The two NUT-like solutions of Ernst equation

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

Wu Yabo; Dong Peng; Deng Xuemei

By applying Ehlers transformation to Schwarzschild and Kerr solutions of Ernst equation and choosing the suitable coordinate transformations, the two NUT-like solutions, i.e., the so called NUT-Taub-like and the Kerr-NUT-like solutions are obtained which not only can, respectively, reduce to Schwarzschild and Kerr solutions when the parameter l{sup '}=0, but also can also reduce to the NUT-Taub metric and Kerr-NUT metric, respectively, when l{sup '} satisfies the some approximation. Meanwhile it is shown that in the NUT-Taub and Kerr-NUT solutions the range of value for the parameter l interpreted as the gravomagnetic monopole cannot be arbitrary and should be confinedmore » by mass of the source to vertical bar l vertical bar<

The Kitaev honeycomb model on surfaces of genus g ≥ 2

NASA Astrophysics Data System (ADS)

Brennan, John; Vala, Jiří

2018-05-01

We present a construction of the Kitaev honeycomb lattice model on an arbitrary higher genus surface. We first generalize the exact solution of the model based on the Jordan–Wigner fermionization to a surface with genus g = 2, and then use this as a basic module to extend the solution to lattices of arbitrary genus. We demonstrate our method by calculating the ground states of the model in both the Abelian doubled {Z}}}2 phase and the non-Abelian Ising topological phase on lattices with the genus up to g = 6. We verify the expected ground state degeneracy of the system in both topological phases and further illuminate the role of fermionic parity in the Abelian phase.

Time Dependent Channel Packet Calculation of Two Nucleon Scattering Matrix Elements

DTIC Science & Technology

2010-03-01

solutions, 46 ( ) ( )1 1 11 ( ) cos sinL L L L Lr Akr j kr krψ δ η δ= −   (3.70) Here, A is an arbitrary constant, Lδ is the phase shift...iv AFIT/DS/ENP/10-M03 Abstract A new approach to calculating nucleon-nucleon scattering matrix...elements using a proven atomic time-dependent wave packet technique is investigated. Using this technique, reactant and product wave packets containing

Comment on "the one dimensional acoustic field with arbitrary mean axial temperature gradient and mean flow" (J.Li and A.S.Morgans, Journal of Sound and Vibration 400 (2017) 248-269)

NASA Astrophysics Data System (ADS)

Dokumaci, Erkan

2017-12-01

In a recent study, Li and Morgans [1] present an ingenious WKB approximation for the acoustic plane wave field in a straight uniform duct with mean temperature gradient and mean flow. The authors state that the previous solutions are limited to small linear mean temperature gradients and low mean flow Mach numbers and claim that their solution applies for arbitrary mean temperature profiles and moderate-to-large mean flow velocity Mach numbers at both low and high frequencies.

A Self-Stabilizing Hybrid-Fault Tolerant Synchronization Protocol

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

2014-01-01

In this report we present a strategy for solving the Byzantine general problem for self-stabilizing a fully connected network from an arbitrary state and in the presence of any number of faults with various severities including any number of arbitrary (Byzantine) faulty nodes. Our solution applies to realizable systems, while allowing for differences in the network elements, provided that the number of arbitrary faults is not more than a third of the network size. The only constraint on the behavior of a node is that the interactions with other nodes are restricted to defined links and interfaces. Our solution does not rely on assumptions about the initial state of the system and no central clock nor centrally generated signal, pulse, or message is used. Nodes are anonymous, i.e., they do not have unique identities. We also present a mechanical verification of a proposed protocol. A bounded model of the protocol is verified using the Symbolic Model Verifier (SMV). The model checking effort is focused on verifying correctness of the bounded model of the protocol as well as confirming claims of determinism and linear convergence with respect to the self-stabilization period. We believe that our proposed solution solves the general case of the clock synchronization problem.

General Linewidth Formula for Steady-State Multimode Lasing in Arbitrary Cavities

NASA Astrophysics Data System (ADS)

Chong, Y. D.; Stone, A. Douglas

2012-08-01

A formula for the laser linewidth of arbitrary cavities in the multimode nonlinear regime is derived from a scattering analysis of the solutions to semiclassical laser theory. The theory generalizes previous treatments of the effects of gain and openness described by the Petermann factor. The linewidth is expressed using quantities based on the nonlinear scattering matrix, which can be computed from steady-state ab initio laser theory; unlike previous treatments, no passive cavity or phenomenological parameters are involved. We find that low cavity quality factor, combined with significant dielectric dispersion, can cause substantial deviations from the Shawlow-Townes-Petermann theory.

Approximate bound-state solutions of the Dirac equation for the generalized yukawa potential plus the generalized tensor interaction

NASA Astrophysics Data System (ADS)

Ikot, Akpan N.; Maghsoodi, Elham; Hassanabadi, Hassan; Obu, Joseph A.

2014-05-01

In this paper, we obtain the approximate analytical bound-state solutions of the Dirac particle with the generalized Yukawa potential within the framework of spin and pseudospin symmetries for the arbitrary к state with a generalized tensor interaction. The generalized parametric Nikiforov-Uvarov method is used to obtain the energy eigenvalues and the corresponding wave functions in closed form. We also report some numerical results and present figures to show the effect of the tensor interaction.

Singular perturbation solutions of steady-state Poisson-Nernst-Planck systems.

PubMed

Wang, Xiang-Sheng; He, Dongdong; Wylie, Jonathan J; Huang, Huaxiong

2014-02-01

We study the Poisson-Nernst-Planck (PNP) system with an arbitrary number of ion species with arbitrary valences in the absence of fixed charges. Assuming point charges and that the Debye length is small relative to the domain size, we derive an asymptotic formula for the steady-state solution by matching outer and boundary layer solutions. The case of two ionic species has been extensively studied, the uniqueness of the solution has been proved, and an explicit expression for the solution has been obtained. However, the case of three or more ions has received significantly less attention. Previous work has indicated that the solution may be nonunique and that even obtaining numerical solutions is a difficult task since one must solve complicated systems of nonlinear equations. By adopting a methodology that preserves the symmetries of the PNP system, we show that determining the outer solution effectively reduces to solving a single scalar transcendental equation. Due to the simple form of the transcendental equation, it can be solved numerically in a straightforward manner. Our methodology thus provides a standard procedure for solving the PNP system and we illustrate this by solving some practical examples. Despite the fact that for three ions, previous studies have indicated that multiple solutions may exist, we show that all except for one of these solutions are unphysical and thereby prove the existence and uniqueness for the three-ion case.

Solutions of the Helmholtz equation with boundary conditions for force-free magnetic fields

NASA Technical Reports Server (NTRS)

Rasband, S. N.; Turner, L.

1981-01-01

It is shown that the solution, with one ignorable coordinate, for the Taylor minimum energy state (resulting in a force-free magnetic field) in either a straight cylindrical or a toroidal geometry with arbitrary cross section can be reduced to the solution of either an inhomogeneous Helmholtz equation or a Grad-Shafranov equation with simple boundary conditions. Standard Green's function theory is, therefore, applicable. Detailed solutions are presented for the Taylor state in toroidal and cylindrical domains having a rectangular cross section. The focus is on solutions corresponding to the continuous eigenvalue spectra. Singular behavior at 90 deg corners is explored in detail.

Nonlinear system guidance in the presence of transmission zero dynamics

NASA Technical Reports Server (NTRS)

Meyer, G.; Hunt, L. R.; Su, R.

1995-01-01

An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.

Quantifying entanglement properties of qudit mixed states with incomplete permutation symmetry

NASA Astrophysics Data System (ADS)

Barasiński, Artur; Nowotarski, Mateusz

2017-04-01

The characterization of entanglement properties in mixed states is important from both a theoretical and a practical point of view. While the estimation of entanglement of bipartite pure states is well established, for mixed states it is a considerably much harder task. The key elements of the mixed-state entanglement theory are given by the exact solutions which sometimes are possible for special states of high symmetry problems. In this paper, we present the exact investigation on the entanglement properties for a five-parameter family of highly symmetric two-qudit mixed states with equal but arbitrary finite local Hilbert space dimension. We achieve this by extensive analysis of various conditions of separability and the entanglement classification with respect to stochastic local operations and classical communication. Furthermore, our results can be used for an arbitrary state by proper application of the proposed twirling operator.

Use of Invariant Manifolds for Transfers Between Three-Body Systems

NASA Technical Reports Server (NTRS)

Beckman, Mark; Howell, Kathleen

2003-01-01

The Lunar L1 and L2 libration points have been proposed as gateways granting inexpensive access to interplanetary space. To date, only individual solutions to the transfer between three-body systems have been found. The methodology to solve the problem for arbitrary three-body systems and entire families of orbits does not exist. This paper presents the initial approaches to solve the general problem for single and multiple impulse transfers. Two different methods of representing and storing 7-dimensional invariant manifold data are presented. Some particular solutions are presented for the transfer problem, though the emphasis is on developing methodology for solving the general problem.

Representations of Invariant Manifolds for Applications in Three-Body Systems

NASA Technical Reports Server (NTRS)

Howell, K.; Beckman, M.; Patterson, C.; Folta, D.

2004-01-01

The Lunar L1 and L2 libration points have been proposed as gateways granting inexpensive access to interplanetary space. To date, only individual solutions to the transfer between three-body systems have been found. The methodology to solve the problem for arbitrary three-body systems and entire families of orbits is currently being studied. This paper presents an initial approach to solve the general problem for single and multiple impulse transfers. Two different methods of representing and storing the invariant manifold data are presented. Some particular solutions are presented for two types of transfer problems, though the emphasis is on developing the methodology for solving the general problem.

Full analytical solution of the bloch equation when using a hyperbolic-secant driving function.

PubMed

Zhang, Jinjin; Garwood, Michael; Park, Jang-Yeon

2017-04-01

The frequency-swept pulse known as the hyperbolic-secant (HS) pulse is popular in NMR for achieving adiabatic spin inversion. The HS pulse has also shown utility for achieving excitation and refocusing in gradient-echo and spin-echo sequences, including new ultrashort echo-time imaging (e.g., Sweep Imaging with Fourier Transform, SWIFT) and B 1 mapping techniques. To facilitate the analysis of these techniques, the complete theoretical solution of the Bloch equation, as driven by the HS pulse, was derived for an arbitrary state of initial magnetization. The solution of the Bloch-Riccati equation for transverse and longitudinal magnetization for an arbitrary initial state was derived analytically in terms of HS pulse parameters. The analytical solution was compared with the solutions using both the Runge-Kutta method and the small-tip approximation. The analytical solution was demonstrated on different initial states at different frequency offsets with/without a combination of HS pulses. Evolution of the transverse magnetization was influenced significantly by the choice of HS pulse parameters. The deviation of the magnitude of the transverse magnetization, as obtained by comparing the small-tip approximation to the analytical solution, was < 5% for flip angles < 30 °, but > 10% for the flip angles > 40 °. The derived analytical solution provides insights into the influence of HS pulse parameters on the magnetization evolution. Magn Reson Med 77:1630-1638, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

The entrainment matrix of a superfluid nucleon mixture at finite temperatures

NASA Astrophysics Data System (ADS)

Leinson, Lev B.

2018-06-01

It is considered a closed system of non-linear equations for the entrainment matrix of a non-relativistic mixture of superfluid nucleons at arbitrary temperatures below the onset of neutron superfluidity, which takes into account the essential dependence of the superfluid energy gap in the nucleon spectra on the velocities of superfluid flows. It is assumed that the protons condense into the isotropic 1S0 state, and the neutrons are paired into the spin-triplet 3P2 state. It is derived an analytic solution to the non-linear equations for the entrainment matrix under temperatures just below the critical value for the neutron superfluidity onset. In general case of an arbitrary temperature of the superfluid mixture the non-linear equations are solved numerically and fitted by simple formulas convenient for a practical use with an arbitrary set of the Landau parameters.

A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2002-01-01

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

First Born amplitude for transitions from a circular state to a state of large (l, m)

NASA Astrophysics Data System (ADS)

Dewangan, D. P.

2005-01-01

The use of cylindrical polar coordinates instead of the conventional spherical polar coordinates enables us to derive compact expressions of the first Born amplitude for some selected sets of transitions from an arbitrary initial circular \\big|\\psi_{n_i,n_i-1,n_i-1}\\big\\rangle state to a final \\big|\\psi_{n_f,l_f,m_f}\\big\\rangle state of large (lf, mf). The formulae for \\big|\\psi_{n_i,n_i-1,n_i-1}\\big\\rangle \\longrightarrow \\big|\\psi_{n_f,n_f-1,n_f-2}\\big\\rangle and \\big|\\psi_{n_i,n_i-1,n_i-1}\\big\\rangle \\longrightarrow \\big|\\psi_{n_f,n_f-1,n_f-3}\\big\\rangle transitions are expressed in terms of the Jacobi polynomials which serve as suitable starting points for constructing complete solutions over the bound energy levels of hydrogen-like atoms. The formulae for \\big|\\psi_{n_i,n_i-1,n_i-1}\\big\\rangle \\longrightarrow \\big|\\psi_{n_f,n_f-1,-(n_f-2)}\\big\\rangle and \\big|\\psi_{n_i,n_i-1,n_i-1}\\big\\rangle \\longrightarrow \\big|\\psi_{n_f,n_f-1,-(n_f-3)}\\big\\rangle transitions are in simple algebraic forms and are directly applicable to all possible values of ni and nf. It emerges that the method can be extended to evaluate the first Born amplitude for many other transitions involving states of large (l, m).

Spin imbalance effect on the Larkin-Ovchinnikov-Fulde-Ferrel state

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

Yoshii, Ryosuke; Tsuchiya, Shunji; Research and Education Center for Natural Sciences, Keio University, 4-1-1 Hiyoshi, Kanagawa 223-8521

2011-07-01

We study spin imbalance effects on the Larkin-Ovchinnikov-Fulde-Ferrel (LOFF) state relevant for superconductors under a strong magnetic field and spin polarized ultracold Fermi gas. We obtain the exact solution for the condensates with arbitrary spin imbalance and the fermion spectrum perturbatively in the presence of small spin imbalance. We also obtain fermion zero mode exactly without perturbation theory.

Analytical solutions of the Schroedinger equation for a two-dimensional exciton in magnetic field of arbitrary strength

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

Hoang-Do, Ngoc-Tram; Hoang, Van-Hung; Le, Van-Hoang

2013-05-15

The Feranchuk-Komarov operator method is developed by combining with the Levi-Civita transformation in order to construct analytical solutions of the Schroedinger equation for a two-dimensional exciton in a uniform magnetic field of arbitrary strength. As a result, analytical expressions for the energy of the ground and excited states are obtained with a very high precision of up to four decimal places. Especially, the precision is uniformly stable for the whole range of the magnetic field. This advantage appears due to the consideration of the asymptotic behaviour of the wave-functions in strong magnetic field. The results could be used for variousmore » physical analyses and the method used here could also be applied to other atomic systems.« less

A System of Poisson Equations for a Nonconstant Varadhan Functional on a Finite State Space

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

Cavazos-Cadena, Rolando; Hernandez-Hernandez, Daniel

2006-01-15

Given a discrete-time Markov chain with finite state space and a stationary transition matrix, a system of 'local' Poisson equations characterizing the (exponential) Varadhan's functional J(.) is given. The main results, which are derived for an arbitrary transition structure so that J(.) may be nonconstant, are as follows: (i) Any solution to the local Poisson equations immediately renders Varadhan's functional, and (ii) a solution of the system always exist. The proof of this latter result is constructive and suggests a method to solve the local Poisson equations.

Transient potentials in dendritic systems of arbitrary geometry.

PubMed

Butz, E G; Cowan, J D

1974-09-01

A simple graphical calculus is developed that generates analytic solutions for membrane potential transforms at any point on the dendritic tree of neurons with arbitrary dendritic geometries, in response to synaptic "current" inputs. Such solutions permit the computation of transients in neurons with arbitrary geometry and may facilitate analysis of the role of dendrites in such cells.

Probabilistically Perfect Cloning of Two Pure States: Geometric Approach.

PubMed

Yerokhin, V; Shehu, A; Feldman, E; Bagan, E; Bergou, J A

2016-05-20

We solve the long-standing problem of making n perfect clones from m copies of one of two known pure states with minimum failure probability in the general case where the known states have arbitrary a priori probabilities. The solution emerges from a geometric formulation of the problem. This formulation reveals that cloning converges to state discrimination followed by state preparation as the number of clones goes to infinity. The convergence exhibits a phenomenon analogous to a second-order symmetry-breaking phase transition.

2D Slightly Compressible Ideal Flow in an Exterior Domain

NASA Astrophysics Data System (ADS)

Secchi, Paolo

2006-12-01

We consider the Euler equations of barotropic inviscid compressible fluids in the exterior domain. It is well known that, as the Mach number goes to zero, the compressible flows approximate the solution of the equations of motion of inviscid, incompressible fluids. In dimension 2 such limit solution exists on any arbitrary time interval, with no restriction on the size of the initial data. It is then natural to expect the same for the compressible solution, if the Mach number is sufficiently small. First we study the life span of smooth irrotational solutions, i.e. the largest time interval T(ɛ) of existence of classical solutions, when the initial data are a small perturbation of size ɛ from a constant state. Then, we study the nonlinear interaction between the irrotational part and the incompressible part of a general solution. This analysis yields the existence of smooth compressible flow on any arbitrary time interval and with no restriction on the size of the initial velocity, for any Mach number sufficiently small. Finally, the approach is applied to the study of the incompressible limit. For the proofs we use a combination of energy estimates and a decay estimate for the irrotational part.

Transient Potentials in Dendritic Systems of Arbitrary Geometry

PubMed Central

Butz, Edward G.; Cowan, Jack D.

1974-01-01

A simple graphical calculus is developed that generates analytic solutions for membrane potential transforms at any point on the dendritic tree of neurons with arbitrary dendritic geometries, in response to synaptic “current” inputs. Such solutions permit the computation of transients in neurons with arbitrary geometry and may facilitate analysis of the role of dendrites in such cells. PMID:4416699

Tables of branching ratios for electric dipole transitions between arbitrary levels of hydrogen-like atoms

NASA Technical Reports Server (NTRS)

Omidvar, K.

1977-01-01

The branching ratios in hydrogen-like atoms due to the electric-dipole transitions are tabulated for the initial principal and azimuthal quantum numbers n prime l prime, and final principal and azimuthal quantum numbers n l. Average values with respect to l prime are given. The branching ratios not tabulated, including the initial states n prime yields infinity l prime corresponding to the threshold of the continuum, could be obtained by extrapolation.

Invariant Functions, Symmetries and Primary Branch Solutions of First Order Autonomous Systems

NASA Astrophysics Data System (ADS)

Lou, Sen-Yue; Yao, Ruo-Xia

2017-07-01

An invariant function (IF) is defined as a multiplier of a symmetry that means a symmetry multiplied by an IF is still a symmetry. Primary branch solutions of arbitrary first order scalar systems can be obtained by means of the IF and its related symmetry approach. Especially, one recursion operator and some sets of infinitely many high order symmetries are also explicitly given for arbitrary (1+1)-dimensional first order autonomous systems. Because of the intrusion of the arbitrary function, various implicit special exact solutions can be found by fixing the arbitrary functions and selecting different seed solutions. Supported by the National Natural Science Foundations of China under Grant Nos. 11435005, 11471004, 11175092, and 11205092, Shanghai Knowledge Service Platform for Trustworthy Internet of Things No. ZF1213 and K. C. Wong Magna Fund in Ningbo University

Surf Zone Currents. Volume I. State of Knowledge.

DTIC Science & Technology

1982-09-01

elevation above an arbitrary datum a angle between wave crest and bottom contour a angle between wave crest and the shoreline . ab angle between breaking...b- Note that neglecting wave setup, refraction and for small ab , equation (74) reduces to that employed by Longuet-Higgins (eq. 48). These researchers...28. As ab o (Note that ab = o means theory reduces to original order (zero order) solution given by Longuet-Higgins, 1970, the triangular solution is

Ordering process in the diffusively coupled logistic lattice

NASA Astrophysics Data System (ADS)

Conrado, Claudine V.; Bohr, Tomas

1991-08-01

We study the ordering process in a lattice of diffusively coupled logistic maps for increasing lattice size. Within a window of parameters, the system goes into a weakly chaotic state with long range "antiferromagnetic" order. This happens for arbitrary lattice size L and the ordering time behaves as t ~ L2 as we would expect from a picture of diffusing defects.

