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

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

Continuous family of finite-dimensional representations of a solvable Lie algebra arising from singularities

PubMed Central

Yau, Stephen S.-T.

1983-01-01

A natural mapping from the set of complex analytic isolated hypersurface singularities to the set of finite dimensional Lie algebras is first defined. It is proven that the image under this natural mapping is contained in the set of solvable Lie algebras. This approach gives rise to a continuous inequivalent family of finite dimensional representations of a solvable Lie algebra. PMID:16593401

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.

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.

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

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

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

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

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…

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).

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.

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.

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.

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.

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 large class of solvable multistate Landau–Zener models and quantum integrability

NASA Astrophysics Data System (ADS)

Chernyak, Vladimir Y.; Sinitsyn, Nikolai A.; Sun, Chen

2018-06-01

The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians (Sinitsyn et al 2018 Phys. Rev. Lett. 120 190402). Within the multistate Landau–Zener (MLZ) theory, however, there has been a successful alternative approach to identify and solve complex time-dependent models (Sinitsyn and Chernyak 2017 J. Phys. A: Math. Theor. 50 255203). Here we compare both methods by applying them to a new class of exactly solvable MLZ models. This class contains systems with an arbitrary number of interacting states and shows quick growth with N number of exact adiabatic energy crossing points, which appear at different moments of time. At each N, transition probabilities in these systems can be found analytically and exactly but complexity and variety of solutions in this class also grow with N quickly. We illustrate how common features of solvable MLZ systems appear from quantum integrability and develop an approach to further classification of solvable MLZ problems.

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 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

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.

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.

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.

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.

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.

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.

Analysis of Eigenvalue and Eigenfunction of Klein Gordon Equation Using Asymptotic Iteration Method for Separable Non-central Cylindrical Potential

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Lilis Elviyanti, Isnaini

2018-04-01

Analysis of relativistic energy and wave function for zero spin particles using Klein Gordon equation was influenced by separable noncentral cylindrical potential was solved by asymptotic iteration method (AIM). By using cylindrical coordinates, the Klein Gordon equation for the case of symmetry spin was reduced to three one-dimensional Schrodinger like equations that were solvable using variable separation method. The relativistic energy was calculated numerically with Matlab software, and the general unnormalized wave function was expressed in hypergeometric terms.

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.

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.

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.

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.

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.

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.

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.

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.

Timing variation in an analytically solvable chaotic system

NASA Astrophysics Data System (ADS)

Blakely, J. N.; Milosavljevic, M. S.; Corron, N. J.

2017-02-01

We present analytic solutions for a chaotic dynamical system that do not have the regular timing characteristic of recently reported solvable chaotic systems. The dynamical system can be viewed as a first order filter with binary feedback. The feedback state may be switched only at instants defined by an external clock signal. Generalizing from a period one clock, we show analytic solutions for period two and higher period clocks. We show that even when the clock 'ticks' randomly the chaotic system has an analytic solution. These solutions can be visualized in a stroboscopic map whose complexity increases with the complexity of the clock. We provide both analytic results as well as experimental data from an electronic circuit implementation of the system. Our findings bridge the gap between the irregular timing of well known chaotic systems such as Lorenz and Rossler and the well regulated oscillations of recently reported solvable chaotic systems.

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.

Large-scale semidefinite programming for many-electron quantum mechanics.

PubMed

Mazziotti, David A

2011-02-25

The energy of a many-electron quantum system can be approximated by a constrained optimization of the two-electron reduced density matrix (2-RDM) that is solvable in polynomial time by semidefinite programming (SDP). Here we develop a SDP method for computing strongly correlated 2-RDMs that is 10-20 times faster than previous methods [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. We illustrate with (i) the dissociation of N(2) and (ii) the metal-to-insulator transition of H(50). For H(50) the SDP problem has 9.4×10(6) variables. This advance also expands the feasibility of large-scale applications in quantum information, control, statistics, and economics. © 2011 American Physical Society

Large-Scale Semidefinite Programming for Many-Electron Quantum Mechanics

NASA Astrophysics Data System (ADS)

Mazziotti, David A.

2011-02-01

The energy of a many-electron quantum system can be approximated by a constrained optimization of the two-electron reduced density matrix (2-RDM) that is solvable in polynomial time by semidefinite programming (SDP). Here we develop a SDP method for computing strongly correlated 2-RDMs that is 10-20 times faster than previous methods [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.213001]. We illustrate with (i) the dissociation of N2 and (ii) the metal-to-insulator transition of H50. For H50 the SDP problem has 9.4×106 variables. This advance also expands the feasibility of large-scale applications in quantum information, control, statistics, and economics.

On the rational monodromy-free potentials with sextic growth

NASA Astrophysics Data System (ADS)

Gibbons, J.; Veselov, A. P.

2009-01-01

We study the rational potentials V(x ), with sextic growth at infinity, such that the corresponding one-dimensional Schrödinger equation has no monodromy in the complex domain for all values of the spectral parameter. We investigate in detail the subclass of such potentials which can be constructed by the Darboux transformations from the well-known class of quasiexactly solvable potentials V =x6-νx2+l(l +1)/x2. We show that, in contrast with the case of quadratic growth, there are monodromy-free potentials which have quasirational eigenfunctions, but which cannot be given by this construction. We discuss the relations between the corresponding algebraic varieties and present some elementary solutions of the Calogero-Moser problem in the external field with sextic potential.

Class of exactly solvable scattering potentials in two dimensions, entangled-state pair generation, and a grazing-angle resonance effect

NASA Astrophysics Data System (ADS)

Loran, Farhang; Mostafazadeh, Ali

2017-12-01

We provide an exact solution of the scattering problem for the potentials of the form v (x ,y ) =χa(x ) [v0(x ) +v1(x ) ei α y] , where χa(x ) :=1 for x ∈[0 ,a ] , χa(x ) :=0 for x ∉[0 ,a ] , vj(x ) are real or complex-valued functions, χa(x ) v0(x ) is an exactly solvable scattering potential in one dimension, and α is a positive real parameter. If α exceeds the wave number k of the incident wave, the scattered wave does not depend on the choice of v1(x ) . In particular, v (x ,y ) is invisible if v0(x ) =0 and k <α . For k >α and v1(x ) ≠0 , the scattered wave consists of a finite number of coherent plane-wave pairs ψn± with wave vector: kn=(±√{k2-[nα ] 2 },n α ) , where n =0 ,1 ,2 ,...

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

Integrable Time-Dependent Quantum Hamiltonians

NASA Astrophysics Data System (ADS)

Sinitsyn, Nikolai A.; Yuzbashyan, Emil A.; Chernyak, Vladimir Y.; Patra, Aniket; Sun, Chen

2018-05-01

We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

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.

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 , ∞).

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

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.

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.

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.

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.

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.

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.

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.

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.

Matrix superpotentials

NASA Astrophysics Data System (ADS)

Nikitin, Anatoly G.; Karadzhov, Yuri

2011-07-01

We present a collection of matrix-valued shape invariant potentials which give rise to new exactly solvable problems of SUSY quantum mechanics. It includes all irreducible matrix superpotentials of the generic form W=kQ+\\frac{1}{k} R+P, where k is a variable parameter, Q is the unit matrix multiplied by a real-valued function of independent variable x, and P and R are the Hermitian matrices depending on x. In particular, we recover the Pron'ko-Stroganov 'matrix Coulomb potential' and all known scalar shape invariant potentials of SUSY quantum mechanics. In addition, five new shape invariant potentials are presented. Three of them admit a dual shape invariance, i.e. the related Hamiltonians can be factorized using two non-equivalent superpotentials. We find discrete spectrum and eigenvectors for the corresponding Schrödinger equations and prove that these eigenvectors are normalizable.

Deformation of supersymmetric and conformal quantum mechanics through affine transformations

NASA Technical Reports Server (NTRS)

Spiridonov, Vyacheslav

1993-01-01

Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.

D term and the structure of pointlike and composed spin-0 particles

NASA Astrophysics Data System (ADS)

Hudson, Jonathan; Schweitzer, Peter

2017-12-01

This work deals with form factors of the energy-momentum tensor (EMT) of spin-0 particles and the unknown particle property D term related to the EMT, and it is divided into three parts. The first part explores free, weakly and strongly interacting theories to study EMT form factors with the following findings. (i) The free Klein-Gordon theory predicts for the D term D =-1 . (ii) Even infinitesimally small interactions can drastically impact D . (iii) In strongly interacting theories one can encounter large negative D though notable exceptions exist, which include Goldstone bosons of chiral symmetry breaking. (iv) Contrary to common belief one cannot arbitrarily add "total derivatives" to the EMT. Rather the EMT must be defined in an unambiguous way. The second part deals with the interpretation of the information content of EMT form factors in terms of 3D densities with the following results. (i) The 3D-density formalism is internally consistent. (ii) The description is subject to relativistic corrections but those are acceptably small in phenomenologically relevant situations including nucleons and nuclei. (iii) The free-field result D =-1 persists when a spin-0 boson is not pointlike but "heuristically given some internal structure." The third part investigates the question of whether such "giving of an extended structure" can be implemented dynamically, and it has the following insights. (i) We construct a consistent microscopic theory which, in a certain parametric limit, interpolates between extended and pointlike solutions. (ii) This theory is exactly solvable which is rare in 3 +1 dimensions, admits nontopological solitons of Q -ball type, and has a Gaussian field amplitude. (iii) The interaction of this theory belongs to a class of logarithmic potentials which were discussed in the literature, albeit in different contexts including beyond-standard-model phenomenology, cosmology, and Higgs physics.

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.

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.

Solution of second order supersymmetrical intertwining relations in Minkowski plane

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

Ioffe, M. V., E-mail: m.ioffe@spbu.ru; Kolevatova, E. V., E-mail: e.v.kolev@yandex.ru; Nishnianidze, D. N., E-mail: cutaisi@yahoo.com

2016-08-15

Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the “metric” matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of “metric” matrices, and their properties are discussed.

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

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.

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.

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.

Solvability conditions for dendritic growth in the boundary-layer model with capillary anisotropy

NASA Technical Reports Server (NTRS)

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

1986-01-01

This paper is concerned primarily with the development of an analytic approach to the theory of steady-state velocity selection in the boundary-layer model of dendritic solidification. The two-dimensional version of this model with a fourfold crystalline anisotropy alpha in the surface tension is considered. By extending a WKB method introduced in an earlier paper, the alpha dependence of the selected growth rate is determined in the limit of small alpha; and this rate is studied for large alphas in the limit in which the dimensionless undercooling approaches unity. Portions of the paper are devoted to a reinterpretation of the mathematical structure of the solvability condition in problems of this kind.

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.

Analytically solvable chaotic oscillator based on a first-order filter.

PubMed

Corron, Ned J; Cooper, Roy M; Blakely, Jonathan N

2016-02-01

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.

Analytically solvable chaotic oscillator based on a first-order filter

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

Corron, Ned J.; Cooper, Roy M.; Blakely, Jonathan N.

2016-02-15

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform formore » any stable infinite-impulse response filter is chaotic.« less

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.

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

Inverse problems in quantum chemistry

NASA Astrophysics Data System (ADS)

Karwowski, Jacek

Inverse problems constitute a branch of applied mathematics with well-developed methodology and formalism. A broad family of tasks met in theoretical physics, in civil and mechanical engineering, as well as in various branches of medical and biological sciences has been formulated as specific implementations of the general theory of inverse problems. In this article, it is pointed out that a number of approaches met in quantum chemistry can (and should) be classified as inverse problems. Consequently, the methodology used in these approaches may be enriched by applying ideas and theorems developed within the general field of inverse problems. Several examples, including the RKR method for the construction of potential energy curves, determining parameter values in semiempirical methods, and finding external potentials for which the pertinent Schrödinger equation is exactly solvable, are discussed in detail.

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 Duffin-Kemmer-Petiau oscillator

NASA Technical Reports Server (NTRS)

Nedjadi, Youcef; Barrett, Roger

1995-01-01

In view of current interest in relativistic spin-one systems and the recent work on the Dirac Oscillator, we introduce the Duffin-Kemmer-Petiau (DKP) equation obtained by using an external potential linear in r. Since, in the non-relativistic limit, the spin 1 representation leads to a harmonic oscillator with a spin-orbit coupling of the Thomas form, we call the equation the DKP oscillator. This oscillator is a relativistic generalization of the quantum harmonic oscillator for scalar and vector bosons. We show that it conserves total angular momentum and that it is exactly solvable. We calculate and discuss the eigenspectrum of the DKP oscillator in the spin 1 representation.

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.

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.

The impact of finite-area inhomogeneities on resistive and Hall measurement

NASA Astrophysics Data System (ADS)

Koon, Daniel

2013-03-01

I derive an iterative expression for the electric potential in an otherwise homogeneous thin specimen as the result of a finite-area inhomogeneity in either the direct conductance, the Hall conductance, or both. This expression extends to the finite-area regime the calculation of the effect of such inhomogeneities on the measurement error in the sheet resistance and Hall sheet resistance. I then test these results on the exactly-solvable case of a circular inhomogeneity equally distant from the four electrodes of either a square four-point-probe array on an infinitely large conducting specimen or a circular van der Pauw specimen with symmetrically-placed electrodes.

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.

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

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.

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.

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.

The construction of partner potential from the general potential Rosen-Morse and Manning Rosen in 4 dimensional Schrodinger system

NASA Astrophysics Data System (ADS)

Nathalia Wea, Kristiana; Suparmi, A.; Cari, C.; Wahyulianti

2017-11-01

The solution of the Schrodinger equation with physical potential is the important part in quantum physics. Many methods have been developed to resolve the Schrodinger equation. The Nikiforov-Uvarov method and supersymmetric method are the most methods that interesting to be explored. The supersymmetric method not only used to solve the Schrodinger equation but also used to construct the partner potential from a general potential. In this study, the Nikiforov-Uvarov method was used to solve the Schrodinger equation while the supersymmetric method was used to construction partner potential. The study about the construction of the partner potential from general potential Rosen-Morse and Manning Rosen in D-dimensional Schrodinger system has been done. The partner potential was obtained are solvable. By using the Nikiforov-Uvarov method the eigenfunction of the Schrodinger equation in D-dimensional system with general potential Rosen-Morse and Manning Rosen and the Schrodinger equation in D-dimensional system with partner potential Rosen-Morse and Manning Rosen are determined. The eigenfunctions are different between the Schrodinger equation with general potential and the Schrodinger potential with the partner potential.

Neutrino conversion in a neutrino flux: towards an effective theory of collective oscillations

NASA Astrophysics Data System (ADS)

Hansen, Rasmus S. L.; Smirnov, Alexei Yu.

2018-04-01

Collective oscillations of supernova neutrinos above the neutrino sphere can be completely described by the propagation of individual neutrinos in external potentials and are in this sense a linear phenomenon. An effective theory of collective oscillations can be developed based on certain assumptions about time dependence of these potentials. General conditions for strong flavor transformations are formulated and these transformations can be interpreted as parametric resonance effects induced by periodic modulations of the potentials. We study a simplified and solvable example, where a probe neutrino is propagating in a flux of collinear neutrinos, such that ν ν‑ interactions in the flux are absent. Still, this example retains the main feature—the coherent flavor exchange. Properties of the parametric resonance are studied, and it is shown that integrations over energies and emission points of the flux neutrinos suppress modulations of the potentials and therefore strong transformations. The transformations are also suppressed by changes in densities of background neutrinos and electrons.

Escape rate of Brownian particles from a metastable potential well under time derivative Ornstein-Uhlenbeck noise

NASA Astrophysics Data System (ADS)

Bai, Zhan-Wu; Wang, Ping

2016-03-01

We investigate the escape rate of Brownian particles that move in a cubic metastable potential subjected to an internal time derivative Ornstein-Uhlenbeck noise (DOUN). This noise can induce the ballistic diffusion of force-free Brownian particles. Some new features are found. The escape rate for DOUN shows qualitative different dependence on potential well width compared with OUN which induces normal diffusion. As the potential barrier height decreases, the escape rate of DOUN deviates from Arrhenius law considerably earlier than that of Ornstein-Uhlenbeck noise (OUN). The Brownian particles escape faster under DOUN than that under OUN. A quasi-periodic oscillation occurs in transient state. A solvable case is presented to demonstrate the significant cancellation behavior in the barrier region that governs most of these phenomena. The physical mechanism of the findings can be clarified by the noise features. These characteristics should be common for internal noises that induce superdiffusion, especially the ballistic diffusion.

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.

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.

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.

Two- and three-photon ionization in the noble gases

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

McGuire, E.J.

1981-08-01

By using a characteristic Green's function for an exactly solvable Schroedinger equation with an approximation to the central potential of Hermann and Skillman, the cross section for nonresonant two- and three-photon ionization of Ne, Ar, Kr, and Xe were calculated in jl coupling. Expressions for cross sections in jl coupling are given. Comparison with the Ar two-photon cross section of Pindzola and Kelly, calculated using the many-body theory, the dipole-length approximation, and LS coupling shows a disagreement of as much as a factor of 2. The disagreement appears to arise from distortion introduced by shifting the Green's-function resonances to experimentalmore » values.« less

New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials

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

Marquette, Ian; Quesne, Christiane

2013-04-15

In recent years, many exceptional orthogonal polynomials (EOP) were introduced and used to construct new families of 1D exactly solvable quantum potentials, some of which are shape invariant. In this paper, we construct from Hermite and Laguerre EOP and their related quantum systems new 2D superintegrable Hamiltonians with higher-order integrals of motion and the polynomial algebras generated by their integrals of motion. We obtain the finite-dimensional unitary representations of the polynomial algebras and the corresponding energy spectrum. We also point out a new type of degeneracies of the energy levels of these systems that is associated with holes in sequencesmore » of EOP.« less

Relativistic energy-dispersion relations of 2D rectangular lattices

NASA Astrophysics Data System (ADS)

Ata, Engin; Demirhan, Doğan; Büyükkılıç, Fevzi

2017-04-01

An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters V0, core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.

Effective photon mass and exact translating quantum relativistic structures

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

Haas, Fernando, E-mail: fernando.haas@ufrgs.br; Manrique, Marcos Antonio Albarracin, E-mail: sagret10@hotmail.com

2016-04-15

Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can reveal a localization in the radial direction perpendicular to the wave packet propagation, thanks to a non-vanishing scalar potential. The external electromagnetic field, the particle current density, and the charge density are determined. The stability analysis of the solutions is performed by means of numerical simulations. The results are useful for the description of a charged quantum test particle in the relativistic regime, provided spinmore » effects are not decisive.« less

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.

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.

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.

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.

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.

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.

Position-Dependent Mass Schrödinger Equation for the Morse Potential

NASA Astrophysics Data System (ADS)

Ovando, G.; Peña, J. J.; Morales, J.; López-Bonilla, J.

2017-01-01

The position dependent mass Schrödinger equation (PDMSE) has a wide range of quantum applications such as the study of semiconductors, quantum wells, quantum dots and impurities in crystals, among many others. On the other hand, the Morse potential is one of the most important potential models used to study the electronic properties of diatomic molecules. In this work, the solution of the effective mass one-dimensional Schrödinger equation for the Morse potential is presented. This is done by means of the canonical transformation method in algebraic form. The PDMSE is solved for any model of the proposed kinetic energy operators as for example the BenDaniel-Duke, Gora-Williams, Zhu-Kroemer or Li-Kuhn. Also, in order to solve the PDMSE with Morse potential, we consider a superpotential leading to a special form of the exactly solvable Schrödinger equation of constant mass for a class of multiparameter exponential-type potential along with a proper mass distribution. The proposed approach is general and can be applied in the search of new potentials suitable on science of materials by looking into the viable choices of the mass function.

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.

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.

Protecting coherence by environmental decoherence: a solvable paradigmatic model

NASA Astrophysics Data System (ADS)

Torres, Juan Mauricio; Seligman, Thomas H.

2017-11-01

We consider a particularly simple exactly solvable model for a qubit coupled to sequentially nested environments. The purpose is to exemplify the coherence conserving effect of a central system, that has been reported as a result of increasing the coupling between near and far environment. The paradigmatic example is the Jaynes-Cummings Hamiltonian, which we introduce into a Kossakowski-Lindblad master equation using alternatively the lowering operator of the oscillator or its number operator as Lindblad operators. The harmonic oscillator is regarded as the near environment of the qubit, while effects of a far environment are accounted for by the two options for the dissipative part of the master equation. The exact solution allows us to cover the entire range of coupling strength from the perturbative regime to strong coupling analytically. The coherence conserving effect of the coupling to the far environment is confirmed throughout.

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.

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.

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.

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.

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.

Electron-nuclear corellations for photoinduced dynamics in molecular dimers

NASA Astrophysics Data System (ADS)

Kilin, Dmitri S.; Pereversev, Yuryi V.; Prezhdo, Oleg V.

2003-03-01

Ultrafast photoinduced dynamics of electronic excitation in molecular dimers is drastically affected by dynamic reorganization of of inter- and intra- molecular nuclear configuration modelled by quantized nuclear degree of freedom [1]. The dynamics of the electronic population and nuclear coherence is analyzed with help of both numerical solution of the chain of coupled differential equations for mean coordinate, population inversion, electronic-vibrational correlation etc.[2] and by propagating the Gaussian wavepackets in relevant adiabatic potentials. Intriguing results were obtained in the approximation of small energy difference and small change of nuclear equilibrium configuration for excited electronic states. In the limiting case of resonance between electronic states energy difference and frequency of the nuclear mode these results have been justified by comparison to exactly solvable Jaynes-Cummings model. It has been found that the photoinduced processes in dimer are arranged according to their time scales:(i) fast scale of nuclear motion,(ii) intermediate scale of dynamical redistribution of electronic population between excited states as well as growth and dynamics of electronic -nuclear correlation,(iii) slow scale of electronic population approaching to the quasiequilibrium distribution, decay of electronic-nuclear correlation, and diminishing the amplitude of mean coordinate oscillations, accompanied by essential growth of the nuclear coordinate dispersion associated with the overall nuclear wavepacket width. Demonstrated quantum-relaxational features of photoinduced vibronic dinamical processess in molecular dimers are obtained by simple method, applicable to large biological systems with many degrees of freedom. [1] J. A. Cina, D. S. Kilin, T. S. Humble, J. Chem. Phys. (2003) in press. [2] O. V. Prezhdo, J. Chem. Phys. 117, 2995 (2002).

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.

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)

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.

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.

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.

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.

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.

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.

Eigenfunctions and Eigenvalues for a Scalar Riemann-Hilbert Problem Associated to Inverse Scattering

NASA Astrophysics Data System (ADS)

Pelinovsky, Dmitry E.; Sulem, Catherine

A complete set of eigenfunctions is introduced within the Riemann-Hilbert formalism for spectral problems associated to some solvable nonlinear evolution equations. In particular, we consider the time-independent and time-dependent Schrödinger problems which are related to the KdV and KPI equations possessing solitons and lumps, respectively. Non-standard scalar products, orthogonality and completeness relations are derived for these problems. The complete set of eigenfunctions is used for perturbation theory and bifurcation analysis of eigenvalues supported by the potentials under perturbations. We classify two different types of bifurcations of new eigenvalues and analyze their characteristic features. One type corresponds to thresholdless generation of solitons in the KdV equation, while the other predicts a threshold for generation of lumps in the KPI equation.

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

An Exactly Solvable Model for the Spread of Disease

ERIC Educational Resources Information Center

Mickens, Ronald E.

2012-01-01

We present a new SIR epidemiological model whose exact analytical solution can be calculated. In this model, unlike previous models, the infective population becomes zero at a finite time. Remarkably, these results can be derived from only an elementary knowledge of differential equations.

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.

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.

Analytically Solvable Model of Spreading Dynamics with Non-Poissonian Processes

NASA Astrophysics Data System (ADS)

Jo, Hang-Hyun; Perotti, Juan I.; Kaski, Kimmo; Kertész, János

2014-01-01

Non-Poissonian bursty processes are ubiquitous in natural and social phenomena, yet little is known about their effects on the large-scale spreading dynamics. In order to characterize these effects, we devise an analytically solvable model of susceptible-infected spreading dynamics in infinite systems for arbitrary inter-event time distributions and for the whole time range. Our model is stationary from the beginning, and the role of the lower bound of inter-event times is explicitly considered. The exact solution shows that for early and intermediate times, the burstiness accelerates the spreading as compared to a Poisson-like process with the same mean and same lower bound of inter-event times. Such behavior is opposite for late-time dynamics in finite systems, where the power-law distribution of inter-event times results in a slower and algebraic convergence to a fully infected state in contrast to the exponential decay of the Poisson-like process. We also provide an intuitive argument for the exponent characterizing algebraic convergence.

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.

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

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.

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.

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.

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.

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.

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.

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.

Solvable four-state Landau-Zener model of two interacting qubits with path interference

DOE PAGES

Sinitsyn, Nikolai A.

2015-11-30

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

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.

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.

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

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.

