both static and dynamical levels and the system satisfies the fluctuation-dissipation theorem. Our analysis is focused on the exactly solvable model of a weakly interacting driven-dissipative Bose gas in presence of frequency-dependent particle pumping and losses, and is based on a quantum Langevin theory, which we derive starting from a microscopical quantum optics model. For generic non-Markovian reservoirs, we demonstrate that the emergence of thermal properties occurs in the range of frequencies corresponding to low-energy excitations. For the specific case of non-Markovian baths verifying the Kennard-Stepanov relation, we show that pseudothermalization can instead occur at all energy scales. The possible implications regarding the interpretation of thermal laws in low-temperature exciton-polariton experiments are discussed. We finally show that the presence of either a saturable pumping or a dispersive environment leads to a breakdown of the pseudothermalization effect.

Single-crossover recombination in discrete time.

PubMed

von Wangenheim, Ute; Baake, Ellen; Baake, Michael

2010-05-01

Modelling the process of recombination leads to a large coupled nonlinear dynamical system. Here, we consider a particular case of recombination in discrete time, allowing only for single crossovers. While the analogous dynamics in continuous time admits a closed solution (Baake and Baake in Can J Math 55:3-41, 2003), this no longer works for discrete time. A more general model (i.e. without the restriction to single crossovers) has been studied before (Bennett in Ann Hum Genet 18:311-317, 1954; Dawson in Theor Popul Biol 58:1-20, 2000; Linear Algebra Appl 348:115-137, 2002) and was solved algorithmically by means of Haldane linearisation. Using the special formalism introduced by Baake and Baake (Can J Math 55:3-41, 2003), we obtain further insight into the single-crossover dynamics and the particular difficulties that arise in discrete time. We then transform the equations to a solvable system in a two-step procedure: linearisation followed by diagonalisation. Still, the coefficients of the second step must be determined in a recursive manner, but once this is done for a given system, they allow for an explicit solution valid for all times.

Scaling laws describe memories of host-pathogen riposte in the HIV population.

PubMed

Barton, John P; Kardar, Mehran; Chakraborty, Arup K

2015-02-17

The enormous genetic diversity and mutability of HIV has prevented effective control of this virus by natural immune responses or vaccination. Evolution of the circulating HIV population has thus occurred in response to diverse, ultimately ineffective, immune selection pressures that randomly change from host to host. We show that the interplay between the diversity of human immune responses and the ways that HIV mutates to evade them results in distinct sets of sequences defined by similar collectively coupled mutations. Scaling laws that relate these sets of sequences resemble those observed in linguistics and other branches of inquiry, and dynamics reminiscent of neural networks are observed. Like neural networks that store memories of past stimulation, the circulating HIV population stores memories of host-pathogen combat won by the virus. We describe an exactly solvable model that captures the main qualitative features of the sets of sequences and a simple mechanistic model for the origin of the observed scaling laws. Our results define collective mutational pathways used by HIV to evade human immune responses, which could guide vaccine design.

Computer simulation of two-dimensional unsteady flows in estuaries and embayments by the method of characteristics : basic theory and the formulation of the numerical method

USGS Publications Warehouse

Lai, Chintu

1977-01-01

Two-dimensional unsteady flows of homogeneous density in estuaries and embayments can be described by hyperbolic, quasi-linear partial differential equations involving three dependent and three independent variables. A linear combination of these equations leads to a parametric equation of characteristic form, which consists of two parts: total differentiation along the bicharacteristics and partial differentiation in space. For its numerical solution, the specified-time-interval scheme has been used. The unknown, partial space-derivative terms can be eliminated first by suitable combinations of difference equations, converted from the corresponding differential forms and written along four selected bicharacteristics and a streamline. Other unknowns are thus made solvable from the known variables on the current time plane. The computation is carried to the second-order accuracy by using trapezoidal rule of integration. Means to handle complex boundary conditions are developed for practical application. Computer programs have been written and a mathematical model has been constructed for flow simulation. The favorable computer outputs suggest further exploration and development of model worthwhile. (Woodard-USGS)

Separation of ion types in tandem mass spectrometry data interpretation -- a graph-theoretic approach.