The Scaling Group of the 1-D Invisicid Euler Equations

NASA Astrophysics Data System (ADS)

Schmidt, Emma; Ramsey, Scott; Boyd, Zachary; Baty, Roy

2017-11-01

The one dimensional (1-D) compressible Euler equations in non-ideal media support scale invariant solutions under a variety of initial conditions. Famous scale invariant solutions include the Noh, Sedov, Guderley, and collapsing cavity hydrodynamic test problems. We unify many classical scale invariant solutions under a single scaling group analysis. The scaling symmetry group generator provides a framework for determining all scale invariant solutions emitted by the 1-D Euler equations for arbitrary geometry, initial conditions, and equation of state. We approach the Euler equations from a geometric standpoint, and conduct scaling analyses for a broad class of materials.

Solutions to an advanced functional partial differential equation of the pantograph type

PubMed Central

Zaidi, Ali A.; Van Brunt, B.; Wake, G. C.

2015-01-01

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained. PMID:26345391

Solutions to an advanced functional partial differential equation of the pantograph type.

PubMed

Zaidi, Ali A; Van Brunt, B; Wake, G C

2015-07-08

A model for cells structured by size undergoing growth and division leads to an initial boundary value problem that involves a first-order linear partial differential equation with a functional term. Here, size can be interpreted as DNA content or mass. It has been observed experimentally and shown analytically that solutions for arbitrary initial cell distributions are asymptotic as time goes to infinity to a certain solution called the steady size distribution. The full solution to the problem for arbitrary initial distributions, however, is elusive owing to the presence of the functional term and the paucity of solution techniques for such problems. In this paper, we derive a solution to the problem for arbitrary initial cell distributions. The method employed exploits the hyperbolic character of the underlying differential operator, and the advanced nature of the functional argument to reduce the problem to a sequence of simple Cauchy problems. The existence of solutions for arbitrary initial distributions is established along with uniqueness. The asymptotic relationship with the steady size distribution is established, and because the solution is known explicitly, higher-order terms in the asymptotics can be readily obtained.

Growth or decay of cosmological inhomogeneities as a function of their equation of state

NASA Astrophysics Data System (ADS)

Comer, G. L.; Deruelle, Nathalie; Langlois, David; Parry, Joe

1994-03-01

We expand Einstein's equations in the synchronous gauge in terms of a purely space-dependent, ``seed,'' metric. The (nonlinear) solution accurately describes a universe inhomogeneous at scales larger than the Hubble radius. We show that the inhomogeneities grow or decay, as time increases, depending on the equation of state for the matter (supposed to be a perfect fluid). We then consider the case when matter is a scalar field with an arbitrary potential. Finally we discuss the generality of the model and show that it is an attractor for a class of generic solutions of Einstein's equations.

Solutions of the Bethe ansatz equations for XXX antiferromagnet of arbitrary spin in the case of a finite number of sites

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

Avdeev, L.V.; Doerfel, B.D.

1987-11-01

The exactly integrable isotropic Heisenberg chain of N spins s is studied, and numerical solutions to the Bethe ansatz equations corresponding to the antiferromagnetic vacuum (for sN less than or equal to 128) and the simplest excitations have been obtained. For s = 1, a complete set of states for N = 6 is given, and the vacuum solution for finite N is estimated analytically. The deviations from the string picture at large N are discussed.

Collective Yu-Shiba-Rusinov states in magnetic clusters at superconducting surfaces

NASA Astrophysics Data System (ADS)

Körber, Simon; Trauzettel, Björn; Kashuba, Oleksiy

2018-05-01

We study the properties of collective Yu-Shiba-Rusinov (YSR) states generated by multiple magnetic adatoms (clusters) placed on the surface of a superconductor. For magnetic clusters with equal distances between their constituents, we demonstrate the formation of effectively spin-unpolarized YSR states with subgap energies independent of the spin configuration of the magnetic impurities. We solve the problem analytically for arbitrary spin structure and analyze both spin-polarized (dispersive energy levels) and spin-unpolarized (pinned energy levels) solutions. While the energies of the spin-polarized solutions can be characterized solely by the net magnetic moment of the cluster, the wave functions of the spin-unpolarized solutions effectively decouple from it. This decoupling makes them stable against thermal fluctuation and detectable in scanning tunneling microscopy experiments.

Momentum fractionation on superstrata

DOE PAGES

Bena, Iosif; Martinec, Emil; Turton, David; ...

2016-05-11

Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical three-charge states reside in highdegree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifoldmore » singularities. Upon taking the AdS3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Lastly, our construction establishes the very nontrivial fact that large classes of CFT states with momentum fractionation can be realized in the bulk as smooth horizonless supergravity solutions.« less

A robust, efficient equidistribution 2D grid generation method

NASA Astrophysics Data System (ADS)

Chacon, Luis; Delzanno, Gian Luca; Finn, John; Chung, Jeojin; Lapenta, Giovanni

2007-11-01

We present a new cell-area equidistribution method for two- dimensional grid adaptation [1]. The method is able to satisfy the equidistribution constraint to arbitrary precision while optimizing desired grid properties (such as isotropy and smoothness). The method is based on the minimization of the grid smoothness integral, constrained to producing a given positive-definite cell volume distribution. The procedure gives rise to a single, non-linear scalar equation with no free-parameters. We solve this equation numerically with the Newton-Krylov technique. The ellipticity property of the linearized scalar equation allows multigrid preconditioning techniques to be effectively used. We demonstrate a solution exists and is unique. Therefore, once the solution is found, the adapted grid cannot be folded due to the positivity of the constraint on the cell volumes. We present several challenging tests to show that our new method produces optimal grids in which the constraint is satisfied numerically to arbitrary precision. We also compare the new method to the deformation method [2] and show that our new method produces better quality grids. [1] G.L. Delzanno, L. Chac'on, J.M. Finn, Y. Chung, G. Lapenta, A new, robust equidistribution method for two-dimensional grid generation, in preparation. [2] G. Liao and D. Anderson, A new approach to grid generation, Appl. Anal. 44, 285--297 (1992).

Quantum Discord for d⊗2 Systems

PubMed Central

Ma, Zhihao; Chen, Zhihua; Fanchini, Felipe Fernandes; Fei, Shao-Ming

2015-01-01

We present an analytical solution for classical correlation, defined in terms of linear entropy, in an arbitrary system when the second subsystem is measured. We show that the optimal measurements used in the maximization of the classical correlation in terms of linear entropy, when used to calculate the quantum discord in terms of von Neumann entropy, result in a tight upper bound for arbitrary systems. This bound agrees with all known analytical results about quantum discord in terms of von Neumann entropy and, when comparing it with the numerical results for 106 two-qubit random density matrices, we obtain an average deviation of order 10−4. Furthermore, our results give a way to calculate the quantum discord for arbitrary n-qubit GHZ and W states evolving under the action of the amplitude damping noisy channel. PMID:26036771

A new shock-capturing numerical scheme for ideal hydrodynamics

NASA Astrophysics Data System (ADS)

Fecková, Z.; Tomášik, B.

2015-05-01

We present a new algorithm for solving ideal relativistic hydrodynamics based on Godunov method with an exact solution of Riemann problem for an arbitrary equation of state. Standard numerical tests are executed, such as the sound wave propagation and the shock tube problem. Low numerical viscosity and high precision are attained with proper discretization.

New Exact Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Fireballs

NASA Astrophysics Data System (ADS)

Csörgő, Tamás; Kasza, Gábor; Csanád, Máté; Jiang, Zefang

2018-06-01

We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables like the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton-proton and heavy ion collision data at RHIC and LHC. In the longitudinally boost-invariant limit, these new solutions approach the Hwa-Bjorken solution and the corresponding rapidity distributions approach a rapidity plateaux.

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

Bena, Iosif; Bobev, Nikolay; Warner, Nicholas P.

We discuss 'spectral-flow' coordinate transformations that take asymptotically four-dimensional solutions into other asymptotically four-dimensional solutions. We find that spectral flow can relate smooth three-charge solutions with a multicenter Taub-NUT base to solutions where one or several Taub-NUT centers are replaced by two-charge supertubes, and vice versa. We further show that multiparameter spectral flows can map such Taub-NUT centers to more singular centers that are either D2-D0 or pure D0-brane sources. Since supertubes can depend on arbitrary functions, we establish that the moduli space of smooth horizonless black-hole microstate solutions is classically of infinite dimension. We also use the physics ofmore » supertubes to argue that some multicenter solutions that appear to be bound states from a four-dimensional perspective are in fact not bound states when considered from a five- or six-dimensional perspective.« less

Solution to the mean king's problem with mutually unbiased bases for arbitrary levels

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

Kimura, Gen; Tanaka, Hajime; Ozawa, Masanao

2006-05-15

The mean king's problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi et al. [Phys. Rev. A 71, 052331 (2005)] related the problem to the existence of a maximal set of d-1 mutually orthogonal Latin squares, in their restricted setting that allows only measurements of projection-valued measures. However, we then cannot find a solution to the problem when, e.g., d=6 or d=10. In contrast to their result, we show that the king's problem always has a solution for arbitrary levels if we also allow positive operator-valued measures. In constructing the solution, we use orthogonal arrays in combinatorialmore » design theory.« less

Exploring Lovelock theory moduli space for Schrödinger solutions

NASA Astrophysics Data System (ADS)

Jatkar, Dileep P.; Kundu, Nilay

2016-09-01

We look for Schrödinger solutions in Lovelock gravity in D > 4. We span the entire parameter space and determine parametric relations under which the Schrödinger solution exists. We find that in arbitrary dimensions pure Lovelock theories have Schrödinger solutions of arbitrary radius, on a co-dimension one locus in the Lovelock parameter space. This co-dimension one locus contains the subspace over which the Lovelock gravity can be written in the Chern-Simons form. Schrödinger solutions do not exist outside this locus and on this locus they exist for arbitrary dynamical exponent z. This freedom in z is due to the degeneracy in the configuration space. We show that this degeneracy survives certain deformation away from the Lovelock moduli space.

State space truncation with quantified errors for accurate solutions to discrete Chemical Master Equation

PubMed Central

Cao, Youfang; Terebus, Anna; Liang, Jie

2016-01-01

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEG), we truncate the state space by limiting the total molecular copy numbers in each MEG. We further describe a theoretical framework for analysis of the truncation error in the steady state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of 1) the birth and death model, 2) the single gene expression model, 3) the genetic toggle switch model, and 4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate out theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks. PMID:27105653

State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation

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

Cao, Youfang; Terebus, Anna; Liang, Jie

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEGs), we truncate the state space by limiting the total molecular copy numbers in each MEG. Wemore » further describe a theoretical framework for analysis of the truncation error in the steady-state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of (1) the birth and death model, (2) the single gene expression model, (3) the genetic toggle switch model, and (4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady-state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate our theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.« less

State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation

DOE PAGES

Cao, Youfang; Terebus, Anna; Liang, Jie

2016-04-22

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEGs), we truncate the state space by limiting the total molecular copy numbers in each MEG. Wemore » further describe a theoretical framework for analysis of the truncation error in the steady-state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of (1) the birth and death model, (2) the single gene expression model, (3) the genetic toggle switch model, and (4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady-state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate our theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.« less

Exact analytical solution of a classical Josephson tunnel junction problem

NASA Astrophysics Data System (ADS)

Kuplevakhsky, S. V.; Glukhov, A. M.

2010-10-01

We give an exact and complete analytical solution of the classical problem of a Josephson tunnel junction of arbitrary length W ɛ(0,∞) in the presence of external magnetic fields and transport currents. Contrary to a wide-spread belief, the exact analytical solution unambiguously proves that there is no qualitative difference between so-called "small" (W≪1) and "large" junctions (W≫1). Another unexpected physical implication of the exact analytical solution is the existence (in the current-carrying state) of unquantized Josephson vortices carrying fractional flux and located near one of the edges of the junction. We also refine the mathematical definition of critical transport current.

A Self-Stabilizing Hybrid Fault-Tolerant Synchronization Protocol

NASA Technical Reports Server (NTRS)

Malekpour, Mahyar R.

2015-01-01

This paper presents a strategy for solving the Byzantine general problem for self-stabilizing a fully connected network from an arbitrary state and in the presence of any number of faults with various severities including any number of arbitrary (Byzantine) faulty nodes. The strategy consists of two parts: first, converting Byzantine faults into symmetric faults, and second, using a proven symmetric-fault tolerant algorithm to solve the general case of the problem. A protocol (algorithm) is also present that tolerates symmetric faults, provided that there are more good nodes than faulty ones. The solution applies to realizable systems, while allowing for differences in the network elements, provided that the number of arbitrary faults is not more than a third of the network size. The only constraint on the behavior of a node is that the interactions with other nodes are restricted to defined links and interfaces. The solution does not rely on assumptions about the initial state of the system and no central clock nor centrally generated signal, pulse, or message is used. Nodes are anonymous, i.e., they do not have unique identities. A mechanical verification of a proposed protocol is also present. A bounded model of the protocol is verified using the Symbolic Model Verifier (SMV). The model checking effort is focused on verifying correctness of the bounded model of the protocol as well as confirming claims of determinism and linear convergence with respect to the self-stabilization period.

Improved analytical approximation to arbitrary l-state solutions of the Schrödinger equation for the hyperbolical potentials

NASA Astrophysics Data System (ADS)

Sánchez López, Elena H.

2018-04-01

Water has been traditionally highlighted (together with fish and salt) as one of the essential elements in fish processing. Indeed, the need for large quantities of fresh water for the production of salted fish and fish sauces in Roman times is commonly asserted. This paper analyses water-related structures within Roman halieutic installations, arguing that their common presence in the best known fish processing installations in the Western Roman world should be taken as evidence of the use of fresh water during the production processes, even if its role in the activities carried out in those installations is not clear. In addition, the text proposes some first estimates on the amount of water that could be needed by those fish processing complexes for their functioning, concluding that water needs to be taken into account when reconstructing fish-salting recipes.

The general solution to the classical problem of finite Euler Bernoulli beam

NASA Technical Reports Server (NTRS)

Hussaini, M. Y.; Amba-Rao, C. L.

1977-01-01

An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.

Semi-analytical solution for the generalized absorbing boundary condition in molecular dynamics simulations

NASA Astrophysics Data System (ADS)

Lee, Chung-Shuo; Chen, Yan-Yu; Yu, Chi-Hua; Hsu, Yu-Chuan; Chen, Chuin-Shan

2017-07-01

We present a semi-analytical solution of a time-history kernel for the generalized absorbing boundary condition in molecular dynamics (MD) simulations. To facilitate the kernel derivation, the concept of virtual atoms in real space that can conform with an arbitrary boundary in an arbitrary lattice is adopted. The generalized Langevin equation is regularized using eigenvalue decomposition and, consequently, an analytical expression of an inverse Laplace transform is obtained. With construction of dynamical matrices in the virtual domain, a semi-analytical form of the time-history kernel functions for an arbitrary boundary in an arbitrary lattice can be found. The time-history kernel functions for different crystal lattices are derived to show the generality of the proposed method. Non-equilibrium MD simulations in a triangular lattice with and without the absorbing boundary condition are conducted to demonstrate the validity of the solution.

Optimal port-based teleportation

NASA Astrophysics Data System (ADS)

Mozrzymas, Marek; Studziński, Michał; Strelchuk, Sergii; Horodecki, Michał

2018-05-01

Deterministic port-based teleportation (dPBT) protocol is a scheme where a quantum state is guaranteed to be transferred to another system without unitary correction. We characterise the best achievable performance of the dPBT when both the resource state and the measurement is optimised. Surprisingly, the best possible fidelity for an arbitrary number of ports and dimension of the teleported state is given by the largest eigenvalue of a particular matrix—Teleportation Matrix. It encodes the relationship between a certain set of Young diagrams and emerges as the optimal solution to the relevant semidefinite programme.

Heating a plasma by a broadband stream of fast electrons: Fast ignition, shock ignition, and Gbar shock wave applications

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

Gus’kov, S. Yu., E-mail: guskov@sci.lebedev.ru; Nicolai, Ph.; Ribeyre, X.

2015-09-15

An exact analytic solution is found for the steady-state distribution function of fast electrons with an arbitrary initial spectrum irradiating a planar low-Z plasma with an arbitrary density distribution. The solution is applied to study the heating of a material by fast electrons of different spectra such as a monoenergetic spectrum, a step-like distribution in a given energy range, and a Maxwellian spectrum, which is inherent in laser-produced fast electrons. The heating of shock- and fast-ignited precompressed inertial confinement fusion (ICF) targets as well as the heating of a target designed to generate a Gbar shock wave for equation ofmore » state (EOS) experiments by laser-produced fast electrons with a Maxwellian spectrum is investigated. A relation is established between the energies of two groups of Maxwellian fast electrons, which are responsible for generation of a shock wave and heating the upstream material (preheating). The minimum energy of the fast and shock igniting beams as well as of the beam for a Gbar shock wave generation increases with the spectral width of the electron distribution.« less

Generalized analytical solutions to sequentially coupled multi-species advective-dispersive transport equations in a finite domain subject to an arbitrary time-dependent source boundary condition

NASA Astrophysics Data System (ADS)

Chen, Jui-Sheng; Liu, Chen-Wuing; Liang, Ching-Ping; Lai, Keng-Hsin

2012-08-01

SummaryMulti-species advective-dispersive transport equations sequentially coupled with first-order decay reactions are widely used to describe the transport and fate of the decay chain contaminants such as radionuclide, chlorinated solvents, and nitrogen. Although researchers attempted to present various types of methods for analytically solving this transport equation system, the currently available solutions are mostly limited to an infinite or a semi-infinite domain. A generalized analytical solution for the coupled multi-species transport problem in a finite domain associated with an arbitrary time-dependent source boundary is not available in the published literature. In this study, we first derive generalized analytical solutions for this transport problem in a finite domain involving arbitrary number of species subject to an arbitrary time-dependent source boundary. Subsequently, we adopt these derived generalized analytical solutions to obtain explicit analytical solutions for a special-case transport scenario involving an exponentially decaying Bateman type time-dependent source boundary. We test the derived special-case solutions against the previously published coupled 4-species transport solution and the corresponding numerical solution with coupled 10-species transport to conduct the solution verification. Finally, we compare the new analytical solutions derived for a finite domain against the published analytical solutions derived for a semi-infinite domain to illustrate the effect of the exit boundary condition on coupled multi-species transport with an exponential decaying source boundary. The results show noticeable discrepancies between the breakthrough curves of all the species in the immediate vicinity of the exit boundary obtained from the analytical solutions for a finite domain and a semi-infinite domain for the dispersion-dominated condition.

Norm overlap between many-body states: Uncorrelated overlap between arbitrary Bogoliubov product states

NASA Astrophysics Data System (ADS)

Bally, B.; Duguet, T.

2018-02-01

Background: State-of-the-art multi-reference energy density functional calculations require the computation of norm overlaps between different Bogoliubov quasiparticle many-body states. It is only recently that the efficient and unambiguous calculation of such norm kernels has become available under the form of Pfaffians [L. M. Robledo, Phys. Rev. C 79, 021302 (2009), 10.1103/PhysRevC.79.021302]. Recently developed particle-number-restored Bogoliubov coupled-cluster (PNR-BCC) and particle-number-restored Bogoliubov many-body perturbation (PNR-BMBPT) ab initio theories [T. Duguet and A. Signoracci, J. Phys. G 44, 015103 (2017), 10.1088/0954-3899/44/1/015103] make use of generalized norm kernels incorporating explicit many-body correlations. In PNR-BCC and PNR-BMBPT, the Bogoliubov states involved in the norm kernels differ specifically via a global gauge rotation. Purpose: The goal of this work is threefold. We wish (i) to propose and implement an alternative to the Pfaffian method to compute unambiguously the norm overlap between arbitrary Bogoliubov quasiparticle states, (ii) to extend the first point to explicitly correlated norm kernels, and (iii) to scrutinize the analytical content of the correlated norm kernels employed in PNR-BMBPT. Point (i) constitutes the purpose of the present paper while points (ii) and (iii) are addressed in a forthcoming paper. Methods: We generalize the method used in another work [T. Duguet and A. Signoracci, J. Phys. G 44, 015103 (2017), 10.1088/0954-3899/44/1/015103] in such a way that it is applicable to kernels involving arbitrary pairs of Bogoliubov states. The formalism is presently explicated in detail in the case of the uncorrelated overlap between arbitrary Bogoliubov states. The power of the method is numerically illustrated and benchmarked against known results on the basis of toy models of increasing complexity. Results: The norm overlap between arbitrary Bogoliubov product states is obtained under a closed-form expression allowing its computation without any phase ambiguity. The formula is physically intuitive, accurate, and versatile. It equally applies to norm overlaps between Bogoliubov states of even or odd number parity. Numerical applications illustrate these features and provide a transparent representation of the content of the norm overlaps. Conclusions: The complex norm overlap between arbitrary Bogoliubov states is computed, without any phase ambiguity, via elementary linear algebra operations. The method can be used in any configuration mixing of orthogonal and non-orthogonal product states. Furthermore, the closed-form expression extends naturally to correlated overlaps at play in PNR-BCC and PNR-BMBPT. As such, the straight overlap between Bogoliubov states is the zero-order reduction of more involved norm kernels to be studied in a forthcoming paper.

Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach

NASA Astrophysics Data System (ADS)

Trinkle, Dallas R.

2017-10-01

A general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the vacancy lattice Green function reduces to the sum of a few analytic functions and numerical integration of a smooth function over the Brillouin zone for arbitrary crystals. The Dyson equation solves for the Green function in the presence of a solute with arbitrary but finite interaction range to compute the transport coefficients accurately, efficiently and automatically, including cases with very large differences in solute-vacancy exchange rates. The methodology takes advantage of the space group symmetry of a crystal to reduce the complexity of the matrix inversion in the Dyson equation. An open-source implementation of the algorithm is available, and numerical results are presented for the convergence of the integration error of the bare vacancy Green function, and tracer correlation factors for a variety of crystals including wurtzite (hexagonal diamond) and garnet.

Finite-Length Diocotron Modes in a Non-neutral Plasma Column

NASA Astrophysics Data System (ADS)

Walsh, Daniel; Dubin, Daniel

2017-10-01

Diocotron modes are 2D distortions of a non-neutral plasma column that propagate azimuthally via E × B drifts. While the infinite-length theory of diocotron modes is well-understood for arbitrary azimuthal mode number l, the finite-length mode frequency is less developed (with some exceptions), and is naturally of relevance to experiments. In this poster, we present an approach to address finite length effects, such as temperature dependence of the mode frequency. We use a bounce-averaged solution to the Vlasov Equation, in which the Vlasov Equation is solved using action-angle variables of the unperturbed Hamiltonian. We write the distribution function as a Fourier series in the bounce-angle variable ψ, keeping only the bounce-averaged term. We demonstrate a numerical solution to this equation for a realistic plasma with a finite Debye Length, compare to the existing l = 1 theory, and discuss possible extensions of the existing theory to l ≠ 1 . Supported by NSF/DOE Partnership Grants PHY1414570 and DESC0002451.

A multistage time-stepping scheme for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, E.

1985-01-01

A class of explicit multistage time-stepping schemes is used to construct an algorithm for solving the compressible Navier-Stokes equations. Flexibility in treating arbitrary geometries is obtained with a finite-volume formulation. Numerical efficiency is achieved by employing techniques for accelerating convergence to steady state. Computer processing is enhanced through vectorization of the algorithm. The scheme is evaluated by solving laminar and turbulent flows over a flat plate and an NACA 0012 airfoil. Numerical results are compared with theoretical solutions or other numerical solutions and/or experimental data.

Abundant closed form solutions of the conformable time fractional Sawada-Kotera-Ito equation using (G‧ / G) -expansion method

NASA Astrophysics Data System (ADS)

Al-Shawba, Altaf Abdulkarem; Gepreel, K. A.; Abdullah, F. A.; Azmi, A.

2018-06-01

In current study, we use the (G‧ / G) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.

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

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

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

2013-10-15

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

Length filtration of the separable states.

PubMed

Chen, Lin; Ðoković, Dragomir Ž

2016-11-01

We investigate the separable states ρ of an arbitrary multi-partite quantum system with Hilbert space [Formula: see text] of dimension d . The length L ( ρ ) of ρ is defined as the smallest number of pure product states having ρ as their mixture. The length filtration of the set of separable states, [Formula: see text], is the increasing chain [Formula: see text], where [Formula: see text]. We define the maximum length, [Formula: see text], critical length, L crit , and yet another special length, L c , which was defined by a simple formula in one of our previous papers. The critical length indicates the first term in the length filtration whose dimension is equal to [Formula: see text]. We show that in general d ≤ L c ≤ L crit ≤ L max ≤ d 2 . We conjecture that the equality L crit = L c holds for all finite-dimensional multi-partite quantum systems. Our main result is that L crit = L c for the bipartite systems having a single qubit as one of the parties. This is accomplished by computing the rank of the Jacobian matrix of a suitable map having [Formula: see text] as its range.

Exact solution of the generalized Peierls equation for arbitrary n-fold screw dislocation

NASA Astrophysics Data System (ADS)

Wang, Shaofeng; Hu, Xiangsheng

2018-05-01

The exact solution of the generalized Peierls equation is presented and proved for arbitrary n-fold screw dislocation. The displacement field, stress field and the energy of the n-fold dislocation are also evaluated explicitly. It is found that the solution defined on each individual fold is given by the tail cut from the original Peierls solution. In viewpoint of energetics, a screw dislocation has a tendency to spread the distribution on all possible slip planes which are contained in the dislocation line zone. Based on the exact solution, the approximated solution of the improved Peierls equation is proposed for the modified γ-surface.

Optical solitons in nematic liquid crystals: model with saturation effects

NASA Astrophysics Data System (ADS)

Borgna, Juan Pablo; Panayotaros, Panayotis; Rial, Diego; de la Vega, Constanza Sánchez F.

2018-04-01

We study a 2D system that couples a Schrödinger evolution equation to a nonlinear elliptic equation and models the propagation of a laser beam in a nematic liquid crystal. The nonlinear elliptic equation describes the response of the director angle to the laser beam electric field. We obtain results on well-posedness and solitary wave solutions of this system, generalizing results for a well-studied simpler system with a linear elliptic equation for the director field. The analysis of the nonlinear elliptic problem shows the existence of an isolated global branch of solutions with director angles that remain bounded for arbitrary electric field. The results on the director equation are also used to show local and global existence, as well as decay for initial conditions with sufficiently small L 2-norm. For sufficiently large L 2-norm we show the existence of energy minimizing optical solitons with radial, positive and monotone profiles.

FIBER OPTICS: Method of calculation of the propagation constant for guided modes

NASA Astrophysics Data System (ADS)

Ardasheva, L. I.; Sadykov, Nail R.; Chernyakov, V. E.

1992-09-01

A new method of calculating the propagation constants and wave eigenfunctions of guided modes is proposed for axisymmetric translationally invariant fiber-optic waveguides with arbitrary refractive index profiles. The method is based on solving a parabolic scalar wave equation. A comparison is made between the numerical solution under steady-state conditions and the eigenfunctions of single-mode and multimode waveguides.

Group analysis of dynamics equations of self-gravitating polytropic gas

NASA Astrophysics Data System (ADS)

Klebanov, I.; Panov, A.; Ivanov, S.; Maslova, O.

2018-06-01

The Lie algebras admitted by the dynamics equations of self-gravitating gas for an arbitrary equation of state and a polytropic gas are calculated. A spherically symmetric submodel is constructed for the case of a polytropic gas. The Lie algebras and the optimal system of subalgebras for a spherically symmetric submodel are computed. An invariant solution describing the steady motion is obtained.

Supersonic flow past oscillating airfoils including nonlinear thickness effects

NASA Technical Reports Server (NTRS)

Van Dyke, Milton D

1954-01-01

A solution to second order in thickness is derived for harmonically oscillating two-dimensional airfoils in supersonic flow. For slow oscillations of an arbitrary profile, the result is found as a series including the third power of frequency. For arbitrary frequencies, the method of solution for any specific profile is indicated, and the explicit solution derived for a single wedge. Nonlinear thickness effects are found generally to reduce the torsional damping, and so enlarge the range of Mach numbers within which torsional instability is possible.

Feedback quantum control of molecular electronic population transfer

NASA Astrophysics Data System (ADS)

Bardeen, Christopher J.; Yakovlev, Vladislav V.; Wilson, Kent R.; Carpenter, Scott D.; Weber, Peter M.; Warren, Warren S.

1997-11-01

Feedback quantum control, where the sample `teaches' a computer-controlled arbitrary lightform generator to find the optimal light field, is experimentally demonstrated for a molecular system. Femtosecond pulses tailored by a computer-controlled acousto-optic pulse shaper excite fluorescence from laser dye molecules in solution. Fluorescence and laser power are monitored, and the computer uses the experimental data and a genetic algorithm to optimize population transfer from ground to first excited state. Both efficiency (the ratio of excited state population to laser energy) and effectiveness (total excited state population) are optimized. Potential use as an `automated theory tester' is discussed.

Density matrix solutions for the susceptibilities of a three-level system with arbitrary relaxation rates and field strengths

NASA Technical Reports Server (NTRS)

Ryan, J. C.; Lawandy, N. M.

1986-01-01

The susceptibilities for a three-level system with arbitrary pump and signal field strengths are derived for arbitrary longitudinal and transverse relaxation rates. The results are of interest in connection with the calculation of the Raman gain in systems where resonance enhancement plays a dominant role.

A free energy satisfying discontinuous Galerkin method for one-dimensional Poisson-Nernst-Planck systems

NASA Astrophysics Data System (ADS)

Liu, Hailiang; Wang, Zhongming

2017-01-01

We design an arbitrary-order free energy satisfying discontinuous Galerkin (DG) method for solving time-dependent Poisson-Nernst-Planck systems. Both the semi-discrete and fully discrete DG methods are shown to satisfy the corresponding discrete free energy dissipation law for positive numerical solutions. Positivity of numerical solutions is enforced by an accuracy-preserving limiter in reference to positive cell averages. Numerical examples are presented to demonstrate the high resolution of the numerical algorithm and to illustrate the proven properties of mass conservation, free energy dissipation, as well as the preservation of steady states.

An integral equation-based numerical solver for Taylor states in toroidal geometries

NASA Astrophysics Data System (ADS)

O'Neil, Michael; Cerfon, Antoine J.

2018-04-01

We present an algorithm for the numerical calculation of Taylor states in toroidal and toroidal-shell geometries using an analytical framework developed for the solution to the time-harmonic Maxwell equations. Taylor states are a special case of what are known as Beltrami fields, or linear force-free fields. The scheme of this work relies on the generalized Debye source representation of Maxwell fields and an integral representation of Beltrami fields which immediately yields a well-conditioned second-kind integral equation. This integral equation has a unique solution whenever the Beltrami parameter λ is not a member of a discrete, countable set of resonances which physically correspond to spontaneous symmetry breaking. Several numerical examples relevant to magnetohydrodynamic equilibria calculations are provided. Lastly, our approach easily generalizes to arbitrary geometries, both bounded and unbounded, and of varying genus.

Energy repartition in the nonequilibrium steady state

NASA Astrophysics Data System (ADS)

Yan, Peng; Bauer, Gerrit E. W.; Zhang, Huaiwu

2017-01-01

The concept of temperature in nonequilibrium thermodynamics is an outstanding theoretical issue. We propose an energy repartition principle that leads to a spectral (mode-dependent) temperature in steady-state nonequilibrium systems. The general concepts are illustrated by analytic solutions of the classical Heisenberg spin chain connected to Langevin heat reservoirs with arbitrary temperature profiles. Gradients of external magnetic fields are shown to localize spin waves in a Wannier-Zeemann fashion, while magnon interactions renormalize the spectral temperature. Our generic results are applicable to other thermodynamic systems such as Newtonian liquids, elastic solids, and Josephson junctions.

Solving general gauge theories on inner product spaces

NASA Astrophysics Data System (ADS)

Batalin, Igor; Marnelius, Robert

1995-02-01

By means of a generalized quartet mechanism we show in a model independent way that a BRST quantization on an inner product space leads to physical states of the form ph> = exp [ Q, ψ]ph> 0 where Q is the nilpotent BRST operator, ψ a hermitian fermionic gauge-fixing operator, and ph> o BRST invariant states determined by a hermitian set of BRST doublets in involution. ph> 0 does not belong to an inner product space although ph> does. Since the BRST quartets are split into two sets of hermitian BRST doublets there are two choices for ph> 0 and the corresponding ψ. When applied to general, both irreducible and reducible, gauge theories of arbitrary rank within the BFV formulation we find that ph> 0 are trivial BRST invariant states which only depend on the matter variables for one set of solutions, and for the other set ph> 0 are solutions of a Dirac quantization. This generalizes previous Lie group solutions obtained by means of a bigrading.

Adaptive reconnection-based arbitrary Lagrangian Eulerian method

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

Bo, Wurigen; Shashkov, Mikhail

We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less

Adaptive reconnection-based arbitrary Lagrangian Eulerian method

DOE PAGES

Bo, Wurigen; Shashkov, Mikhail

2015-07-21

We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less

Rarefaction waves in van der Waals fluids with an arbitrary number of degrees of freedom

DOE PAGES

Yuen, Albert; Barnard, John J.

2015-09-30

The isentropic expansion of an instantaneously and homogeneously heated foil is calculated using a 1D fluid model. The initial temperature and density are assumed to be in the vicinity of the critical temperature and solid density, respectively. The fluid is assumed to satisfy the van der Waals equation of state with an arbitrary number of degrees of freedom. Self-similar Riemann solutions are found. With a larger number of degrees of freedom f, depending on the initial dimensionless entropymore » $$˜\\atop{s_0}$$, a richer family of foil expansion behaviors have been found. We calculate the domain in parameter space where these behaviors occur. In total, eight types of rarefaction waves are found and described.« less

Tripartite Controlled Teleportation via a Seven-Qubit Entangled State

NASA Astrophysics Data System (ADS)

Nie, Yi-you; Sang, Ming-huang; Li, Song-song

2017-09-01

We demonstrate that a seven-qubit entangled state can be used to realize the deterministic tripartite controlled teleportation by performing Bell-state measurements, where Alice wants to teleport an arbitrary single-qubit state of qubit a to Bob, Charlie wants to teleport an arbitrary single-qubit state of qubit b to David and at the same time Edison wants to teleport an arbitrary single-qubit state of qubit c to Ford via the control of the supervisor Tom.

Recursive analytical solution describing artificial satellite motion perturbed by an arbitrary number of zonal terms

NASA Technical Reports Server (NTRS)

Mueller, A. C.

1977-01-01

An analytical first order solution has been developed which describes the motion of an artificial satellite perturbed by an arbitrary number of zonal harmonics of the geopotential. A set of recursive relations for the solution, which was deduced from recursive relations of the geopotential, was derived. The method of solution is based on Von-Zeipel's technique applied to a canonical set of two-body elements in the extended phase space which incorporates the true anomaly as a canonical element. The elements are of Poincare type, that is, they are regular for vanishing eccentricities and inclinations. Numerical results show that this solution is accurate to within a few meters after 500 revolutions.

A coordinate free description of magnetohydrostatic equilibria

NASA Technical Reports Server (NTRS)

Martens, P. C. H.

1986-01-01

The question what geometrical restrictions are imposed on static magnetic fields by the magnetohydrostatic (MHS) equation is addressed. The general mathematical problem is therefore to determine the solutions of the MHS equations in the corona subject to an arbitrary normal component of the magnetic field at the boundary and arbitrary connectivity. What constraints the MHS equations impose on the geometry of the solutions, expressed in metric tensors, will be determined.

On generalized Melvin solution for the Lie algebra E_6

NASA Astrophysics Data System (ADS)

Bolokhov, S. V.; Ivashchuk, V. D.

2017-10-01

A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra G is considered. The gravitational model in D dimensions, D ≥ 4, contains n 2-forms and l ≥ n scalar fields, where n is the rank of G. The solution is governed by a set of n functions H_s(z) obeying n ordinary differential equations with certain boundary conditions imposed. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). The polynomials H_s(z), s = 1,\\ldots ,6, for the Lie algebra E_6 are obtained and a corresponding solution for l = n = 6 is presented. The polynomials depend upon integration constants Q_s, s = 1,\\ldots ,6. They obey symmetry and duality identities. The latter ones are used in deriving asymptotic relations for solutions at large distances. The power-law asymptotic relations for E_6-polynomials at large z are governed by the integer-valued matrix ν = A^{-1} (I + P), where A^{-1} is the inverse Cartan matrix, I is the identity matrix and P is a permutation matrix, corresponding to a generator of the Z_2-group of symmetry of the Dynkin diagram. The 2-form fluxes Φ ^s, s = 1,\\ldots ,6, are calculated.

Generalized Buneman Pruning for Inferring the Most Parsimonious Multi-state Phylogeny

NASA Astrophysics Data System (ADS)

Misra, Navodit; Blelloch, Guy; Ravi, R.; Schwartz, Russell

Accurate reconstruction of phylogenies remains a key challenge in evolutionary biology. Most biologically plausible formulations of the problem are formally NP-hard, with no known efficient solution. The standard in practice are fast heuristic methods that are empirically known to work very well in general, but can yield results arbitrarily far from optimal. Practical exact methods, which yield exponential worst-case running times but generally much better times in practice, provide an important alternative. We report progress in this direction by introducing a provably optimal method for the weighted multi-state maximum parsimony phylogeny problem. The method is based on generalizing the notion of the Buneman graph, a construction key to efficient exact methods for binary sequences, so as to apply to sequences with arbitrary finite numbers of states with arbitrary state transition weights. We implement an integer linear programming (ILP) method for the multi-state problem using this generalized Buneman graph and demonstrate that the resulting method is able to solve data sets that are intractable by prior exact methods in run times comparable with popular heuristics. Our work provides the first method for provably optimal maximum parsimony phylogeny inference that is practical for multi-state data sets of more than a few characters.

Alfven waves in spiral interplanetary field

NASA Technical Reports Server (NTRS)

Whang, Y. C.

1973-01-01

A theoretical study is presented of the Alfven waves in the spiral interplanetary magnetic field. The Alfven waves under consideration are arbitrary, large amplitude, non-monochromatic, microscale waves of any polarization. They superpose on a mesoscale background flow of thermally anisotropic plasma. Using WKB approximation, an analytical solution for the amplitude vectors is obtained as a function of the background flow properties: density, velocity, Alfven speed, thermal anisotropy, and the spiral angel. The necessary condition for the validity of the WKB solution is discussed. The intensity of fluctuations is calculated as a function of heliocentric distance. Relative intensity of fluctuations as compared with the magnitude of the background field has its maximum in the region near l au. Thus outside of this region, the solar wind is less turbulent.

Characterization of the startup transient electrokinetic flow in rectangular channels of arbitrary dimensions, zeta potential distribution, and time-varying pressure gradient.

PubMed

Miller, Andrew; Villegas, Arturo; Diez, F Javier

2015-03-01

The solution to the startup transient EOF in an arbitrary rectangular microchannel is derived analytically and validated experimentally. This full 2D transient solution describes the evolution of the flow through five distinct periods until reaching a final steady state. The derived analytical velocity solution is validated experimentally for different channel sizes and aspect ratios under time-varying pressure gradients. The experiments used a time resolved micro particle image velocimetry technique to calculate the startup transient velocity profiles. The measurements captured the effect of time-varying pressure gradient fields derived in the analytical solutions. This is tested by using small reservoirs at both ends of the channel which allowed a time-varying pressure gradient to develop with a time scale on the order of the transient EOF. Results showed that under these common conditions, the effect of the pressure build up in the reservoirs on the temporal development of the transient startup EOF in the channels cannot be neglected. The measurements also captured the analytical predictions for channel walls made of different materials (i.e., zeta potentials). This was tested in channels that had three PDMS and one quartz wall, resulting in a flow with an asymmetric velocity profile due to variations in the zeta potential between the walls. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

Fast Preparation of Critical Ground States Using Superluminal Fronts

NASA Astrophysics Data System (ADS)

Agarwal, Kartiek; Bhatt, R. N.; Sondhi, S. L.

2018-05-01

We propose a spatiotemporal quench protocol that allows for the fast preparation of ground states of gapless models with Lorentz invariance. Assuming the system initially resides in the ground state of a corresponding massive model, we show that a superluminally moving "front" that locally quenches the mass, leaves behind it (in space) a state arbitrarily close to the ground state of the gapless model. Importantly, our protocol takes time O (L ) to produce the ground state of a system of size ˜Ld (d spatial dimensions), while a fully adiabatic protocol requires time ˜O (L2) to produce a state with exponential accuracy in L . The physics of the dynamical problem can be understood in terms of relativistic rarefaction of excitations generated by the mass front. We provide proof of concept by solving the proposed quench exactly for a system of free bosons in arbitrary dimensions, and for free fermions in d =1 . We discuss the role of interactions and UV effects on the free-theory idealization, before numerically illustrating the usefulness of the approach via simulations on the quantum Heisenberg spin chain.

The in-phase states of Josephson junctions stacks as attractors

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

Hristov, I.; Dimova, S.; Hristova, R.