Coherent scattering from semi-infinite non-Hermitian potentials

NASA Astrophysics Data System (ADS)

Ahmed, Zafar; Ghosh, Dona; Kumar, Sachin

2018-02-01

When two identical (coherent) beams are injected at a semi-infinite non-Hermitian medium from left and right, we show that both reflection (rL,rR) and transmission (tL,tR) amplitudes are nonreciprocal. In a parametric domain, there exists spectral singularity (SS) at a real energy E =E*=k*2 and the determinant of the time-reversed two port scattering matrix, i.e., |det(S (-k ) ) |=| tL(-k ) tR(-k ) -rL(-k ) rR(-k ) | , vanishes sharply at k =k* , displaying the phenomenon of coherent perfect absorption (CPA). In the complementary parametric domain, the potential becomes either left or right reflectionless at E =Ez . We rule out the existence of invisibility despite rR(Ei) =0 and tR(Ei) =1 but T (Ei)≠1 , in this avenue. We present two simple exactly solvable models where expressions for E*, Ez, Ei, and parametric conditions on the potential have been obtained in explicit and simple forms. Earlier, the phenomena of SS and CPA have been found to occur only in the scattering complex potentials which are spatially localized (vanish asymptotically) and have tL=tR .

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.

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…

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.

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

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

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…

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

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…

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…

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.

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.

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.

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.

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.

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

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.

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

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.

Neutron whispering gallery

NASA Astrophysics Data System (ADS)

Nesvizhevsky, Valery V.; Voronin, Alexei Yu.; Cubitt, Robert; Protasov, Konstantin V.

2010-02-01

The `whispering gallery' effect has been known since ancient times for sound waves in air, later in water and more recently for a broad range of electromagnetic waves: radio, optics, Roentgen and so on. It consists of wave localization near a curved reflecting surface and is expected for waves of various natures, for instance, for atoms and neutrons. For matter waves, it would include a new feature: a massive particle would be settled in quantum states, with parameters depending on its mass. Here, we present for the first time the quantum whispering-gallery effect for cold neutrons. This phenomenon provides an example of an exactly solvable problem analogous to the `quantum bouncer'; it is complementary to the recently discovered gravitationally bound quantum states of neutrons . These two phenomena provide a direct demonstration of the weak equivalence principle for a massive particle in a pure quantum state. Deeply bound whispering-gallery states are long-living and weakly sensitive to surface potential; highly excited states are short-living and very sensitive to the wall potential shape. Therefore, they are a promising tool for studying fundamental neutron-matter interactions, quantum neutron optics and surface physics effects.

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

Novel quantum phase transition from bounded to extensive entanglement

PubMed Central

Zhang, Zhao; Ahmadain, Amr

2017-01-01

The nature of entanglement in many-body systems is a focus of intense research with the observation that entanglement holds interesting information about quantum correlations in large systems and their relation to phase transitions. In particular, it is well known that although generic, many-body states have large, extensive entropy, ground states of reasonable local Hamiltonians carry much smaller entropy, often associated with the boundary length through the so-called area law. Here we introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states and uncover a remarkable quantum phase transition whereby the entanglement scaling changes from area law into extensively large entropy. This transition shows that entanglement in many-body systems may be enhanced under special circumstances with a potential for generating “useful” entanglement for the purpose of quantum computing and that the full implications of locality and its restrictions on possible ground states may hold further surprises. PMID:28461464

Novel quantum phase transition from bounded to extensive entanglement.

PubMed

Zhang, Zhao; Ahmadain, Amr; Klich, Israel

2017-05-16

The nature of entanglement in many-body systems is a focus of intense research with the observation that entanglement holds interesting information about quantum correlations in large systems and their relation to phase transitions. In particular, it is well known that although generic, many-body states have large, extensive entropy, ground states of reasonable local Hamiltonians carry much smaller entropy, often associated with the boundary length through the so-called area law. Here we introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states and uncover a remarkable quantum phase transition whereby the entanglement scaling changes from area law into extensively large entropy. This transition shows that entanglement in many-body systems may be enhanced under special circumstances with a potential for generating "useful" entanglement for the purpose of quantum computing and that the full implications of locality and its restrictions on possible ground states may hold further surprises.

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

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.

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.

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…

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.

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…

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…

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…

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…

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.

Non-cooperative Brownian donkeys: A solvable 1D model

NASA Astrophysics Data System (ADS)

Jiménez de Cisneros, B.; Reimann, P.; Parrondo, J. M. R.

2003-12-01

A paradigmatic 1D model for Brownian motion in a spatially symmetric, periodic system is tackled analytically. Upon application of an external static force F the system's response is an average current which is positive for F < 0 and negative for F > 0 (absolute negative mobility). Under suitable conditions, the system approaches 100% efficiency when working against the external force F.

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.

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.

Interplay of non-Markov and internal friction effects in the barrier crossing kinetics of biopolymers: insights from an analytically solvable model.

PubMed

Makarov, Dmitrii E

2013-01-07

Conformational rearrangements in biomolecules (such as protein folding or enzyme-ligand binding) are often interpreted in terms of low-dimensional models of barrier crossing such as Kramers' theory. Dimensionality reduction, however, entails memory effects; as a result, the effective frictional drag force along the reaction coordinate nontrivially depends on the time scale of the transition. Moreover, when both solvent and "internal" friction effects are important, their interplay results in a highly nonlinear dependence of the effective friction on solvent viscosity that is not captured by common phenomenological models of barrier crossing. Here, these effects are illustrated using an analytically solvable toy model of an unstructured polymer chain involved in an inter- or intramolecular transition. The transition rate is calculated using the Grote-Hynes and Langer theories, which--unlike Kramers' theory--account for memory. The resulting effective frictional force exerted by the polymer along the reaction coordinate can be rationalized in terms of the effective number of monomers engaged in the transition. Faster transitions (relative to the polymer reconfiguration time scale) involve fewer monomers and, correspondingly, lower friction forces, because the polymer chain does not have enough time to reconfigure in response to the transition.

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.

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.

The harmonic oscillator and the position dependent mass Schroedinger equation: isospectral partners and factorization operators

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

Morales, J.; Ovando, G.; Pena, J. J.

2010-12-23

One of the most important scientific contributions of Professor Marcos Moshinsky has been his study on the harmonic oscillator in quantum theory vis a vis the standard Schroedinger equation with constant mass [1]. However, a simple description of the motion of a particle interacting with an external environment such as happen in compositionally graded alloys consist of replacing the mass by the so-called effective mass that is in general variable and dependent on position. Therefore, honoring in memoriam Marcos Moshinsky, in this work we consider the position-dependent mass Schrodinger equations (PDMSE) for the harmonic oscillator potential model as former potentialmore » as well as with equi-spaced spectrum solutions, i.e. harmonic oscillator isospectral partners. To that purpose, the point canonical transformation method to convert a general second order differential equation (DE), of Sturm-Liouville type, into a Schroedinger-like standard equation is applied to the PDMSE. In that case, the former potential associated to the PDMSE and the potential involved in the Schroedinger-like standard equation are related through a Riccati-type relationship that includes the equivalent of the Witten superpotential to determine the exactly solvable positions-dependent mass distribution (PDMD)m(x). Even though the proposed approach is exemplified with the harmonic oscillator potential, the procedure is general and can be straightforwardly applied to other DEs.« less

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.

Single-particle trajectories reveal two-state diffusion-kinetics of hOGG1 proteins on DNA.

PubMed

Vestergaard, Christian L; Blainey, Paul C; Flyvbjerg, Henrik

2018-03-16

We reanalyze trajectories of hOGG1 repair proteins diffusing on DNA. A previous analysis of these trajectories with the popular mean-squared-displacement approach revealed only simple diffusion. Here, a new optimal estimator of diffusion coefficients reveals two-state kinetics of the protein. A simple, solvable model, in which the protein randomly switches between a loosely bound, highly mobile state and a tightly bound, less mobile state is the simplest possible dynamic model consistent with the data. It yields accurate estimates of hOGG1's (i) diffusivity in each state, uncorrupted by experimental errors arising from shot noise, motion blur and thermal fluctuations of the DNA; (ii) rates of switching between states and (iii) rate of detachment from the DNA. The protein spends roughly equal time in each state. It detaches only from the loosely bound state, with a rate that depends on pH and the salt concentration in solution, while its rates for switching between states are insensitive to both. The diffusivity in the loosely bound state depends primarily on pH and is three to ten times higher than in the tightly bound state. We propose and discuss some new experiments that take full advantage of the new tools of analysis presented here.

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.

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.

Consumer Search, Rationing Rules, and the Consequence for Competition

NASA Astrophysics Data System (ADS)

Ruebeck, Christopher S.

Firms' conjectures about demand are consequential in oligopoly games. Through agent-based modeling of consumers' search for products, we can study the rationing of demand between capacity-constrained firms offering homogeneous products and explore the robustness of analytically solvable models' results. After algorithmically formalizing short-run search behavior rather than assuming a long-run average, this study predicts stronger competition in a two-stage capacity-price game.

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.

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.

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.

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'.

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

Low Energy Spectrum of Proximate Kitaev Spin Liquid α -RuCl3 by Terahertz Spectroscopy

NASA Astrophysics Data System (ADS)

Little, Arielle; Wu, Liang; Kelley, Paige; Banerjee, Arnab; Bridges, Craig; Yan, Jiaqiang; Nagler, Stephen; Mandrus, David; Orenstein, Joseph

A Quantum Spin Liquid (QSL) is an ultra-quantum state of matter with no ordered ground state. Recently, a route to a QSL identified by Kitaev has received a great deal of attention. The compound α -RuCl3, in which Ru atoms form a honeycomb lattice, has been shown to possess Kitaev exchange interactions, although a smaller Heisenberg interaction exists and leads to a zig-zag antiferromagnetic state below 7 K. Because of proximity to the exactly-solvable Kitaev spin-liquid model, this material is considered a potential host for Majorana-like modes. In this work, we use time-domain terahertz (THz) Spectroscopy to probe the low-energy excitations of α -RuCl3. We observe the emergence of a sharp magnetic spin-wave absorption peak below the AFM ordering temperature at 7 K on top of a broad continuum that persists up to room temperature. Additionally we report the polarization dependence of the THz absorption, which reveals optical birefringence, indicating the presence of large monoclinic domains.

Synthetic electromagnetic knot in a three-dimensional skyrmion

PubMed Central

Lee, Wonjae; Gheorghe, Andrei H.; Tiurev, Konstantin; Ollikainen, Tuomas; Möttönen, Mikko; Hall, David S.

2018-01-01

Classical electromagnetism and quantum mechanics are both central to the modern understanding of the physical world and its ongoing technological development. Quantum simulations of electromagnetic forces have the potential to provide information about materials and systems that do not have conveniently solvable theoretical descriptions, such as those related to quantum Hall physics, or that have not been physically observed, such as magnetic monopoles. However, quantum simulations that simultaneously implement all of the principal features of classical electromagnetism have thus far proved elusive. We experimentally realize a simulation in which a charged quantum particle interacts with the knotted electromagnetic fields peculiar to a topological model of ball lightning. These phenomena are induced by precise spatiotemporal control of the spin field of an atomic Bose-Einstein condensate, simultaneously creating a Shankar skyrmion—a topological excitation that was theoretically predicted four decades ago but never before observed experimentally. Our results reveal the versatile capabilities of synthetic electromagnetism and provide the first experimental images of topological three-dimensional skyrmions in a quantum system. PMID:29511735

Dynamics of Fermionic Impurity in One Dimension

NASA Astrophysics Data System (ADS)

Guan, Huijie; Andrei, Natan

2014-03-01

We study the dynamics of a fermionic impurity propagating in a one dimensional infinite line. The system is described by the Gaudin-Yang Model and is exactly solvable by the Nested Bethe Ansatz. Starting from a generic initial state, we obtain the time evolution of the wavefunction by the Yudson Approach in which we expand the initial state with the Nested Bethe Ansatz solutions. One situation that we are interested in is where, initially, the impurity is embedded in host fermions with a lattice configuration and one remove the periodic potential at time zero. We calculate the density profile and correlation functions at a later time. Another situation is to shoot an impurity into a cloud of fermions and calculate the probability for it to pass through. While the repulsive case has been studied already[1], we extend it to the attractive case and study the role of bound states in the evolution. We are also interested in boson impurity problem, where not only impurity interacts with host particles, all host particles interact with each other.

Quantum Brownian motion and its conflict with the second law

NASA Astrophysics Data System (ADS)

Nieuwenhuizen, Theo M.; Allahverdyan, Armen E.

2002-11-01

The Brownian motion of a harmonically bound quantum particle and coupled to a harmonic quantum bath is exactly solvable. At low enough temperatures the stationary state is non-Gibbsian due to an entanglement with the bath. This happens when a cloud of bath modes around the particle is formed. Equilibrium thermodynamics for particle plus bath together, does not imply standard thermodynamics for the particle itself at low T. Various formulations of the second law are then invalid. First, the Clausius inequality can be violated. Second, when the width of the confining potential is suddenly changed, there occurs a relaxation to equilibrium during which the rate of entropy production is partly negative. Third, for non-adiabatic changes of system parameters the rate of energy dissipation can be negative, and, out of equilibrium, cyclic processes are possible which extract work from the bath. Conditions are put forward under which perpetuum mobile of the second kind, having several work extraction cycles, enter the realm of condensed matter physics.

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.

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.

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.

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.

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.

A hidden analytic structure of the Rabi model

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

Moroz, Alexander, E-mail: wavescattering@yahoo.com

2014-01-15

The Rabi model describes the simplest interaction between a cavity mode with a frequency ω{sub c} and a two-level system with a resonance frequency ω{sub 0}. It is shown here that the spectrum of the Rabi model coincides with the support of the discrete Stieltjes integral measure in the orthogonality relations of recently introduced orthogonal polynomials. The exactly solvable limit of the Rabi model corresponding to Δ=ω{sub 0}/(2ω{sub c})=0, which describes a displaced harmonic oscillator, is characterized by the discrete Charlier polynomials in normalized energy ϵ, which are orthogonal on an equidistant lattice. A non-zero value of Δ leads tomore » non-classical discrete orthogonal polynomials ϕ{sub k}(ϵ) and induces a deformation of the underlying equidistant lattice. The results provide a basis for a novel analytic method of solving the Rabi model. The number of ca. 1350 calculable energy levels per parity subspace obtained in double precision (cca 16 digits) by an elementary stepping algorithm is up to two orders of magnitude higher than is possible to obtain by Braak’s solution. Any first n eigenvalues of the Rabi model arranged in increasing order can be determined as zeros of ϕ{sub N}(ϵ) of at least the degree N=n+n{sub t}. The value of n{sub t}>0, which is slowly increasing with n, depends on the required precision. For instance, n{sub t}≃26 for n=1000 and dimensionless interaction constant κ=0.2, if double precision is required. Given that the sequence of the lth zeros x{sub nl}’s of ϕ{sub n}(ϵ)’s defines a monotonically decreasing discrete flow with increasing n, the Rabi model is indistinguishable from an algebraically solvable model in any finite precision. Although we can rigorously prove our results only for dimensionless interaction constant κ<1, numerics and exactly solvable example suggest that the main conclusions remain to be valid also for κ≥1. -- Highlights: •A significantly simplified analytic solution of the Rabi model. •The spectrum is the lattice of discrete orthogonal polynomials. •Up to 1350 levels in double precision can be obtained for a given parity. •Omission of any level can be easily detected.« less

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.

Pilot weather advisor

NASA Technical Reports Server (NTRS)

Kilgore, W. A.; Seth, S.; Crabill, N. L.; Shipley, S. T.; Graffman, I.; Oneill, J.

1992-01-01

The results of the work performed by ViGYAN, Inc., to demonstrate the Pilot Weather Advisor cockpit weather data system using a broadcast satellite communication system are presented. The Pilot Weather Advisor demonstrated that the technical problems involved with transmitting significant amount of weather data to an aircraft in-flight or on-the-ground via satellite are solvable with today's technology. The Pilot Weather Advisor appears to be a viable solution for providing accurate and timely weather information for general aviation aircraft.

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.

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.

Integrable mappings with transcendental invariants

NASA Astrophysics Data System (ADS)

Grammaticos, B.; Ramani, A.

2007-06-01

We examine a family of integrable mappings which possess rational invariants involving polynomials of arbitrarily high degree. Next we extend these mappings to the case where their parameters are functions of the independent variable. The resulting mappings do not preserve any invariant but are solvable by linearisation. Using this result we then proceed to construct the solution of the initial autonomous mappings and use it to explicitly construct the invariant, which turns out to be transcendental in the generic case.

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)).

Sixth-Order Lie Group Integrators

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

Forest, E.

1990-03-01

In this paper we present the coefficients of several 6th order symplectic integrator of the type developed by R. Ruth. To get these results we fully exploit the connection with Lie groups. This integrator, as well as all the explicit integrators of Ruth, may be used in any equation where some sort of Lie bracket is preserved. In fact, if the Lie operator governing the equation of motion is separable into two solvable parts, the Ruth integrators can be used.

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.

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.

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.

Computerized Attendance Accounting and Emergency Assistance Communications: Viable Tools in Secondary School Administration

NASA Technical Reports Server (NTRS)

Roberts, Vasel W.

1971-01-01

In the late 1968, the Space Technology Application Office at the Jet Propulsion Laboratory (JPL) initiated a pilot study to determine whether technological aids could be developed that would help secondary school administrators cope with the volatile and chaotic situations that often accompany student activism, disorders, and riots. The study was conducted in cooperation with the Sacramento City Unified School District (SCUSD) and at the John F. Kennedy Senior High School (JFK) in Sacramento, California. The problems at JFK and in the SCUSD were identified and described to the JPL team by members of the Kennedy staff and personnel at various levels and departments within the school district. The JPL team of engineers restricted their scope to problems that appeared solvable, or at least partially solvable, through the use of technological systems. Thus far, two hardware systems have been developed for use in the school. The first, a personal emergency assistance communication system, has already been tested operationally at JFK and has met the objectives established for it. The second technological aid developed was a computerized attendance accounting system. This system has been fabricated, tested, and installed at JFK. Full-scale operational testing began in April 1971. While studies and hardware tests were in progress at JFK, contacts were made with several other schools in order that, insofar as practicable, hardware designs could allow for possible adaptation to schools other than JFK.

Entanglement entropy production in gravitational collapse: covariant regularization and solvable models

NASA Astrophysics Data System (ADS)

Bianchi, Eugenio; De Lorenzo, Tommaso; Smerlak, Matteo

2015-06-01

We study the dynamics of vacuum entanglement in the process of gravitational collapse and subsequent black hole evaporation. In the first part of the paper, we introduce a covariant regularization of entanglement entropy tailored to curved spacetimes; this regularization allows us to propose precise definitions for the concepts of black hole "exterior entropy" and "radiation entropy." For a Vaidya model of collapse we find results consistent with the standard thermodynamic properties of Hawking radiation. In the second part of the paper, we compute the vacuum entanglement entropy of various spherically-symmetric spacetimes of interest, including the nonsingular black hole model of Bardeen, Hayward, Frolov and Rovelli-Vidotto and the "black hole fireworks" model of Haggard-Rovelli. We discuss specifically the role of event and trapping horizons in connection with the behavior of the radiation entropy at future null infinity. We observe in particular that ( i) in the presence of an event horizon the radiation entropy diverges at the end of the evaporation process, ( ii) in models of nonsingular evaporation (with a trapped region but no event horizon) the generalized second law holds only at early times and is violated in the "purifying" phase, ( iii) at late times the radiation entropy can become negative (i.e. the radiation can be less correlated than the vacuum) before going back to zero leading to an up-down-up behavior for the Page curve of a unitarily evaporating black hole.

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.

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.

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.

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

Dufour, F., E-mail: dufour@math.u-bordeaux1.fr; Prieto-Rumeau, T., E-mail: tprieto@ccia.uned.es

We consider a discrete-time constrained discounted Markov decision process (MDP) with Borel state and action spaces, compact action sets, and lower semi-continuous cost functions. We introduce a set of hypotheses related to a positive weight function which allow us to consider cost functions that might not be bounded below by a constant, and which imply the solvability of the linear programming formulation of the constrained MDP. In particular, we establish the existence of a constrained optimal stationary policy. Our results are illustrated with an application to a fishery management problem.

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.

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.

The rid-redundant procedure in C-Prolog

NASA Technical Reports Server (NTRS)

Chen, Huo-Yan; Wah, Benjamin W.

1987-01-01

C-Prolog can conveniently be used for logical inferences on knowledge bases. However, as similar to many search methods using backward chaining, a large number of redundant computation may be produced in recursive calls. To overcome this problem, the 'rid-redundant' procedure was designed to rid all redundant computations in running multi-recursive procedures. Experimental results obtained for C-Prolog on the Vax 11/780 computer show that there is an order of magnitude improvement in the running time and solvable problem size.

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.

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.

Making classical and quantum canonical general relativity computable through a power series expansion in the inverse cosmological constant.

PubMed

Gambini, R; Pullin, J

2000-12-18

We consider general relativity with a cosmological constant as a perturbative expansion around a completely solvable diffeomorphism invariant field theory. This theory is the lambda --> infinity limit of general relativity. This allows an explicit perturbative computational setup in which the quantum states of the theory and the classical observables can be explicitly computed. An unexpected relationship arises at a quantum level between the discrete spectrum of the volume operator and the allowed values of the cosmological constant.

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.

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.

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.

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.”

Tidal disruption of viscous bodies

NASA Technical Reports Server (NTRS)

Sridhar, S.; Tremaine, S.

1992-01-01

Tidal disruptions are investigated in viscous-fluid planetesimals whose radius is small relative to the distance of closest (parabolic-orbit) approach to a planet. The planetesimal surface is in these conditions always ellipsoidal, facilitating treatment by coupled ODEs which are solvable with high accuracy. While the disrupted planetesimals evolve into needlelike ellipsoids, their density does not decrease. The validity of viscous fluid treatment holds for solid (ice or rock) planetesimals in cases where tidal stresses are greater than material strength, but integrity is maintained by self-gravity.

Convergence analysis of a monotonic penalty method for American option pricing

NASA Astrophysics Data System (ADS)

Zhang, Kai; Yang, Xiaoqi; Teo, Kok Lay

2008-12-01

This paper is devoted to study the convergence analysis of a monotonic penalty method for pricing American options. A monotonic penalty method is first proposed to solve the complementarity problem arising from the valuation of American options, which produces a nonlinear degenerated parabolic PDE with Black-Scholes operator. Based on the variational theory, the solvability and convergence properties of this penalty approach are established in a proper infinite dimensional space. Moreover, the convergence rate of the combination of two power penalty functions is obtained.

Instationary Generalized Stokes Equations in Partially Periodic Domains

NASA Astrophysics Data System (ADS)

Sauer, Jonas

2018-06-01

We consider an instationary generalized Stokes system with nonhomogeneous divergence data under a periodic condition in only some directions. The problem is set in the whole space, the half space or in (after an identification of the periodic directions with a torus) bounded domains with sufficiently regular boundary. We show unique solvability for all times in Muckenhoupt weighted Lebesgue spaces. The divergence condition is dealt with by analyzing the associated reduced Stokes system and in particular by showing maximal regularity of the partially periodic reduced Stokes operator.

Assessing system reliability and allocating resources: a bayesian approach that integrates multi-level data

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

Graves, Todd L; Hamada, Michael S

2008-01-01

Good estimates of the reliability of a system make use of test data and expert knowledge at all available levels. Furthermore, by integrating all these information sources, one can determine how best to allocate scarce testing resources to reduce uncertainty. Both of these goals are facilitated by modern Bayesian computational methods. We apply these tools to examples that were previously solvable only through the use of ingenious approximations, and use genetic algorithms to guide resource allocation.

ORNL`s war on crime, technically speaking

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

Xiques, P.

This paper describes research being carried out by the Center for Applied Science and Technology for Law Enforcement (CASTLE), at Oak Ridge National Laboratory. This program works on projects which are solvable, affordable, and outside the scope of the private sector. Examples are presented of work related to: the lifetime of childrens fingerprints compared to adults; the development of ways of providing cooler body armor; digital enhancement technology applied to security-camera images from crime scenes; victim identification by skeletal reconstruction for use by forensic anthropologists.

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.

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.

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.

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.

Elementary wave interactions in blood flow through artery

NASA Astrophysics Data System (ADS)

Raja Sekhar, T.; Minhajul

2017-10-01

In this paper, we consider the Riemann problem and interaction of elementary waves for the quasilinear hyperbolic system of conservation laws that arises in blood flow through arteries. We study the properties of solution involving shocks and rarefaction waves and establish the existence and uniqueness conditions. We show that the Riemann problem is solvable for arbitrary initial data under certain condition and construct the condition for no-feasible solution. Finally, we present numerical examples with different initial data and discuss all possible interactions of elementary waves.

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

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

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.

N=2 supersymmetric quantum mechanics of N Lieb-Liniger-Yang bosons on a line

NASA Astrophysics Data System (ADS)

Mateos Guilarte, J.; Moreno Mosquera, A.