PubMed

Yan, Bo; Pan, Chongle; Olman, Victor N; Hettich, Robert L; Xu, Ying

2004-01-01

Mass spectrometry is one of the most popular analytical techniques for identification of individual proteins in a protein mixture, one of the basic problems in proteomics. It identifies a protein through identifying its unique mass spectral pattern. While the problem is theoretically solvable, it remains a challenging problem computationally. One of the key challenges comes from the difficulty in distinguishing the N- and C-terminus ions, mostly b- and y-ions respectively. In this paper, we present a graph algorithm for solving the problem of separating bfrom y-ions in a set of mass spectra. We represent each spectral peak as a node and consider two types of edges: a type-1 edge connects two peaks possibly of the same ion types and a type-2 edge connects two peaks possibly of different ion types, predicted based on local information. The ion-separation problem is then formulated and solved as a graph partition problem, which is to partition the graph into three subgraphs, namely b-, y-ions and others respectively, so to maximize the total weight of type-1 edges while minimizing the total weight of type-2 edges within each subgraph. We have developed a dynamic programming algorithm for rigorously solving this graph partition problem and implemented it as a computer program PRIME. We have tested PRIME on 18 data sets of high accurate FT-ICR tandem mass spectra and found that it achieved ~90% accuracy for separation of b- and y- ions.

Nonlocal Symmetry and Interaction Solutions of a Generalized Kadomtsev—Petviashvili Equation

NASA Astrophysics Data System (ADS)

Huang, Li-Li; Chen, Yong; Ma, Zheng-Yi

2016-08-01

A generalized Kadomtsev—Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion (CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev—Petviashvili equation, some Bäcklund transformations (BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further, by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev—Petviashvili equation is proved consistent Riccati expansion (CRE) solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of under Grant Nos. 11275072 and 11435005, Doctoral Program of Higher Education of China under Grant No. 20120076110024, the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No. 61321064, and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213, and Zhejiang Provincial Natural Science Foundation of China under Grant No. LY14A010005

Statistically qualified neuro-analytic failure detection method and system

DOEpatents

Vilim, Richard B.; Garcia, Humberto E.; Chen, Frederick W.

2002-03-02

An apparatus and method for monitoring a process involve development and application of a statistically qualified neuro-analytic (SQNA) model to accurately and reliably identify process change. The development of the SQNA model is accomplished in two stages: deterministic model adaption and stochastic model modification of the deterministic model adaptation. Deterministic model adaption involves formulating an analytic model of the process representing known process characteristics, augmenting the analytic model with a neural network that captures unknown process characteristics, and training the resulting neuro-analytic model by adjusting the neural network weights according to a unique scaled equation error minimization technique. Stochastic model modification involves qualifying any remaining uncertainty in the trained neuro-analytic model by formulating a likelihood function, given an error propagation equation, for computing the probability that the neuro-analytic model generates measured process output. Preferably, the developed SQNA model is validated using known sequential probability ratio tests and applied to the process as an on-line monitoring system. Illustrative of the method and apparatus, the method is applied to a peristaltic pump system.

Generalized model of electromigration with 1:1 (analyte:selector) complexation stoichiometry: part I. Theory.

PubMed

Dubský, Pavel; Müllerová, Ludmila; Dvořák, Martin; Gaš, Bohuslav

2015-03-06

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. Copyright © 2015 Elsevier B.V. All rights reserved.

Correlation of ground tests and analyses of a dynamically scaled Space Station model configuration

NASA Technical Reports Server (NTRS)

Javeed, Mehzad; Edighoffer, Harold H.; Mcgowan, Paul E.

1993-01-01

Verification of analytical models through correlation with ground test results of a complex space truss structure is demonstrated. A multi-component, dynamically scaled space station model configuration is the focus structure for this work. Previously established test/analysis correlation procedures are used to develop improved component analytical models. Integrated system analytical models, consisting of updated component analytical models, are compared with modal test results to establish the accuracy of system-level dynamic predictions. Design sensitivity model updating methods are shown to be effective for providing improved component analytical models. Also, the effects of component model accuracy and interface modeling fidelity on the accuracy of integrated model predictions is examined.