2014-11-12

The aim of this investigation is to show that the coherent, in-phase states of intrinsic Josephson junctions stacks are attractors of the stacks' states when the applied external magnetic field h{sub e} and the external current γ vary within certain domains. Mathematically the problem is to find the solutions of the system of perturbed sine-Gordon equations for fixed other parameters and zero or random initial conditions. We determine the region in the plane (h{sub e}, γ), where the in-phase states are attractors of the stack's states for arbitrary initial perturbations. This is important, because the in-phase states are required formore » achieving terahertz radiation from the Josephson stacks.« less

Global stability of steady states in the classical Stefan problem for general boundary shapes

PubMed Central

Hadžić, Mahir; Shkoller, Steve

2015-01-01

The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady-state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of such steady states, assuming a sufficient degree of smoothness on the initial domain, but without any a priori restriction on the convexity properties of the initial shape. This is an extension of our previous result (Hadžić & Shkoller 2014 Commun. Pure Appl. Math. 68, 689–757 (doi:10.1002/cpa.21522)) in which we studied nearly spherical shapes. PMID:26261359

Too hot to handle? Analytic solutions for massive neutrino or warm dark matter cosmologies

NASA Astrophysics Data System (ADS)

Slepian, Zachary; Portillo, Stephen K. N.

2018-05-01

We obtain novel closed-form solutions to the Friedmann equation for cosmological models containing a component whose equation of state is that of radiation (w = 1/3) at early times and that of cold pressureless matter (w = 0) at late times. The equation of state smoothly transitions from the early to late-time behavior and exactly describes the evolution of a species with a Dirac Delta function distribution in momentum magnitudes |p_0| (i.e. all particles have the same |p_0|). Such a component, here termed "hot matter", is an approximate model for both neutrinos and warm dark matter. We consider it alone and in combination with cold matter and with radiation, also obtaining closed-form solutions for the growth of super-horizon perturbations in each case. The idealized model recovers t(a) to better than 1.5% accuracy for all a relative to a Fermi-Dirac distribution (as describes neutrinos). We conclude by adding the second moment of the distribution to our exact solution and then generalizing to include all moments of an arbitrary momentum distribution in a closed-form solution.

Too hot to handle? Analytic solutions for massive neutrino or warm dark matter cosmologies

NASA Astrophysics Data System (ADS)

Slepian, Zachary; Portillo, Stephen K. N.

2018-07-01

We obtain novel closed-form solutions to the Friedmann equation for cosmological models containing a component whose equation of state is that of radiation (w = 1/3) at early times and that of cold pressureless matter (w= 0) at late times. The equation of state smoothly transitions from the early- to late-time behaviour and exactly describes the evolution of a species with a Dirac delta function distribution in momentum magnitudes |{p}_0| (i.e. all particles have the same |{p}_0|). Such a component, here termed `hot matter', is an approximate model for both neutrinos and warm dark matter. We consider it alone and in combination with cold matter and with radiation, also obtaining closed-form solutions for the growth of superhorizon perturbations in each case. The idealized model recovers t(a) to better than 1.5 per cent accuracy for all a relative to a Fermi-Dirac distribution (as describes neutrinos). We conclude by adding the second moment of the distribution to our exact solution and then generalizing to include all moments of an arbitrary momentum distribution in a closed-form solution.

Multiparty-controlled Joint Remote Preparation of an Arbitrary m-qudit State with d-dimensional Greenberger-Horne-Zeilinger States

NASA Astrophysics Data System (ADS)

Lv, Shu-Xin; Zhao, Zheng-Wei; Zhou, Ping

2018-01-01

We present a scheme for multiparty-controlled joint remote preparation of an arbitrary m-qudit state by using d-dimensional Greenberger-Horne-Zeilinger (GHZ) states as the quantum channel. An arbitrary m-qudit state can be transmitted from two senders to a remote receiver in a quantum communication network under the controller's control. The senders perform m-qudit measurements according to their information of prepared state, the controllers only need perform single-particle projective measurements. The receiver can prepare the original state on his quantum system by performing corresponding unitary operation according the measurement results of the senders and controllers. It is shown that an arbitrary m-qudit state in general form can be controlled joint remote prepared if and only if the receiver cooperates with all the senders and controllers.

Phase equilibria and formation of vesicles of dioleoylphosphatidylcholine in glycerol/water mixtures.

PubMed

Johansson, L B; Kalman, B; Wikander, G; Fransson, A; Fontell, K; Bergenståhl, B; Lindblom, G

1993-07-04

The lipid 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) forms a lamellar liquid crystalline phase (L alpha) in arbitrary mixtures of glycerol and water. The phase has been characterized by means of X-ray diffraction, 31P-NMR spectroscopy and differential scanning calorimetry (DSC). In the L alpha state, and for DOPC concentrations greater than 50% (w/w), the thickness of the lipid bilayer decreases, while the area of the polar head group increases with increasing glycerol concentration. The phase transition from gel to L alpha state occurs in the range of 240 to 260 K. Contrary to a previous (McDaniel, R.V., McIntosh, T.J. and Simon, S.A. (1983) Biochim. Biophys. Acta 731, 97) study of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) we find that in the gel state, the thickness of the DOPC lipid bilayer is greater than that in the L alpha state. This suggests that in the gel state, the lipid acyl chains of DOPC are in extended configuration. The lamellar phase reaches its maximum swelling at about 50% (w/w) of DOPC. At lower DOPC concentrations a two-phase system is formed where the lamellar phase exists in equilibrium with excess of solvent. Unilamellar vesicles can be prepared from a diluted suspension of the lamellar phase either by using the sonicator or extruder technique. We show this by means of 31P-NMR, EPR and fluorescence spectroscopy. The mean radius of the vesicles, prepared by a sonicator, has been determined at different glycerol/water mixtures. It is found to decrease continuously from 100 A at 100% water to a minimum of 75 A at about 50% water in the solvent mixture. By further decreasing the water content in the solution, the radius rapidly increases, and a mean radius of 450 A is estimated at a water content of 10%. The rotational relaxation times of a fluorescent probe and two EPR spin probes, solubilized in DOPC vesicles, have been measured at different glycerol/water mixtures. It is found that the rotational rates are always much slower in the systems containing glycerol.

Static Einstein-Maxwell Black Holes with No Spatial Isometries in AdS Space.

PubMed

Herdeiro, Carlos A R; Radu, Eugen

2016-11-25

We explicitly construct static black hole solutions to the fully nonlinear, D=4, Einstein-Maxwell-anti-de Sitter (AdS) equations that have no continuous spatial symmetries. These black holes have a smooth, topologically spherical horizon (section), but without isometries, and approach, asymptotically, global AdS spacetime. They are interpreted as bound states of a horizon with the Einstein-Maxwell-AdS solitons recently discovered, for appropriate boundary data. In sharp contrast to the uniqueness results for a Minkowski electrovacuum, the existence of these black holes shows that single, equilibrium, black hole solutions in an AdS electrovacuum admit an arbitrary multipole structure.

Multiparty-controlled teleportation of an arbitrary GHZ-class state by using a d-dimensional ( N+2)-particle nonmaximally entangled state as the quantum channel

NASA Astrophysics Data System (ADS)

Long, LiuRong; Li, HongWei; Zhou, Ping; Fan, Chao; Yin, CaiLiu

2011-03-01

We present a scheme for multiparty-controlled teleportation of an arbitrary high-dimensional GHZ-class state with a d-dimensional ( N+2)-particle GHZ state following some ideas from the teleportation (Chinese Physics B, 2007, 16: 2867). This scheme has the advantage of transmitting much fewer particles for controlled teleportation of an arbitrary multiparticle GHZ-class state. Moreover, we discuss the application of this scheme by using a nonmaximally entangled state as its quantum channel.

Generalized transformations and coordinates for static spherically symmetric general relativity

NASA Astrophysics Data System (ADS)

Hill, James M.; O'Leary, Joseph

2018-04-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.

Generalized transformations and coordinates for static spherically symmetric general relativity.

PubMed

Hill, James M; O'Leary, Joseph

2018-04-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington-Finkelstein transformation and the Kruskal-Szekeres coordinates.

Generalized transformations and coordinates for static spherically symmetric general relativity

PubMed Central

2018-01-01

We examine a static, spherically symmetric solution of the empty space field equations of general relativity with a non-orthogonal line element which gives rise to an opportunity that does not occur in the standard derivations of the Schwarzschild solution. In these derivations, convenient coordinate transformations and dynamical assumptions inevitably lead to the Schwarzschild solution. By relaxing these conditions, a new solution possibility arises and the resulting formalism embraces the Schwarzschild solution as a special case. The new solution avoids the coordinate singularity associated with the Schwarzschild solution and is achieved by obtaining a more suitable coordinate chart. The solution embodies two arbitrary constants, one of which can be identified as the Newtonian gravitational potential using the weak field limit. The additional arbitrary constant gives rise to a situation that allows for generalizations of the Eddington–Finkelstein transformation and the Kruskal–Szekeres coordinates. PMID:29765624

The D-dimensional non-relativistic particle in the Scarf Trigonometry plus Non-Central Rosen-Morse Potentials

NASA Astrophysics Data System (ADS)

Deta, U. A.; Lestari, N. A.; Yantidewi, M.; Suparmi, A.; Cari, C.

2018-03-01

The D-Dimensional Non-Relativistic Particle Properties in the Scarf Trigonometry plus Non-Central Rosen-Morse Potentials was investigated using an analytical method. The bound state energy is given approximately in the closed form. The approximate wave function for arbitrary l-state in D-dimensions are expressed in the form of generalised Jacobi Polynomials. The energy spectra of the particle are increased when the dimensions are higher. The relationship between the orbital number in each dimension is recursive. The special case in 3 dimensions is given to the ground state.

Generalized Kinetic Description of Steady-State Collisionless Plasmas

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Liemohn, M. W.; Krivorutsky, E. N.

1997-01-01

We present a general solution to the collisionless Boltzmann (Vlasov) equation for a free-flowing plasma along a magnetic field line using Liouville's theorem, allowing for an arbitrary potential structure including non-monotonicities. The constraints of the existing collisionless kinetic transport models are explored, and the need for a more general approach to the problem of self- consistent potential energy calculations is described. Then a technique that handles an arbitrary potential energy distribution along the field line is presented and discussed. For precipitation of magnetospherically trapped hot plasma, this model yields moment calculations that vary by up to a factor of two for various potential energy structures with the same total potential drop. The differences are much greater for the high-latitude outflow scenario, giving order of magnitude variations depending on the shape of the potential energy distribution.

Approximate arbitrary κ-state solutions of Dirac equation with Schiöberg and Manning-Rosen potentials within the coulomb-like Yukawa-like and generalized tensor interactions

NASA Astrophysics Data System (ADS)

Ikot, Akpan N.; Hassanabadi, Hassan; Obong, Hillary Patrick; Mehraban, H.; Yazarloo, Bentol Hoda

2015-07-01

The effects of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT) and generalized tensor (GLT) interactions are investigated in the Dirac theory with Schiöberg and Manning-Rosen potentials within the framework of spin and pseudospin symmetries using the Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions have been approximately obtained in the case of spin and pseudospin symmetries. We have also reported some numerical results and figures to show the effects these tensor interactions.

Analytic Solution of the Problem of Additive Formation of an Inhomogeneous Elastic Spherical Body in an Arbitrary Nonstationary Central Force Field

NASA Astrophysics Data System (ADS)

Parshin, D. A.

2017-09-01

We study the processes of additive formation of spherically shaped rigid bodies due to the uniform accretion of additional matter to their surface in an arbitrary centrally symmetric force field. A special case of such a field can be the gravitational or electrostatic force field. We consider the elastic deformation of the formed body. The body is assumed to be isotropic with elasticmoduli arbitrarily varying along the radial coordinate.We assume that arbitrary initial circular stresses can arise in the additional material added to the body in the process of its formation. In the framework of linear mechanics of growing bodies, the mathematical model of the processes under study is constructed in the quasistatic approximation. The boundary value problems describing the development of stress-strain state of the object under study before the beginning of the process and during the entire process of its formation are posed. The closed analytic solutions of the posed problems are constructed by quadratures for some general types of material inhomogeneity. Important typical characteristics of the mechanical behavior of spherical bodies additively formed in the central force field are revealed. These characteristics substantially distinguish such bodies from the already completely composed bodies similar in dimensions and properties which are placed in the force field and are described by problems of mechanics of deformable solids in the classical statement disregarding the mechanical aspects of additive processes.

Segmented strings and the McMillan map

DOE PAGES

Gubser, Steven S.; Parikh, Sarthak; Witaszczyk, Przemek

2016-07-25

We present new exact solutions describing motions of closed segmented strings in AdS 3 in terms of elliptic functions. The existence of analytic expressions is due to the integrability of the classical equations of motion, which in our examples reduce to instances of the McMillan map. Here, we also obtain a discrete evolution rule for the motion in AdS 3 of arbitrary bound states of fundamental strings and D1-branes in the test approximation.

Entropy of N=2 black holes and their M-brane description

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

Behrndt, K.; Mohaupt, T.

1997-08-01

In this paper we discuss the M-brane description for an N=2 black hole. This solution is a result of the compactification of M-5-brane configurations over a Calabi-Yau threefold with arbitrary intersection numbers C{sub ABC}. In analogy with the D-brane description where one counts open string states we count here open M-2-branes which end on the M-5-brane. {copyright} {ital 1997} {ital The American Physical Society}

Simulation of a Single-Element Lean-Direct Injection Combustor Using Arbitrary Polyhedral Mesh

NASA Technical Reports Server (NTRS)

Wey, Thomas; Liu, Nan-Suey

2012-01-01

This paper summarizes procedures of generating the arbitrary polyhedral mesh as well as presents sample results from its application to the numerical solution of a single-element LDI combustor using a preliminary version of the new OpenNCC.

Type II universal spacetimes

NASA Astrophysics Data System (ADS)

Hervik, S.; Málek, T.; Pravda, V.; Pravdová, A.

2015-12-01

We study type II universal metrics of the Lorentzian signature. These metrics simultaneously solve vacuum field equations of all theories of gravitation with the Lagrangian being a polynomial curvature invariant constructed from the metric, the Riemann tensor and its covariant derivatives of an arbitrary order. We provide examples of type II universal metrics for all composite number dimensions. On the other hand, we have no examples for prime number dimensions and we prove the non-existence of type II universal spacetimes in five dimensions. We also present type II vacuum solutions of selected classes of gravitational theories, such as Lovelock, quadratic and L({{Riemann}}) gravities.

Controlled Remote State Preparation of an Arbitrary Two-Qubit State by Using GHZ States

NASA Astrophysics Data System (ADS)

Huang, Li; Zhao, Hong-xia

2017-03-01

In this paper, we demonstrate that two Greenberger-Horne-Zeilinger (GHZ) states can be used to realize the perfect and deterministic controlled remote state preparation of an arbitrary two-qubit state by performing only the two-qubit projective measurements and appropriate unitary operations.

Nonlinear Fano interferences in open quantum systems: An exactly solvable model

NASA Astrophysics Data System (ADS)

Finkelstein-Shapiro, Daniel; Calatayud, Monica; Atabek, Osman; Mujica, Vladimiro; Keller, Arne

2016-06-01

We obtain an explicit solution for the stationary-state populations of a dissipative Fano model, where a discrete excited state is coupled to a continuum set of states; both excited sets of states are reachable by photoexcitation from the ground state. The dissipative dynamic is described by a Liouville equation in Lindblad form and the field intensity can take arbitrary values within the model. We show that the population of the continuum states as a function of laser frequency can always be expressed as a Fano profile plus a Lorentzian function with effective parameters whose explicit expressions are given in the case of a closed system coupled to a bath as well as for the original Fano scattering framework. Although the solution is intricate, it can be elegantly expressed as a linear transformation of the kernel of a 4 ×4 matrix which has the meaning of an effective Liouvillian. We unveil key notable processes related to the optical nonlinearity and which had not been reported to date: electromagnetic-induced transparency, population inversions, power narrowing and broadening, as well as an effective reduction of the Fano asymmetry parameter.

Joint remote control of an arbitrary single-qubit state by using a multiparticle entangled state as the quantum channel

NASA Astrophysics Data System (ADS)

Lv, Shu-Xin; Zhao, Zheng-Wei; Zhou, Ping

2018-01-01

We present a scheme for joint remote implementation of an arbitrary single-qubit operation following some ideas in one-way quantum computation. All the senders share the information of implemented quantum operation and perform corresponding single-qubit measurements according to their information of implemented operation. An arbitrary single-qubit operation can be implemented upon the remote receiver's quantum system if the receiver cooperates with all the senders. Moreover, we study the protocol of multiparty joint remote implementation of an arbitrary single-qubit operation with many senders by using a multiparticle entangled state as the quantum channel.

Optimal Joint Remote State Preparation of Arbitrary Equatorial Multi-qudit States

NASA Astrophysics Data System (ADS)

Cai, Tao; Jiang, Min

2017-03-01

As an important communication technology, quantum information transmission plays an important role in the future network communication. It involves two kinds of transmission ways: quantum teleportation and remote state preparation. In this paper, we put forward a new scheme for optimal joint remote state preparation (JRSP) of an arbitrary equatorial two-qudit state with hybrid dimensions. Moreover, the receiver can reconstruct the target state with 100 % success probability in a deterministic manner via two spatially separated senders. Based on it, we can extend it to joint remote preparation of arbitrary equatorial multi-qudit states with hybrid dimensions using the same strategy.

Radiation and scattering by thin-wire structures in the complex frequency domain. [electromagnetic theory for thin-wire antennas

NASA Technical Reports Server (NTRS)

Richmond, J. H.

1974-01-01

Piecewise-sinusoidal expansion functions and Galerkin's method are employed to formulate a solution for an arbitrary thin-wire configuration in a homogeneous conducting medium. The analysis is performed in the real or complex frequency domain. In antenna problems, the solution determines the current distribution, impedance, radiation efficiency, gain and far-field patterns. In scattering problems, the solution determines the absorption cross section, scattering cross section and the polarization scattering matrix. The electromagnetic theory is presented for thin wires and the forward-scattering theorem is developed for an arbitrary target in a homogeneous conducting medium.

Numerical solutions of 3-dimensional Navier-Stokes equations for closed bluff-bodies

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallelepiped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDc VPS 32 computer. The codes are written in 32-bit (half word) FORTRAN, which provides an approximate factor of two decreasing in computational time and doubles the memory size compared to the 54-bit word size.

A Conditionally Integrable Bi-confluent Heun Potential Involving Inverse Square Root and Centrifugal Barrier Terms

NASA Astrophysics Data System (ADS)

Ishkhanyan, Tigran A.; Krainov, Vladimir P.; Ishkhanyan, Artur M.

2018-05-01

We present a conditionally integrable potential, belonging to the bi-confluent Heun class, for which the Schrödinger equation is solved in terms of the confluent hypergeometric functions. The potential involves an attractive inverse square root term x-1/2 with arbitrary strength and a repulsive centrifugal barrier core x-2 with the strength fixed to a constant. This is a potential well defined on the half-axis. Each of the fundamental solutions composing the general solution of the Schrödinger equation is written as an irreducible linear combination, with non-constant coefficients, of two confluent hypergeometric functions. We present the explicit solution in terms of the non-integer order Hermite functions of scaled and shifted argument and discuss the bound states supported by the potential. We derive the exact equation for the energy spectrum and approximate that by a highly accurate transcendental equation involving trigonometric functions. Finally, we construct an accurate approximation for the bound-state energy levels.

Infinite stream of Hele--Shaw bubbles

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

Burgess, D.; Tanveer, S.

1991-03-01

Exact solutions are presented for a steady stream of bubbles in a Hele--Shaw cell when the effect of surface tension is neglected. These solutions form a three-parameter family. For specified area and distance between bubbles, the speed of the bubble remains arbitrary when surface tension is neglected. However, numerical and analytical evidence indicates that this arbitrariness is removed by the effect of surface tension. The branch of solutions that corresponds to the McLean--Saffman finger solution were primarily studied. A dramatic increase was observed in bubble speeds when the distance between bubbles is on the order of a bubble diameter, whichmore » may have relevance to experiments done by Maxworthy (J. Fluid Mech. {bold 173}, 95 (1986)).« less

Arbitrary norm support vector machines.