2017-02-01

A supersymmetric generalization of the Lieb-Liniger-Yang dynamics governing N massive bosons moving on a line with delta interactions among them at coinciding points is developed. The analysis of the delicate balance between integrability and-supersymmetry, starting from the exactly solvable non-supersymmetric LLY system, is one of the paper main concerns. Two extreme regimes of the N parameter are explored: 1) For few bosons we fall in the realm of supersymmetric quantum mechanics with a short number of degrees of freedom, e.g., the SUSY Pösch-Teller potentials if N = 1 . 2) For large N we deal with supersymmetric extensions of many-body systems in the thermodynamic limit akin, e.g., to the supersymmetric Calogero-Sutherland systems. Emphasis will be put in the investigation of the ground-state structure of these quantum mechanical systems enjoying {N}=2 extended supersymmetry without spoiling integrability. The decision about wether or not supersymmetry is spontaneously broken, a central question in SUSY quantum mechanics determined from the ground-state structure, is another goal of the paper.

An analytically solvable three-body break-up model problem in hyperspherical coordinates

NASA Astrophysics Data System (ADS)

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

2012-10-01

An analytically solvable S-wave model for three particles break-up processes is presented. The scattering process is represented by a non-homogeneous Coulombic Schrödinger equation where the driven term is given by a Coulomb-like interaction multiplied by the product of a continuum wave function and a bound state in the particles coordinates. The closed form solution is derived in hyperspherical coordinates leading to an analytic expression for the associated scattering transition amplitude. The proposed scattering model contains most of the difficulties encountered in real three-body scattering problem, e.g., non-separability in the electrons' spherical coordinates and Coulombic asymptotic behavior. Since the coordinates' coupling is completely different, the model provides an alternative test to that given by the Temkin-Poet model. The knowledge of the analytic solution provides an interesting benchmark to test numerical methods dealing with the double continuum, in particular in the asymptotic regions. An hyperspherical Sturmian approach recently developed for three-body collisional problems is used to reproduce to high accuracy the analytical results. In addition to this, we generalized the model generating an approximate wave function possessing the correct radial asymptotic behavior corresponding to an S-wave three-body Coulomb problem. The model allows us to explore the typical structure of the solution of a three-body driven equation, to identify three regions (the driven, the Coulombic and the asymptotic), and to analyze how far one has to go to extract the transition amplitude.

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.

Practice makes perfect: familiarity of task determines success in solvable tasks for free-ranging dogs (Canis lupus familiaris).

PubMed

Bhattacharjee, Debottam; Dasgupta, Sandipan; Biswas, Arpita; Deheria, Jayshree; Gupta, Shreya; Nikhil Dev, N; Udell, Monique; Bhadra, Anindita

2017-07-01

Domestic dogs' (Canis lupus familiaris) socio-cognitive faculties have made them highly sensitive to human social cues. While dogs often excel at understanding human communicative gestures, they perform comparatively poorly in problem-solving and physical reasoning tasks. This difference in their behaviour could be due to the lifestyle and intense socialization, where problem solving and physical cognition are less important than social cognition. Free-ranging dogs live in human-dominated environments, not under human supervision and are less socialized. Being scavengers, they often encounter challenges where problem solving is required in order to get access to food. We tested Indian street dogs in familiar and unfamiliar independent solvable tasks and quantified their persistence and dependence on a novel human experimenter, in addition to their success in solving a task. Our results indicate that free-ranging dogs succeeded and persisted more in the familiar task as compared to the unfamiliar one. They showed negligible amount of human dependence in the familiar task, but showed prolonged gazing and considerable begging behaviour to the human experimenter in the context of the unfamiliar task. Cognitive abilities of free-ranging dogs thus play a pivotal role in determining task-associated behaviours based on familiarity. In addition to that, these dogs inherently tend to socialize with and depend on humans, even if they are strangers. Our results also illustrate free-ranging dogs' low competence at physical cognitive tasks.

Fast and Accurate Multivariate Gaussian Modeling of Protein Families: Predicting Residue Contacts and Protein-Interaction Partners

PubMed Central

Feinauer, Christoph; Procaccini, Andrea; Zecchina, Riccardo; Weigt, Martin; Pagnani, Andrea

2014-01-01

In the course of evolution, proteins show a remarkable conservation of their three-dimensional structure and their biological function, leading to strong evolutionary constraints on the sequence variability between homologous proteins. Our method aims at extracting such constraints from rapidly accumulating sequence data, and thereby at inferring protein structure and function from sequence information alone. Recently, global statistical inference methods (e.g. direct-coupling analysis, sparse inverse covariance estimation) have achieved a breakthrough towards this aim, and their predictions have been successfully implemented into tertiary and quaternary protein structure prediction methods. However, due to the discrete nature of the underlying variable (amino-acids), exact inference requires exponential time in the protein length, and efficient approximations are needed for practical applicability. Here we propose a very efficient multivariate Gaussian modeling approach as a variant of direct-coupling analysis: the discrete amino-acid variables are replaced by continuous Gaussian random variables. The resulting statistical inference problem is efficiently and exactly solvable. We show that the quality of inference is comparable or superior to the one achieved by mean-field approximations to inference with discrete variables, as done by direct-coupling analysis. This is true for (i) the prediction of residue-residue contacts in proteins, and (ii) the identification of protein-protein interaction partner in bacterial signal transduction. An implementation of our multivariate Gaussian approach is available at the website http://areeweb.polito.it/ricerca/cmp/code. PMID:24663061

Whispering gallery states of neutrons and anti-hydrogen atoms and their applications to fundamental and surface physics

NASA Astrophysics Data System (ADS)

Nesvizhevsky, Valery

2013-03-01

The `whispering gallery' effect has been known since ancient times for sound waves in air, later in water and more recently for a broad range of electromagnetic waves: radio, optics, Roentgen and so on. It is intensively used and explored due to its numerous crucial applications. It consists of wave localization near a curved reflecting surface and is expected for waves of various natures, for instance, for neutrons and (anti)atoms. For (anti)matter waves, it includes a new feature: a massive particle is settled in quantum states, with parameters depending on its mass. In this talk, we present the first observation of the quantum whispering-gallery effect for matter particles (cold neutrons) 1-2. This phenomenon provides an example of an exactly solvable problem analogous to the `quantum bouncer'; it is complementary to recently discovered gravitational quantum states of neutrons3. These two phenomena provide a direct demonstration of the weak equivalence principle for a massive particle in a quantum state. Deeply bound long-living states are weakly sensitive to surface potential; highly excited short-living states are very sensitive to the wall nuclear potential shape. Therefore, they are a promising tool for studying fundamental neutron-matter interactions, quantum neutron optics and surface physics effects. Analogous phenomena could be measured with atoms and anti-atoms 4-5.

Ab Initio Optimized Effective Potentials for Real Molecules in Optical Cavities: Photon Contributions to the Molecular Ground State

PubMed Central

2018-01-01

We introduce a simple scheme to efficiently compute photon exchange-correlation contributions due to the coupling to transversal photons as formulated in the newly developed quantum-electrodynamical density-functional theory (QEDFT).1−5 Our construction employs the optimized-effective potential (OEP) approach by means of the Sternheimer equation to avoid the explicit calculation of unoccupied states. We demonstrate the efficiency of the scheme by applying it to an exactly solvable GaAs quantum ring model system, a single azulene molecule, and chains of sodium dimers, all located in optical cavities and described in full real space. While the first example is a two-dimensional system and allows to benchmark the employed approximations, the latter two examples demonstrate that the correlated electron-photon interaction appreciably distorts the ground-state electronic structure of a real molecule. By using this scheme, we not only construct typical electronic observables, such as the electronic ground-state density, but also illustrate how photon observables, such as the photon number, and mixed electron-photon observables, for example, electron–photon correlation functions, become accessible in a density-functional theory (DFT) framework. This work constitutes the first three-dimensional ab initio calculation within the new QEDFT formalism and thus opens up a new computational route for the ab initio study of correlated electron–photon systems in quantum cavities. PMID:29594185

Two dimensional J-matrix approach to quantum scattering

NASA Astrophysics Data System (ADS)

Olumegbon, Ismail Adewale

We present an extension of the J-matrix method of scattering to two dimensions in cylindrical coordinates. In the J-matrix approach we select a zeroth order Hamiltonian, H0, which is exactly solvable in the sense that we select a square integrable basis set that enable us to have an infinite tridiagonal representation for H0. Expanding the wavefunction in this basis makes the wave equation equivalent to a three-term recursion relation for the expansion coefficients. Consequently, finding solutions of the recursion relation is equivalent to solving the original H0 problem (i.e., determining the expansion coefficients of the system's wavefunction). The part of the original potential interaction which cannot be brought to an exact tridiagonal form is cut in an NxN basis space and its matrix elements are computed numerically using Gauss quadrature approach. Hence, this approach embodies powerful tools in the analysis of solutions of the wave equation by exploiting the intimate connection and interplay between tridiagonal matrices and the theory of orthogonal polynomials. In such analysis, one is at liberty to employ a wide range of well established methods and numerical techniques associated with these settings such as quadrature approximation and continued fractions. To demonstrate the utility, usefulness, and accuracy of the extended method we use it to obtain the bound states for an illustrative short range potential problem.

Two dimensional J-matrix approach to quantum scattering

NASA Astrophysics Data System (ADS)

Olumegbon, Ismail Adewale

2013-01-01

We present an extension of the J-matrix method of scattering to two dimensions in cylindrical coordinates. In the J-matrix approach we select a zeroth order Hamiltonian, H0, which is exactly solvable in the sense that we select a square integrable basis set that enable us to have an infinite tridiagonal representation for H0. Expanding the wavefunction in this basis makes the wave equation equivalent to a three-term recursion relation for the expansion coefficients. Consequently, finding solutions of the recursion relation is equivalent to solving the original H0 problem (i.e., determining the expansion coefficients of the system's wavefunction). The part of the original potential interaction which cannot be brought to an exact tridiagonal form is cut in an NxN basis space and its matrix elements are computed numerically using Gauss quadrature approach. Hence, this approach embodies powerful tools in the analysis of solutions of the wave equation by exploiting the intimate connection and interplay between tridiagonal matrices and the theory of orthogonal polynomials. In such analysis, one is at liberty to employ a wide range of well established methods and numerical techniques associated with these settings such as quadrature approximation and continued fractions. To demonstrate the utility, usefulness, and accuracy of the extended method we use it to obtain the bound states for an illustrative short range potential problem.

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.

A Class of Solvable Stopping Games

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

Alvarez, Luis H. R.

We consider a class of Dynkin games in the case where the underlying process evolves according to a one-dimensional but otherwise general diffusion. We establish general conditions under which both the value and the saddle point equilibrium exist and under which the exercise boundaries characterizing the saddle point strategy can be explicitly characterized in terms of a pair of standard first order necessary conditions for optimality. We also analyze those cases where an extremal pair of boundaries exists and investigate the overall impact of increased volatility on the equilibrium stopping strategies and their values.

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.

Resonant Perturbation Theory of Decoherence and Relaxation of Quantum Bits

DOE PAGES

Merkli, M.; Berman, G. P.; Sigal, I. M.

2010-01-01

We describe our recenmore » t results on the resonant perturbation theory of decoherence and relaxation for quantum systems with many qubits. The approach represents a rigorous analysis of the phenomenon of decoherence and relaxation for general N -level systems coupled to reservoirs of bosonic fields. We derive a representation of the reduced dynamics valid for all times t ≥ 0 and for small but fixed interaction strength. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.« less

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.

Solving Lauricella string scattering amplitudes through recurrence relations

NASA Astrophysics Data System (ADS)

Lai, Sheng-Hong; Lee, Jen-Chi; Lee, Taejin; Yang, Yi

2017-09-01

We show that there exist infinite number of recurrence relations valid for all energies among the open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA. Moreover, these infinite number of recurrence relations can be used to solve all the Lauricella SSA and express them in terms of one single four tachyon amplitude. These results extend the solvability of SSA at the high energy, fixed angle scattering limit and those at the Regge scattering limit discovered previously to all kinematic regimes.

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.

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.

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.

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.

Nonlocal symmetry and explicit solutions from the CRE method of the Boussinesq equation

NASA Astrophysics Data System (ADS)

Zhao, Zhonglong; Han, Bo

2018-04-01

In this paper, we analyze the integrability of the Boussinesq equation by using the truncated Painlevé expansion and the CRE method. Based on the truncated Painlevé expansion, the nonlocal symmetry and Bäcklund transformation of this equation are obtained. A prolonged system is introduced to localize the nonlocal symmetry to the local Lie point symmetry. It is proved that the Boussinesq equation is CRE solvable. The two-solitary-wave fusion solutions, single soliton solutions and soliton-cnoidal wave solutions are presented by means of the Bäcklund transformations.

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.

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.

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.

Output regulation control for switched stochastic delay systems with dissipative property under error-dependent switching

NASA Astrophysics Data System (ADS)

Li, L. L.; Jin, C. L.; Ge, X.

2018-01-01

In this paper, the output regulation problem with dissipative property for a class of switched stochastic delay systems is investigated, based on an error-dependent switching law. Under the assumption that none subsystem is solvable for the problem, a sufficient condition is derived by structuring multiple Lyapunov-Krasovskii functionals with respect to multiple supply rates, via designing error feedback regulators. The condition is also established when dissipative property reduces to passive property. Finally, two numerical examples are given to demonstrate the feasibility and efficiency of the present method.

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.

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.

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.

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.

Spectral function from Reduced Density Matrix Functional Theory

NASA Astrophysics Data System (ADS)

Romaniello, Pina; di Sabatino, Stefano; Berger, Jan A.; Reining, Lucia

2015-03-01

In this work we focus on the calculation of the spectral function, which determines, for example, photoemission spectra, from reduced density matrix functional theory. Starting from its definition in terms of the one-body Green's function we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the two-body as well as higher-order density matrices. Various approximations to this expression are explored by using the exactly solvable Hubbard chains.

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.

The {sech}( {\\hat{ξ }} ) -Type Profiles: A Swiss-Army Knife for Exact Analytical Modeling of Thermal Diffusion and Wave Propagation in Graded Media

NASA Astrophysics Data System (ADS)

Krapez, J.-C.

2018-07-01

This work deals with the exact analytical modeling of transfer phenomena in heterogeneous materials exhibiting one-dimensional continuous variations of their properties. Regarding heat transfer, it has recently been shown that by applying a Liouville transformation and multiple Darboux transformations, infinite sequences of solvable profiles of thermal effusivity can be constructed together with the associated temperature (exact) solutions, all in closed-form expressions (vs. the diffusion-time variable and with a growing number of parameters). In addition, a particular class of profiles, the so-called {sech}( {\\hat{ξ }} ) -type profiles, exhibit high agility and at the same time parsimony. In this paper we delve further into the description of these solvable profiles and their properties. Most importantly, their quadrupole formulation is provided, enabling smooth synthetic profiles of effusivity of arbitrary complexity to be built, and allowing the corresponding temperature dynamic response to be obtained very easily thereafter. Examples are given with increasing variability of the effusivity and an increasing number of elementary profiles. These highly flexible profiles are equally relevant to providing an exact analytical solution to wave propagation problems in 1D graded media (i.e., Maxwell's equations, the acoustic equation, the telegraph equation, etc.). From now on, whether it be for diffusion-like or wave-like problems, when the leading properties present (possibly piecewise-) continuously heterogeneous profiles, the classical staircase model can be advantageously replaced by a "high-level" quadrupole model consisting of one or more {sech}( {\\hat{ξ }} ) -type profiles, which makes the latter a true Swiss-Army knife for analytical modeling.

Theoretical analysis of oscillatory terms in lattice heat-current time correlation functions and their contributions to thermal conductivity

NASA Astrophysics Data System (ADS)

Pereverzev, Andrey; Sewell, Tommy

2018-03-01

Lattice heat-current time correlation functions for insulators and semiconductors obtained using molecular dynamics (MD) simulations exhibit features of both pure exponential decay and oscillatory-exponential decay. For some materials the oscillatory terms contribute significantly to the lattice heat conductivity calculated from the correlation functions. However, the origin of the oscillatory terms is not well understood, and their contribution to the heat conductivity is accounted for by fitting them to empirical functions. Here, a translationally invariant expression for the heat current in terms of creation and annihilation operators is derived. By using this full phonon-picture definition of the heat current and applying the relaxation-time approximation we explain, at least in part, the origin of the oscillatory terms in the lattice heat-current correlation function. We discuss the relationship between the crystal Hamiltonian and the magnitude of the oscillatory terms. A solvable one-dimensional model is used to illustrate the potential importance of terms that are omitted in the commonly used phonon-picture expression for the heat current. While the derivations are fully quantum mechanical, classical-limit expressions are provided that enable direct contact with classical quantities obtainable from MD.

Exact, E = 0, classical and quantum solutions for general power-law oscillators

NASA Technical Reports Server (NTRS)

Nieto, Michael Martin; Daboul, Jamil

1995-01-01

For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.

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.

Protein Crystals as Novel Catalytic Materials.

PubMed

Margolin, Alexey L.; Navia, Manuel A.

2001-06-18

In this era of molecular biology, protein crystallization is often considered to be a necessary first step in obtaining structural information through X-ray diffraction analysis. In a different light, protein crystals can also be thought of as materials, whose chemical and physical properties make them broadly attractive and useful across a larger spectrum of disciplines. The full potential of these protein crystalline materials has been severely restricted in practice, however, both by their inherent fragility, and by strongly held skepticism concerning their routine and predictable growth, formulation, and practical application. Fortunately, these problems have turned out to be solvable. A systematic exploration of the biophysics and biochemistry of protein crystallization has shown that one can dependably create new protein crystalline materials more or less at will. In turn, these crystals can be readily strengthened, both chemically and mechanically, to make them suitable for practical commercialization. Today, these novel materials are used as industrial catalysts on a commercial scale, in bioremediation and "green chemistry" applications, and in enantioselective chromatography of pharmaceuticals and fine chemicals. In the near future, their utility will expand, to include the purification of protein drugs, formulation of direct protein therapeutics, and development of adjuvant-less vaccines.

Quantization of charged fields in the presence of critical potential steps

NASA Astrophysics Data System (ADS)

Gavrilov, S. P.; Gitman, D. M.

2016-02-01

QED with strong external backgrounds that can create particles from the vacuum is well developed for the so-called t -electric potential steps, which are time-dependent external electric fields that are switched on and off at some time instants. However, there exist many physically interesting situations where external backgrounds do not switch off at the time infinity. E.g., these are time-independent nonuniform electric fields that are concentrated in restricted space areas. The latter backgrounds represent a kind of spatial x -electric potential steps for charged particles. They can also create particles from the vacuum, the Klein paradox being closely related to this process. Approaches elaborated for treating quantum effects in the t -electric potential steps are not directly applicable to the x -electric potential steps and their generalization for x -electric potential steps was not sufficiently developed. We believe that the present work represents a consistent solution of the latter problem. We have considered a canonical quantization of the Dirac and scalar fields with x -electric potential step and have found in- and out-creation and annihilation operators that allow one to have particle interpretation of the physical system under consideration. To identify in- and out-operators we have performed a detailed mathematical and physical analysis of solutions of the relativistic wave equations with an x -electric potential step with subsequent QFT analysis of correctness of such an identification. We elaborated a nonperturbative (in the external field) technique that allows one to calculate all characteristics of zero-order processes, such, for example, scattering, reflection, and electron-positron pair creation, without radiation corrections, and also to calculate Feynman diagrams that describe all characteristics of processes with interaction between the in-, out-particles and photons. These diagrams have formally the usual form, but contain special propagators. Expressions for these propagators in terms of in- and out-solutions are presented. We apply the elaborated approach to two popular exactly solvable cases of x -electric potential steps, namely, to the Sauter potential and to the Klein step.

First Experimental Realization of the Dirac Oscillator

NASA Astrophysics Data System (ADS)

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

2013-10-01

We present the first experimental microwave realization of the one-dimensional Dirac oscillator, a paradigm in exactly solvable relativistic systems. The experiment relies on a relation of the Dirac oscillator to a corresponding tight-binding system. This tight-binding system is implemented as a microwave system by a chain of coupled dielectric disks, where the coupling is evanescent and can be adjusted appropriately. The resonances of the finite microwave system yield the spectrum of the one-dimensional Dirac oscillator with and without a mass term. The flexibility of the experimental setup allows the implementation of other one-dimensional Dirac-type equations.

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.

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.

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.

Solving fractional optimal control problems within a Chebyshev-Legendre operational technique

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Ezz-Eldien, S. S.; Doha, E. H.; Abdelkawy, M. A.; Baleanu, D.

2017-06-01

In this manuscript, we report a new operational technique for approximating the numerical solution of fractional optimal control (FOC) problems. The operational matrix of the Caputo fractional derivative of the orthonormal Chebyshev polynomial and the Legendre-Gauss quadrature formula are used, and then the Lagrange multiplier scheme is employed for reducing such problems into those consisting of systems of easily solvable algebraic equations. We compare the approximate solutions achieved using our approach with the exact solutions and with those presented in other techniques and we show the accuracy and applicability of the new numerical approach, through two numerical examples.

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.

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.

Early predictors of helpless thoughts and behaviors in children: developmental precursors to depressive cognitions.

PubMed

Cole, David A; Warren, Dana E; Dallaire, Danielle H; Lagrange, Beth; Travis, Rebekah; Ciesla, Jeffrey A

2007-04-01

Learned helplessness behavior and cognitions were assessed in 95 kindergarten-age children during a series of impossible puzzle trials followed by a solvable puzzle trial. Latent growth curve analysis revealed reliable individual differences in the trajectories of children's affect, motivation, and self-cognitions over time. Parents' reports of negative life events, harsh/negative parenting, and warm/positive parenting were associated with their children's learned helplessness behavioral trajectories and outcomes over the course of the puzzle trials. Results support speculations about the developmental origins of depressive explanatory or attributional style in children.

Metaphorical motion in mathematical reasoning: further evidence for pre-motor implementation of structure mapping in abstract domains.

PubMed

Fields, Chris

2013-08-01

The theory of computation and category theory both employ arrow-based notations that suggest that the basic metaphor "state changes are like motions" plays a fundamental role in all mathematical reasoning involving formal manipulations. If this is correct, structure-mapping inferences implemented by the pre-motor action planning system can be expected to be involved in solving any mathematics problems not solvable by table lookups and number line manipulations alone. Available functional imaging studies of multi-digit arithmetic, algebra, geometry and calculus problem solving are consistent with this expectation.

A tensor Banach algebra approach to abstract kinetic equations

NASA Astrophysics Data System (ADS)

Greenberg, W.; van der Mee, C. V. M.

The study deals with a concrete algebraic construction providing the existence theory for abstract kinetic equation boundary-value problems, when the collision operator A is an accretive finite-rank perturbation of the identity operator in a Hilbert space H. An algebraic generalization of the Bochner-Phillips theorem is utilized to study solvability of the abstract boundary-value problem without any regulatory condition. A Banach algebra in which the convolution kernel acts is obtained explicitly, and this result is used to prove a perturbation theorem for bisemigroups, which then plays a vital role in solving the initial equations.

Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method

NASA Astrophysics Data System (ADS)

Schnack, J.; Wendland, O.

2010-12-01

The very interesting magnetic properties of frustrated magnetic molecules are often hardly accessible due to the prohibitive size of the related Hilbert spaces. The finite-temperature Lanczos method is able to treat spin systems for Hilbert space sizes up to 109. Here we first demonstrate for exactly solvable systems that the method is indeed accurate. Then we discuss the thermal properties of one of the biggest magnetic molecules synthesized to date, the icosidodecahedron with antiferromagnetically coupled spins of s = 1/2. We show how genuine quantum features such as the magnetization plateau behave as a function of temperature.

Parallel Implementation of Numerical Solution of Few-Body Problem Using Feynman's Continual Integrals

NASA Astrophysics Data System (ADS)

Naumenko, Mikhail; Samarin, Viacheslav

2018-02-01

Modern parallel computing algorithm has been applied to the solution of the few-body problem. The approach is based on Feynman's continual integrals method implemented in C++ programming language using NVIDIA CUDA technology. A wide range of 3-body and 4-body bound systems has been considered including nuclei described as consisting of protons and neutrons (e.g., 3,4He) and nuclei described as consisting of clusters and nucleons (e.g., 6He). The correctness of the results was checked by the comparison with the exactly solvable 4-body oscillatory system and experimental data.

The Geometric Nature of the Flaschka Transformation

NASA Astrophysics Data System (ADS)

Bloch, Anthony M.; Gay-Balmaz, François; Ratiu, Tudor S.

2017-06-01

We show that the Flaschka map, originally introduced to analyze the dynamics of the integrable Toda lattice system, is the inverse of a momentum map. We discuss the geometrical setting of the map and apply it to the generalized Toda lattice systems on semisimple Lie algebras, the rigid body system on Toda orbits, and to coadjoint orbits of semidirect products groups. In addition, we develop an infinite-dimensional generalization for the group of area preserving diffeomorphisms of the annulus and apply it to the analysis of the dispersionless Toda lattice PDE and the solvable rigid body PDE.

Nonlocal symmetries, solitary waves and cnoidal periodic waves of the (2+1)-dimensional breaking soliton equation

NASA Astrophysics Data System (ADS)

Zou, Li; Tian, Shou-Fu; Feng, Lian-Li

2017-12-01

In this paper, we consider the (2+1)-dimensional breaking soliton equation, which describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. By virtue of the truncated Painlevé expansion method, we obtain the nonlocal symmetry, Bäcklund transformation and Schwarzian form of the equation. Furthermore, by using the consistent Riccati expansion (CRE), we prove that the breaking soliton equation is solvable. Based on the consistent tan-function expansion, we explicitly derive the interaction solutions between solitary waves and cnoidal periodic waves.

Simple analytical model of a thermal diode

NASA Astrophysics Data System (ADS)

Kaushik, Saurabh; Kaushik, Sachin; Marathe, Rahul

2018-05-01

Recently there is a lot of attention given to manipulation of heat by constructing thermal devices such as thermal diodes, transistors and logic gates. Many of the models proposed have an asymmetry which leads to the desired effect. Presence of non-linear interactions among the particles is also essential. But, such models lack analytical understanding. Here we propose a simple, analytically solvable model of a thermal diode. Our model consists of classical spins in contact with multiple heat baths and constant external magnetic fields. Interestingly the magnetic field is the only parameter required to get the effect of heat rectification.

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.

Determination of formal redox potentials in aqueous solution of copper(II) complexes with ligands having nitrogen and oxygen donor atoms and comparison with their EPR and UV-Vis spectral features.

PubMed

Tabbì, Giovanni; Giuffrida, Alessandro; Bonomo, Raffaele P

2013-11-01

Formal redox potentials in aqueous solution were determined for copper(II) complexes with ligands having oxygen and nitrogen as donor atoms. All the chosen copper(II) complexes have well-known stereochemistries (pseudo-octahedral, square planar, square-based pyramidal, trigonal bipyramidal or tetrahedral) as witnessed by their reported spectroscopic, EPR and UV-visible (UV-Vis) features, so that a rough correlation between the measured redox potential and the typical geometrical arrangement of the copper(II) complex could be established. Negative values have been obtained for copper(II) complexes in tetragonally elongated pseudo-octahedral geometries, when measured against Ag/AgCl reference electrode. Copper(II) complexes in tetrahedral environments (or flattened tetrahedral geometries) show positive redox potential values. There is a region, always in the field of negative redox potentials which groups the copper(II) complexes exhibiting square-based pyramidal arrangements. Therefore, it is suggested that a measurement of the formal redox potential could be of great help, when some ambiguities might appear in the interpretation of spectroscopic (EPR and UV-Vis) data. Unfortunately, when the comparison is made between copper(II) complexes in square-based pyramidal geometries and those in square planar environments (or a pseudo-octahedral) a little perturbed by an equatorial tetrahedral distortion, their redox potentials could fall in the same intermediate region. In this case spectroscopic data have to be handled with great care in order to have an answer about a copper complex geometrical characteristics. © 2013.

Redox characterization of the Fe(II)-catalyzed transformation of ferrihydrite to goethite

NASA Astrophysics Data System (ADS)

Jones, Adele M.; Collins, Richard N.; Waite, T. David

2017-12-01

The reduction potential of Fe(II)-Fe(III) (oxyhydr)oxide systems provides an important control on the biogeochemical cycling of redox-sensitive elements such as carbon and nitrogen as well as trace metals and organic contaminants in natural systems. As such, an in-depth understanding of the factors controlling the reduction potential of such systems is critical to predicting the likely transformation, transport and fate of these species in natural and perturbed environments. In this study the mineralogy and reduction potential of ferrihydrite suspensions at pH 6.50 and pH 7.00 were determined over the course of their Fe(II)-catalyzed transformation to lepidocrocite and goethite using X-ray absorption spectroscopy and mediated electrochemical approaches. The measured reduction potentials were compared to those of analogous Fe(II)-Fe(III) (oxyhydr)oxide suspensions reacted for 5 min containing pure ferrihydrite (Fh), lepidocrocite (L) and goethite (Gt). The reduction potentials of the pure Fe(II)-Fe(III) (oxyhydr)oxide suspensions were, respectively, +47.5, -13.5 and -122.3 mV vs. SHE at pH 6.5, and -22.9, -84.1 and -189.7 mV vs. SHE at pH 7. These values are in good agreement with reduction potentials calculated using the Nernst equation and reported thermodynamic solubility products indicating that these suspensions had reached equilibrium within 5 min. The reduction potential of the pH 6.50 Fe(II)-ferrihydrite suspension decreased from +47.4 mV to -126.4 mV over a week, and from -20.1 mV to -188.4 mV (all vs. SHE) after 24 h at pH 7. The changes in reduction potential over time matched well to those calculated from the relative proportion of each pure Fe(III) (oxyhydr)oxide present suggesting that Fe3+ activity was influenced by the mix of iron oxides present rather than the most insoluble solid species. Finally, evidence is provided that adsorbed Fe(II) has the capacity to reduce a significantly larger fraction of a reducible species than the aqueous Fe(II) species with which it is in equilibrium. As an Fe(III) (oxyhydr)oxide suspension in equilibrium with aqueous and adsorbed Fe(II) species possesses a single, unique reduction potential, this suggests that adsorbed Fe(II) is a more facile reductant than aqueous Fe(II).

Adaptive multiconfigurational wave functions.

PubMed

Evangelista, Francesco A

2014-03-28

A method is suggested to build simple multiconfigurational wave functions specified uniquely by an energy cutoff Λ. These are constructed from a model space containing determinants with energy relative to that of the most stable determinant no greater than Λ. The resulting Λ-CI wave function is adaptive, being able to represent both single-reference and multireference electronic states. We also consider a more compact wave function parameterization (Λ+SD-CI), which is based on a small Λ-CI reference and adds a selection of all the singly and doubly excited determinants generated from it. We report two heuristic algorithms to build Λ-CI wave functions. The first is based on an approximate prescreening of the full configuration interaction space, while the second performs a breadth-first search coupled with pruning. The Λ-CI and Λ+SD-CI approaches are used to compute the dissociation curve of N2 and the potential energy curves for the first three singlet states of C2. Special attention is paid to the issue of energy discontinuities caused by changes in the size of the Λ-CI wave function along the potential energy curve. This problem is shown to be solvable by smoothing the matrix elements of the Hamiltonian. Our last example, involving the Cu2O2(2+) core, illustrates an alternative use of the Λ-CI method: as a tool to both estimate the multireference character of a wave function and to create a compact model space to be used in subsequent high-level multireference coupled cluster computations.

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.

Cell-type-dependent action potentials and voltage-gated currents in mouse fungiform taste buds.

PubMed

Kimura, Kenji; Ohtubo, Yoshitaka; Tateno, Katsumi; Takeuchi, Keita; Kumazawa, Takashi; Yoshii, Kiyonori

2014-01-01

Taste receptor cells fire action potentials in response to taste substances to trigger non-exocytotic neurotransmitter release in type II cells and exocytotic release in type III cells. We investigated possible differences between these action potentials fired by mouse taste receptor cells using in situ whole-cell recordings, and subsequently we identified their cell types immunologically with cell-type markers, an IP3 receptor (IP3 R3) for type II cells and a SNARE protein (SNAP-25) for type III cells. Cells not immunoreactive to these antibodies were examined as non-IRCs. Here, we show that type II cells and type III cells fire action potentials using different ionic mechanisms, and that non-IRCs also fire action potentials with either of the ionic mechanisms. The width of action potentials was significantly narrower and their afterhyperpolarization was deeper in type III cells than in type II cells. Na(+) current density was similar in type II cells and type III cells, but it was significantly smaller in non-IRCs than in the others. Although outwardly rectifying current density was similar between type II cells and type III cells, tetraethylammonium (TEA) preferentially suppressed the density in type III cells and the majority of non-IRCs. Our mathematical model revealed that the shape of action potentials depended on the ratio of TEA-sensitive current density and TEA-insensitive current one. The action potentials of type II cells and type III cells under physiological conditions are discussed. © 2013 Federation of European Neuroscience Societies and John Wiley & Sons Ltd.

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.

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

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.

Exploring potential applications of a novel extracellular polymeric substance synthesizing bacterium (Bacillus licheniformis) isolated from gut contents of earthworm (Metaphire posthuma) in environmental remediation.

PubMed

Biswas, Jayanta Kumar; Banerjee, Anurupa; Rai, Mahendra Kumar; Rinklebe, Jörg; Shaheen, Sabry M; Sarkar, Santosh Kumar; Dash, Madhab Chandra; Kaviraj, Anilava; Langer, Uwe; Song, Hocheol; Vithanage, Meththika; Mondal, Monojit; Niazi, Nabeel Khan

2018-05-22

The aim was to isolate, characterize, and explore potentials of gut bacteria from the earthworm (Metaphire posthuma) and imply these bacteria for remediation of Cu(II) and Zn(II). An extracellular polymeric substance (EPS) producing gut bacteria (Bacillus licheniformis strain KX657843) was isolated and identified based on 16S rRNA sequencing and phylogenetic analysis. The strain showed maximum tolerance of 8 and 6 mM for Cu(II) and Zn(II) respectively. It removed 34.5% of Cu(II) and 54.4% of Zn(II) at 25 mg L -1 after 72 and 96 h incubation respectively. The bacteria possessed a great potential to produce indole acetic acid (38.49 μg mL -1 ) at 5 mg mL -1 L-tryptophan following 12 days incubation. The sterilized seeds of mung beans (Vigna radiata) displayed greater germination and growth under bacterium enriched condition. We observed that the bacterial strain phosphate solubilization ability with a maximum of 204.2 mg L -1 in absence of Cu(II) and Zn(II). Endowed with biosurfactant property the bacterium exhibited 24% emulsification index. The bacterium offered significant potential of plant growth promotion, Cu(II) and Zn(II) removal, and as such this study is the first report on EPS producing B. licheniformis KX657843 from earthworm which can be applied as powerful tool in remediation programs of Cu(II) and Zn(II) contaminated sites.

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.

Solving the emergency care crisis in America: the power of the law and storytelling.

PubMed

Maa, John

2012-01-01

An Emergency Department visit that ended tragically prompted my yearlong journey to Washington, DC, and emergency rooms across the country to search for solutions to the national crisis in emergency care. I reached the conclusion that the crisis is entirely solvable, and I developed a three-part solution that includes 1) nationally standardizing and coordinating care, 2) prioritizing resources and incentives in the delivery of emergency care, and 3) inspiring young clinicians to careers in emergency care. Physicians across America should now harness the power of storytelling to strengthen both the delivery of patient care and health care reform efforts on Capitol Hill.

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.

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.

Exact folded-band chaotic oscillator.

PubMed

Corron, Ned J; Blakely, Jonathan N

2012-06-01

An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.

Reimagining NEPA: choices for environmentalists

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

Pollack, S.

1985-01-01

Five years after the end of the environmental decade the movement has split into those whose strategy is to enhance opportunities for grassroots organizing and those whose strategy is to increase internal expertise. The positions of the technocratic and grassroots proponents over the National Environmental Policy Act (NEPA) show that one sees NEPA as a way to empower a new class of professionals, while the other uses NEPA to elevate the importance of citizen's participation in decision making. A third, or deep ecology, perspective criticizes both approaches and treats environmental degradation as a symptom of deeper societal problems, solvable onlymore » by massive changes in current values and institutions.« less

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.

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.

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.

Conditioned invariant subspaces, disturbance decoupling and solutions of rational matrix equations

NASA Technical Reports Server (NTRS)

Li, Z.; Sastry, S. S.

1986-01-01

Conditioned invariant subspaces are introduced both in terms of output injection and in terms of state estimation. Various properties of these subspaces are explored and the problem of disturbance decoupling by output injection (OIP) is defined. It is then shown that OIP is equivalent to the problem of disturbance decoupled estimation as introduced in Willems (1982) and Willems and Commault (1980). Both solvability conditions and a description of solutions for a class of rational matrix equations of the form X(s)M(s) = Q(s) on several ways are given in state-space form. Finally, the problem of output stabilization with respect to a disturbance is briefly addressed.

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.

Failure detection and identification

NASA Technical Reports Server (NTRS)

Massoumnia, Mohammad-Ali; Verghese, George C.; Willsky, Alan S.

1989-01-01

Using the geometric concept of an unobservability subspace, a solution is given to the problem of detecting and identifying control system component failures in linear, time-invariant systems. Conditions are developed for the existence of a causal, linear, time-invariant processor that can detect and uniquely identify a component failure, first for the case where components can fail simultaneously, and then for the case where they fail only one at a time. Explicit design algorithms are provided when these conditions are satisfied. In addition to time-domain solvability conditions, frequency-domain interpretations of the results are given, and connections are drawn with results already available in the literature.

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.

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.

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.

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.

Hypovitaminosis A: international programmatic issues.

PubMed

Underwood, B A

1994-08-01

The virtual elimination of vitamin A deficiency and all its consequences is high on the political agenda as a solvable public health problem by the end of the decade. Five to six times more children in the developing world are likely to be subclinically than clinically deficient. Subclinical deficiency can be detected by newer methodological approaches. Subclinically deficient children are at increased risk of severe and fatal infections. The problem at a population level is avoidable by the appropriate selection and application of a mix of available interventions. Countries are challenged to assess, analyze and take actions to incorporate nutrition concerns into development planning to attain end-of-decade goals.

Solving the Emergency Care Crisis in America: The Power of the Law and Storytelling

PubMed Central

Maa, John

2012-01-01

An Emergency Department visit that ended tragically prompted my yearlong journey to Washington, DC, and emergency rooms across the country to search for solutions to the national crisis in emergency care. I reached the conclusion that the crisis is entirely solvable, and I developed a three-part solution that includes 1) nationally standardizing and coordinating care, 2) prioritizing resources and incentives in the delivery of emergency care, and 3) inspiring young clinicians to careers in emergency care. Physicians across America should now harness the power of storytelling to strengthen both the delivery of patient care and health care reform efforts on Capitol Hill. PMID:23012606

Realization theory and quadratic optimal controllers for systems defined over Banach and Frechet algebras

NASA Technical Reports Server (NTRS)

Byrnes, C. I.

1980-01-01

It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.

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 ).

Reduction of aqueous transition metal species on the surfaces of Fe(II)-containing oxides

USGS Publications Warehouse

White, A.F.; Peterson, M.L.

1996-01-01

Experimental studies demonstrate that structural Fe(II) in magnetite and ilmenite heterogeneously reduce aqueous ferric, cupric, vanadate, and chromate ions at the oxide surfaces over a pH range of 1-7 at 25??C. For an aqueous transition metal m, such reactions are 3[Fe2+Fe3+2]O4(magnetite) + 2/nmz ??? 4[Fe3+2]O3(maghemite) + Fe2+ + 2/nmz-n and 3[Fe2+Ti]O3(ilmenite) + 2/nmz ??? Fe3+2Ti3O9(pseudorutile) + Fe2+ + 2/nmz-n, where z is the valance state and n is the charge transfer number. The half cell potential range for solid state oxidation [Fe(II)] ??? [Fe(III)] is -0.34 to -0.65 V, making structural Fe(II) a stronger reducing agent than aqueous Fe2+ (-0.77 V). Reduction rates for aqueous metal species are linear with time (up to 36 h), decrease with pH, and have rate constants between 0.1 and 3.3 ?? 10-10 mol m-2 s-1. Iron is released to solution both from the above reactions and from dissolution of the oxide surface. In the presence of chromate, Fe2+ is oxidized homogeneously in solution to Fe3+. X-ray photoelectron spectroscopy (XPS) denotes a Fe(III) oxide surface containing reduced Cr(III) and V(IV) species. Magnetite and ilmenite electrode potentials are insensitive to increases in divalent transition metals including Zn(II), Co(II), Mn(II), and Ni(II) and reduced V(IV) and Cr(III) but exhibit a log-linear concentration-potential response to Fe(III) and Cu(II). Complex positive electrode responses occur with increasing Cr(VI) and V(V) concentrations. Potential dynamic scans indicate that the high oxidation potential of dichromate is capable of suppressing the cathodic reductive dissolution of magnetite. Oxide electrode potentials are determined by the Fe(II)/Fe(III) composition of the oxide surface and respond to aqueous ion potentials which accelerate this oxidation process. Natural magnetite sands weathered under anoxic conditions are electrochemically reactive as demonstrated by rapid chromate reduction and the release of aqueous Fe(III) to experimental solution. In contrast, magnetite weathered under oxidizing vadose conditions show minimum reactivity toward chromate ions. The ability of Fe(II) oxides to reduce transition metals in soils and groundwaters will be strongly dependent on the redox environment.

Reduction of aqueous transition metal species on the surfaces of Fe(II) -containing oxides

NASA Astrophysics Data System (ADS)

White, Art F.; Peterson, Maria L.

1996-10-01

Experimental studies demonstrate that structural Fe(II) in magnetite and ilmenite heterogeneously reduce aqueous ferric, cupric, vanadate, and chromate ions at the oxide surfaces over a pH range of 1-7 at 25°C. For an aqueous transition metal m, such reactions are 3[FeFe23+]O+2/nm→4[Fe23+]O+Fe+2/nm and 3[FeTi]O+→Fe23+TiO+Fe+2/nm, where z is the valance state and n is the charge transfer number. The half cell potential range for solid state oxidation [Fe(II)] → [Fe(III)] is -0.34 to -0.65 V, making structural Fe(II) a stronger reducing agent than aqueous Fe 2+ (-0.77 V). Reduction rates for aqueous metal species are linear with time (up to 36 h), decrease with pH, and have rate constants between 0.1 and 3.3 × 10 -10 mol m -2 s -1. Iron is released to solution both from the above reactions and from dissolution of the oxide surface. In the presence of chromate, Fe 2+ is oxidized homogeneously in solution to Fe 3+. X-ray photoelectron spectroscopy (XPS) denotes a Fe(III) oxide surface containing reduced Cr(III) and V(IV) species. Magnetite and ilmenite electrode potentials are insensitive to increases in divalent transition metals including Zn(II), Co(II), Mn(II), and Ni(II) and reduced V(IV) and Cr(III) but exhibit a log-linear concentration-potential response to Fe(III) and Cu(II). Complex positive electrode responses occur with increasing Cr(VI) and V(V) concentrations. Potential dynamic scans indicate that the high oxidation potential of dichromate is capable of suppressing the cathodic reductive dissolution of magnetite. Oxide electrode potentials are determined by the Fe(II)/Fe(III) composition of the oxide surface and respond to aqueous ion potentials which accelerate this oxidation process. Natural magnetite sands weathered under anoxic conditions are electrochemically reactive as demonstrated by rapid chromate reduction and the release of aqueous Fe(III) to experimental solution. In contrast, magnetite weathered under oxidizing vadose conditions show minimum reactivity toward chromate ions. The ability of Fe(II) oxides to reduce transition metals in soils and groundwaters will be strongly dependent on the redox environment.

CD4+ T cell-mediated cytotoxicity is associated with MHC class II expression on malignant CD19+ B cells in diffuse large B cell lymphoma.

PubMed

Zhou, Yong; Zha, Jie; Lin, Zhijuan; Fang, Zhihong; Zeng, Hanyan; Zhao, Jintao; Luo, Yiming; Li, Zhifeng; Xu, Bing

2018-01-15

Diffuse large B cell lymphoma (DLBCL) is a common B cell malignancy with approximately 30% of patients present relapsed or refractory disease after first-line therapy. Research of further treatment options is needed. Cytotoxic CD4 + T cells express cytolytic molecules and have potential antitumor function. Here, we showed that the CD19 + cells from DLBCL patients presented significantly reduced expression of MHC II molecules than those from healthy controls. Three years after the first-line treatment, patients that presented relapsed disease had significantly lower MHC II expression on their CD19 + cells than patients who did not show recurrence. Examining cytotoxic CD4 + T cells show that DLBCL patients presented significantly elevated frequencies of granzyme A-, granzyme B-, and/or perforin-expressing cytotoxic CD4 + T cells. Also, frequency of cytotoxic CD4 + T cells in DLBCL patients was positively correlated with the MHC II expression level. Subsequently, the cytotoxic potential of CD4 + T cells against autologous CD19 + cells was investigated. We found that the cytotoxic potential of CD4 + T cells was highest in MHC II-high, intermediate in MHC II-mid, and lowest in MHC II-low patients. The percentage of MHC II-expressing viable CD19 + cells presented a significant reduction after longer incubation with cytotoxic CD4 + T cells, suggesting that cytotoxic CD4 + T cells preferentially eliminated MHC II-expressing CD19 + cells. Blocking MHC II on CD19 + cells significantly reduced the cytolytic capacity of CD4 + T cells. Despite these discoveries, the frequency of cytotoxic CD4 + T cells did not predict the clinical outcome of DLBCL patients. Together, these results demonstrated that cytotoxic CD4 + T cells presented an MHC II-dependent cytotoxic potential against autologous CD19 + cells and could potentially represent a future treatment option for DLBCL. Copyright © 2017 Elsevier Inc. All rights reserved.

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.

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.

Nine Criteria for a Measure of Scientific Output

PubMed Central

Kreiman, Gabriel; Maunsell, John H. R.

2011-01-01

Scientific research produces new knowledge, technologies, and clinical treatments that can lead to enormous returns. Often, the path from basic research to new paradigms and direct impact on society takes time. Precise quantification of scientific output in the short-term is not an easy task but is critical for evaluating scientists, laboratories, departments, and institutions. While there have been attempts to quantifying scientific output, we argue that current methods are not ideal and suffer from solvable difficulties. Here we propose criteria that a metric should have to be considered a good index of scientific output. Specifically, we argue that such an index should be quantitative, based on robust data, rapidly updated and retrospective, presented with confidence intervals, normalized by number of contributors, career stage and discipline, impractical to manipulate, and focused on quality over quantity. Such an index should be validated through empirical testing. The purpose of quantitatively evaluating scientific output is not to replace careful, rigorous review by experts but rather to complement those efforts. Because it has the potential to greatly influence the efficiency of scientific research, we have a duty to reflect upon and implement novel and rigorous ways of evaluating scientific output. The criteria proposed here provide initial steps toward the systematic development and validation of a metric to evaluate scientific output. PMID:22102840

Looking back at 'looking back': operationalising referential gaze for dingoes in an unsolvable task.

PubMed

Smith, Bradley Philip; Litchfield, Carla Anita

2013-11-01

This paper examined the performance of dingoes (Canis dingo) on the rope-pulling task, previously used by Miklósi et al. (Curr Biol 13:763-766, 2003) to highlight a key distinction in the problem-solving behaviour of wolves compared to dogs when in the company of humans. That is, when dogs were confronted with an unsolvable task, following a solvable version of the task they looked back or gazed at the human, whereas, wolves did not. We replicated the rope-pulling task using 12 sanctuary-housed dingoes and used the Miklósi et al. (Curr Biol 13:763-766, 2003) definition of looking back behaviour to analyse the data. However, at least three different types of look backs were observed in our study. We, then developed a more accurate operational definition of looking back behaviour that was task specific and reanalysed the data. We found that the operational definition employed greatly influences the results, with vague definitions potentially overestimating the prevalence of looking back behaviour. Thus, caution must be taken when interpreting the results of studies utilising looking back as behaviour linked to assistance seeking during problem solving. We present a more stringent definition and make suggestions for future research.

Beyond the cold hit: measuring the impact of the national DNA data bank on public safety at the city and county level.

PubMed

Gabriel, Matthew; Boland, Cherisse; Holt, Cydne

2010-01-01

Over the past decade, the Combined DNA Index System (CODIS) has increased solvability of violent crimes by linking evidence DNA profiles to known offenders. At present, an in-depth analysis of the United States National DNA Data Bank effort has not assessed the success of this national public safety endeavor. Critics of this effort often focus on laboratory and police investigators unable to provide timely investigative support as a root cause(s) of CODIS' failure to increase public safety. By studying a group of nearly 200 DNA cold hits obtained in SFPD criminal investigations from 2001-2006, three key performance metrics (Significance of Cold Hits, Case Progression & Judicial Resolution, and Potential Reduction of Future Criminal Activity) provide a proper context in which to define the impact of CODIS at the City and County level. Further, the analysis of a recidivist group of cold hit offenders and their past interaction with law enforcement established five noteworthy criminal case resolution trends; these trends signify challenges to CODIS in achieving meaningful case resolutions. CODIS' effectiveness and critical activities to support case resolutions are the responsibility of all criminal justice partners in order to achieve long-lasting public safety within the United States.

Challenges and Opportunities for Advancing Work on Climate Change and Public Health.

PubMed

Gould, Solange; Rudolph, Linda

2015-12-09

Climate change poses a major threat to public health. Strategies that address climate change have considerable potential to benefit health and decrease health inequities, yet public health engagement at the intersection of public health, equity, and climate change has been limited. This research seeks to understand the barriers to and opportunities for advancing work at this nexus. We conducted semi-structured in-depth interviews (N = 113) with public health and climate change professionals and thematic analysis. Barriers to public health engagement in addressing climate change include individual perceptions that climate change is not urgent or solvable and insufficient understanding of climate change's health impacts and programmatic connections. Institutional barriers include a lack of public health capacity, authority, and leadership; a narrow framework for public health practice that limits work on the root causes of climate change and health; and compartmentalization within and across sectors. Opportunities include integrating climate change into current public health practice; providing inter-sectoral support for climate solutions with health co-benefits; and using a health frame to engage and mobilize communities. Efforts to increase public health sector engagement should focus on education and communications, building leadership and funding, and increasing work on the shared root causes of climate change and health inequities.