PubMed

Huang, Kaizhu; Zheng, Danian; King, Irwin; Lyu, Michael R

2009-02-01

Support vector machines (SVM) are state-of-the-art classifiers. Typically L2-norm or L1-norm is adopted as a regularization term in SVMs, while other norm-based SVMs, for example, the L0-norm SVM or even the L(infinity)-norm SVM, are rarely seen in the literature. The major reason is that L0-norm describes a discontinuous and nonconvex term, leading to a combinatorially NP-hard optimization problem. In this letter, motivated by Bayesian learning, we propose a novel framework that can implement arbitrary norm-based SVMs in polynomial time. One significant feature of this framework is that only a sequence of sequential minimal optimization problems needs to be solved, thus making it practical in many real applications. The proposed framework is important in the sense that Bayesian priors can be efficiently plugged into most learning methods without knowing the explicit form. Hence, this builds a connection between Bayesian learning and the kernel machines. We derive the theoretical framework, demonstrate how our approach works on the L0-norm SVM as a typical example, and perform a series of experiments to validate its advantages. Experimental results on nine benchmark data sets are very encouraging. The implemented L0-norm is competitive with or even better than the standard L2-norm SVM in terms of accuracy but with a reduced number of support vectors, -9.46% of the number on average. When compared with another sparse model, the relevance vector machine, our proposed algorithm also demonstrates better sparse properties with a training speed over seven times faster.

Single-Photon Emission of a Hydrogenlike Atom

NASA Astrophysics Data System (ADS)

Skobelev, V. V.

2016-11-01

Implementing a previously obtained, original solution of the Dirac equation for an electron in the field of a nucleus ( Ze) expressed in terms of the wave function of the corresponding Schrödinger equation and its derivatives in spherical coordinates and the spin projection operator Σ3 associated with the eigenfunction, taking into account in each component of the spinor the leading term of the expansion in the small parameter ( Zα), α = e 2 / ħc ≈ 1 / 137, the partial probabilities W of emission of a photon ( Zα)* → ( Zα) + γ have been calculated. Here two orthogonal states of the linear polarization of the photon, and also the spin states of the electron, which previously had not been taken into consideration, have been taken into account in the transverse gauge. It turns out that the probabilities W of emission of a photon per unit time for any allowed transitions are proportional to (Zα)4, as was previously accepted, and the selection rules for the quantum number m have the usual form Δ m = 0,±1. It was found that a spin flip does not take place during emission. In contrast to the customary situation with the selection rules for the quantum number l being of the form Δ l = ±1, for Δ m = ±1 there also exist integrals over dcosθ which are not equal to zero for undetermined odd values of Δ l. In this, and also in a fundamentally different dependence of the amplitude on the quantum numbers consist the differences from the traditional approach to the problem. Necessary conditions are formulated, under the fulfillment of which the selection rules for l are not changed, having values Δ l = ±1 for arbitrary Δ m, but it was not possible, however, to give a complete proof of these rules.

A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids

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

Hong Luo; Luqing Luo; Robert Nourgaliev

2012-11-01

A reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, a variant of P1P2 method, is presented for the solution of the compressible Euler equations on arbitrary grids. In this method, an in-cell reconstruction, designed to enhance the accuracy of the discontinuous Galerkin method, is used to obtain a quadratic polynomial solution (P2) from the underlying linear polynomial (P1) discontinuous Galerkin solution using a least-squares method. The stencils used in the reconstruction involve only the von Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The developed RDG method is used to compute a variety of flow problems onmore » arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG(P1P2) method is third-order accurate, and outperforms the third-order DG method (DG(P2)) in terms of both computing costs and storage requirements.« less

Potential flow about arbitrary biplane wing sections

NASA Technical Reports Server (NTRS)

Garrick, I E

1937-01-01

A rigorous treatment is given of the problem of determining the two-dimensional potential flow around arbitrary biplane cellules. The analysis involves the use of elliptic functions and is sufficiently general to include the effects of such elements as the section shapes, the chord ratio, gap, stagger, and decalage, which elements may be specified arbitrarily. The flow problem is resolved by making use of the methods of conformal representation. Thus the solution of the problem of transforming conformally two arbitrary contours into two circles is expressed by a pair of simultaneous integral equations, for which a method of numerical solution is outlined. As an example of the numerical process, the pressure distribution over certain arrangements of the NACA 4412 airfoil in biplane combinations is presented and compared with the monoplane pressure distribution.

Theory of ion-matrix-sheath dynamics

NASA Astrophysics Data System (ADS)

Kos, L.; Tskhakaya, D. D.

2018-01-01

The time evolution of a one-dimensional, uni-polar ion sheath (an "ion matrix sheath") is investigated. The analytical solutions for the ion-fluid and Poisson's equations are found for an arbitrary time dependence of the wall-applied negative potential. In the case that the wall potential is large and remains constant after its ramp-up application, the explicit time dependencies of the sheath's parameters during the initial stage of the process are given. The characteristic rate of approaching the stationary state, satisfying the Child-Langmuir law, is determined.

Solution of a Plane Hydrofracture Problem with Stress Contrast

NASA Astrophysics Data System (ADS)

Gladkov, I. O.; Linkov, A. M.

2018-03-01

A plane hydrofracture problem for the Khristianovich-Geertsma-de Klerk model is extended and solved in the case where a confining stress closing a fracture is not constant in the direction of its propagation. A method is developed for solving the problem with an arbitrary stress contrast. It is stated that the transition through a contact with positive (negative) contrast occurs with fracture arresting (acceleration), whose intensity is controlled by a dimensionless parameter derived from theoretical considerations and numerical results.

Bidirectional Quantum Teleportation by Using Five-qubit Cluster State

NASA Astrophysics Data System (ADS)

Sang, Ming-huang

2016-03-01

We propose a scheme for bidirectional quantum teleportation by using a five-qubit cluster state. In our scheme, Alice can transmit an arbitrary two-qubit entangled state to Bob and at the same time Bob can teleport an arbitrary single-qubit state to Alice.

Video event classification and image segmentation based on noncausal multidimensional hidden Markov models.

PubMed

Ma, Xiang; Schonfeld, Dan; Khokhar, Ashfaq A

2009-06-01

In this paper, we propose a novel solution to an arbitrary noncausal, multidimensional hidden Markov model (HMM) for image and video classification. First, we show that the noncausal model can be solved by splitting it into multiple causal HMMs and simultaneously solving each causal HMM using a fully synchronous distributed computing framework, therefore referred to as distributed HMMs. Next we present an approximate solution to the multiple causal HMMs that is based on an alternating updating scheme and assumes a realistic sequential computing framework. The parameters of the distributed causal HMMs are estimated by extending the classical 1-D training and classification algorithms to multiple dimensions. The proposed extension to arbitrary causal, multidimensional HMMs allows state transitions that are dependent on all causal neighbors. We, thus, extend three fundamental algorithms to multidimensional causal systems, i.e., 1) expectation-maximization (EM), 2) general forward-backward (GFB), and 3) Viterbi algorithms. In the simulations, we choose to limit ourselves to a noncausal 2-D model whose noncausality is along a single dimension, in order to significantly reduce the computational complexity. Simulation results demonstrate the superior performance, higher accuracy rate, and applicability of the proposed noncausal HMM framework to image and video classification.

Application of low-order potential solutions to higher-order vertical traction boundary problems in an elastic half-space

PubMed Central

Taylor, Adam G.

2018-01-01

New solutions of potential functions for the bilinear vertical traction boundary condition are derived and presented. The discretization and interpolation of higher-order tractions and the superposition of the bilinear solutions provide a method of forming approximate and continuous solutions for the equilibrium state of a homogeneous and isotropic elastic half-space subjected to arbitrary normal surface tractions. Past experimental measurements of contact pressure distributions in granular media are reviewed in conjunction with the application of the proposed solution method to analysis of elastic settlement in shallow foundations. A numerical example is presented for an empirical ‘saddle-shaped’ traction distribution at the contact interface between a rigid square footing and a supporting soil medium. Non-dimensional soil resistance is computed as the reciprocal of normalized surface displacements under this empirical traction boundary condition, and the resulting internal stresses are compared to classical solutions to uniform traction boundary conditions. PMID:29892456

Quantum Teleportation of an Arbitrary N-qubit State via GHZ-like States

NASA Astrophysics Data System (ADS)

Zhang, Bo; Liu, Xing-tong; Wang, Jian; Tang, Chao-jing

2016-03-01

Recently Zhu (Int. J. Theor. Phys. 53, 4095, 2014) had shown that using GHZ-like states as quantum channel, it is possible to teleport an arbitrary unknown two-qubit state. We investigate this channel for the teleportation of an arbitrary N-qubit state. The strict proof through mathematical induction is presented and the rule for the receiver to reconstruct the desired state is explicitly derived in the most general case. We also discuss that if a system of quantum secret sharing of classical message is established, our protocol can be transformed to a N-qubit perfect controlled teleportation scheme from the controller's point of view.

Exact solution of a one-dimensional model of strained epitaxy on a periodically modulated substrate

NASA Astrophysics Data System (ADS)

Tokar, V. I.; Dreyssé, H.

2005-03-01

We consider a one-dimensional lattice gas model of strained epitaxy with the elastic strain accounted for through a finite number of cluster interactions comprising contiguous atomic chains. Interactions of this type arise in the models of strained epitaxy based on the Frenkel-Kontorova model. Furthermore, the deposited atoms interact with the substrate via an arbitrary periodic potential of period L . This model is solved exactly with the use of an appropriately adopted technique developed recently in the theory of protein folding. The advantage of the proposed approach over the standard transfer-matrix method is that it reduces the problem to finding the largest eigenvalue of a matrix of size L instead of 2L-1 , which is vital in the case of nanostructures where L may measure in hundreds of interatomic distances. Our major conclusion is that the substrate modulation always facilitates the size calibration of self-assembled nanoparticles in one- and two-dimensional systems.

Exact solution for four-order acousto-optic Bragg diffraction with arbitrary initial conditions.

PubMed

Pieper, Ron; Koslover, Deborah; Poon, Ting-Chung

2009-03-01

An exact solution to the four-order acousto-optic (AO) Bragg diffraction problem with arbitrary initial conditions compatible with exact Bragg angle incident light is developed. The solution, obtained by solving a 4th-order differential equation, is formalized into a transition matrix operator predicting diffracted light orders at the exit of the AO cell in terms of the same diffracted light orders at the entrance. It is shown that the transition matrix is unitary and that this unitary matrix condition is sufficient to guarantee energy conservation. A comparison of analytical solutions with numerical predictions validates the formalism. Although not directly related to the approach used to obtain the solution, it was discovered that all four generated eigenvalues from the four-order AO differential matrix operator are expressed simply in terms of Euclid's Divine Proportion.

Digging into the Elusive Localised Solutions of (2+1) Dimensional sine-Gordon Equation

NASA Astrophysics Data System (ADS)

Radha, R.; Senthil Kumar, C.

2018-05-01

In this paper, we revisit the (2+1) dimensional sine-Gordon equation analysed earlier [R. Radha and M. Lakshmanan, J. Phys. A Math. Gen. 29, 1551 (1996)] employing the Truncated Painlevé Approach. We then generate the solutions in terms of lower dimensional arbitrary functions of space and time. By suitably harnessing the arbitrary functions present in the closed form of the solution, we have constructed dromion solutions and studied their collisional dynamics. We have also constructed dromion pairs and shown that the dynamics of the dromion pairs can be turned ON or OFF desirably. In addition, we have also shown that the orientation of the dromion pairs can be changed. Apart from the above classes of solutions, we have also generated compactons, rogue waves and lumps and studied their dynamics.

Solution to a gene divergence problem under arbitrary stable nucleotide transition probabilities

NASA Technical Reports Server (NTRS)

Holmquist, R.

1976-01-01

A nucleic acid chain, L nucleotides in length, with the specific base sequence B(1)B(2) ... B(L) is defined by the L-dimensional vector B = (B(1), B(2), ..., B(L)). For twelve given constant non-negative transition probabilities that, in a specified position, the base B is replaced by the base B' in a single step, an exact analytical expression is derived for the probability that the position goes from base B to B' in X steps. Assuming that each base mutates independently of the others, an exact expression is derived for the probability that the initial gene sequence B goes to a sequence B' = (B'(1), B'(2), ..., B'(L)) after X = (X(1), X(2), ..., X(L)) base replacements. The resulting equations allow a more precise accounting for the effects of Darwinian natural selection in molecular evolution than does the idealized (biologically less accurate) assumption that each of the four nucleotides is equally likely to mutate to and be fixed as one of the other three. Illustrative applications of the theory to some problems of biological evolution are given.

Teleportation of a two-qubit arbitrary unknown state using a four-qubit genuine entangled state with the combination of bell-state measurements

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

Dong, Li; Xiu, Xiao-Ming, E-mail: xiuxiaomingdl@126.com; Ren, Yuan-Peng

2013-01-15

We propose a protocol transferring an arbitrary unknown two-qubit state using the quantum channel of a four-qubit genuine entangled state. Simplifying the four-qubit joint measurement to the combination of Bell-state measurements, it can be realized more easily with currently available technologies.

General form of genuine multipartite entanglement quantum channels for teleportation

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

Chen Pingxing; Key Laboratory of Quantum Communication and Quantum Computation, University of Science and Technology of China, Hefei 230026; Department of Physics, National University of Defense Technology, Changsha 410073

2006-09-15

Recently Yeo and Chua [Phys. Rev. Lett. 96, 060502 (2006)] presented an explicit protocol for faithfully teleporting an arbitrary two-qubit state via a genuine four-qubit entanglement channel. Here we generalize completely their results to teleporting an arbitrary N-qubit state via genuine N-qubit entanglement channels. And we present the general form of the genuine multipartite entanglement channels, namely, the sufficient and necessary condition the genuine N-qubit entanglement channels must satisfy to teleport an arbitrary N-qubit state.

Inertial nonvacuum states viewed from the Rindler frame

NASA Astrophysics Data System (ADS)

Lochan, Kinjalk; Padmanabhan, T.

2015-02-01

The appearance of the inertial vacuum state in Rindler frame has been extensively studied in the literature, both from the point of view of quantum field theory developed using Rindler foliation and using the response of an Unruh-Dewitt detector. In comparison, less attention has been devoted to the study of inertial nonvacuum states when viewed from the Rindler frame. We provide a comprehensive study of this issue in this paper. We first present a general formalism describing the characterization of arbitrary inertial state (i) when described using an arbitrary foliation and (ii) using the response of an Unruh-DeWitt detector moving along an arbitrary trajectory. This allows us to calculate the mean number of particles in an arbitrary inertial state, when the QFT is described using an arbitrary foliation of spacetime or when the state is probed by a detector moving along an arbitrary trajectory. We use this formalism to explicitly compute the results for the Rindler frame and uniformly accelerated detectors. Any arbitrary inertial state will always have a thermal component in the Rindler frame with additional contributions arising from the nonvacuum nature. We classify the nature of the additional contributions in terms of functions characterizing the inertial state. We establish that for all physically well-behaved normalizable inertial states, the correction terms decrease rapidly with the energy of the Rindler mode so that the high frequency limit is dominated by the thermal noise in any normalizable inertial state. However, inertial states which are not strictly normalizable like, for example, the one-particle state with definite momentum, lead to a constant contribution at all high frequencies in the Rindler frame. We show that a similar behavior arises in the response of the Unruh-DeWitt detector as well. In the case of the detector response, we provide a physical interpretation for the constant contribution at high frequencies in terms of total detection rate of comoving inertial detectors. We also describe two different approaches for defining a transition rate for the Unruh-DeWitt detector, when the two-point function lacks the time translation invariance, and discuss several features of different definitions of transition rates. The implications are discussed.

Long-term motion of resonant satellites with arbitrary eccentricity and inclination

NASA Technical Reports Server (NTRS)

Nacozy, P. E.; Diehl, R. E.

1982-01-01

A first-order, semi-analytical method for the long-term motion of resonant satellites is introduced. The method provides long-term solutions, valid for nearly all eccentricities and inclinations, and for all commensurability ratios. The method allows the inclusion of all zonal and tesseral harmonics of a nonspherical planet. We present here an application of the method to a synchronous satellite including J2 and J22 harmonics. Global, long-term solutions for this problem are given for arbitrary values of eccentricity, argument of perigee and inclination.

Interior radiances in optically deep absorbing media. I - Exact solutions for one-dimensional model.

NASA Technical Reports Server (NTRS)

Kattawar, G. W.; Plass, G. N.

1973-01-01

An exact analytic solution to the one-dimensional scattering problem with arbitrary single scattering albedo and arbitrary surface albedo is presented. Expressions are given for the emergent flux from a homogeneous layer, the internal flux within the layer, and the radiative heating. A comparison of these results with the values calculated from the matrix operator theory indicates an exceedingly high accuracy. A detailed study is made of the error in the matrix operator results and its dependence on the accuracy of the starting value.

Analytical solution of the optimal three dimensional reentry problem using Chapman's exact equations

NASA Technical Reports Server (NTRS)

Vinh, N. X.; Busemann, A.; Culp, R. D.

1974-01-01

This paper presents the general solution for the optimal three dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere. A set of dimensionless variables is introduced, and the resulting exact equations of motion have the distinctive advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a general lift-drag polar is used to define the aerodynamic control. Hence, the results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary polar and entering any planetary atmosphere.

Steering, Entanglement, Nonlocality, and the EPR Paradox

NASA Astrophysics Data System (ADS)

Wiseman, Howard; Jones, Steve; Andrew, Doherty

2007-06-01

The concept of steering was introduced by Schroedinger in 1935 as a generalization of the EPR paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and Isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell-nonlocality. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original EPR paradox.

Laplace-Runge-Lenz vector for arbitrary spin

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

Nikitin, A. G.

2013-12-15

A countable set of superintegrable quantum mechanical systems is presented which admit the dynamical symmetry with respect to algebra so(4). This algebra is generated by the Laplace-Runge-Lenz vector generalized to the case of arbitrary spin. The presented systems describe neutral particles with non-trivial multipole momenta. Their spectra can be found algebraically like in the case of hydrogen atom. Solutions for the systems with spins 1/2 and 1 are presented explicitly, solutions for spin 3/2 can be expressed via solutions of an ordinary differential equation of first order. A more extended version of this paper including detailed calculations is published asmore » an e-print arXiv:1308.4279.« less

Probabilistic Teleportation of an Arbitrary Three-Level Two-Particle State and Classical Communication Cost

NASA Astrophysics Data System (ADS)

Dai, Hong-Yi; Kuang, Le-Man; Li, Cheng-Zu

2005-07-01

We propose a scheme to probabilistically teleport an unknown arbitrary three-level two-particle state by using two partial entangled two-particle states of three-level as the quantum channel. The classical communication cost required in the ideal probabilistic teleportation process is also calculated. This scheme can be directly generalized to teleport an unknown and arbitrary three-level K-particle state by using K partial entangled two-particle states of three-level as the quantum channel. The project supported by National Fundamental Research Program of China under Grant No. 2001CB309310, National Natural Science Foundation of China under Grant Nos. 10404039 and 10325523

The fundamental closed-form solution of control-related states of kth order S3PR system with left-side non-sharing resource places of Petri nets

NASA Astrophysics Data System (ADS)

Chao, Daniel Yuh; Yu, Tsung Hsien

2016-01-01

Due to the state explosion problem, it has been unimaginable to enumerate reachable states for Petri nets. Chao broke the barrier earlier by developing the very first closed-form solution of the number of reachable and other states for marked graphs and the kth order system. Instead of using first-met bad marking, we propose 'the moment to launch resource allocation' (MLR) as a partial deadlock avoidance policy for a large, real-time dynamic resource allocation system. Presently, we can use the future deadlock ratio of the current state as the indicator of MLR due to which the ratio can be obtained real-time by a closed-form formula. This paper progresses the application of an MLR concept one step further on Gen-Left kth order systems (one non-sharing resource place in any position of the left-side process), which is also the most fundamental asymmetric net structure, by the construction of the system's closed-form solution of the control-related states (reachable, forbidden, live and deadlock states) with a formula depending on the parameters of k and the location of the non-sharing resource. Here, we kick off a new era of real-time, dynamic resource allocation decisions by constructing a generalisation formula of kth order systems (Gen-Left) with r* on the left side but at arbitrary locations.

Propagation of waves from an arbitrary shaped surface-A generalization of the Fresnel diffraction integral

NASA Astrophysics Data System (ADS)

Feshchenko, R. M.; Vinogradov, A. V.; Artyukov, I. A.

2018-04-01

Using the method of Laplace transform the field amplitude in the paraxial approximation is found in the two-dimensional free space using initial values of the amplitude specified on an arbitrary shaped monotonic curve. The obtained amplitude depends on one a priori unknown function, which can be found from a Volterra first kind integral equation. In a special case of field amplitude specified on a concave parabolic curve the exact solution is derived. Both solutions can be used to study the light propagation from arbitrary surfaces including grazing incidence X-ray mirrors. They can find applications in the analysis of coherent imaging problems of X-ray optics, in phase retrieval algorithms as well as in inverse problems in the cases when the initial field amplitude is sought on a curved surface.