Challenges and Opportunities for Advancing Work on Climate Change and Public Health

PubMed Central

Gould, Solange; Rudolph, Linda

2015-01-01

Climate change poses a major threat to public health. Strategies that address climate change have considerable potential to benefit health and decrease health inequities, yet public health engagement at the intersection of public health, equity, and climate change has been limited. This research seeks to understand the barriers to and opportunities for advancing work at this nexus. We conducted semi-structured in-depth interviews (N = 113) with public health and climate change professionals and thematic analysis. Barriers to public health engagement in addressing climate change include individual perceptions that climate change is not urgent or solvable and insufficient understanding of climate change’s health impacts and programmatic connections. Institutional barriers include a lack of public health capacity, authority, and leadership; a narrow framework for public health practice that limits work on the root causes of climate change and health; and compartmentalization within and across sectors. Opportunities include integrating climate change into current public health practice; providing inter-sectoral support for climate solutions with health co-benefits; and using a health frame to engage and mobilize communities. Efforts to increase public health sector engagement should focus on education and communications, building leadership and funding, and increasing work on the shared root causes of climate change and health inequities. PMID:26690194

Phase diagram of the disordered Bose-Hubbard model

NASA Astrophysics Data System (ADS)

Gurarie, V.; Pollet, L.; Prokof'Ev, N. V.; Svistunov, B. V.; Troyer, M.

2009-12-01

We establish the phase diagram of the disordered three-dimensional Bose-Hubbard model at unity filling which has been controversial for many years. The theorem of inclusions, proven by Pollet [Phys. Rev. Lett. 103, 140402 (2009)] states that the Bose-glass phase always intervenes between the Mott insulating and superfluid phases. Here, we note that assumptions on which the theorem is based exclude phase transitions between gapped (Mott insulator) and gapless phases (Bose glass). The apparent paradox is resolved through a unique mechanism: such transitions have to be of the Griffiths type when the vanishing of the gap at the critical point is due to a zero concentration of rare regions where extreme fluctuations of disorder mimic a regular gapless system. An exactly solvable random transverse field Ising model in one dimension is used to illustrate the point. A highly nontrivial overall shape of the phase diagram is revealed with the worm algorithm. The phase diagram features a long superfluid finger at strong disorder and on-site interaction. Moreover, bosonic superfluidity is extremely robust against disorder in a broad range of interaction parameters; it persists in random potentials nearly 50 (!) times larger than the particle half-bandwidth. Finally, we comment on the feasibility of obtaining this phase diagram in cold-atom experiments, which work with trapped systems at finite temperature.

A relativistically interacting exactly solvable multi-time model for two massless Dirac particles in 1 + 1 dimensions

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

Lienert, Matthias, E-mail: lienert@math.lmu.de

2015-04-15

The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e., a map from (space-time){sup N} to a spin space. This concept was originally proposed by Dirac as the basis of relativistic quantum mechanics. In such a view, interaction potentials are mathematically inconsistent. This fact motivates the search for new mechanisms for relativistic interactions. In this paper, we explore the idea that relativistic interaction can be described by boundary conditions on the set of coincidence points of two particles in space-time. This extends ideas from zero-range physics to amore » relativistic setting. We illustrate the idea at the simplest model which still possesses essential physical properties like Lorentz invariance and a positive definite density: two-time equations for massless Dirac particles in 1 + 1 dimensions. In order to deal with a spatio-temporally non-trivial domain, a necessity in the multi-time picture, we develop a new method to prove existence and uniqueness of classical solutions: a generalized version of the method of characteristics. Both mathematical and physical considerations are combined to precisely formulate and answer the questions of probability conservation, Lorentz invariance, interaction, and antisymmetry.« 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.

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

On the emergence of molecular structure from atomic shape in the 1/r2 harmonium model.

PubMed

Müller-Herold, Ulrich

2006-01-07

The formal similarity of the three-body Hamiltonians for helium and the hydrogen molecule ion is used to demonstrate the unfolding of a rotating dumbbell-like proton distribution from a (1s)2-type electron distribution by smooth variation of the particles' masses in the 1/r2 harmonium model. The 1/r2 harmonium is an exactly solvable modification of the harmonium model (also known as Hooke's law atom) where the attraction between different particles is harmonic and the repulsion between the two equal particles is given by a 1/r2 potential. The dumbbell-like molecular structure appears as an expression of increasing spatial correlation due to increasing mass. It gradually appears in the one-density distribution of the two equal particles if their mass exceeds a critical value depending on the mass of the third particle. For large mass of the equal particles, their one-density distribution approaches an asymptotic form derived from the Born-Oppenheimer treatment of H2+ in the 1/r2 harmonium model. Below the critical value, the one density is a spherical, Gaussian-type atomic density distribution with a maximum at the center of mass. The topological transition at the critical value separates molecular structure and atomic shape as two qualitatively different manifestations of spatial structure.

Black Hole on a Chip: Proposal for a Physical Realization of the Sachdev-Ye-Kitaev model in a Solid-State System

NASA Astrophysics Data System (ADS)

Pikulin, D. I.; Franz, M.

2017-07-01

A system of Majorana zero modes with random infinite-range interactions—the Sachdev-Ye-Kitaev (SYK) model—is thought to exhibit an intriguing relation to the horizons of extremal black holes in two-dimensional anti-de Sitter space. This connection provides a rare example of holographic duality between a solvable quantum-mechanical model and dilaton gravity. Here, we propose a physical realization of the SYK model in a solid-state system. The proposed setup employs the Fu-Kane superconductor realized at the interface between a three-dimensional topological insulator and an ordinary superconductor. The requisite N Majorana zero modes are bound to a nanoscale hole fabricated in the superconductor that is threaded by N quanta of magnetic flux. We show that when the system is tuned to the surface neutrality point (i.e., chemical potential coincident with the Dirac point of the topological insulator surface state) and the hole has sufficiently irregular shape, the Majorana zero modes are described by the SYK Hamiltonian. We perform extensive numerical simulations to demonstrate that the system indeed exhibits physical properties expected of the SYK model, including thermodynamic quantities and two-point as well as four-point correlators, and discuss ways in which these can be observed experimentally.

Redox potential of pheophytin a in photosystem II of two cyanobacteria having the different special pair chlorophylls.

PubMed

Allakhverdiev, Suleyman I; Tomo, Tatsuya; Shimada, Yuichiro; Kindo, Hayato; Nagao, Ryo; Klimov, Vyacheslav V; Mimuro, Mamoru

2010-02-23

Water oxidation by photosystem (PS) II in oxygenic photosynthetic organisms is a major source of energy on the earth, leading to the production of a stable reductant. Mechanisms generating a high oxidation potential for water oxidation have been a major focus of photosynthesis research. This potential has not been estimated directly but has been measured by the redox potential of the primary electron acceptor, pheophytin (Phe) a. However, the reported values for Phe a are still controversial. Here, we measured the redox potential of Phe a under physiological conditions (pH 7.0; 25 degrees C) in two cyanobacteria with different special pair chlorophylls (Chls): Synechocystis sp. PCC 6803, whose special pair for PS II consists of Chl a, and Acaryochloris marina MBIC 11017, whose special pair for PS II consists of Chl d. We obtained redox potentials of -536 +/- 8 mV for Synechocystis sp. PCC 6803 and -478 +/- 24 mV for A. marina on PS II complexes in the presence of 1.0 M betaine. The difference in the redox potential of Phe a between the two species closely corresponded with the difference in the light energy absorbed by Chl a versus Chl d. We estimated the potentials of the special pair of PS II to be 1.20 V and 1.18 V for Synechocystis sp. PCC 6803 (P680) and A. marina (P713), respectively. This clearly indicates conservation in the properties of water-oxidation systems in oxygenic photosynthetic organisms, irrespective of the special-pair chlorophylls.

Action potentials and ion conductances in wild-type and CALHM1-knockout type II taste cells

PubMed Central

Saung, Wint Thu; Foskett, J. Kevin

2017-01-01

Taste bud type II cells fire action potentials in response to tastants, triggering nonvesicular ATP release to gustatory neurons via voltage-gated CALHM1-associated ion channels. Whereas CALHM1 regulates mouse cortical neuron excitability, its roles in regulating type II cell excitability are unknown. In this study, we compared membrane conductances and action potentials in single identified TRPM5-GFP-expressing circumvallate papillae type II cells acutely isolated from wild-type (WT) and Calhm1 knockout (KO) mice. The activation kinetics of large voltage-gated outward currents were accelerated in cells from Calhm1 KO mice, and their associated nonselective tail currents, previously shown to be highly correlated with ATP release, were completely absent in Calhm1 KO cells, suggesting that CALHM1 contributes to all of these currents. Calhm1 deletion did not significantly alter resting membrane potential or input resistance, the amplitudes and kinetics of Na+ currents either estimated from action potentials or recorded from steady-state voltage pulses, or action potential threshold, overshoot peak, afterhyperpolarization, and firing frequency. However, Calhm1 deletion reduced the half-widths of action potentials and accelerated the deactivation kinetics of transient outward currents, suggesting that the CALHM1-associated conductance becomes activated during the repolarization phase of action potentials. NEW & NOTEWORTHY CALHM1 is an essential ion channel component of the ATP neurotransmitter release mechanism in type II taste bud cells. Its contribution to type II cell resting membrane properties and excitability is unknown. Nonselective voltage-gated currents, previously associated with ATP release, were absent in cells lacking CALHM1. Calhm1 deletion was without effects on resting membrane properties or voltage-gated Na+ and K+ channels but contributed modestly to the kinetics of action potentials. PMID:28202574

Action potentials and ion conductances in wild-type and CALHM1-knockout type II taste cells.

PubMed

Ma, Zhongming; Saung, Wint Thu; Foskett, J Kevin

2017-05-01

Taste bud type II cells fire action potentials in response to tastants, triggering nonvesicular ATP release to gustatory neurons via voltage-gated CALHM1-associated ion channels. Whereas CALHM1 regulates mouse cortical neuron excitability, its roles in regulating type II cell excitability are unknown. In this study, we compared membrane conductances and action potentials in single identified TRPM5-GFP-expressing circumvallate papillae type II cells acutely isolated from wild-type (WT) and Calhm1 knockout (KO) mice. The activation kinetics of large voltage-gated outward currents were accelerated in cells from Calhm1 KO mice, and their associated nonselective tail currents, previously shown to be highly correlated with ATP release, were completely absent in Calhm1 KO cells, suggesting that CALHM1 contributes to all of these currents. Calhm1 deletion did not significantly alter resting membrane potential or input resistance, the amplitudes and kinetics of Na + currents either estimated from action potentials or recorded from steady-state voltage pulses, or action potential threshold, overshoot peak, afterhyperpolarization, and firing frequency. However, Calhm1 deletion reduced the half-widths of action potentials and accelerated the deactivation kinetics of transient outward currents, suggesting that the CALHM1-associated conductance becomes activated during the repolarization phase of action potentials. NEW & NOTEWORTHY CALHM1 is an essential ion channel component of the ATP neurotransmitter release mechanism in type II taste bud cells. Its contribution to type II cell resting membrane properties and excitability is unknown. Nonselective voltage-gated currents, previously associated with ATP release, were absent in cells lacking CALHM1. Calhm1 deletion was without effects on resting membrane properties or voltage-gated Na + and K + channels but contributed modestly to the kinetics of action potentials. Copyright © 2017 the American Physiological Society.

Potential Energy Surface Database of Group II Dimer

National Institute of Standards and Technology Data Gateway

SRD 143 NIST Potential Energy Surface Database of Group II Dimer (Web, free access)   This database provides critical atomic and molecular data needed in order to evaluate the feasibility of using laser cooled and trapped Group II atomic species (Mg, Ca, Sr, and Ba) for ultra-precise optical clocks or quantum information processing devices.

Adaptive multiconfigurational wave functions

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

Evangelista, Francesco A., E-mail: francesco.evangelista@emory.edu

2014-03-28

A method is suggested to build simple multiconfigurational wave functions specified uniquely by an energy cutoff Λ. These are constructed from a model space containing determinants with energy relative to that of the most stable determinant no greater than Λ. The resulting Λ-CI wave function is adaptive, being able to represent both single-reference and multireference electronic states. We also consider a more compact wave function parameterization (Λ+SD-CI), which is based on a small Λ-CI reference and adds a selection of all the singly and doubly excited determinants generated from it. We report two heuristic algorithms to build Λ-CI wave functions.more » The first is based on an approximate prescreening of the full configuration interaction space, while the second performs a breadth-first search coupled with pruning. The Λ-CI and Λ+SD-CI approaches are used to compute the dissociation curve of N{sub 2} and the potential energy curves for the first three singlet states of C{sub 2}. Special attention is paid to the issue of energy discontinuities caused by changes in the size of the Λ-CI wave function along the potential energy curve. This problem is shown to be solvable by smoothing the matrix elements of the Hamiltonian. Our last example, involving the Cu{sub 2}O{sub 2}{sup 2+} core, illustrates an alternative use of the Λ-CI method: as a tool to both estimate the multireference character of a wave function and to create a compact model space to be used in subsequent high-level multireference coupled cluster computations.« less

Properties of an intermediate-duration inactivation process of the voltage-gated sodium conductance in rat hippocampal CA1 neurons.

PubMed

French, Christopher R; Zeng, Zhen; Williams, David A; Hill-Yardin, Elisa L; O'Brien, Terence J

2016-02-01

Rapid transmembrane flow of sodium ions produces the depolarizing phase of action potentials (APs) in most excitable tissue through voltage-gated sodium channels (NaV). Macroscopic currents display rapid activation followed by fast inactivation (IF) within milliseconds. Slow inactivation (IS) has been subsequently observed in several preparations including neuronal tissues. IS serves important physiological functions, but the kinetic properties are incompletely characterized, especially the operative timescales. Here we present evidence for an "intermediate inactivation" (II) process in rat hippocampal CA1 neurons with time constants of the order of 100 ms. The half-inactivation potentials (V0.5) of steady-state inactivation curves were hyperpolarized by increasing conditioning pulse duration from 50 to 500 ms and could be described by a sum of Boltzmann relations. II state transitions were observed after opening as well as subthreshold potentials. Entry into II after opening was relatively insensitive to membrane potential, and recovery of II became more rapid at hyperpolarized potentials. Removal of fast inactivation with cytoplasmic papaine revealed time constants of INa decay corresponding to II and IS with long depolarizations. Dynamic clamp revealed attenuation of trains of APs over the 10(2)-ms timescale, suggesting a functional role of II in repetitive firing accommodation. These experimental findings could be reproduced with a five-state Markov model. It is likely that II affects important aspects of hippocampal neuron response and may provide a drug target for sodium channel modulation. Copyright © 2016 the American Physiological Society.

40 CFR 98.356 - Data reporting requirements.

Code of Federal Regulations, 2014 CFR

2014-07-01

...) Maximum CH4 production potential (B0) used as an input to Equation II-1 or II-2 of this subpart, from Table II-1 to this subpart. (4) Methane conversion factor (MCF) used as an input to Equation II-1 or II...

40 CFR 98.356 - Data reporting requirements.

Code of Federal Regulations, 2012 CFR

2012-07-01

...) Maximum CH4 production potential (B0) used as an input to Equation II-1 or II-2 of this subpart, from Table II-1 to this subpart. (4) Methane conversion factor (MCF) used as an input to Equation II-1 or II...

40 CFR 98.356 - Data reporting requirements.

Code of Federal Regulations, 2013 CFR

2013-07-01

...) Maximum CH4 production potential (B0) used as an input to Equation II-1 or II-2 of this subpart, from Table II-1 to this subpart. (4) Methane conversion factor (MCF) used as an input to Equation II-1 or II...

Formal language constrained path problems

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

Barrett, C.; Jacob, R.; Marathe, M.

1997-07-08

In many path finding problems arising in practice, certain patterns of edge/vertex labels in the labeled graph being traversed are allowed/preferred, while others are disallowed. Motivated by such applications as intermodal transportation planning, the authors investigate the complexity of finding feasible paths in a labeled network, where the mode choice for each traveler is specified by a formal language. The main contributions of this paper include the following: (1) the authors show that the problem of finding a shortest path between a source and destination for a traveler whose mode choice is specified as a context free language is solvablemore » efficiently in polynomial time, when the mode choice is specified as a regular language they provide algorithms with improved space and time bounds; (2) in contrast, they show that the problem of finding simple paths between a source and a given destination is NP-hard, even when restricted to very simple regular expressions and/or very simple graphs; (3) for the class of treewidth bounded graphs, they show that (i) the problem of finding a regular language constrained simple path between source and a destination is solvable in polynomial time and (ii) the extension to finding context free language constrained simple paths is NP-complete. Several extensions of these results are presented in the context of finding shortest paths with additional constraints. These results significantly extend the results in [MW95]. As a corollary of the results, they obtain a polynomial time algorithm for the BEST k-SIMILAR PATH problem studied in [SJB97]. The previous best algorithm was given by [SJB97] and takes exponential time in the worst case.« less

Invariant Chain Complexes and Clusters as Platforms for MIF Signaling

PubMed Central

Lindner, Robert

2017-01-01

Invariant chain (Ii/CD74) has been identified as a surface receptor for migration inhibitory factor (MIF). Most cells that express Ii also synthesize major histocompatibility complex class II (MHC II) molecules, which depend on Ii as a chaperone and a targeting factor. The assembly of nonameric complexes consisting of one Ii trimer and three MHC II molecules (each of which is a heterodimer) has been regarded as a prerequisite for efficient delivery to the cell surface. Due to rapid endocytosis, however, only low levels of Ii-MHC II complexes are displayed on the cell surface of professional antigen presenting cells and very little free Ii trimers. The association of Ii and MHC II has been reported to block the interaction with MIF, thus questioning the role of surface Ii as a receptor for MIF on MHC II-expressing cells. Recent work offers a potential solution to this conundrum: Many Ii-complexes at the cell surface appear to be under-saturated with MHC II, leaving unoccupied Ii subunits as potential binding sites for MIF. Some of this work also sheds light on novel aspects of signal transduction by Ii-bound MIF in B-lymphocytes: membrane raft association of Ii-MHC II complexes enables MIF to target Ii-MHC II to antigen-clustered B-cell-receptors (BCR) and to foster BCR-driven signaling and intracellular trafficking. PMID:28208600

78 FR 20616 - Western Pacific Fishery Management Council; Public Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2013-04-05

... Northern Mariana Islands i. Coral reef fisheries ii. Bottomfish fisheries iii. Potential use of Bio... iii. Potential use of Bio-Sampling data to improve fishery data iv. Update of fishery dependent and... and crustacean fisheries ii. Bottomfish fisheries iii. Potential use of Bio-Sampling data to improve...

Synthesis, structural characterization, and pro-apoptotic activity of 1-indanone thiosemicarbazone platinum(II) and palladium(II) complexes: potential as antileukemic agents.

PubMed

Gómez, Natalia; Santos, Diego; Vázquez, Ramiro; Suescun, Leopoldo; Mombrú, Alvaro; Vermeulen, Monica; Finkielsztein, Liliana; Shayo, Carina; Moglioni, Albertina; Gambino, Dinorah; Davio, Carlos

2011-08-01

In the search for alternative chemotherapeutic strategies against leukemia, various 1-indanone thiosemicarbazones, as well as eight novel platinum(II) and palladium(II) complexes, with the formula [MCl₂(HL)] and [M(HL)(L)]Cl, derived from two 1-indanone thiosemicarbazones were synthesized and tested for antiproliferative activity against the human leukemia U937 cell line. The crystal structure of [Pt(HL1)(L1)]Cl·2MeOH, where L1=1-indanone thiosemicarbazone, was solved by X-ray diffraction. Free thiosemicarbazone ligands showed no antiproliferative effect, but the corresponding platinum(II) and palladium(II) complexes inhibited cell proliferation and induced apoptosis. Platinum(II) complexes also displayed selective apoptotic activity in U937 cells but not in peripheral blood monocytes or the human hepatocellular carcinoma HepG2 cell line used to screen for potential hepatotoxicity. Present findings show that, in U937 cells, 1-indanone thiosemicarbazones coordinated to palladium(II) were more cytotoxic than those complexed with platinum(II), although the latter were found to be more selective for leukemic cells suggesting that they are promising compounds with potential therapeutic application against hematological malignancies. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Angiotensin II-aldosterone interaction in human coronary microarteries involves GPR30, EGFR, and endothelial NO synthase.

PubMed

Batenburg, Wendy W; Jansen, Pieter M; van den Bogaerdt, Antoon J; J Danser, Alexander H

2012-04-01

The aim of this study was to investigate the aldosterone-angiotensin (Ang) II interaction in human coronary microarteries (HCMAs). HCMAs, obtained from 75 heart-beating organ donors, were mounted in myographs and exposed to Ang II, either directly or following a 30-min pre-incubation with aldosterone, 17β-oestradiol, hydrocortisone, the p38 mitogen-activated protein kinase (MAPK) inhibitor SB203580, the extracellular regulated kinase 1/2 (ERK1/2) inhibitor PD98059, the GPR30 antagonist G15, or the epidermal growth factor receptor (EGFR) antagonist AG1478. Ang II constricted HCMAs in a concentration-dependent manner. All steroids, at nanomolar levels, potentiated Ang II and G15 prevented this effect. The potentiation disappeared or was reversed into Ang II antagonism at micromolar steroid levels. NO synthase (NOS) inhibition prevented the latter antagonism in the case of 17β-oestradiol, whereas both aldosterone and 17β-oestradiol at micro- (but not nano-) molar levels induced endothelial NOS phosphorylation in human umbilical vein endothelial cells. AG1478, but not SB203580 or PD98059, abolished the Ang II-induced contraction in the presence of aldosterone or 17β-oestradiol, and none of these drugs affected Ang II alone. Steroids including aldosterone affect Ang II-induced vasoconstriction in a biphasic manner. Potentiation occurs at nanomolar steroid levels and depends on GPR30 and EGFR transactivation. At micromolar steroid levels, this potentiation either disappears (aldosterone and hydrocortisone) or is reversed into an inhibition (17β-oestradiol), and this is due to the endothelial NOS activation that occurs at such concentrations.

Potentiometric and electrokinetic signatures of iron(II) interactions with (α,γ)-Fe2O3.

PubMed

Toczydłowska, Diana; Kędra-Królik, Karolina; Nejbert, Krzysztof; Preočanin, Tajana; Rosso, Kevin M; Zarzycki, Piotr

2015-10-21

The electrochemical signatures of Fe(II) interactions with iron(III) oxides are poorly understood, despite their importance in controlling the amount of mobilized iron. Here, we report the potentiometric titration of α,γ-Fe2O3 oxides exposed to Fe(II) ions. We monitored in situ surface and ζ potentials, the ratio of mobilized ferric to ferrous, and the periodically analyzed nanoparticle crystal structure using X-ray diffraction. Electrokinetic potential reveals weak but still noticeable specific sorption of Fe(II) to the oxide surface under acidic conditions, and pronounced adsorption under alkaline conditions that results in a surface potential reversal. By monitoring the aqueous iron(II/III) fraction, we found that the addition of Fe(II) ions produces platinum electrode response consistent with the iron solubility-activity curve. Although, XRD analysis showed no evidence of γ-Fe2O3 transformations along the titration pathway despite iron cycling between aqueous and solid reservoirs, the magnetite formation cannot be ruled out.

Calcium/calmodulin-dependent protein kinase II activity regulates the proliferative potential of growth plate chondrocytes.

PubMed

Li, Yuwei; Ahrens, Molly J; Wu, Amy; Liu, Jennifer; Dudley, Andrew T

2011-01-01

For tissues that develop throughout embryogenesis and into postnatal life, the generation of differentiated cells to promote tissue growth is at odds with the requirement to maintain the stem cell/progenitor cell population to preserve future growth potential. In the growth plate cartilage, this balance is achieved in part by establishing a proliferative phase that amplifies the number of progenitor cells prior to terminal differentiation into hypertrophic chondrocytes. Here, we show that endogenous calcium/calmodulin-dependent protein kinase II (CamkII, also known as Camk2) activity is upregulated prior to hypertrophy and that loss of CamkII function substantially blocks the transition from proliferation to hypertrophy. Wnt signaling and Pthrp-induced phosphatase activity negatively regulate CamkII activity. Release of this repression results in activation of multiple effector pathways, including Runx2- and β-catenin-dependent pathways. We present an integrated model for the regulation of proliferation potential by CamkII activity that has important implications for studies of growth control and adult progenitor/stem cell populations.

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.

Finite-time H∞ control for linear continuous system with norm-bounded disturbance

NASA Astrophysics Data System (ADS)

Meng, Qingyi; Shen, Yanjun

2009-04-01

In this paper, the definition of finite-time H∞ control is presented. The system under consideration is subject to time-varying norm-bounded exogenous disturbance. The main aim of this paper is focused on the design a state feedback controller which ensures that the closed-loop system is finite-time bounded (FTB) and reduces the effect of the disturbance input on the controlled output to a prescribed level. A sufficient condition is presented for the solvability of this problem, which can be reduced to a feasibility problem involving linear matrix inequalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

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.

Transmission of isotropic light across a dielectric surface in two and three dimensions.

NASA Technical Reports Server (NTRS)

Allen, W. A.

1973-01-01

Average transmittance of polarized diffuse light across a dielectric surface is calculated in both two and three dimensions. The incident light in both cases is confined to an angular range measured from the surface normal. Limiting values in three dimensions correspond to known results for two cases, (1) normal incidence, and (2) diffuse light incident from a 180 deg cone. The two-dimensional formulation is solvable in terms of elliptic functions and incomplete elliptic integrals of the first, second, and third kinds. Results are displayed graphically for values of transmittances in excess of 0.9 associated with relative indices of refraction in the range m = 1.0 to m = 2.6.

Statistical Analysis for Collision-free Boson Sampling.

PubMed

Huang, He-Liang; Zhong, Han-Sen; Li, Tan; Li, Feng-Guang; Fu, Xiang-Qun; Zhang, Shuo; Wang, Xiang; Bao, Wan-Su

2017-11-10

Boson sampling is strongly believed to be intractable for classical computers but solvable with photons in linear optics, which raises widespread concern as a rapid way to demonstrate the quantum supremacy. However, due to its solution is mathematically unverifiable, how to certify the experimental results becomes a major difficulty in the boson sampling experiment. Here, we develop a statistical analysis scheme to experimentally certify the collision-free boson sampling. Numerical simulations are performed to show the feasibility and practicability of our scheme, and the effects of realistic experimental conditions are also considered, demonstrating that our proposed scheme is experimentally friendly. Moreover, our broad approach is expected to be generally applied to investigate multi-particle coherent dynamics beyond the boson sampling.

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.

The differential equation of an arbitrary reflecting surface

NASA Astrophysics Data System (ADS)

Melka, Richard F.; Berrettini, Vincent D.; Yousif, Hashim A.

2018-05-01

A differential equation describing the reflection of a light ray incident upon an arbitrary reflecting surface is obtained using the law of reflection. The derived equation is written in terms of a parameter and the value of this parameter determines the nature of the reflecting surface. Under various parametric constraints, the solution of the differential equation leads to the various conic surfaces but is not generally solvable. In addition, the dynamics of the light reflections from the conic surfaces are executed in the Mathematica software. Our derivation is the converse of the traditional approach and our analysis assumes a relation between the object distance and the image distance. This leads to the differential equation of the reflecting surface.

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.

Mean-field description of topological charge 4e superconductors

NASA Astrophysics Data System (ADS)

Gabriele, Victoria; Luo, Jing; Teo, Jeffrey C. Y.

BCS superconductors can be understood by a mean-field approximation of two-body interacting Hamiltonians, whose ground states break charge conservation spontaneously by allowing non-vanishing expectation values of charge 2e Cooper pairs. Topological superconductors, such as one-dimensional p-wave wires, have non-trivial ground states that support robust gapless boundary excitations. We construct a four-body Hamiltonian in one dimension and perform a mean-field analysis. The mean-field Hamiltonian is now quartic in fermions but is still exactly solvable. The ground state exhibits 4-fermion expectation values instead of Cooper pair ones. There also exists a topological phase, where the charge 4e superconductor carries exotic zero energy boundary excitations.

Separation of Variables and Superintegrability; The symmetry of solvable systems

NASA Astrophysics Data System (ADS)

Kalnins, Ernest G.; Kress, Jonathan M.; Miller, Willard, Jr.

2018-06-01

Separation of variables methods for solving partial differential equations are of immense theoretical and practical importance in mathematical physics. They are the most powerful tool known for obtaining explicit solutions of the partial differential equations of mathematical physics. The purpose of this book is to give an up-to-date presentation of the theory of separation of variables and its relation to superintegrability. Collating and presenting it in a unified, updated and a more accessible manner, the results scattered in the literature that the authors have prepared is an invaluable resource for mathematicians and mathematical physicists in particular, as well as science, engineering, geological and biological researchers interested in explicit solutions.

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.

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).

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.

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.

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.

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.

PCLIPS: Parallel CLIPS

NASA Technical Reports Server (NTRS)

Gryphon, Coranth D.; Miller, Mark D.

1991-01-01

PCLIPS (Parallel CLIPS) is a set of extensions to the C Language Integrated Production System (CLIPS) expert system language. PCLIPS is intended to provide an environment for the development of more complex, extensive expert systems. Multiple CLIPS expert systems are now capable of running simultaneously on separate processors, or separate machines, thus dramatically increasing the scope of solvable tasks within the expert systems. As a tool for parallel processing, PCLIPS allows for an expert system to add to its fact-base information generated by other expert systems, thus allowing systems to assist each other in solving a complex problem. This allows individual expert systems to be more compact and efficient, and thus run faster or on smaller machines.

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.

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.

Advanced study of global oceanographic requirements for EOS A/B: Technical volume

NASA Technical Reports Server (NTRS)

1972-01-01

Characteristics of the ocean are considered in terms of U.S. social, scientific and ecomomic priorities and in terms of the measurements that can best be made from a spacecraft. The kinds of information needed to advance the basic ocean sciences, to improve marine transportation and fisheries operations, and to provide information for pollution control are discussed. These information needs were related to sensor concepts and an optimum sensor complement is presented, together with orbital considerations. The data-gathering capabilities of an oceanographic spacecraft were considered in relation to those of terrestrial oceanographic programs, using airborne, surface, and submarine platforms. Data management problems are discussed and are considered to be solvable with current technology.

Quantum stochastic calculus associated with quadratic quantum noises

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

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr; Sinha, Kalyan B., E-mail: kbs-jaya@yahoo.co.in

2016-02-15

We first study a class of fundamental quantum stochastic processes induced by the generators of a six dimensional non-solvable Lie †-algebra consisting of all linear combinations of the generalized Gross Laplacian and its adjoint, annihilation operator, creation operator, conservation, and time, and then we study the quantum stochastic integrals associated with the class of fundamental quantum stochastic processes, and the quantum Itô formula is revisited. The existence and uniqueness of solution of a quantum stochastic differential equation is proved. The unitarity conditions of solutions of quantum stochastic differential equations associated with the fundamental processes are examined. The quantum stochastic calculusmore » extends the Hudson-Parthasarathy quantum stochastic calculus.« less

Integrable scalar cosmologies. II. Can they fit into Gauged Extended Supergravity or be encoded in N=1 superpotentials?

NASA Astrophysics Data System (ADS)

Fré, P.; Sorin, A. S.; Trigiante, M.

2014-04-01

The question whether the integrable one-field cosmologies classified in a previous paper by Fré, Sagnotti and Sorin can be embedded as consistent one-field truncations into Extended Gauged Supergravity or in N=1 supergravity gauged by a superpotential without the use of D-terms is addressed in this paper. The answer is that such an embedding is very difficult and rare but not impossible. Indeed, we were able to find two examples of integrable models embedded in supergravity in this way. Both examples are fitted into N=1 supergravity by means of a very specific and interesting choice of the superpotential W(z). The question whether there are examples of such an embedding in Extended Gauged Supergravity remains open. In the present paper, relying on the embedding tensor formalism we classified all gaugings of the N=2 STU model, confirming, in the absence on hypermultiplets, the uniqueness of the stable de Sitter vacuum found several years ago by Fré, Trigiante and Van Proeyen and excluding the embedding of any integrable cosmological model. A detailed analysis of the space of exact solutions of the first supergravity-embedded integrable cosmological model revealed several new features worth an in-depth consideration. When the scalar potential has an extremum at a negative value, the Universe necessarily collapses into a Big Crunch notwithstanding its spatial flatness. The causal structure of these Universes is quite different from that of the closed, positive curved, Universe: indeed, in this case the particle and event horizons do not coincide and develop complicated patterns. The cosmological consequences of this unexpected mechanism deserve careful consideration. The Cartan fieldshi associated with the Cartan generators of the Lie algebra G, whose number equals the rank r of G/H. For instance, in models associated with toroidal or orbifold compactifications, fields of this type are generically interpreted as radii of the underlying multi-tori. The axion fieldsbI associated with the roots of the Lie algebra G. The kinetic terms of Cartan scalars have the canonical form ∑ir α/i22 ∂μhi∂μ hi, up to constant coefficients, while for the axion scalars entering solvable coset representatives, the αi2 factors leave way to exponential functions exp[βihi] of Cartan fields. The scalar potentials of Gauged Supergravity are polynomial functions of the coset representatives, so that after the truncation to Cartan sectors, setting the axions to constant values, one is led naturally to combinations of exponentials of the type encountered in [1]. Yet the devil lies in the details, since the integrable potentials do result from exponential functions exp[βh], but with rigidly fixed ratios between the βi entering the exponents and the αi entering the kinetic terms. The candidate potentials are displayed in Tables 1 and 2 following the notations and the nomenclature of [1]. As a result, the possible role of integrable potentials in Gauged Supergravity theories is not evident a priori, and actually, the required ratios are quite difficult to be obtained. Notwithstanding these difficulties we were able to identify a pair of examples, showing that although rare, supergravity integrable cosmological models based on G/H scalar manifolds

Actions and mechanisms of action of novel analogues of sotalol on guinea-pig and rabbit ventricular cells.

PubMed Central

Connors, S. P.; Gill, E. W.; Terrar, D. A.

1992-01-01

1. The actions and mechanisms of action of novel analogues of sotalol which prolong cardiac action potentials were investigated in guinea-pig and rabbit isolated ventricular cells. 2. In guinea-pig and rabbit cells the compounds significantly prolonged action potential duration at 20% and 90% repolarization levels without affecting resting membrane potential. In guinea-pig but not rabbit cells there was an increase in action potential amplitude and in rabbit cells there was no change in the shape or position of the 'notch' in the action potential. 3. Possible mechanisms of action were studied in more detail in the case of compound II (1-(4-methanesulphonamidophenoxy)-3-(N-methyl 3,4 dichlorophenylethylamino)-2-propanol). Prolongation of action potential duration continued to occur in the presence of nisoldipine, and calcium currents recorded under voltage-clamp conditions were not reduced by compound II (1 microM). Action potential prolongation by compound II was also unaffected in the presence of 10 microM tetrodotoxin. 4. Compound II (1 microM) did not influence IK1 assessed from the current during ramp changes in membrane potential (20 mV s-1) over the range -90 to -10 mV. 5. Compound II (1 microM) blocked time-dependent delayed rectifier potassium current (IK) activated by step depolarizations and recorded as an outward tail following repolarization. When a submaximal concentration (50 nM) was applied there was no change in the apparent reversal potential of IK.(ABSTRACT TRUNCATED AT 250 WORDS) PMID:1393293

Activation of Group II Metabotropic Glutamate Receptors Induces Depotentiation in Amygdala Slices and Reduces Fear-Potentiated Startle in Rats

ERIC Educational Resources Information Center

Lin, Chia-Ho; Lee, Chia-Ching; Huang, Ya-Chun; Wang, Su-Jane; Gean, Po-Wu

2005-01-01

There is a close correlation between long-term potentiation (LTP) in the synapses of lateral amygdala (LA) and fear conditioning in animals. We predict that reversal of LTP (depotentiation) in this area of the brain may ameliorate conditioned fear. Activation of group II metabotropic glutamate receptors (mGluR II) with DCG-IV induces…

Adsorption of Cd(II) and Pb(II) by in situ oxidized Fe3O4 membrane grafted on 316L porous stainless steel filter tube and its potential application for drinking water treatment.

PubMed

Zhu, Mengfei; Zhu, Li; Wang, Jianlong; Yue, Tianli; Li, Ronghua; Li, Zhonghong

2017-07-01

Removing heavy metal ions from aqueous solutions is one of the most challenging separations. In situ oxidized Fe 3 O 4 membranes using 316L porous stainless steel filter tube have shown great potential for removing anion Cr(VI). Here we report the performances of the in situ oxidized Fe 3 O 4 membranes for removing two toxic cations Cd(II) and Pb(II) commonly existing in water and their potential applications for drinking water purification. The membranes exhibited high removal efficiency: 97% at pH 9.0 for Cd(II) of 1.0 mg/L initial concentration and 100% at pH 5.0-6.0 for Pb(II) of 5.0 mg/L initial concentration. The maximum adsorption capabilities were estimated at 0.800 mg/g and 2.251 mg/g respectively for Cd(II) and Pb(II) at 318 K by the Langmuir model. Results of batch tests revealed the existence of electrostatic attraction and chemisorption. XRD and FT-IR analyses indicated that the chemisorption might be the insertion of Cd(II) and Pb(II) into the Fe 3 O 4 crystal faces of 311 and 511 to form mononuclear or binuclear coordination with O atoms of Fe-O 6 groups. Competitive adsorption of Cd(II) and Pb(II) in binary solutions revealed a preferential adsorption for Pb(II). Na 2 EDTA solution was used to regenerate the membranes, and the maximum desorption ratio was 90.29% and 99.75% respectively for Cd(II) and Pb(II). The membranes were able to efficiently lower Cd(II) and Pb(II) concentrations to meet the drinking water standards recommended by the World Health Organization and are promising for engineering applications aimed at drinking water purification. Copyright © 2017 Elsevier Ltd. All rights reserved.

Extending Romanovski polynomials in quantum mechanics

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

Quesne, C.

2013-12-15

Some extensions of the (third-class) Romanovski polynomials (also called Romanovski/pseudo-Jacobi polynomials), which appear in bound-state wavefunctions of rationally extended Scarf II and Rosen-Morse I potentials, are considered. For the former potentials, the generalized polynomials satisfy a finite orthogonality relation, while for the latter an infinite set of relations among polynomials with degree-dependent parameters is obtained. Both types of relations are counterparts of those known for conventional polynomials. In the absence of any direct information on the zeros of the Romanovski polynomials present in denominators, the regularity of the constructed potentials is checked by taking advantage of the disconjugacy properties ofmore » second-order differential equations of Schrödinger type. It is also shown that on going from Scarf I to Scarf II or from Rosen-Morse II to Rosen-Morse I potentials, the variety of rational extensions is narrowed down from types I, II, and III to type III only.« less

Spectroscopic, electrochemical and photovoltaic properties of Pt(ii) and Pd(ii) complexes of a chelating 1,10-phenanthroline appended perylene diimide.

PubMed

Işık Büyükekşi, Sebile; Şengül, Abdurrahman; Erdönmez, Seda; Altındal, Ahmet; Orman, Efe Baturhan; Özkaya, Ali Rıza

2018-02-20

In this study, a bis-chelating bridging perylene diimide ditopic ligand, namely N,N'-di(1,10-phenanthroline)-1,6,7,12-tetrakis-(4-methoxyphenoxy)perylene tetracarboxylic acid diimide (1), was synthesized and characterized. Further reactions of 1 with d 8 metal ions such as Pt(ii) and Pd(ii) having preferential square-planar geometry afforded the novel triads [(Cl 2 )M(ii)-(1)-M(ii)(Cl 2 )] where M(ii) = Pt(ii) (2), and Pd(ii) (3), respectively. The isolated triads and the key precursor were fully characterized by FT-IR, 1D-NMR ( 1 H NMR and 13 C DEPT NMR), 2D-NMR ( 1 H- 1 H COSY, 1 H- 13 C HSQC, 1 H- 13 C HMBC), MALDI-TOF mass and UV/Vis spectroscopy. The electrochemical properties of 1, 2 and 3 were investigated by cyclic voltammetry as well as in situ spectroelectrochemistry and also in situ electrocolorimetric measurements. These compounds were shown to exhibit net colour changes suitable for electrochromic applications. The compounds exhibited remarkably narrow HOMO-LUMO gaps, leading to their ease of reduction at low negative potentials. More importantly, dye-sensitized solar cells (DSSCs) were also fabricated using 1-3 to clarify the potential use of these complexes as a sensitizer. Analysis of the experimental data indicated that 2 has good potential as a sensitizer material for DSSCs.

Tuning of the ionization potential of paddlewheel diruthenium(II, II) complexes with fluorine atoms on the benzoate ligands.

PubMed

Miyasaka, Hitoshi; Motokawa, Natsuko; Atsuumi, Ryo; Kamo, Hiromichi; Asai, Yuichiro; Yamashita, Masahiro

2011-01-21

A series of paddlewheel diruthenium(ii, ii) complexes with various fluorine-substituted benzoate ligands were isolated as THF adducts and structurally characterized: [Ru(2)(F(x)PhCO(2))(4)(THF)(2)] (F(x)PhCO(2)(-) = o-fluorobenzoate, o-F; m-fluorobenzoate, m-F; p-fluorobenzoate, p-F; 2,6-difluorobenzoate, 2,6-F(2); 3,4-difluorobenzoate, 3,4-F(2); 3,5-difluorobenzoate, 3,5-F(2); 2,3,4-trifluorobenzoate, 2,3,4-F(3); 2,3,6-trifluorobenzoate, 2,3,6-F(3); 2,4,5-trifluorobenzoate, 2,4,5-F(3); 2,4,6-trifluorobenzoate, 2,4,6-F(3); 3,4,5-trifluorobenzoate, 3,4,5-F(3); 2,3,4,5-tetrafluorobenzoate, 2,3,4,5-F(4); 2,3,5,6-tetrafluorobenzoate, 2,3,5,6-F(4); pentafluorobenzoate, F(5)). By adding fluorine atoms on the benzoate ligands, it was possible to tune the redox potential (E(1/2)) for [Ru(2)(II,II)]/[Ru(2)(II,III)](+) over a wide range of potentials from -40 mV to 350 mV (vs. Ag/Ag(+) in THF). 2,3,6-F(3), 2,3,4,5-F(4), 2,3,5,6-F(4) and F(5) were relatively air-stable compounds even though they are [Ru(2)(II,II)] species. The redox potential in THF was dependent on an electronic effect rather than on a structural (steric) effect of the o-F atoms, although more than one substituent in the m- and p-positions shifted E(1/2) to higher potentials in relation to the general Hammett equation. A quasi-Hammett parameter for an o-F atom (σ(o)) was estimated to be ∼0.2, and a plot of E(1/2)vs. a sum of Hammett parameters including σ(o) was linear. In addition, the HOMO energy levels, which was calculated based on atomic coordinates of solid-state structures, as well as the redox potential were affected by adding F atoms. Nevertheless, a steric contribution stabilizing their static structures in the solid state was present in addition to the electronic effect. On the basis of the electronic effect, the redox potential of these complexes is correlated to the HOMO energy level, and the electronic effect of F atoms is the main factor controlling the ionization potential of the complexes with ligands free from the rotational constraint, i.e. complexes in solution.

Measurement Space Drill Support

DTIC Science & Technology

2015-08-30

II) H-47 Block II (I) *H-47 Block II (II) AVN FVL Att (I) * AVN FVL Att (II) TRAC- MTRY F2025B Logistic Flow MS Drill Support FY15 Research...does not have to use other AVN /ground assets to cover the area, freeing these assets to perform other missions and potentially enhancing the

Risk Factors for Dog Relinquishment to a Los Angeles Municipal Animal Shelter

PubMed Central

Dolan, Emily D.; Scotto, Jamie; Slater, Margaret; Weiss, Emily

2015-01-01

Simple Summary Low income has been reported to be a risk factor for dog relinquishment to shelters in the U.S. The majority of people with lower incomes, however, do not relinquish. Risk factors for relinquishment in a low socioeconomic region of Los Angeles were examined. Cost was associated with relinquishment, and most people were not aware of available assistance. Those who relinquished reported emotional attachment to the dog and higher perceived stress than a comparison group. The majority of reasons for relinquishment were likely solvable with assistance, highlighting an opportunity to provide community-specific alternatives to relinquishment. Abstract Dog relinquishment is a large component of shelter intake in the United States. Research has shown traits of the dog are associated with relinquishment as well as general characteristics of those relinquishing. Low income is often cited as a risk factor for relinquishment. The majority of people with lower incomes, however, do not relinquish. A group of people accessing a shelter in a low socioeconomic region of Los Angeles to relinquish their dogs was surveyed. This study examined risk factors for relinquishment, controlling for household income, compared to a group utilizing low cost spay/neuter services. A total of 76.9% of those relinquishing noted cost as a reason for relinquishment. Of participants in the relinquishment group, 80.7% reported not being aware of any services available to them. Most notable in the findings was that the odds of relinquishment were generally higher as the amount of perceived stress in the home in the past three months increased. The majority of people in both groups reported being emotionally attached to the dog. In this sample from a South Los Angeles community, the majority of reasons for relinquishment were likely solvable with assistance. These findings highlight an opportunity to assess community needs and provide community specific alternatives to relinquishment. PMID:26690483

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.

Zodiac II: Debris Disk Imaging Potential

NASA Technical Reports Server (NTRS)

Traub Wesley; Bryden, Geoff; Stapelfeldt, Karl; Chen, Pin; Trauger, John

2011-01-01

Zodiac II is a proposed coronagraph on a balloon-borne platform, for the purpose of observing debris disks around nearby stars. Zodiac II will have a 1.2-m diameter telescope mounted in a balloon-borne gondola capable of arcsecond quality pointing, and with the capability to make long-duration (several week) flights. Zodiac II will have a coronagraph able to make images of debris disks, meaning that its scattered light speckles will be at or below an average contrast level of about 10(exp -7) in three narrow (7 percent) bands centered on the V band, and one broad (20%) one at I band. We will discuss the potential science to be done with Zodiac II.

Remediation potential of mulch for removing lead.

PubMed

Jang, A; Bishop, P L

2012-01-01

Hardwood bark mulch has good physicochemical properties for the adsorption of lead (Pb(II)). Batch tests were conducted to obtain the sorption coefficient of Pb(II) in mulch. The results of the Freundlich model were not in as good agreement as for the case of the Langmuir model. In addition, a laboratory-scale mulch permeable reactive barrier (PRB) system was designed for the treatment of Pb(II)-contaminated groundwater. The mulch PRB system, using a mulch layer, can potentially be used in the subsurface for cost-effective and in situ transformation of the Pb(II) into environmentally acceptable forms. From the Pb(II) breakthrough curve, the mulch becomes saturated more quickly at higher flow rates.

40 CFR 98.356 - Data reporting requirements.

Code of Federal Regulations, 2011 CFR

2011-07-01

...) Maximum CH4 production potential (B0) used as an input to Equation II-1 or II-2 of this subpart. (4) Methane conversion factor (MCF) used as an input to Equation II-1 or II-2 of this subpart. (5) Annual mass...

Potential for microbial oxidation of ferrous iron in basaltic glass.

PubMed

Xiong, Mai Yia; Shelobolina, Evgenya S; Roden, Eric E

2015-05-01

Basaltic glass (BG) is an amorphous ferrous iron [Fe(II)]-containing material present in basaltic rocks, which are abundant on rocky planets such as Earth and Mars. Previous research has suggested that Fe(II) in BG can serve as an energy source for chemolithotrophic microbial metabolism, which has important ramifications for potential past and present microbial life on Mars. However, to date there has been no direct demonstration of microbially catalyzed oxidation of Fe(II) in BG. In this study, three different culture systems were used to investigate the potential for microbial oxidation of Fe(II) in BG, including (1) the chemolithoautotrophic Fe(II)-oxidizing, nitrate-reducing "Straub culture"; (2) the mixotrophic Fe(II)-oxidizing, nitrate-reducing organism Desulfitobacterium frappieri strain G2; and (3) indigenous microorganisms from a streambed Fe seep in Wisconsin. The BG employed consisted of clay and silt-sized particles of freshly quenched lava from the TEB flow in Kilauea, Hawaii. Soluble Fe(II) or chemically reduced NAu-2 smectite (RS) were employed as positive controls to verify Fe(II) oxidation activity in the culture systems. All three systems demonstrated oxidation of soluble Fe(II) and/or structural Fe(II) in RS, whereas no oxidation of Fe(II) in BG material was observed. The inability of the Straub culture to oxidize Fe(II) in BG was particularly surprising, as this culture can oxidize other insoluble Fe(II)-bearing minerals such as biotite, magnetite, and siderite. Although the reason for the resistance of the BG toward enzymatic oxidation remains unknown, it seems possible that the absence of distinct crystal faces or edge sites in the amorphous glass renders the material resistant to such attack. These findings have implications with regard to the idea that Fe(II)-Si-rich phases in basalt rocks could provide a basis for chemolithotrophic microbial life on Mars, specifically in neutral-pH environments where acid-promoted mineral dissolution and utilization of dissolved Fe(II) as an energy source is not likely to take place.

Bernoulli potential in type-I and weak type-II superconductors: II. Surface dipole

NASA Astrophysics Data System (ADS)

Lipavský, P.; Morawetz, K.; Koláček, J.; Mareš, J. J.; Brandt, E. H.; Schreiber, M.

2004-09-01

The Budd-Vannimenus theorem is modified to apply to superconductors in the Meissner state. The obtained identity links the surface value of the electrostatic potential to the density of free energy at the surface which allows one to evaluate the electrostatic potential observed via the capacitive pickup without the explicit solution of the charge profile.