Electroosmotic flow in microchannels with arbitrary geometry and arbitrary distribution of wall charge.

PubMed

Xuan, Xiangchun; Li, Dongqing

2005-09-01

General solutions are developed for direct current (DC) and alternating current (AC) electroosmotic flows in microfluidic channels with arbitrary cross-sectional geometry and arbitrary distribution of wall charge (zeta potential). The applied AC electric field can also be of arbitrary waveform. By proposing a nondimensional time scale varpi defined as the ratio of the diffusion time of momentum across the electric double-layer thickness to the period of the applied electric field, we demonstrate analytically that the Helmholtz-Smoluchowski electroosmotic velocity is an appropriate slip condition for AC electroosmotic flows in typical microfluidic applications. With this slip condition approach, electroosmotic flows in rectangular and asymmetric trapezoidal microchannels with nonuniform wall charge, as examples, are investigated. The unknown constants in the proposed general solutions are numerically determined with a least-squares method through matching the boundary conditions. We find that the wall charge affects significantly the electroosmotic flow while the channel geometry does not. Moreover, the flow feature is characterized by another nondimensional time scale Omega defined as the ratio of the diffusion time of momentum across the channel hydraulic radius to the period of the applied electric field. The onset of phase shift between AC electroosmotic velocity and applied electric field is also examined analytically.

Necessary and sufficient conditions on n-qudit state for perfect teleportation of an arbitrary single qudit state

NASA Astrophysics Data System (ADS)

Shang-Guan, Li-Ying; Sun, Hong-Xiang; Wen, Qiao-Yan; Zhu, Fu-Chen

2009-12-01

Firstly, we investigate the necessary and sufficient conditions that an entangled channel of n-qubits should satisfy to carry out perfect teleportation of an arbitrary single qubit state and dense coding. It is shown that the sender can transmit two classical bits of information by sending one qubit. Further, the case of high-dimension quantum state is also considered. Utilizing n-qudit state as quantum channel, it is proposed that the necessary and sufficient conditions are {(d+2)(d-1)}/{2} in all to teleport an arbitrary single qudit state. The sender can transmit 2log2d classical bits of information to the receiver conditioned on the constraints.

Quantum Teleportation of a Three-qubit State using a Five-qubit Cluster State

NASA Astrophysics Data System (ADS)

Liu, Zhong-min; Zhou, Lin

2014-12-01

Recently Muralidharan and Panigrahi (Phys. Rev. A 78, 062333 2008) had shown that using a five-qubit cluster state as quantum channel, it is possible to teleport an arbitrary single-qubit state and an arbitrary two-qubit state. In this paper, we investigate this channel for the teleportation of a special form of three-qubit state.

Stability and minimum size of colloidal clusters on a liquid-air interface.

PubMed

Pergamenshchik, V M

2012-02-01

A vertical force applied to each of two colloids, trapped at a liquid-air interface, induces their logarithmic pairwise attraction. I recently showed [Phys. Rev. E 79, 011407 (2009)] that in clusters of size R much larger than the capillary length λ, the attraction changes to that of a power law and is much stronger due to a many-body effect, and I derived two equations that describe the equilibrium coarse-grained meniscus profile and colloid density in such clusters. In this paper, this theory is shown also to describe small clusters with R≪ λ provided the number N of colloids therein is sufficiently large. An analytical solution for a small circular cluster with an arbitrary short-range power-law pairwise repulsion is found. The energy of a cluster is obtained as a function of its radius R and colloid number N. As in large clusters, the attraction force and energy universally scale with the distance L between colloids as L(-3) and L(-2), respectively, for any repulsion forces. The states of an equilibrium cluster, predicted by the theory, are shown to be stable with respect to small perturbations of the meniscus profile and colloid density. The minimum number of colloids in a circular cluster, which sustains the thermal motion, is estimated. For standard parameters, it can be very modest, e.g., in the range 20-200, which is in line with experimental findings on reversible clusterization on a liquid-air interface. © 2012 American Physical Society

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

Chu, S.; Wang, K.; Layton, E.

In this paper we accomplish three goals. First, we present new nonperturbative results of complex quasi-energies (shifts and widths) for several low-lying excited states of atomic H in strong fields, using the {ital L}{sup 2} non-Hermitian Floquet matrix technique. Second, we present a new nonperturbative {ital L}{sup 2} technique for the treatment of ac Stark shifts of arbitrary excited states. We found that all the Rydberg states in weak fields are upshifted and closely follow the quadratic field dependence described by the ponderomotive potential {ital e}{sup 2}{ital F}{sup 2}/4{ital mgw}{sup 2}. Large deviation from the ponderomotive shift and intricate level-shiftmore » behaviors, however, occur in strong fields. Finally, we present a classical nonperturbative treatment of the electronic motion in intense laser fields. We show that the spectral analysis of classical trajectories can provide detailed insights regarding the mechanisms responsible for the multiple-harmonic generation recently observed in high-intensity experiments.« less

Optimal Low-Thrust Limited-Power Transfers between Arbitrary Elliptic Coplanar Orbits

NASA Technical Reports Server (NTRS)

daSilvaFernandes, Sandro; dasChagasCarvalho, Francisco

2007-01-01

In this work, a complete first order analytical solution, which includes the short periodic terms, for the problem of optimal low-thrust limited-power transfers between arbitrary elliptic coplanar orbits in a Newtonian central gravity field is obtained through Hamilton-Jacobi theory and a perturbation method based on Lie series.

New generalized Noh solutions for HEDP hydrocode verification

NASA Astrophysics Data System (ADS)

Velikovich, A. L.; Giuliani, J. L.; Zalesak, S. T.; Tangri, V.

2017-10-01

The classic Noh solution describing stagnation of a cold ideal gas in a strong accretion shock wave has been the workhorse of compressible hydrocode verification for over three decades. We describe a number of its generalizations available for HEDP code verification. First, for an ideal gas, we have obtained self-similar solutions that describe adiabatic convergence either of a finite-pressure gas into an empty cavity or of a finite-amplitude sound wave into a uniform resting gas surrounding the center or axis of symmetry. At the moment of collapse such a flow produces a uniform gas whose velocity at each point is constant and directed towards the axis or the center, i. e. the initial condition similar to the classic solution but with a finite pressure of the converging gas. After that, a constant-velocity accretion shock propagates into the incident gas whose pressure and velocity profiles are not flat, in contrast with the classic solution. Second, for an arbitrary equation of state, we demonstrate the existence of self-similar solutions of the Noh problem in cylindrical and spherical geometry. Examples of such solutions with a three-term equation of state that includes cold, thermal ion/lattice, and thermal electron contributions are presented for aluminum and copper. These analytic solutions are compared to our numerical simulation results as an example of their use for code verification. Work supported by the US DOE/NNSA.

Multi-component Wronskian solution to the Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Xu, Tao; Sun, Fu-Wei; Zhang, Yi; Li, Juan

2014-01-01

It is known that the Kadomtsev-Petviashvili (KP) equation can be decomposed into the first two members of the coupled Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy by the binary non-linearization of Lax pairs. In this paper, we construct the N-th iterated Darboux transformation (DT) for the second- and third-order m-coupled AKNS systems. By using together the N-th iterated DT and Cramer's rule, we find that the KPII equation has the unreduced multi-component Wronskian solution and the KPI equation admits a reduced multi-component Wronskian solution. In particular, based on the unreduced and reduced two-component Wronskians, we obtain two families of fully-resonant line-soliton solutions which contain arbitrary numbers of asymptotic solitons as y → ∓∞ to the KPII equation, and the ordinary N-soliton solution to the KPI equation. In addition, we find that the KPI line solitons propagating in parallel can exhibit the bound state at the moment of collision.

Deep Learning Fluid Mechanics

NASA Astrophysics Data System (ADS)

Barati Farimani, Amir; Gomes, Joseph; Pande, Vijay

2017-11-01

We have developed a new data-driven model paradigm for the rapid inference and solution of the constitutive equations of fluid mechanic by deep learning models. Using generative adversarial networks (GAN), we train models for the direct generation of solutions to steady state heat conduction and incompressible fluid flow without knowledge of the underlying governing equations. Rather than using artificial neural networks to approximate the solution of the constitutive equations, GANs can directly generate the solutions to these equations conditional upon an arbitrary set of boundary conditions. Both models predict temperature, velocity and pressure fields with great test accuracy (>99.5%). The application of our framework for inferring and generating the solutions of partial differential equations can be applied to any physical phenomena and can be used to learn directly from experiments where the underlying physical model is complex or unknown. We also have shown that our framework can be used to couple multiple physics simultaneously, making it amenable to tackle multi-physics problems.

A satellite relative motion model including J_2 and J_3 via Vinti's intermediary

NASA Astrophysics Data System (ADS)

Biria, Ashley D.; Russell, Ryan P.

2018-03-01

Vinti's potential is revisited for analytical propagation of the main satellite problem, this time in the context of relative motion. A particular version of Vinti's spheroidal method is chosen that is valid for arbitrary elliptical orbits, encapsulating J_2, J_3, and generally a partial J_4 in an orbit propagation theory without recourse to perturbation methods. As a child of Vinti's solution, the proposed relative motion model inherits these properties. Furthermore, the problem is solved in oblate spheroidal elements, leading to large regions of validity for the linearization approximation. After offering several enhancements to Vinti's solution, including boosts in accuracy and removal of some singularities, the proposed model is derived and subsequently reformulated so that Vinti's solution is piecewise differentiable. While the model is valid for the critical inclination and nonsingular in the element space, singularities remain in the linear transformation from Earth-centered inertial coordinates to spheroidal elements when the eccentricity is zero or for nearly equatorial orbits. The new state transition matrix is evaluated against numerical solutions including the J_2 through J_5 terms for a wide range of chief orbits and separation distances. The solution is also compared with side-by-side simulations of the original Gim-Alfriend state transition matrix, which considers the J_2 perturbation. Code for computing the resulting state transition matrix and associated reference frame and coordinate transformations is provided online as supplementary material.

A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

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

Hong Luo; Luqing Luo; Robert Nourgaliev

2010-09-01

A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier–Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier–Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need tomore » judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi–Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier–Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier–Stokes equations.« less

A Reconstructed Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations on Arbitrary Grids

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

Hong Luo; Luqing Luo; Robert Nourgaliev

2010-01-01

A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need tomore » judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.« less

Nodal-line dynamics via exact polynomial solutions for coherent waves traversing aberrated imaging systems.

PubMed

Paganin, David M; Beltran, Mario A; Petersen, Timothy C

2018-03-01

We obtain exact polynomial solutions for two-dimensional coherent complex scalar fields propagating through arbitrary aberrated shift-invariant linear imaging systems. These solutions are used to model nodal-line dynamics of coherent fields output by such systems.

Polyelectrolyte multilayers: preparation and applications

NASA Astrophysics Data System (ADS)

Izumrudov, V. A.; Mussabayeva, B. Kh; Murzagulova, K. B.

2018-02-01

The review concerns the results of studies on the synthesis of polyelectrolyte coatings on charged surfaces. These coatings represent nanostructured systems with clearly defined tendency to self-assembly and self-adjustment, which is of particular interest for materials science, biomedicine and pharmacology. A breakthrough in this area of knowledge is due to the development and introduction of a new technique, so-called layer-by-layer (LbL) deposition of nanofilms. The technique is very simple, viz., multilayers are formed as a result of alternating treatment of a charged substrate of arbitrary shape with water-salt solutions of differently charged polyelectrolytes. Nevertheless, efficient use of the LbL method to fabricate nanofilms requires meeting certain conditions and limitations that were revealed in the course of research on model systems. Prospects for applications of polyelectrolyte layers in various fields are discussed. The bibliography includes 58 references.

Preparing Greenberger-Horne-Zeilinger and W states on a long-range Ising spin model by global controls

NASA Astrophysics Data System (ADS)

Chen, Jiahui; Zhou, Hui; Duan, Changkui; Peng, Xinhua

2017-03-01

Entanglement, a unique quantum resource with no classical counterpart, remains at the heart of quantum information. The Greenberger-Horne-Zeilinger (GHZ) and W states are two inequivalent classes of multipartite entangled states which cannot be transformed into each other by means of local operations and classic communication. In this paper, we present the methods to prepare the GHZ and W states via global controls on a long-range Ising spin model. For the GHZ state, general solutions are analytically obtained for an arbitrary-size spin system, while for the W state, we find a standard way to prepare the W state that is analytically illustrated in three- and four-spin systems and numerically demonstrated for larger-size systems. The number of parameters required in the numerical search increases only linearly with the size of the system.

Analytic Reflected Lightcurves for Exoplanets

NASA Astrophysics Data System (ADS)

Haggard, Hal M.; Cowan, Nicolas B.

2018-04-01

The disk-integrated reflected brightness of an exoplanet changes as a function of time due to orbital and rotational motion coupled with an inhomogeneous albedo map. We have previously derived analytic reflected lightcurves for spherical harmonic albedo maps in the special case of a synchronously-rotating planet on an edge-on orbit (Cowan, Fuentes & Haggard 2013). In this letter, we present analytic reflected lightcurves for the general case of a planet on an inclined orbit, with arbitrary spin period and non-zero obliquity. We do so for two different albedo basis maps: bright points (δ-maps), and spherical harmonics (Y_l^m-maps). In particular, we use Wigner D-matrices to express an harmonic lightcurve for an arbitrary viewing geometry as a non-linear combination of harmonic lightcurves for the simpler edge-on, synchronously rotating geometry. These solutions will enable future exploration of the degeneracies and information content of reflected lightcurves, as well as fast calculation of lightcurves for mapping exoplanets based on time-resolved photometry. To these ends we make available Exoplanet Analytic Reflected Lightcurves (EARL), a simple open-source code that allows rapid computation of reflected lightcurves.

Asymmetric Bidirectional Controlled Teleportation by Using Six-qubit Cluster State

NASA Astrophysics Data System (ADS)

Li, Yuan-hua; Nie, Li-ping; Li, Xiao-lan; Sang, Ming-huang

2016-06-01

We propose a scheme for asymmetric bidirectional controlled teleportation by using a six-qubit cluster state as quantum channel. In our scheme, Alice can transmit an arbitrary two-qubit entangled state to Bob and at the same time Bob can teleport an arbitrary single-qubit state to Alice under the control of the supervisor Charlie.

Generation of an arbitrary concatenated Greenberger-Horne-Zeilinger state with single photons

NASA Astrophysics Data System (ADS)

Chen, Shan-Shan; Zhou, Lan; Sheng, Yu-Bo

2017-02-01

The concatenated Greenberger-Horne-Zeilinger (C-GHZ) state is a new kind of logic-qubit entangled state, which may have extensive applications in future quantum communication. In this letter, we propose a protocol for constructing an arbitrary C-GHZ state with single photons. We exploit the cross-Kerr nonlinearity for this purpose. This protocol has some advantages over previous protocols. First, it only requires two kinds of cross-Kerr nonlinearities to generate single phase shifts  ±θ. Second, it is not necessary to use sophisticated m-photon Toffoli gates. Third, this protocol is deterministic and can be used to generate an arbitrary C-GHZ state. This protocol may be useful in future quantum information processing based on the C-GHZ state.

Conservative-variable average states for equilibrium gas multi-dimensional fluxes

NASA Technical Reports Server (NTRS)

Iannelli, G. S.

1992-01-01

Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified.

The pulsar force-free magnetosphere linked to its striped wind: time-dependent pseudo-spectral simulations

NASA Astrophysics Data System (ADS)

Pétri, J.

2012-07-01

Pulsar activity and its related radiation mechanism are usually explained by invoking some plasma processes occurring inside the magnetosphere, be it polar caps, outer/slot gaps or the transition region between the quasi-static magnetic dipole regime and the wave zone, like the striped wind. Despite many detailed local investigations, the global electrodynamics around those neutron stars remains poorly described with only little quantitative studies on the largest scales, i.e. of several light-cylinder radii rL. A better understanding of these compact objects requires a deep and accurate knowledge of their immediate electromagnetic surrounding within the magnetosphere and its link to the relativistic pulsar wind. This is compulsory to make any reliable predictions about the whole electric circuit, energy losses, sites of particle acceleration and the possibly associated emission mechanisms. The aim of this work is to present accurate solutions to the nearly stationary force-free pulsar magnetosphere and its link to the striped wind, for various spin periods and arbitrary inclination. To this end, the time-dependent Maxwell equations are solved in spherical geometry in the force-free approximation using a vector spherical harmonic expansion of the electromagnetic field. An exact analytical enforcement of the divergencelessness of the magnetic part is obtained by a projection method. Special care has been given to designing an algorithm able to look deeply into the magnetosphere with physically realistic ratios of stellar R* to light-cylinder rL radius. However, currently available computational resources allow us only to set R*/rL= 10-1 corresponding to pulsars with a period of 2 ms. The spherical geometry permits a proper and mathematically well-posed imposition of self-consistent physical boundary conditions on the stellar crust. We checked our code against several analytical solutions, like the Deutsch vacuum rotator solution and the Michel monopole field. We also retrieve energy losses comparable to the magnetodipole radiation formula and consistent with previous similar works. Finally, for arbitrary obliquity, we give an expression for the total electric charge of the system. It does not vanish except for the perpendicular rotator. This is due to the often ignored point charge located at the centre of the neutron star. It is questionable if such solutions with huge electric charges could exist in reality except for configurations close to an orthogonal rotator. The charge spread over the stellar crust is not a tunable parameter as often hypothesized.

An exact solution for the history-dependent material and delamination behavior of laminated plates subjected to cylindrical bending

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

Williams, Todd O

2009-01-01

The exact solution for the history-dependent behavior of laminated plates subjected to cylindrical bending is presented. The solution represents the extension of Pagano's solution to consider arbitrary types of constitutive behaviors for the individual lamina as well as arbitrary types of cohesive zones models for delamination behavior. Examples of the possible types of material behavior are plasticity, viscoelasticity, viscoplasticity, and damaging. Examples of possible CZMs that can be considered are linear, nonlinear hardening, as well as nonlinear with softening. The resulting solution is intended as a benchmark solution for considering the predictive capabilities of different plate theories. Initial results aremore » presented for several types of history-dependent material behaviors. It is shown that the plate response in the presence of history-dependent behaviors can differ dramatically from the elastic response. These results have strong implications for what constitutes an appropriate plate theory for modeling such behaviors.« less

BLUES function method in computational physics

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Müller-Nedebock, Kristian K.

2018-04-01

We introduce a computational method in physics that goes ‘beyond linear use of equation superposition’ (BLUES). A BLUES function is defined as a solution of a nonlinear differential equation (DE) with a delta source that is at the same time a Green’s function for a related linear DE. For an arbitrary source, the BLUES function can be used to construct an exact solution to the nonlinear DE with a different, but related source. Alternatively, the BLUES function can be used to construct an approximate piecewise analytical solution to the nonlinear DE with an arbitrary source. For this alternative use the related linear DE need not be known. The method is illustrated in a few examples using analytical calculations and numerical computations. Areas for further applications are suggested.

A note on the radial solutions for the supercritical Hénon equation

NASA Astrophysics Data System (ADS)

Barutello, Vivina; Secchi, Simone; Serra, Enrico

2008-05-01

We prove the existence of a positive radial solution for the Hénon equation with arbitrary growth. The solution is found by means of a shooting method and turns out to be an increasing function of the radial variable. Some numerical experiments suggest the existence of many positive oscillating solutions.

New 2D dilaton gravity for nonsingular black holes

NASA Astrophysics Data System (ADS)

Kunstatter, Gabor; Maeda, Hideki; Taves, Tim

2016-05-01

We construct a two-dimensional action that is an extension of spherically symmetric Einstein-Lanczos-Lovelock (ELL) gravity. The action contains arbitrary functions of the areal radius and the norm squared of its gradient, but the field equations are second order and obey Birkhoff’s theorem. In complete analogy with spherically symmetric ELL gravity, the field equations admit the generalized Misner-Sharp mass as the first integral that determines the form of the vacuum solution. The arbitrary functions in the action allow for vacuum solutions that describe a larger class of interesting nonsingular black hole spacetimes than previously available.