Minimal string theories and integrable hierarchies

NASA Astrophysics Data System (ADS)

Iyer, Ramakrishnan

Well-defined, non-perturbative formulations of the physics of string theories in specific minimal or superminimal model backgrounds can be obtained by solving matrix models in the double scaling limit. They provide us with the first examples of completely solvable string theories. Despite being relatively simple compared to higher dimensional critical string theories, they furnish non-perturbative descriptions of interesting physical phenomena such as geometrical transitions between D-branes and fluxes, tachyon condensation and holography. The physics of these theories in the minimal model backgrounds is succinctly encoded in a non-linear differential equation known as the string equation, along with an associated hierarchy of integrable partial differential equations (PDEs). The bosonic string in (2,2m-1) conformal minimal model backgrounds and the type 0A string in (2,4 m) superconformal minimal model backgrounds have the Korteweg-de Vries system, while type 0B in (2,4m) backgrounds has the Zakharov-Shabat system. The integrable PDE hierarchy governs flows between backgrounds with different m. In this thesis, we explore this interesting connection between minimal string theories and integrable hierarchies further. We uncover the remarkable role that an infinite hierarchy of non-linear differential equations plays in organizing and connecting certain minimal string theories non-perturbatively. We are able to embed the type 0A and 0B (A,A) minimal string theories into this single framework. The string theories arise as special limits of a rich system of equations underpinned by an integrable system known as the dispersive water wave hierarchy. We find that there are several other string-like limits of the system, and conjecture that some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain how these and several other string-like special points arise and are connected. In some cases, the framework endows the theories with a non-perturbative definition for the first time. Notably, we discover that the Painleve IV equation plays a key role in organizing the string theory physics, joining its siblings, Painleve I and II, whose roles have previously been identified in this minimal string context. We then present evidence that the conjectured type II theories have smooth non-perturbative solutions, connecting two perturbative asymptotic regimes, in a 't Hooft limit. Our technique also demonstrates evidence for new minimal string theories that are not apparent in a perturbative analysis.

Landscape Potential Analysis for Ecotourism Destination in the Resort Ii Salak Mountain, Halimun-Salak National Park

NASA Astrophysics Data System (ADS)

Kusumoarto, A.; Gunawan, A.; Nurazizah, G. R.

2017-10-01

The Resort II Salak Mountain has variety of landscape potential for created as ecotourism destination, especially the potential of the waterfall (curug) and sulphur crater (Kawah Ratu). The aim of this study was to identify and analyze the potential resources of the landscape to be created as ecotourism destination, Resort II Salak Mountain. This research was conducted through two phases: 1) identification of the attractions location that have potential resources for ecotourism destination, and 2) analysis of the level of potential resource of the landscape in each location using Analysis of Tourist Attraction Operational Destination (ATAOD). The study showed Resort II Salak Mountain has many ecotourism objects which have been used for ecotourism activities, such as hot spring baths, Curug Cigamea, Curug Ngumpet, Curug Seribu, Curug Pangeran, Curug Muara, Curug Cihurang, Kawah Ratu, camping ground, Curug Kondang and Curug Alami. The location of all waterfalls -curug, spread widely in the core zone for ecotourism. In the other hand, camping ground is located in the business zone, while Kawah Ratu is located in the natural forest, which is included in the buffer zone of Halimun-Salak National Park (HSNP). The result showed that the ecotourism objects with the highest potential value are Kawah Ratu, Curug Seribu, Curug Muara, Curug Kondang and Curug Ngumpet.

Protein social behavior makes a stronger signal for partner identification than surface geometry

PubMed Central

Laine, Elodie

2016-01-01

ABSTRACT Cells are interactive living systems where proteins movements, interactions and regulation are substantially free from centralized management. How protein physico‐chemical and geometrical properties determine who interact with whom remains far from fully understood. We show that characterizing how a protein behaves with many potential interactors in a complete cross‐docking study leads to a sharp identification of its cellular/true/native partner(s). We define a sociability index, or S‐index, reflecting whether a protein likes or not to pair with other proteins. Formally, we propose a suitable normalization function that accounts for protein sociability and we combine it with a simple interface‐based (ranking) score to discriminate partners from non‐interactors. We show that sociability is an important factor and that the normalization permits to reach a much higher discriminative power than shape complementarity docking scores. The social effect is also observed with more sophisticated docking algorithms. Docking conformations are evaluated using experimental binding sites. These latter approximate in the best possible way binding sites predictions, which have reached high accuracy in recent years. This makes our analysis helpful for a global understanding of partner identification and for suggesting discriminating strategies. These results contradict previous findings claiming the partner identification problem being solvable solely with geometrical docking. Proteins 2016; 85:137–154. © 2016 Wiley Periodicals, Inc. PMID:27802579

Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations

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

Chen Xie; Liu Zhengxin; Wen Xiaogang

2011-12-15

Topological insulators in free fermion systems have been well characterized and classified. However, it is not clear in strongly interacting boson or fermion systems what symmetry-protected topological orders exist. In this paper, we present a model in a two-dimensional (2D) interacting spin system with nontrivial onsite Z{sub 2} symmetry-protected topological order. The order is nontrivial because we can prove that the one-dimensional (1D) system on the boundary must be gapless if the symmetry is not broken, which generalizes the gaplessness of Wess-Zumino-Witten model for Lie symmetry groups to any discrete symmetry groups. The construction of this model is related tomore » a nontrivial 3-cocycle of the Z{sub 2} group and can be generalized to any symmetry group. It potentially leads to a complete classification of symmetry-protected topological orders in interacting boson and fermion systems of any dimension. Specifically, this exactly solvable model has a unique gapped ground state on any closed manifold and gapless excitations on the boundary if Z{sub 2} symmetry is not broken. We prove the latter by developing the tool of a matrix product unitary operator to study the nonlocal symmetry transformation on the boundary and reveal the nontrivial 3-cocycle structure of this transformation. Similar ideas are used to construct a 2D fermionic model with onsite Z{sub 2} symmetry-protected topological order.« less

Spectroscopy of a one-dimensional V-shaped quantum well with a point impurity

NASA Astrophysics Data System (ADS)

Fassari, S.; Gadella, M.; Glasser, M. L.; Nieto, L. M.

2018-02-01

We consider the one-dimensional Hamiltonian with a V-shaped potential H0 = 1/2 [ -d2/dx2 + | x | ], decorated with a point impurity of either δ-type, or local δ‧-type or even nonlocal δ‧-type, thus yielding three exactly solvable models. We analyse the behaviour of the change in the energy levels when an interaction of the type - λ δ(x) or - λ δ(x -x0) is switched on. In the first case, even energy levels, pertaining to antisymmetric bound states, remain invariant with respect to λ even though odd energy levels, pertaining to symmetric bound states, decrease as λ increases. In the second, all energy levels decrease when the factor λ increases. A similar study has been performed for the so-called nonlocal δ‧ interaction, requiring a coupling constant renormalisation, which implies the replacement of the form factor λ by a renormalised form factor β. In terms of β, odd energy levels are unchanged. However, we show the existence of level crossings: after a fixed value of β the energy of each even level, with the natural exception of the first one, becomes lower than the constant energy of the previous odd level. Finally, we consider an interaction of the type - λδ(x) + μδ‧(x) , and analyse in detail the discrete spectrum of the resulting self-adjoint Hamiltonian.

ERRATUM: Papers published in incorrect sections

NASA Astrophysics Data System (ADS)

2004-04-01

A number of J. Phys. A: Math. Gen. articles have mistakenly been placed in the wrong subject section in recent issues of the journal. We would like to apologize to the authors of these articles for publishing their papers in the Fluid and Plasma Theory section. The correct section for each article is given below. Statistical Physics Issue 4: Microcanonical entropy for small magnetizations Behringer H 2004 J. Phys. A: Math. Gen. 37 1443 Mathematical Physics Issue 9: On the solution of fractional evolution equations Kilbas A A, Pierantozzi T, Trujillo J J and Vázquez L 2004 J. Phys. A: Math. Gen. 37 3271 Quantum Mechanics and Quantum Information Theory Issue 6: New exactly solvable isospectral partners for PT-symmetric potentials Sinha A and Roy P 2004 J. Phys. A: Math. Gen. 37 2509 Issue 9: Symplectically entangled states and their applications to coding Vourdas A 2004 J. Phys. A: Math. Gen. 37 3305 Classical and Quantum Field Theory Issue 6: Pairing of parafermions of order 2: seniority model Nelson C A 2004 J. Phys. A: Math. Gen. 37 2497 Issue 7: Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization Mota R D, Xicoténcatl M A and Granados V D 2004 J. Phys. A: Math. Gen. 37 2835 Issue 9: Could only fermions be elementary? Lev F M 2004 J. Phys. A: Math. Gen. 37 3285

Protein social behavior makes a stronger signal for partner identification than surface geometry.

PubMed

Laine, Elodie; Carbone, Alessandra

2017-01-01

Cells are interactive living systems where proteins movements, interactions and regulation are substantially free from centralized management. How protein physico-chemical and geometrical properties determine who interact with whom remains far from fully understood. We show that characterizing how a protein behaves with many potential interactors in a complete cross-docking study leads to a sharp identification of its cellular/true/native partner(s). We define a sociability index, or S-index, reflecting whether a protein likes or not to pair with other proteins. Formally, we propose a suitable normalization function that accounts for protein sociability and we combine it with a simple interface-based (ranking) score to discriminate partners from non-interactors. We show that sociability is an important factor and that the normalization permits to reach a much higher discriminative power than shape complementarity docking scores. The social effect is also observed with more sophisticated docking algorithms. Docking conformations are evaluated using experimental binding sites. These latter approximate in the best possible way binding sites predictions, which have reached high accuracy in recent years. This makes our analysis helpful for a global understanding of partner identification and for suggesting discriminating strategies. These results contradict previous findings claiming the partner identification problem being solvable solely with geometrical docking. Proteins 2016; 85:137-154. © 2016 Wiley Periodicals, Inc. © 2016 The Authors Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

"Squishy capacitor" model for electrical double layers and the stability of charged interfaces.

PubMed

Partenskii, Michael B; Jordan, Peter C

2009-07-01

Negative capacitance (NC), predicted by various electrical double layer (EDL) theories, is critically reviewed. Physically possible for individual components of the EDL, the compact or diffuse layer, it is strictly prohibited for the whole EDL or for an electrochemical cell with two electrodes. However, NC is allowed for the artificial conditions of sigma control, where an EDL is described by the equilibrium electric response of electrolyte to a field of fixed, and typically uniform, surface charge-density distributions, sigma. The contradiction is only apparent; in fact local sigma cannot be set independently, but is established by the equilibrium response to physically controllable variables, i.e., applied voltage phi (phi control) or total surface charge q (q control). NC predictions in studies based on sigma control signify potential instabilities and phase transitions for physically realizable conditions. Building on our previous study of phi control [M. B. Partenskii and P. C. Jordan, Phys. Rev. E 77, 061117 (2008)], here we analyze critical behavior under q control, clarifying the basic picture using an exactly solvable "squishy capacitor" toy model. We find that phi can change discontinuously in the presence of a lateral transition, specify stability conditions for an electrochemical cell, analyze the origin of the EDL's critical point in terms of compact and diffuse serial contributions, and discuss perspectives and challenges for theoretical studies not limited by sigma control.

On chirality transfer in electron donor-acceptor complexes. A prediction for the sulfinimine···BF3 system.

PubMed

Rode, Joanna E; Dobrowolski, Jan Cz

2012-01-01

Stabilization energies of the electron donor-acceptor sulfinimine···BF(3) complexes calculated at either the B3LYP/aug-cc-pVTZ or the MP2/aug-cc-pVTZ level do not allow to judge, whether the N- or O-atom in sulfinimine is stronger electron-donor to BF(3) . The problem seems to be solvable because chirality transfer phenomenon between chiral sulfinimine and achiral BF(3) is expected to be vibrational circular dichroism (VCD) active. Moreover, the bands associated with the achiral BF(3) molecule are predicted to be the most intense in the entire spectrum. However, the VCD band robustness analyses show that most of the chirality transfer modes of BF(3) are unreliable. Conversely, variation of VCD intensity with change of intermolecular distance, angle, and selected dihedrals between the complex partners shows that to establish the robustness of chirality transfer mode. It is also necessary to determine the influence of the potential energy surface (PES) shape on the VCD intensity. At the moment, there is still no universal criterion for the chirality transfer mode robustness and the conclusions formulated based on one system cannot be directly transferred even to a quite similar one. However, it is certain that more attention should be focused on relation of PES shape and the VCD mode robustness problem. Copyright © 2011 Wiley Periodicals, Inc.

Squeezing effects applied in nonclassical superposition states for quantum nanoelectronic circuits

NASA Astrophysics Data System (ADS)

Choi, Jeong Ryeol

2017-06-01

Quantum characteristics of a driven series RLC nanoelectronic circuit whose capacitance varies with time are studied using an invariant operator method together with a unitary transformation approach. In particular, squeezing effects and nonclassical properties of a superposition state composed of two displaced squeezed number states of equal amplitude, but 180° out of phase, are investigated in detail. We applied our developments to a solvable specific case obtained from a suitable choice of time-dependent parameters. The pattern of mechanical oscillation of the amount of charges stored in the capacitor, which are initially displaced, has exhibited more or less distortion due to the influence of the time-varying parameters of the system. We have analyzed squeezing effects of the system from diverse different angles and such effects are illustrated for better understanding. It has been confirmed that the degree of squeezing is not constant, but varies with time depending on specific situations. We have found that quantum interference occurs whenever the two components of the superposition meet together during the time evolution of the probability density. This outcome signifies the appearance of nonclassical features of the system. Nonclassicality of dynamical systems can be a potential resource necessary for realizing quantum information technique. Indeed, such nonclassical features of superposition states are expected to play a key role in upcoming information science which has attracted renewed attention recently.

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.

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

Can a pairwise contact potential stabilize native protein folds against decoys obtained by threading?

PubMed

Vendruscolo, M; Najmanovich, R; Domany, E

2000-02-01

We present a method to derive contact energy parameters from large sets of proteins. The basic requirement on which our method is based is that for each protein in the database the native contact map has lower energy than all its decoy conformations that are obtained by threading. Only when this condition is satisfied one can use the proposed energy function for fold identification. Such a set of parameters can be found (by perceptron learning) if Mp, the number of proteins in the database, is not too large. Other aspects that influence the existence of such a solution are the exact definition of contact and the value of the critical distance Rc, below which two residues are considered to be in contact. Another important novel feature of our approach is its ability to determine whether an energy function of some suitable proposed form can or cannot be parameterized in a way that satisfies our basic requirement. As a demonstration of this, we determine the region in the (Rc, Mp) plane in which the problem is solvable, i.e., we can find a set of contact parameters that stabilize simultaneously all the native conformations. We show that for large enough databases the contact approximation to the energy cannot stabilize all the native folds even against the decoys obtained by gapless threading.

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.

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.

Urinary angiotensinogen as a potential biomarker of intrarenal renin-angiotensin system activity in Chinese chronic kidney disease patients.

PubMed

Xu, Z; Xu, B; Xu, C

2015-06-01

Urinary angiotensinogen (AGT) mainly derives from the AGT produced in proximal tubular cells. Evidence exists that supports the correlation between urinary AGT and circulating AGT. To investigate the role of urinary AGT as a potential biomarker of intrarenal renin-angiotensin system activity in Chinese chronic kidney disease (CKD) patients. ELISA-based method used to quantify urinary AGT. Analyzed the relationship between urinary AGT and intrarenal angiotensin II (Ang II) activity in 128 CKD patients. ELISA was applied to measure the urinary and plasma renin activity, AGT, Ang II and aldosterone. Furthermore expression levels of intrarenal renin, AGT, Ang II and Ang II receptor were examined by immunohistochemistry staining (IHCS) in 72 CKD patients undergoing renal biopsy. The logarithmic transformation Log(urinary AGT/UCre) levels showed a normal distribution. Therefore, Log(urinary AGT/UCre) levels were used for the analyses. Average urinary AGT was 2.02 ± 0.55 ng/(mg Cr). Hypertension, urinary protein, urinary Ang II and urinary type IV collagen (Col IV) positively correlated with urinary AGT. Estimated glomerular filtration rate (eGFR), urinary sodium and serum AGT negatively correlated with urinary AGT. Multiple regression analysis indicated that low serum AGT, high urinary protein, urinary Ang II and urinary Col IV correlated significantly with high urinary AGT. We observed positive correlation between urinary AGT and positive IHCS area of AGT, Ang II and Ang II type 1 receptor in renal tissue. These data suggest that urinary AGT might be a potential biomarker of intrarenal Ang II activity in CKD patients.

The use of sugar and alcohol industry waste in the adsorption of potentially toxic metals.

PubMed

Santos, Oseas Silva; Mendonça, André Gustavo Ribeiro; Santos, Josué Carinhanha Caldas; Silva, Amanda Paulina Bezerra; Costa, Silvanio Silverio Lopes; Oliveira, Luciana Camargo; Carmo, Janaina Braga; Botero, Wander Gustavo

2016-01-01

One of the waste products of the industrial process of the sugar and alcohol agribusiness is filter cake (FC). This waste product has high levels of organic matter, mainly proteins and lipids, and is rich in calcium, nitrogen, potassium and phosphorous. In this work we characterized samples of FC from sugar and alcohol industries located in sugarcane-producing regions in Brazil and assessed the adsorption of potentially toxic metals (Cu(II), Cd(II), Pb(II), Ni(II) and Cr(III)) by this waste in mono- and multi-elemental systems, seeking to use FC as an adsorbent in contaminated environments. The characterization of FCs showed significant differences between the samples and the adsorption studies showed retention of over 90% of potentially toxic metals. In a competitive environment (multi-metallic solution), the FC was effective in adsorbing all metals except lead, but less effective compared to the mono-metallic solution. These results show the potential for use of this residue as an adsorbent in contaminated environments.

Langmuir Probe Spacecraft Potential End Item Specification Document

NASA Technical Reports Server (NTRS)

Gilchrist, Brian; Curtis, Leslie (Technical Monitor)

2001-01-01

This document describes the Langmuir Probe Spacecraft Potential (LPSP) investigation of the plasma environment in the vicinity of the ProSEDS Delta II spacecraft. This investigation will employ a group of three (3) Langmuir Probe Assemblies, LPAs, mounted on the Delta II second stage to measure the electron density and temperature (n(sub e) and T(sub e)), the ion density (n(sub i)), and the spacecraft potential (V(sub s)) relative to the surrounding ionospheric plasma. This document is also intended to define the technical requirements and flight-vehicle installation interfaces for the design, development, assembly, testing, qualification, and operation of the LPSP subsystem for the Propulsive Small Expendable Deployer System (ProSEDS) and its associated Ground Support Equipment (GSE). This document also defines the interfaces between the LPSP instrument and the ProSEDS Delta II spacecraft, as well as the design, fabrication, operation, and other requirements established to meet the mission objectives. The LPSP is the primary measurement instrument designed to characterize the background plasma environment and is a supporting instrument for measuring spacecraft potential of the Delta II vehicle used for the ProSEDS mission. Specifically, the LPSP will use the three LPAs equally spaced around the Delta II body to make measurements of the ambient ionospheric plasma during passive operations to aid in validating existing models of electrodynamic-tether propulsion. These same probes will also be used to measure Delta II spacecraft potential when active operations occur. When the electron emitting plasma contractor is on, dense neutral plasma is emitted. Effective operation of the plasma contactor (PC) will mean a low potential difference between the Delta II second stage and the surrounding plasma and represents one of the voltage parameters needed to fully characterize the electrodynamic-tether closed circuit. Given that the LP already needs to be well away from any near-field disturbances around the Delta II, it is possible to use the same probe with a simple reconfiguration of the electronics to measure potential with respect to the ambient plasma. The LP measurement techniques are outlined in the following text and discussed in detail in the Appendix. The scientific goals of the investigation, the physical and electrical characteristics of the instrument, and the on-orbit measurement requirements are also discussed in this document.

Synthesis, spectral characterization, structural investigation and antimicrobial studies of mononuclear Cu(II), Ni(II), Co(II), Zn(II) and Cd(II) complexes of a new potentially hexadentate N2O4 Schiff base ligand derived from salicylaldehyde

NASA Astrophysics Data System (ADS)

Keypour, Hassan; Shayesteh, Maryam; Rezaeivala, Majid; Chalabian, Firoozeh; Elerman, Yalcin; Buyukgungor, Orhan

2013-01-01

A new potentially hexadentate N2O4 Schiff base ligand, H2L derived from condensation reaction of an aromatic diamine and salicylaldehyde, and its metal complexes were characterized by elemental analyses, IR, UV-Vis, EI-MS, 1H and 13C NMR spectra, as well as conductance measurements. It has been originated that the Schiff base ligand with Cu(II), Ni(II), Co(II), Cd(II) and Zn(II) ions form mononuclear complexes on 1:1 (metal:ligand) stoichiometry. The conductivity data confirm the non-electrolytic nature of the complexes. Also the crystal structures of the complexes [ZnL] and [CoL] have also been determined by using X-ray crystallographic technique. The Zn(II) and Co(II) complexes show a tetrahedral configuration. Electronic absorption spectra of the Cu(II) and Ni(II) complexes suggest a square-planar geometry around the central metal ion. The synthesized compounds have antibacterial activity against the three Gram-positive bacteria: Bacillus cereus, Enterococcus faecalis and Listeria monocytogenes and also against the three Gram-negative bacteria: Salmonella paraB, Citrobacter freundii and Enterobacter aerogenes. The results showed that in some cases the antibacterial activity of complexes were more than nalidixic acid and amoxicillin as standards.

Differential games in economic systems with delays

NASA Astrophysics Data System (ADS)

Kim, A. V.; Kormyshev, V. M.; Novikov, M. Yu.; Nikonov, M. A.

2017-11-01

In the paper, we consider application of i-smooth analysis (A.V. Kim, 2015) to differential games with delays in economics (Dockner E.J., et all, 2000; R. Isaacs, 1999). The approach is developed in the framework of the theory of positional differential games (N.N. Krasovskii, A.I. Subbotin, 1988; A.V. Kryazhimskii, Yu.S. Osipov, 1973; Yu.S. Osipov, J. Appl. Math. Mech. Vol. 35, № 1, № 6, 1971) and is based on application of the extremal shift strategy. We consider basic notions and constructions of the approach-evasion problem for linear systems with delays. The necessary and sufficient conditions of solvability the approach-evasion problem in terms of special u-stable sets are presented in another paper.

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.

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

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.

[HPLC-ESI-MS(n) analysis of the water soluble extracts of Fructus Choerospondiatis].

PubMed

Shi, Run-ju; Dai, Yun; Fang, Min-feng; Zhao, Xin; Zheng, Jian-bin; Zheng, Xiao-hui

2007-03-01

To establish an HPLC-ESI-MS(n) method for analyzing the chemical ingredients in the water soluble extracts of Fructus Choerospondiatis. Water-solvable extracts of Fructus Choerospondiatis are obtained by heating recirculation. Multi-stage reaction mode (MRM) of the HPLC-ESI-MS(n) was used to determine the content of Gallic acid, the MS(n) technology was used to obtain the information of characteristic multistage fragment ions so as to identify the chemical structure of peaks in the total current spectrum. Eleven compounds were identified, and one of them is a new unknown ingredient. The method, which has high recovery and specificity, can offer the experimental evidences for the further research of the chemical ingredients extracted from the Fructus Choerospondiatis.

Optimal Protocols and Optimal Transport in Stochastic Thermodynamics

NASA Astrophysics Data System (ADS)

Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2011-06-01

Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

Inverse eigenproblem for R-symmetric matrices and their approximation

NASA Astrophysics Data System (ADS)

Yuan, Yongxin

2009-11-01

Let be a nontrivial involution, i.e., R=R-1[not equal to]±In. We say that is R-symmetric if RGR=G. The set of all -symmetric matrices is denoted by . In this paper, we first give the solvability condition for the following inverse eigenproblem (IEP): given a set of vectors in and a set of complex numbers , find a matrix such that and are, respectively, the eigenvalues and eigenvectors of A. We then consider the following approximation problem: Given an n×n matrix , find such that , where is the solution set of IEP and ||[dot operator]|| is the Frobenius norm. We provide an explicit formula for the best approximation solution by means of the canonical correlation decomposition.

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.

Entanglement in 3D Kitaev spin liquids

NASA Astrophysics Data System (ADS)

Matern, S.; Hermanns, M.

2018-06-01

Quantum spin liquids are highly fascinating quantum liquids in which the spin degrees of freedom fractionalize. An interesting class of spin liquids are the exactly solvable, three-dimensional Kitaev spin liquids. Their fractionalized excitations are Majonara fermions, which may exhibit a variety of topological band structures—ranging from topologically protected Weyl semi-metals over nodal semi-metals to systems with Majorana Fermi surfaces. We study the entanglement spectrum of such Kitaev spin liquids and verify that it is closely related to the topologically protected edge spectrum. Moreover, we find that in some cases the entanglement spectrum contains even more information about the topological features than the surface spectrum, and thus provides a simple and reliable tool to probe the topology of a system.

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).

Optimal protocols and optimal transport in stochastic thermodynamics.

PubMed

Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo

2011-06-24

Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.

Application of the magnetic fluid as a detector for changing the magnetic field

NASA Astrophysics Data System (ADS)

Zyatkov, D.; Yurchenko, A.; Yurchenko, V.; Balashov, V.