Dynamics of the Deformable Aeroplane. Part 1. The Equations of Motion. Part 2. A Study of the Trim State and Longitudinal Stability of the Slender Integrated Aeroplane Configuration

DTIC Science & Technology

1964-01-01

smaller than the lower typical vibration natural frequencies of thc structure. But the vibration frequencies of interest are those of the aeroplane in...C ,. . . ,...".N’.. -.,, -.- .%. ,...’.% : .. REPRODUCED FROM BEST AVAILABLE COpy 11 an analysis in general terms: it is natural that the choice of...it may be emphasised t that the arbitrary nature of the Neumann Solution is quite inadequate to describe the ion of the body because of its necessary

Exact solutions of a hierarchy of mixing speeds models

NASA Astrophysics Data System (ADS)

Cornille, H.; Platkowski, T.

1992-07-01

This paper presents several new aspects of discrete kinetic theory (DKT). First a hierarchy of d-dimensional (d=1,2,3) models is proposed with (2d+3) velocities and three moduli speeds: 0, 2, and a third one that can be arbitrary. It is assumed that the particles at rest have an internal energy which, for microscopic collisions, supplies for the loss of the kinetic energy. In a more general way than usual, collisions are allowed that mix particles with different speeds. Second, for the (1+1)-dimensional restriction of the systems of PDE for these models which have two independent quadratic collision terms we construct different exact solutions. The usual types of exact solutions are studied: periodic solutions and shock wave solutions obtained from the standard linearization of the scalar Riccati equations called Riccatian shock waves. Then other types of solutions of the coupled Riccati equations are found called non-Riccatian shock waves and they are compared with the previous ones. The main new result is that, between the upstream and downstream states, these new solutions are not necessarily monotonous. Further, for the shock problem, a two-dimensional dynamical system of ODE is solved numerically with limit values corresponding to the upstream and downstream states. As a by-product of this study two new linearizations for the Riccati coupled equations with two functions are proposed.

Asymmetric Bidirectional Controlled Teleportation via Seven-Photon Entangled State

NASA Astrophysics Data System (ADS)

Nie, Yi-you; Sang, Ming-huang

2017-11-01

We propose a protocol of asymmetric bidirectional controlled teleportation by using a seven-photon entangled state. In our protocol, Alice can teleport an arbitrary single-photon state to Bob and at the same time Bob can teleport an arbitrary two-photon state to Alice via the control of the supervisor Charlie. In addition, ones only carry out the Bell-state measurements and single-photon measurement.

Static Light Scattering from Concentrated Protein Solutions, I: General Theory for Protein Mixtures and Application to Self-Associating Proteins

PubMed Central

Minton, Allen P.

2007-01-01

Exact expressions for the static light scattering of a solution containing up to three species of point-scattering solutes in highly nonideal solutions at arbitrary concentration are obtained from multicomponent scattering theory. Explicit expressions for thermodynamic interaction between solute molecules, required to evaluate the scattering relations, are obtained using an equivalent hard particle approximation similar to that employed earlier to interpret scattering of a single protein species at high concentration. The dependence of scattering intensity upon total protein concentration is calculated for mixtures of nonassociating proteins and for a single self-associating protein over a range of concentrations up to 200 g/l. An approximate semiempirical analysis of the concentration dependence of scattering intensity is proposed, according to which the contribution of thermodynamic interaction to scattering intensity is modeled as that of a single average hard spherical species. Simulated data containing pseudo-noise comparable in magnitude to actual experimental uncertainty are modeled using relations obtained from the proposed semiempirical analysis. It is shown that by using these relations one can extract from the data reasonably reliable information about underlying weak associations that are manifested only at very high total protein concentration. PMID:17526566

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.

Relativistic symmetries in the Rosen—Morse potential and tensor interaction using the Nikiforov—Uvarov method

NASA Astrophysics Data System (ADS)

Sameer, M. Ikhdair; Majid, Hamzavi

2013-04-01

Approximate analytical bound-state solutions of the Dirac particle in the fields of attractive and repulsive Rosen—Morse (RM) potentials including the Coulomb-like tensor (CLT) potential are obtained for arbitrary spin-orbit quantum number κ. The Pekeris approximation is used to deal with the spin-orbit coupling terms κ (κ± 1)r-2. In the presence of exact spin and pseudospin (p-spin) symmetries, the energy eigenvalues and the corresponding normalized two-component wave functions are found by using the parametric generalization of the Nikiforov—Uvarov (NU) method. The numerical results show that the CLT interaction removes degeneracies between the spin and p-spin state doublets.

Extensional channel flow revisited: a dynamical systems perspective

PubMed Central

Meseguer, Alvaro; Mellibovsky, Fernando; Weidman, Patrick D.

2017-01-01

Extensional self-similar flows in a channel are explored numerically for arbitrary stretching–shrinking rates of the confining parallel walls. The present analysis embraces time integrations, and continuations of steady and periodic solutions unfolded in the parameter space. Previous studies focused on the analysis of branches of steady solutions for particular stretching–shrinking rates, although recent studies focused also on the dynamical aspects of the problems. We have adopted a dynamical systems perspective, analysing the instabilities and bifurcations the base state undergoes when increasing the Reynolds number. It has been found that the base state becomes unstable for small Reynolds numbers, and a transitional region including complex dynamics takes place at intermediate Reynolds numbers, depending on the wall acceleration values. The base flow instabilities are constitutive parts of different codimension-two bifurcations that control the dynamics in parameter space. For large Reynolds numbers, the restriction to self-similarity results in simple flows with no realistic behaviour, but the flows obtained in the transition region can be a valuable tool for the understanding of the dynamics of realistic Navier–Stokes solutions. PMID:28690413

Solution of mixed convection heat transfer from isothermal in-line fins

NASA Technical Reports Server (NTRS)

Khalilollahi, Amir

1993-01-01

Transient and steady state combined natural and forced convective flows over two in-line finite thickness fins (louvers) in a vertical channel are numerically solved using two methods. The first method of solution is based on the 'Simple Arbitrary Lagrangian Eulerian' (SALE) technique which incorporates mainly two computational phases: (1) a Lagrangian phase in which the velocity field is updated by the effects of all forces, and (2) an Eulerian phase that executes all advective fluxes of mass, momentum and energy. The second method of solution uses the finite element code entitled FIDAP. In the first part, comparison of the results by FIDAP, SALE, and available experimental work were done and discussed for steady state forced convection over louvered fins. Good agreements were deduced between the three sets of results especially for the flow over a single fin. In the second part and in the absence of experimental literature, the numerical predictions were extended to the transient transports and to the opposing flow where pressure drop is reversed. Results are presented and discussed for heat transfer and pressure drop in assisting and opposing mixed convection flows.

Long Wave Runup in Asymmetric Bays and in Fjords With Two Separate Heads

NASA Astrophysics Data System (ADS)

Raz, Amir; Nicolsky, Dmitry; Rybkin, Alexei; Pelinovsky, Efim

2018-03-01

Modeling of tsunamis in glacial fjords prompts us to evaluate applicability of the cross-sectionally averaged nonlinear shallow water equations to model propagation and runup of long waves in asymmetrical bays and also in fjords with two heads. We utilize the Tuck-Hwang transformation, initially introduced for the plane beaches and currently generalized for bays with arbitrary cross section, to transform the nonlinear governing equations into a linear equation. The solution of the linearized equation describing the runup at the shore line is computed by taking into account the incident wave at the toe of the last sloping segment. We verify our predictions against direct numerical simulation of the 2-D shallow water equations and show that our solution is valid both for bays with an asymmetric L-shaped cross section, and for fjords with two heads—bays with a W-shaped cross section.

Subsurface solute transport with one-, two-, and three-dimensional arbitrary shape sources

NASA Astrophysics Data System (ADS)

Chen, Kewei; Zhan, Hongbin; Zhou, Renjie

2016-07-01

Solutions with one-, two-, and three-dimensional arbitrary shape source geometries will be very helpful tools for investigating a variety of contaminant transport problems in the geological media. This study proposed a general method to develop new solutions for solute transport in a saturated, homogeneous aquifer (confined or unconfined) with a constant, unilateral groundwater flow velocity. Several typical source geometries, such as arbitrary line sources, vertical and horizontal patch sources, circular and volumetric sources, were considered. The sources can sit on the upper or lower aquifer boundary to simulate light non-aqueous-phase-liquids (LNAPLs) or dense non-aqueous-phase-liquids (DNAPLs), respectively, or can be located anywhere inside the aquifer. The developed new solutions were tested against previous benchmark solutions under special circumstances and were shown to be robust and accurate. Such solutions can also be used as a starting point for the inverse problem of source zone and source geometry identification in the future. The following findings can be obtained from analyzing the solutions. The source geometry, including shape and orientation, generally played an important role for the concentration profile through the entire transport process. When comparing the inclined line sources with the horizontal line sources, the concentration contours expanded considerably along the vertical direction, and shrank considerably along the groundwater flow direction. A planar source sitting on the upper aquifer boundary (such as a LNAPL pool) would lead to significantly different concentration profiles compared to a planar source positioned in a vertical plane perpendicular to the flow direction. For a volumetric source, its dimension along the groundwater flow direction became less important compared to its other two dimensions.

Harmonic arbitrary waveform generator

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

Roberts, Brock Franklin

2017-11-28

High frequency arbitrary waveforms have applications in radar, communications, medical imaging, therapy, electronic warfare, and charged particle acceleration and control. State of the art arbitrary waveform generators are limited in the frequency they can operate by the speed of the Digital to Analog converters that directly create their arbitrary waveforms. The architecture of the Harmonic Arbitrary Waveform Generator allows the phase and amplitude of the high frequency content of waveforms to be controlled without taxing the Digital to Analog converters that control them. The Harmonic Arbitrary Waveform Generator converts a high frequency input, into a precision, adjustable, high frequency arbitrarymore » waveform.« less

Analytical expression for the tunnel current through the redox-mediated tunneling contact in the case of the adiabatic electron transfer at one of the working electrodes and any possible type of the electron transfer at the other electrode

NASA Astrophysics Data System (ADS)

Medvedev, Igor G.

2017-11-01

We study the tunnel current through a one-level redox molecule immersed into the electrolyte solution for the case when the coupling of the molecule to one of the working electrodes is strong while it is arbitrary to the other electrode. Using the Feynman-Vernon influence functional theory and the perturbation expansion of the effective action of the classical oscillator coupled both to the valence level of the redox molecule and to the thermal bath representing the classical fluctuations of the polarization of the solvent, we obtain, following the canonical way, the Langevin equation for the oscillator. It is found that for the aqueous electrolyte solution, the damping and the stochastic forces which arise due to the tunnel current are much smaller than those due to the thermal bath and therefore can be neglected. We estimate the higher-order corrections to the effective action and show that the Langevin dynamics takes place in this case for arbitrary parameters of the tunneling junction under the condition of the strong coupling of the redox molecule to one of the working electrodes. Then the steady-state coordinate distribution function of the oscillator resulting from the corresponding Fokker-Planck equation is the Boltzmann distribution function which is determined by the adiabatic free energy surface arising from the mean current-induced force. It enables us to obtain the expression for the tunnel current in the case when the coupling of the redox molecule to one of the working electrodes is strong while it is arbitrary to the other electrode.

Analytical expression for the tunnel current through the redox-mediated tunneling contact in the case of the adiabatic electron transfer at one of the working electrodes and any possible type of the electron transfer at the other electrode.

PubMed

Medvedev, Igor G

2017-11-21

We study the tunnel current through a one-level redox molecule immersed into the electrolyte solution for the case when the coupling of the molecule to one of the working electrodes is strong while it is arbitrary to the other electrode. Using the Feynman-Vernon influence functional theory and the perturbation expansion of the effective action of the classical oscillator coupled both to the valence level of the redox molecule and to the thermal bath representing the classical fluctuations of the polarization of the solvent, we obtain, following the canonical way, the Langevin equation for the oscillator. It is found that for the aqueous electrolyte solution, the damping and the stochastic forces which arise due to the tunnel current are much smaller than those due to the thermal bath and therefore can be neglected. We estimate the higher-order corrections to the effective action and show that the Langevin dynamics takes place in this case for arbitrary parameters of the tunneling junction under the condition of the strong coupling of the redox molecule to one of the working electrodes. Then the steady-state coordinate distribution function of the oscillator resulting from the corresponding Fokker-Planck equation is the Boltzmann distribution function which is determined by the adiabatic free energy surface arising from the mean current-induced force. It enables us to obtain the expression for the tunnel current in the case when the coupling of the redox molecule to one of the working electrodes is strong while it is arbitrary to the other electrode.

Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles

NASA Astrophysics Data System (ADS)

Deutsch, Ivan

2017-04-01

We study the production of arbitrary superpositions of Dicke states via optimal control. We show that N atomic hyperfine qubits, interacting symmetrically via the Rydberg blockade, are well described by the Jaynes-Cummings Model (JCM), familiar in cavity QED. In this isomorphism, the presence or absence of a collective Rydberg excitation plays the role of the two-level system and the number of symmetric excitations of the hyperfine qubits plays the role of the bosonic excitations of the JCM. This system is fully controllable through the addition of phase-modulated microwaves that drive transitions between the Rydberg-dressed states. In the weak dressing regime, this results in a single-axis twisting Hamiltonian, plus time-dependent rotations of the collective spin. For strong dressing we control the entire Jaynes-Cummings ladder. Using optimal control, we design microwave waveforms that can generate arbitrary states in the symmetric subspace. This includes cat states, Dicke states, and spin squeezed states. With currently feasible parameters, it is possible to generate arbitrary symmetric states of _10 hyperfine qubits in 1 microsec, assuming a fast microwave phase switching time. The same control can be achieved with a ``dressed-ground control'' scheme, which reduces the demands for fast phase switching at the expense of increased total control time. More generally, we can achieve control on larger ensembles of qubits by designing waveforms that are bandwidth limited within the coherence time of the system. We use this to study general questions of the ``quantum speed limit'' and information content in a waveform that is needed to generate arbitrary quantum states.

Similar solutions for the compressible laminar boundary layer with heat transfer and pressure gradient

NASA Technical Reports Server (NTRS)

Cohen, Clarence B; Reshotko, Eli

1956-01-01

Stewartson's transformation is applied to the laminar compressible boundary-layer equations and the requirement of similarity is introduced, resulting in a set of ordinary nonlinear differential equations previously quoted by Stewartson, but unsolved. The requirements of the system are Prandtl number of 1.0, linear viscosity-temperature relation across the boundary layer, an isothermal surface, and the particular distributions of free-stream velocity consistent with similar solutions. This system admits axial pressure gradients of arbitrary magnitude, heat flux normal to the surface, and arbitrary Mach numbers. The system of differential equations is transformed to integral system, with the velocity ratio as the independent variable. For this system, solutions are found by digital computation for pressure gradients varying from that causing separation to the infinitely favorable gradient and for wall temperatures from absolute zero to twice the free-stream stagnation temperature. Some solutions for separated flows are also presented.

Hypersonic shock structure with Burnett terms in the viscous stress and heat flux

NASA Technical Reports Server (NTRS)

Chapman, Dean R.; Fiscko, Kurt A.

1988-01-01

The continuum Navier-Stokes and Burnett equations are solved for one-dimensional shock structure in various monatomic gases. A new numerical method is employed which utilizes the complete time-dependent continuum equations and obtains the steady-state shock structure by allowing the system to relax from arbitrary initial conditions. Included is discussion of numerical difficulties encountered when solving the Burnett equations. Continuum solutions are compared to those obtained utilizing the Direct Simulation Monte Carlo method. Shock solutions are obtained for a hard sphere gas and for argon from Mach 1.3 to Mach 50. Solutions for a Maxwellian gas are obtained from Mach 1.3 to Mach 3.8. It is shown that the Burnett equations yield shock structure solutions in much closer agreement to both Monte Carlo and experimental results than do the Navier-Stokes equations. Shock density thickness, density asymmetry, and density-temperature separation are all more accurately predicted by the Burnett equations than by the Navier-Stokes equations.

An algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equations

NASA Astrophysics Data System (ADS)

Daud, Wan Suhana Wan; Ahmad, Nazihah; Malkawi, Ghassan

2017-11-01

Sylvester matrix equations played a prominent role in various areas including control theory. Considering to any un-certainty problems that can be occurred at any time, the Sylvester matrix equation has to be adapted to the fuzzy environment. Therefore, in this study, an algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equation is constructed. The construction of the algorithm is based on the max-min arithmetic multiplication operation. Besides that, an associated arbitrary matrix equation is modified in obtaining the final solution. Finally, some numerical examples are presented to illustrate the proposed algorithm.

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

Small fan-in is beautiful

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

Beiu, V.; Makaruk, H.E.

1997-09-01

The starting points of this paper are two size-optimal solutions: (1) one for implementing arbitrary Boolean functions; and (2) another one for implementing certain subclasses of Boolean functions. Because VLSI implementations do not cope well with highly interconnected nets -- the area of a chip grows with the cube of the fan-in -- this paper will analyze the influence of limited fan-in on the size optimality for the two solutions mentioned. First, the authors will extend a result from Horne and Hush valid for fan-in {Delta} = 2 to arbitrary fan-in. Second, they will prove that size-optimal solutions are obtainedmore » for small constant fan-ins for both constructions, while relative minimum size solutions can be obtained for fan-ins strictly lower that linear. These results are in agreement with similar ones proving that for small constant fan-ins ({Delta} = 6...9) there exist VLSI-optimal (i.e., minimizing AT{sup 2}) solutions, while there are similar small constants relating to the capacity of processing information.« less

A stationary phase solution for mountain waves with application to mesospheric mountain waves generated by Auckland Island

NASA Astrophysics Data System (ADS)

Broutman, Dave; Eckermann, Stephen D.; Knight, Harold; Ma, Jun

2017-01-01

A relatively general stationary phase solution is derived for mountain waves from localized topography. It applies to hydrostatic, nonhydrostatic, or anelastic dispersion relations, to arbitrary localized topography, and to arbitrary smooth vertically varying background temperature and vector wind profiles. A simple method is introduced to compute the ray Jacobian that quantifies the effects of horizontal geometrical spreading in the stationary phase solution. The stationary phase solution is applied to mesospheric mountain waves generated by Auckland Island during the Deep Propagating Gravity Wave Experiment. The results are compared to a Fourier solution. The emphasis is on interpretations involving horizontal geometrical spreading. The results show larger horizontal geometrical spreading for nonhydrostatic waves than for hydrostatic waves in the region directly above the island; the dominant effect of horizontal geometrical spreading in the lower ˜30 km of the atmosphere, compared to the effects of refraction and background density variation; and the enhanced geometrical spreading due to directional wind in the approach to a critical layer in the mesosphere.

Conditional generation of an arbitrary superposition of coherent states

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

Takeoka, Masahiro; Sasaki, Masahide

2007-06-15

We present a scheme to conditionally generate an arbitrary superposition of a pair of coherent states from a squeezed vacuum by means of the modified photon subtraction where a coherent state ancilla and two on/off type detectors are used. We show that, even including realistic imperfections of the detectors, our scheme can generate a target state with a high fidelity. The amplitude of the generated states can be amplified by conditional homodyne detections.

Bidirectional Controlled Quantum Information Transmission by Using a Five-Qubit Cluster State

NASA Astrophysics Data System (ADS)

Sang, Zhi-wen

2017-11-01

We demonstrate that an entangled five-qubit cluster state can be used to realize the deterministic bidirectional controlled quantum information transmission by performing only Bell-state measurement and single-qubit measurements. In our protocol, Alice can teleport an arbitrary unknown single-qubit state to Bob and at the same time Bob can remotely prepare an arbitrary known single-qubit state for Alice via the control of the supervisor Charlie.

SYMBMAT: Symbolic computation of quantum transition matrix elements

NASA Astrophysics Data System (ADS)

Ciappina, M. F.; Kirchner, T.