2018-05-01

In article the possibility of use of magnetic fluid as a sensitive element for fixing of change of induction of magnetic field in space is considered. Importance of solvable tasks is connected with search of the perspective magnetic substances susceptible to weak magnetic field. The results of a study of the capacitive method for fixing the change in the magnetic field on the basis of a ferromagnetic liquid are presented. The formation of chain structures in the ferrofluid from magnetic particles under the influence of the applied magnetic field leads to a change in the capacitance of the plate condenser. This task has important practical value for development of a magnetosensitive sensor of change of magnetic field.

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.

The relative degree enhancement problem for MIMO nonlinear systems

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

Schoenwald, D.A.; Oezguener, Ue.

1995-07-01

The authors present a result for linearizing a nonlinear MIMO system by employing partial feedback - feedback at all but one input-output channel such that the SISO feedback linearization problem is solvable at the remaining input-output channel. The partial feedback effectively enhances the relative degree at the open input-output channel provided the feedback functions are chosen to satisfy relative degree requirements. The method is useful for nonlinear systems that are not feedback linearizable in a MIMO sense. Several examples are presented to show how these feedback functions can be computed. This strategy can be combined with decentralized observers for amore » completely decentralized feedback linearization result for at least one input-output channel.« less

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.

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.

{\\ {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.

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.

Correlation Decay in Fermionic Lattice Systems with Power-Law Interactions at Nonzero Temperature

NASA Astrophysics Data System (ADS)

Hernández-Santana, Senaida; Gogolin, Christian; Cirac, J. Ignacio; Acín, Antonio

2017-09-01

We study correlations in fermionic lattice systems with long-range interactions in thermal equilibrium. We prove a bound on the correlation decay between anticommuting operators and generalize a long-range Lieb-Robinson-type bound. Our results show that in these systems of spatial dimension D with, not necessarily translation invariant, two-site interactions decaying algebraically with the distance with an exponent α ≥2 D , correlations between such operators decay at least algebraically to 0 with an exponent arbitrarily close to α at any nonzero temperature. Our bound is asymptotically tight, which we demonstrate by a high temperature expansion and by numerically analyzing density-density correlations in the one-dimensional quadratic (free, exactly solvable) Kitaev chain with long-range pairing.

Optimal recombination in genetic algorithms for flowshop scheduling problems

NASA Astrophysics Data System (ADS)

Kovalenko, Julia

2016-10-01

The optimal recombination problem consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We prove NP-hardness of the optimal recombination for various variants of the flowshop scheduling problem with makespan criterion and criterion of maximum lateness. An algorithm for solving the optimal recombination problem for permutation flowshop problems is built, using enumeration of prefect matchings in a special bipartite graph. The algorithm is adopted for the classical flowshop scheduling problem and for the no-wait flowshop problem. It is shown that the optimal recombination problem for the permutation flowshop scheduling problem is solvable in polynomial time for almost all pairs of parent solutions as the number of jobs tends to infinity.

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

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.

Scattering on two Aharonov-Bohm vortices

NASA Astrophysics Data System (ADS)

Bogomolny, E.

2016-12-01

The problem of two Aharonov-Bohm (AB) vortices for the Helmholtz equation is examined in detail. It is demonstrated that the method proposed by Myers (1963 J. Math. Phys. 6 1839) for slit diffraction can be generalised to obtain an explicit solution for AB vortices. Due to the singular nature of AB interaction the Green function and scattering amplitude for two AB vortices obey a series of partial differential equations. Coefficients entering these equations, fulfil ordinary non-linear differential equations whose solutions can be obtained by solving the Painlevé III equation. The asymptotics of necessary functions for very large and very small vortex separations are calculated explicitly. Taken together, this means that the problem of two AB vortices is exactly solvable.

Monomeric, porous type II collagen scaffolds promote chondrogenic differentiation of human bone marrow mesenchymal stem cells in vitro

NASA Astrophysics Data System (ADS)

Tamaddon, M.; Burrows, M.; Ferreira, S. A.; Dazzi, F.; Apperley, J. F.; Bradshaw, A.; Brand, D. D.; Czernuszka, J.; Gentleman, E.

2017-03-01

Osteoarthritis (OA) is a common cause of pain and disability and is often associated with the degeneration of articular cartilage. Lesions to the articular surface, which are thought to progress to OA, have the potential to be repaired using tissue engineering strategies; however, it remains challenging to instruct cell differentiation within a scaffold to produce tissue with appropriate structural, chemical and mechanical properties. We aimed to address this by driving progenitor cells to adopt a chondrogenic phenotype through the tailoring of scaffold composition and physical properties. Monomeric type-I and type-II collagen scaffolds, which avoid potential immunogenicity associated with fibrillar collagens, were fabricated with and without chondroitin sulfate (CS) and their ability to stimulate the chondrogenic differentiation of human bone marrow-derived mesenchymal stem cells was assessed. Immunohistochemical analyses showed that cells produced abundant collagen type-II on type-II scaffolds and collagen type-I on type-I scaffolds. Gene expression analyses indicated that the addition of CS - which was released from scaffolds quickly - significantly upregulated expression of type II collagen, compared to type-I and pure type-II scaffolds. We conclude that collagen type-II and CS can be used to promote a more chondrogenic phenotype in the absence of growth factors, potentially providing an eventual therapy to prevent OA.

Elucidating the Role of Many-Body Forces in Liquid Water. I. Simulations of Water Clusters on the VRT (ASP-W) Potential Surfaces

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

Goldman, N; Saykally, R J

We test the new VRT(ASP-W)II and VRT(ASP-W)III potentials by employing Diffusion Quantum Monte Carlo simulations to calculate the vibrational ground-state properties of water clusters. These potentials are fits of the highly detailed ASP-W ab initio potential to (D{sub 2}O){sub 2} microwave and far-IR data, and along with the SAPT5s potentials, are the most accurate water dimer potential surfaces in the literature. The results from VRT(ASP-W)II and III are compare to those from the original ASP-W potential, the SAPT5s family of potentials, and several bulk water potentials. Only VRT(ASP-W)II and the spectroscopically ''tuned'' SAPT5st (with N-body induction included) accurately reproduce themore » vibrational ground-state structures of water clusters up to the hexamer. Finally, the importance of many-body induction and three-body dispension are examined, and it is shown that the latter can have significant effects on water cluster properties despite its small magnitude.« less

10 CFR Appendix II to Part 960 - NRC and EPA Requirements for Preclosure Repository Performance

Code of Federal Regulations, 2012 CFR

2012-01-01

... 10 Energy 4 2012-01-01 2012-01-01 false NRC and EPA Requirements for Preclosure Repository Performance II Appendix II to Part 960 Energy DEPARTMENT OF ENERGY GENERAL GUIDELINES FOR THE PRELIMINARY SCREENING OF POTENTIAL SITES FOR A NUCLEAR WASTE REPOSITORY Pt. 960, App. II Appendix II to Part 960—NRC and...

10 CFR Appendix II to Part 960 - NRC and EPA Requirements for Preclosure Repository Performance

Code of Federal Regulations, 2011 CFR

2011-01-01

... 10 Energy 4 2011-01-01 2011-01-01 false NRC and EPA Requirements for Preclosure Repository Performance II Appendix II to Part 960 Energy DEPARTMENT OF ENERGY GENERAL GUIDELINES FOR THE PRELIMINARY SCREENING OF POTENTIAL SITES FOR A NUCLEAR WASTE REPOSITORY Pt. 960, App. II Appendix II to Part 960—NRC and...

10 CFR Appendix II to Part 960 - NRC and EPA Requirements for Preclosure Repository Performance

Code of Federal Regulations, 2013 CFR

2013-01-01

... 10 Energy 4 2013-01-01 2013-01-01 false NRC and EPA Requirements for Preclosure Repository Performance II Appendix II to Part 960 Energy DEPARTMENT OF ENERGY GENERAL GUIDELINES FOR THE PRELIMINARY SCREENING OF POTENTIAL SITES FOR A NUCLEAR WASTE REPOSITORY Pt. 960, App. II Appendix II to Part 960—NRC and...

10 CFR Appendix II to Part 960 - NRC and EPA Requirements for Preclosure Repository Performance

Code of Federal Regulations, 2014 CFR

2014-01-01

... 10 Energy 4 2014-01-01 2014-01-01 false NRC and EPA Requirements for Preclosure Repository Performance II Appendix II to Part 960 Energy DEPARTMENT OF ENERGY GENERAL GUIDELINES FOR THE PRELIMINARY SCREENING OF POTENTIAL SITES FOR A NUCLEAR WASTE REPOSITORY Pt. 960, App. II Appendix II to Part 960—NRC and...

The Heme-Based Oxygen Sensor Rhizobium etli FixL: Influence of Auxiliary Ligands on Heme Redox Potential and Implications on the Enzyme Activity.

PubMed

Honorio-Felício, Nathalie; Carepo, Marta S P; de F Paulo, Tércio; de França Lopes, Luiz Gonzaga; Sousa, Eduardo H S; Diógenes, Izaura C N; Bernhardt, Paul V

2016-11-01

Conformational changes associated to sensing mechanisms of heme-based protein sensors are a key molecular event that seems to modulate not only the protein activity but also the potential of the Fe III/II redox couple of the heme domain. In this work, midpoint potentials (E m ) assigned to the Fe III/II redox couple of the heme domain of FixL from Rhizobium etli (ReFixL) in the unliganded and liganded states were determined by spectroelectrochemistry in the presence of inorganic mediators. In comparison to the unliganded ReFixL protein (+19mV), the binding to ligands that switch off the kinase activity induces a negative shift, i. e. E m =-51, -57 and -156mV for O 2 , imidazole and CN - , respectively. Upon binding to CO, which does not affect the kinase active, E m was observed at +21mV. The potential values observed for Fe III/II of the heme domain of ReFixL upon binding to CO and O 2 do not follow the expected trend based on thermodynamics, assuming that positive potential shift would be expected for ligands that bind to and therefore stabilize the Fe II state. Our results suggest that the conformational changes that switch off kinase activity upon O 2 binding have knock-on effects to the local environment of the heme, such as solvent rearrangement, destabilize the Fe II state and counterbalances the Fe II -stabilizing influence of the O 2 ligand. Copyright © 2016 Elsevier Inc. All rights reserved.

48 CFR 30.605 - Processing noncompliances.

Code of Federal Regulations, 2011 CFR

2011-10-01

... with the alleged noncompliance; or (ii) Issue a notice of potential noncompliance to the contractor and provide a copy to the auditor. (2) The notice of potential noncompliance shall— (i) Notify the contractor... difference is increased cost to the Government. (ii) When the negotiated contract or subcontract price is...

48 CFR 30.605 - Processing noncompliances.

Code of Federal Regulations, 2010 CFR

2010-10-01

... with the alleged noncompliance; or (ii) Issue a notice of potential noncompliance to the contractor and provide a copy to the auditor. (2) The notice of potential noncompliance shall— (i) Notify the contractor... difference is increased cost to the Government. (ii) When the negotiated contract or subcontract price is...

48 CFR 30.605 - Processing noncompliances.

Code of Federal Regulations, 2014 CFR

2014-10-01

... with the alleged noncompliance; or (ii) Issue a notice of potential noncompliance to the contractor and provide a copy to the auditor. (2) The notice of potential noncompliance shall— (i) Notify the contractor... difference is increased cost to the Government. (ii) When the negotiated contract or subcontract price is...

48 CFR 30.605 - Processing noncompliances.

Code of Federal Regulations, 2013 CFR

2013-10-01

... with the alleged noncompliance; or (ii) Issue a notice of potential noncompliance to the contractor and provide a copy to the auditor. (2) The notice of potential noncompliance shall— (i) Notify the contractor... difference is increased cost to the Government. (ii) When the negotiated contract or subcontract price is...

48 CFR 30.605 - Processing noncompliances.

Code of Federal Regulations, 2012 CFR

2012-10-01

... with the alleged noncompliance; or (ii) Issue a notice of potential noncompliance to the contractor and provide a copy to the auditor. (2) The notice of potential noncompliance shall— (i) Notify the contractor... difference is increased cost to the Government. (ii) When the negotiated contract or subcontract price is...

Heterobimetallic Complexes with MIII-(μ-OH)-MII Cores (MIII = Fe, Mn, Ga; MII = Ca, Sr, and Ba): Structural, Kinetic, and Redox Properties.

PubMed

Park, Young Jun; Cook, Sarah A; Sickerman, Nathaniel S; Sano, Yohei; Ziller, Joseph W; Borovik, A S

2013-02-01

The effects of redox-inactive metal ions on dioxygen activation were explored using a new Fe II complex containing a tripodal ligand with 3 sulfonamido groups. This iron complex exhibited a faster initial rate for the reduction of O 2 than its Mn II analog. Increases in initial rates were also observed in the presence of group 2 metal ions for both the Fe II and Mn II complexes, which followed the trend NMe 4 + < Ba II < Ca II = Sr II . These studies led to the isolation of heterobimetallic complexes containing Fe III -( μ -OH)-M II cores (M II = Ca, Sr, and Ba) and one with a [Sr II (OH)Mn III ] + motif. The analogous [Ca II (OH)Ga III ] + complex was also prepared and its solid state molecular structure is nearly identical to that of the [Ca II (OH)Fe III ] + system. Nuclear magnetic resonance studies indicated that the diamagnetic [Ca II (OH)Ga III ] + complex retained its structure in solution. Electrochemical measurements on the heterobimetallic systems revealed similar one-electron reduction potentials for the [Ca II (OH)Fe III ] + and [Sr II (OH)Fe III ] + complexes, which were more positive than the potential observed for [Ba II (OH)Fe III ] + . Similar results were obtained for the heterobimetallic Mn II complexes. These findings suggest that Lewis acidity is not the only factor to consider when evaluating the effects of group 2 ions on redox processes, including those within the oxygen-evolving complex of Photosystem II.

Influence of the variation potential on photosynthetic flows of light energy and electrons in pea.

PubMed

Sukhova, Ekaterina; Mudrilov, Maxim; Vodeneev, Vladimir; Sukhov, Vladimir

2018-05-01

Local damage (mainly burning, heating, and mechanical wounding) induces propagation of electrical signals, namely, variation potentials, which are important signals during the life of plants that regulate different physiological processes, including photosynthesis. It is known that the variation potential decreases the rate of CO 2 assimilation by the Calvin-Benson cycle; however, its influence on light reactions has been poorly investigated. The aim of our work was to investigate the influence of the variation potential on the light energy flow that is absorbed, trapped and dissipated per active reaction centre in photosystem II and on the flow of electrons through the chloroplast electron transport chain. We analysed chlorophyll fluorescence in pea leaves using JIP-test and PAM-fluorometry; we also investigated delayed fluorescence. The electrical signals were registered using extracellular electrodes. We showed that the burning-induced variation potential stimulated a nonphotochemical loss of energy in photosystem II under dark conditions. It was also shown that the variation potential gradually increased the flow of light energy absorbed, trapped and dissipated by photosystem II. These changes were likely caused by an increase in the fraction of absorbed light distributed to photosystem II. In addition, the variation potential induced a transient increase in electron flow through the photosynthetic electron transport chain. Some probable mechanisms for the influence of the variation potential on the light reactions of photosynthesis (including the potential role of intracellular pH decrease) are discussed in the work.

Striking hematological abnormalities in patients with microcephalic osteodysplastic primordial dwarfism type II (MOPD II): a potential role of pericentrin in hematopoiesis.

PubMed

Unal, Sule; Alanay, Yasemin; Cetin, Mualla; Boduroglu, Koray; Utine, Eda; Cormier-Daire, Valerie; Huber, Celine; Ozsurekci, Yasemin; Kilic, Esra; Simsek Kiper, Ozlem Pelin; Gumruk, Fatma

2014-02-01

Microcephalic osteodysplastic primordial dwarfism type II (MOPD II) is a rare primordial dwarfism that is similar to Seckel syndrome. Seckel syndrome is known to be associated with various hematological abnormalities; however, hematological findings in MOPD II patients have not been previously reported. The present study aimed to describe the hematological findings in a series of eight patients with MOPD II from a single center. The study included eight patients with MOPD II that were analyzed via molecular testing, and physical and laboratory examinations. Molecular testing showed that seven of the eight patients had pericentrin (PCNT) gene mutations. Hematological evaluation showed that 7 (87.5%) patients had thrombocytosis, 6 (75%) had leukocytosis, 5 (62.5%) had both leukocytosis and thrombocytosis, and 2 (25%) had anemia. We report leukocytosis and thrombocytosis as a common hematologic abnormality in patients with MOPD II. The present findings may improve our understanding of the potential function of the PCNT gene in hematopoietic cell proliferation and differentiation. © 2013 Wiley Periodicals, Inc.

Incorporating INTERACT II Clinical Decision Support Tools into Nursing Home Health Information Technology

PubMed Central

Handler, Steven M.; Sharkey, Siobhan S.; Hudak, Sandra; Ouslander, Joseph G.

2012-01-01

A substantial reduction in hospitalization rates has been associated with the implementation of the Interventions to Reduce Acute Care Transfers (INTERACT) quality improvement intervention using the accompanying paper-based clinical practice tools (INTERACT II). There is significant potential to further increase the impact of INTERACT by integrating INTERACT II tools into nursing home (NH) health information technology (HIT) via standalone or integrated clinical decision support (CDS) systems. This article highlights the process of translating INTERACT II tools from paper to NH HIT. The authors believe that widespread dissemination and integration of INTERACT II CDS tools into various NH HIT products could lead to sustainable improvement in resident and clinician process and outcome measures, including enhanced interclinician communication and a reduction in potentially avoidable hospitalizations. PMID:22267955

EPR Studies of orthorhombic Jahn-Teller effect in single crystal of ferroelectric Cu(II):Cd2(NH4)2 (SO4)3

NASA Astrophysics Data System (ADS)

Benson, Yerima; de, Dilip

In this paper we report the first EPR observation and theoretical explanation of orthorhombic Jahn-Teller effect in Cu(II) doped single crystal of ferroelectric cadmium ammonium sulphate: Cu(II):Cd2(NH4)2 (SO4)3 . The isotropic EPR spectra of the 2D ion (in regular octahedral symmetry) at higher temperature becomes anisotropic at low temperature with clear manifestation of orthorhombic g and hyperfine tensors at 15 K. The static Jahn-Teller(JT) effect can only be explained theoretically by assuming the three JT potential wells energetically inequivalent, unlike the potential wells in most of the Cu(II) doped crystalline materials where JT effect manifests. The measured splitting of the JT potential wells in this ferroelectric crystal fall in the sub millimeter wave region pointing to possible application of the material.

Microbial strategy for potential lead remediation: a review study.

PubMed

Pan, Xiaohong; Chen, Zhi; Li, Lan; Rao, Wenhua; Xu, Zhangyan; Guan, Xiong

2017-02-01

The extensive exploitation and usage of lead compounds result in severe lead(II) pollution in water and soil environments, even in agricultural land, threatening the health of animals and humans via food chains. The recovery and remediation of lead(II) from water and soil environments have been intensively concerned in recent years. Compared with the traditional physic-chemistry treatment, microbial remediation strategy is a promising alternative to remediate lead(II)-contaminated environments due to its cost-effective and environmentally-friendly properties. Various microorganisms are capable of removing or immobilizing lead(II) from water and soil environments through bioaccumulation, precipitation or accelerated transformation of lead(II) into a very stable mineral, resulting in significant effects on lead(II) mobility and bioavailability. In the present review, we investigated a wide diversity of lead(II) bioremediation induced by different microbes and its multi-mechanisms. Moreover, we also discussed the progress and limitations, summarized the common rules of lead(II)-microbe interaction, and evaluated the environmental significance of microbes in lead biogeochemistry process. In addition, we further deliberated the feasibility and potential application of microbes in developing cost-effective, eco-friendly bioremediation or long-term management strategy for lead(II) contaminated repositories.

Heterobimetallic Complexes with MIII-(μ-OH)-MII Cores (MIII = Fe, Mn, Ga; MII = Ca, Sr, and Ba): Structural, Kinetic, and Redox Properties

PubMed Central

Park, Young Jun; Cook, Sarah A.; Sickerman, Nathaniel S.; Sano, Yohei; Ziller, Joseph W.

2013-01-01

The effects of redox-inactive metal ions on dioxygen activation were explored using a new FeII complex containing a tripodal ligand with 3 sulfonamido groups. This iron complex exhibited a faster initial rate for the reduction of O2 than its MnII analog. Increases in initial rates were also observed in the presence of group 2 metal ions for both the FeII and MnII complexes, which followed the trend NMe4+ < BaII < CaII = SrII. These studies led to the isolation of heterobimetallic complexes containing FeIII-(μ-OH)-MII cores (MII = Ca, Sr, and Ba) and one with a [SrII(OH)MnIII]+ motif. The analogous [CaII(OH)GaIII]+ complex was also prepared and its solid state molecular structure is nearly identical to that of the [CaII(OH)FeIII]+ system. Nuclear magnetic resonance studies indicated that the diamagnetic [CaII(OH)GaIII]+ complex retained its structure in solution. Electrochemical measurements on the heterobimetallic systems revealed similar one-electron reduction potentials for the [CaII(OH)FeIII]+ and [SrII(OH)FeIII]+ complexes, which were more positive than the potential observed for [BaII(OH)FeIII]+. Similar results were obtained for the heterobimetallic MnII complexes. These findings suggest that Lewis acidity is not the only factor to consider when evaluating the effects of group 2 ions on redox processes, including those within the oxygen-evolving complex of Photosystem II. PMID:24058726

Nano modification of NZVI with an aquatic plant Azolla filiculoides to remove Pb(II) and Hg(II) from water: Aging time and mechanism study.

PubMed

Arshadi, M; Abdolmaleki, M K; Mousavinia, F; Foroughifard, S; Karimzadeh, A

2017-01-15

This paper reports the preparation and stabilization of nano zero valent iron (NZVI) on a modified aquatic plant, Azolla filiculoides, and investigates its potential for the adsorption/reduction of Pb(II) and Hg(II) ions from aqueous media even after six months of storage in the lab condition. XRD, TEM and zeta potential results demonstrated that the Azolla-NaOH could be a good stabilizer of aged NZVI (six months) and the green support suppressed the oxidation and aggregation of immobilized NZVI. Kinetic and equilibrium models for lead and mercury ions uptake were developed by considering the effect of the initial Pb(II) and Hg(II) concentrations, contact time, adsorbent dosage, initial pH and effect of temperature. The contact time to obtain equilibrium for maximum uptake by Azolla-OH-NZVI was 20min. The removal of toxic metal ions has been monitored in terms of pseudo-first- and -second-order kinetics, and the Freundlich and Langmuir isotherms models have also been utilized to the equilibrium uptake results. The uptake kinetics followed the mechanism of the pseudo-second-order equation for all systems studied, confirming chemical sorption as the rate-limiting step of adsorption mechanisms and not involving a mass transfer in solution. The thermodynamic results confirmed that the uptake of Pb(II) and Hg(II) ions were feasible, spontaneous and endothermic at 25-80°C. XRD and zeta potential data displayed the existence of Pb(0) and Hg(0) on the Azolla-OH-NZVI surface. The nanobioadsorbent revealed high recyclability due to its reasonable uptake efficiency after 7th adsorption-desorption cycles. The proposed nano biocomposite could also be utilized to uptake Pb(II) and Hg(II) ions from the real water (Anzali lagoon water). However, coated NZVI with Azolla filiculoides as a green and environmentally friendly support suppressed rapid oxidation and aggregation of the immobilized NZVI, therefore vastly enhancing the probability of environmental transport and reducing the sedimentation and potential for toxicity. Copyright © 2016 Elsevier Inc. All rights reserved.

Biowaiver extension potential and IVIVC for BCS Class II drugs by formulation design: Case study for cyclosporine self-microemulsifying formulation.

PubMed

Yang, Su-Geun

2010-11-01

The objective of this work was to suggest the biowaiver potential of biopharmaceutical classification system (BCS) Class II drugs in self-microemulsifying drug delivery systems (SMEDDS) which are known to increase the solubility, dissolution and oral absorption of water-insoluble drugs. Cyclosporine was selected as a representative BCS Class II drug. New generic candidate of cyclosporine SMEDDS (test) was applied for the study with brand SMEDDS (reference I) and cyclosporine self-emulsifying drug delivery systems (SEDDS, reference II). Solubility and dissolution of cyclosporine from SMEDDS were critically enhanced, which were the similar behaviors with BCS class I drug. The test showed the identical dissolution rate and the equivalent bioavailability (0.34, 0.42 and 0.68 of p values for AUC₀(→)₂₄(h), C(max) and T(max), respectively) with the reference I. Based on the results, level A in vitro-in vivo correlation (IVIVC) was established from these two SMEDDS formulations. This study serves as a good example for speculating the biowaiver extension potential of BCS Class II drugs specifically in solubilizing formulation such as SMEDDS.

Potential means of cost reduction in grade crossing automatic gate systems. volume II : improved gate arm concepts for railroad/highway grade crossings gate systems

DOT National Transportation Integrated Search

1977-02-28

This report, Volume II of a two-volume study, examines the potential for reduction of the cost of installing and maintaining automatic gates at railroad-highway grade crossings. It includes a review of current practices, equipment, and standards; con...