2012-08-01

We have developed a set of Mathematica notebooks to compute symbolically quantum transition matrices relevant for atomic ionization processes. The utilization of a symbolic language allows us to obtain analytical expressions for the transition matrix elements required in charged-particle and laser induced ionization of atoms. Additionally, by using a few simple commands, it is possible to export these symbolic expressions to standard programming languages, such as Fortran or C, for the subsequent computation of differential cross sections or other observables. One of the main drawbacks in the calculation of transition matrices is the tedious algebraic work required when initial states other than the simple hydrogenic 1s state need to be considered. Using these notebooks the work is dramatically reduced and it is possible to generate exact expressions for a large set of bound states. We present explicit examples of atomic collisions (in First Born Approximation and Distorted Wave Theory) and laser-matter interactions (within the Dipole and Strong Field Approximations and different gauges) using both hydrogenic wavefunctions and Slater-Type Orbitals with arbitrary nlm quantum numbers as initial states. Catalogue identifier: AEMI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMI_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 71 628 No. of bytes in distributed program, including test data, etc.: 444 195 Distribution format: tar.gz Programming language: Mathematica Computer: Single machines using Linux or Windows (with cores with any clock speed, cache memory and bits in a word) Operating system: Any OS that supports Mathematica. The notebooks have been tested under Windows and Linux and with versions 6.x, 7.x and 8.x Classification: 2.6 Nature of problem: The notebooks generate analytical expressions for quantum transition matrix elements required in diverse atomic processes: ionization by ion, electron, or photon impact and ionization within the framework of strong field physics. In charged-particle collisions approaches based on perturbation theory enjoy widespread utilization. Accordingly, we have chosen the First Born Approximation and Distorted Wave theories as examples. In light-matter interactions, the main ingredient for many types of calculations is the dipole transition matrix in its different formulations, i.e. length, velocity, and acceleration gauges. In all these cases the transitions of interest occur between a bound state and a continuum state which can be described in different ways. With the notebooks developed in the present work it is possible to calculate transition matrix elements analytically for any set of quantum numbers nlm of initial hydrogenic states or Slater-Type Orbitals and for plane waves or Coulomb waves as final continuum states. Solution method: The notebooks employ symbolic computation to generate analytical expressions for transition matrix elements used in both collision and light-matter interaction physics. fba_hyd.nb - This notebook computes analytical expressions for the transition matrix of collision-induced ionization in the First Born Approximation (FBA). The transitions considered are from a bound hydrogenic state with arbitrary quantum numbers nlm to a continuum state represented by a plane wave (PW) or a Coulomb wave (CW). distorted_hyd.nb - This notebook computes analytical expressions for the transition matrix of collision-induced ionization in Distorted Wave (DW) theories. The transitions considered are from a (distorted) bound hydrogenic state with arbitrary quantum numbers nlm to a distorted-wave continuum state. The computations are based on scalar and vectorial integrals (see the text for details). dipoleLength_hyd.nb - This notebook computes analytical expressions for the dipole transition matrix in length gauge. The transitions considered are from a bound hydrogenic state with arbitrary quantum numbers nlm to a continuum state represented by a PW (the Strong Field Approximation (SFA)) or a CW (the Coulomb-Volkov Approximation (CVA)). dipoleVelocity_hyd.nb - This notebook computes analytical expressions for the dipole transition matrix in velocity gauge. The transitions considered are from a bound hydrogenic state with arbitrary quantum numbers nlm to a continuum state represented by a PW (the SFA) or a CW (the CVA). dipoleAcceleration_hyd.nb - This notebook computes analytical expressions for the dipole transition matrix in acceleration gauge. The transitions considered are from a bound hydrogenic state with arbitrary quantum numbers nlm to a continuum state represented by a PW (the SFA). For the case of the CVA we only include the transition from the 1s state to a continuum state represented by a CW. fba_STO.nb - This notebook computes analytical expressions for the transition matrix of collision-induced ionization in the FBA. The transitions considered are from a Slater-Type Orbital (STO) with arbitrary quantum numbers nlm to a continuum state represented by a PW or a CW. distorted_STO.nb - This notebook computes analytical expressions for the transition matrix of collision-induced ionization in DW theories. The transitions considered are from a (distorted) STO with arbitrary quantum numbers nlm to a distorted-wave continuum state. The computations are based on scalar and vectorial integrals (see the text for details). dipoleLength_STO.nb - This notebook computes analytical expressions for the dipole transition matrix in length gauge. The transitions considered are from an STO with arbitrary quantum numbers nlm to a continuum state represented by a PW (the SFA) or a CW (the CVA). dipoleVelocity_STO.nb - This notebook computes analytical expressions for the dipole transition matrix in velocity gauge. The transitions considered are from an STO with arbitrary quantum numbers nlm to a continuum state represented by a PW (the SFA) or a CW (the CVA). dipoleAcceleration_STO.nb - This notebook computes analytical expressions for the dipole transition matrix in acceleration gauge. The transitions considered are from an STO with arbitrary quantum numbers nlm to a continuum state represented by a PW (the SFA). The symbolic expressions obtained within each notebook can be exported to standard programming languages such as Fortran or C using the Format.m package (see the text and Ref. Sofroniou (1993) [16] for details). Running time: Computational times vary according to the transition matrix selected and quantum numbers nlm of the initial state used. The typical running time is several minutes, but it will take longer for large values of nlm.

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

Karbanovski, V. V., E-mail: Karbanovski_V_V@mail.ru; Sorokin, O. M.; Nesterova, M. I.

The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.

Unstable spiral waves and local Euclidean symmetry in a model of cardiac tissue.

PubMed

Marcotte, Christopher D; Grigoriev, Roman O

2015-06-01

This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals.

Black holes in an expanding universe.

PubMed

Gibbons, Gary W; Maeda, Kei-ichi

2010-04-02

An exact solution representing black holes in an expanding universe is found. The black holes are maximally charged and the universe is expanding with arbitrary equation of state (P = w rho with -1 < or = for all w < or = 1). It is an exact solution of the Einstein-scalar-Maxwell system, in which we have two Maxwell-type U(1) fields coupled to the scalar field. The potential of the scalar field is an exponential. We find a regular horizon, which depends on one parameter [the ratio of the energy density of U(1) fields to that of the scalar field]. The horizon is static because of the balance on the horizon between gravitational attractive force and U(1) repulsive force acting on the scalar field. We also calculate the black hole temperature.

Use of a variational moment method in calculating propagation constants for waveguides with an arbitrary index profile.

PubMed

Hardy, A; Itzkowitz, M; Griffel, G

1989-05-15

A variational moment method is used to calculate propagation constants of 1-D optical waveguides with an arbitrary index profile. The method is applicable to 2-D waveguides as well, and the index profiles need not be symmetric. Examples are given for the lowest-order and the next higher-order modes and are compared with exact numerical solutions.

Bidirectional Controlled Quantum Communication by Using a Seven-Qubit Entangled State

NASA Astrophysics Data System (ADS)

Sang, Ming-huang; Li, Cong

2018-03-01

We propose a protocol for bidirectional controlled quantum communication by using a seven-qubit entangled state. In our protocol, Alice can teleport an arbitrary unknown two-qubit state to Bob, at the same time Bob can help Alice remotely prepares an arbitrary known single-qubit state. It is shown that, with the help of the controller Charlie, the total success probability of our protocol can reach 100%.

Wave Field Synthesis of moving sources with arbitrary trajectory and velocity profile.

PubMed

Firtha, Gergely; Fiala, Péter

2017-08-01

The sound field synthesis of moving sound sources is of great importance when dynamic virtual sound scenes are to be reconstructed. Previous solutions considered only virtual sources moving uniformly along a straight trajectory, synthesized employing a linear loudspeaker array. This article presents the synthesis of point sources following an arbitrary trajectory. Under high-frequency assumptions 2.5D Wave Field Synthesis driving functions are derived for arbitrary shaped secondary source contours by adapting the stationary phase approximation to the dynamic description of sources in motion. It is explained how a referencing function should be chosen in order to optimize the amplitude of synthesis on an arbitrary receiver curve. Finally, a finite difference implementation scheme is considered, making the presented approach suitable for real-time applications.

On irreversible adsorption of electron-donating compounds in aqueous solution

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

Tamon, Hajime; Atsushi, Masanori; Okazaki, Morio

Activated carbons and synthetic adsorbents have been used for liquid purification and wastewater treatment. The feasibility of an adsorption process depends greatly on the cost of regeneration of spent adsorbents. If irreversible adsorption occurs, regeneration of spent adsorbent is very difficult. Hence, it is very important to understand why irreversible adsorption appears in aqueous solution. In the adsorption of electron-donating compounds such as phenol, aniline, L-phenylalanine, and L-tyrosine from aqueous solution, irreversibility was observed on activated carbon and graphite. The compounds, except L-tyrosine, were reversibly adsorbed on a synthetic adsorbent. In the case where the carbonaceous adsorbents contacted the aqueousmore » solution containing electron-donating compounds for a long time, the irreversible amount adsorbed increased with the contact time. A two-state adsorption model was used to explain why the irreversible adsorption of electron-donating compound appears in aqueous solution. First, the compound is adsorbed in the precursor state for irreversible adsorption, and then moves into its irreversible state over a potential energy barrier after a long contact time. The appearance of irreversible adsorption was qualitatively explained by the two-state adsorption model.« less

Analysis of groundwater flow and stream depletion in L-shaped fluvial aquifers

NASA Astrophysics Data System (ADS)

Lin, Chao-Chih; Chang, Ya-Chi; Yeh, Hund-Der

2018-04-01

Understanding the head distribution in aquifers is crucial for the evaluation of groundwater resources. This article develops a model for describing flow induced by pumping in an L-shaped fluvial aquifer bounded by impermeable bedrocks and two nearly fully penetrating streams. A similar scenario for numerical studies was reported in Kihm et al. (2007). The water level of the streams is assumed to be linearly varying with distance. The aquifer is divided into two subregions and the continuity conditions of the hydraulic head and flux are imposed at the interface of the subregions. The steady-state solution describing the head distribution for the model without pumping is first developed by the method of separation of variables. The transient solution for the head distribution induced by pumping is then derived based on the steady-state solution as initial condition and the methods of finite Fourier transform and Laplace transform. Moreover, the solution for stream depletion rate (SDR) from each of the two streams is also developed based on the head solution and Darcy's law. Both head and SDR solutions in the real time domain are obtained by a numerical inversion scheme called the Stehfest algorithm. The software MODFLOW is chosen to compare with the proposed head solution for the L-shaped aquifer. The steady-state and transient head distributions within the L-shaped aquifer predicted by the present solution are compared with the numerical simulations and measurement data presented in Kihm et al. (2007).

On-chip generation of Einstein-Podolsky-Rosen states with arbitrary symmetry

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

Gräfe, Markus; Heilmann, René; Nolte, Stefan

We experimentally demonstrate a method for integrated-optical generation of two-photon Einstein-Podolsky-Rosen states featuring arbitrary symmetries. In our setting, we employ detuned directional couplers to impose a freely tailorable phase between the two modes of the state. Our results allow to mimic the quantum random walk statistics of bosons, fermions, and anyons, particles with fractional exchange statistics.

Scheme for Implementing Teleporting an Arbitrary Tripartite Entangled State in Cavity QED

NASA Astrophysics Data System (ADS)

Wang, Xue-Wen; Peng, Zhao-Hui

2009-10-01

We propose to teleport an arbitrary tripartite entangled state in cavity QED. In this scheme, the five-qubit Brown state is chosen as the quantum channel. It has been shown that the teleportation protocol can be completed perfectly with two different measurement methods. In the future, our scheme might be realizable based on present experimental technology.

Eshelby's problem of polygonal inclusions with polynomial eigenstrains in an anisotropic magneto-electro-elastic full plane

PubMed Central

Lee, Y.-G.; Zou, W.-N.; Pan, E.

2015-01-01

This paper presents a closed-form solution for the arbitrary polygonal inclusion problem with polynomial eigenstrains of arbitrary order in an anisotropic magneto-electro-elastic full plane. The additional displacements or eigendisplacements, instead of the eigenstrains, are assumed to be a polynomial with general terms of order M+N. By virtue of the extended Stroh formulism, the induced fields are expressed in terms of a group of basic functions which involve boundary integrals of the inclusion domain. For the special case of polygonal inclusions, the boundary integrals are carried out explicitly, and their averages over the inclusion are also obtained. The induced fields under quadratic eigenstrains are mostly analysed in terms of figures and tables, as well as those under the linear and cubic eigenstrains. The connection between the present solution and the solution via the Green's function method is established and numerically verified. The singularity at the vertices of the arbitrary polygon is further analysed via the basic functions. The general solution and the numerical results for the constant, linear, quadratic and cubic eigenstrains presented in this paper enable us to investigate the features of the inclusion and inhomogeneity problem concerning polynomial eigenstrains in semiconductors and advanced composites, while the results can further serve as benchmarks for future analyses of Eshelby's inclusion problem. PMID:26345141

Computation of Coupled Thermal-Fluid Problems in Distributed Memory Environment

NASA Technical Reports Server (NTRS)

Wei, H.; Shang, H. M.; Chen, Y. S.

2001-01-01

The thermal-fluid coupling problems are very important to aerospace and engineering applications. Instead of analyzing heat transfer and fluid flow separately, this study merged two well-accepted engineering solution methods, SINDA for thermal analysis and FDNS for fluid flow simulation, into a unified multi-disciplinary thermal fluid prediction method. A fully conservative patched grid interface algorithm for arbitrary two-dimensional and three-dimensional geometry has been developed. The state-of-the-art parallel computing concept was used to couple SINDA and FDNS for the communication of boundary conditions through PVM (Parallel Virtual Machine) libraries. Therefore, the thermal analysis performed by SINDA and the fluid flow calculated by FDNS are fully coupled to obtain steady state or transient solutions. The natural convection between two thick-walled eccentric tubes was calculated and the predicted results match the experiment data perfectly. A 3-D rocket engine model and a real 3-D SSME geometry were used to test the current model, and the reasonable temperature field was obtained.

The Force-Free Magnetosphere of a Rotating Black Hole

NASA Technical Reports Server (NTRS)

Contopoulos, Ioannis; Kazanas, Demosthenes; Papadopoulos, Demetrios B.

2013-01-01

We revisit the Blandford-Znajek process and solve the fundamental equation that governs the structure of the steady-state force-free magnetosphere around a Kerr black hole. The solution depends on the distributions of the magnetic field angular velocity and the poloidal electric current. These are not arbitrary. They are determined self-consistently by requiring that magnetic field lines cross smoothly the two singular surfaces of the problem: the inner "light surface" located inside the ergosphere and the outer "light surface" which is the generalization of the pulsar light cylinder.We find the solution for the simplest possible magnetic field configuration, the split monopole, through a numerical iterative relaxation method analogous to the one that yields the structure of the steady-state axisymmetric force-free pulsar magnetosphere. We obtain the rate of electromagnetic extraction of energy and confirm the results of Blandford and Znajek and of previous time-dependent simulations. Furthermore, we discuss the physical applicability of magnetic field configurations that do not cross both "light surfaces."

Asymmetric Bidirectional Controlled Quantum Information Transmission via Seven-Particle Entangled State

NASA Astrophysics Data System (ADS)

Sang, Ming-huang; Nie, Li-ping

2017-11-01

We demonstrate that a seven-particle entangled state can be used to realize the deterministic asymmetric bidirectional controlled quantum information transmission by performing only Bell-state measurement and two-particle projective measurement and single-particle measurement. In our protocol, Alice can teleport an arbitrary unknown single-particle state to Bob and at the same time Bob can remotely prepare an arbitrary known two-particle state for Alice via the control of the supervisor Charlie.

Criterion for faithful teleportation with an arbitrary multiparticle channel

NASA Astrophysics Data System (ADS)

Cheung, Chi-Yee; Zhang, Zhan-Jun

2009-08-01

We present a general criterion which allows one to judge if an arbitrary multiparticle entanglement channel can be used to teleport faithfully an unknown quantum state of a given dimension. We also present a general multiparticle teleportation protocol which is applicable for all channel states satisfying this criterion.

Development of response models for the Earth Radiation Budget Experiment (ERBE) sensors. Part 2: Analysis of the ERBE integrating sphere ground calibration

NASA Technical Reports Server (NTRS)

Halyo, Nesim; Taylor, Deborah B.

1987-01-01

An explicit solution of the spectral radiance leaving an arbitrary point on the wall of a spherical cavity with diffuse reflectivity is obtained. The solution is applicable to spheres with an arbitrary number of openings of any size and shape, an arbitrary number of light sources with possible non-diffuse characteristics, a non-uniform sphere wall temperature distribution, non-uniform and non-diffuse sphere wall emissivity and non-uniform but diffuse sphere wall spectral reflectivity. A general measurement equation describing the output of a sensor with a given field of view, angular and spectral response measuring the sphere output is obtained. The results are applied to the Earth Radiation Budget Experiment (ERBE) integrating sphere. The sphere wall radiance uniformity, loading effects and non-uniform wall temperature effects are investigated. It is shown that using appropriate interpretation and processing, a high-accuracy short-wave calibration of the ERBE sensors can be achieved.

On A Problem Of Propagation Of Shock Waves Generated By Explosive Volcanic Eruptions

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

Gusev, V. A.; Sobissevitch, A. L.

2008-06-24

Interdisciplinary study of flows of matter and energy in geospheres has become one of the most significant advances in Earth sciences. It is carried out by means of direct quantitative estimations based on detailed analysis of geological and geophysical observations and experimental data. The actual contribution is the interdisciplinary study of nonlinear acoustics and physical volcanology dedicated to shock wave propagation in a viscous and inhomogeneous medium. The equations governing evolution of shock waves with an arbitrary initial profile and an arbitrary cross-section of a beam are obtained. For the case of low viscous medium, the asymptotic solution meant tomore » calculate a profile of a shock wave in an arbitrary point has been derived. The analytical solution of the problem on propagation of shock pulses from atmosphere into a two-phase fluid-saturated geophysical medium is analysed. Quantitative estimations were carried out with respect to experimental results obtained in the course of real explosive volcanic eruptions.« less

Controlled teleportation of an arbitrary n-qubit quantum information using quantum secret sharing of classical message

NASA Astrophysics Data System (ADS)

Zhang, Zhan-Jun

2006-03-01

I present a scheme which allows an arbitrary 2-qubit quantum state teleportation between two remote parties with control of many agents in a network. Comparisons between the present scheme and the existing scheme proposed recently [F.G. Deng, et al., Phys. Rev. A 72 (2005) 022338] are made. It seems that the present scheme is much simpler and more economic. Then I generalize the scheme to teleport an arbitrary n-qubit quantum state between two remote parties with control of agents in a network.

On the existence of a scaling relation in the evolution of cellular systems

NASA Astrophysics Data System (ADS)

Fortes, M. A.

1994-05-01

A mean field approximation is used to analyze the evolution of the distribution of sizes in systems formed by individual 'cells,' each of which grows or shrinks, in such a way that the total number of cells decreases (e.g. polycrystals, soap froths, precipitate particles in a matrix). The rate of change of the size of a cell is defined by a growth function that depends on the size (x) of the cell and on moments of the size distribution, such as the average size (bar-x). Evolutionary equations for the distribution of sizes and of reduced sizes (i.e. x/bar-x) are established. The stationary (or steady state) solutions of the equations are obtained for various particular forms of the growth function. A steady state of the reduced size distribution is equivalent to a scaling behavior. It is found that there are an infinity of steady state solutions which form a (continuous) one-parameter family of functions, but they are not, in general, reached from an arbitrary initial state. These properties are at variance from those that can be derived from models based on von Neumann-Mullins equation.

Position dependent mass Schroedinger equation and isospectral potentials: Intertwining operator approach

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

Midya, Bikashkali; Roy, B.; Roychoudhury, R.

2010-02-15

Here, we have studied first- and second-order intertwining approaches to generate isospectral partner potentials of position dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as second-order linear differential operator with position dependent coefficients, and the system of equations arising from the intertwining relationship is solved for the coefficients by taking an ansatz. A complete scheme for obtaining general solution is obtained, which is valid for any arbitrary potential and mass function. The proposed technique allows us to generate isospectral potentials with the following spectral modifications: (i) to add new bound state(s), (ii) to removemore » bound state(s), and (iii) to leave the spectrum unaffected. To explain our findings with the help of an illustration, we have used point canonical transformation to obtain the general solution of the position dependent mass Schrodinger equation corresponding to a potential and mass function. It is shown that our results are consistent with the formulation of type A N-fold supersymmetry [T. Tanaka, J. Phys. A 39, 219 (2006); A. Gonzalez-Lopez and T. Tanaka, J. Phys. A 39, 3715 (2006)] for the particular cases N=1 and N=2, respectively.« less

Theory of the corrugation instability of a piston-driven shock wave.

PubMed

Bates, J W

2015-01-01

We analyze the two-dimensional stability of a shock wave driven by a steadily moving corrugated piston in an inviscid fluid with an arbitrary equation of state. For h≤-1 or h>h(c), where h is the D'yakov parameter and h(c) is the Kontorovich limit, we find that small perturbations on the shock front are unstable and grow--at first quadratically and later linearly--with time. Such instabilities are associated with nonequilibrium fluid states and imply a nonunique solution to the hydrodynamic equations. The above criteria are consistent with instability limits observed in shock-tube experiments involving ionizing and dissociating gases and may have important implications for driven shocks in laser-fusion, astrophysical, and/or detonation studies.

Non-linear analysis of stick/slip motion

NASA Astrophysics Data System (ADS)

Pratt, T. K.; Williams, R.

1981-02-01

The steady state relative motion of two masses with dry (Coulomb) friction contact is investigated. The bodies are assumed to have the same mass and stiffness and are subjected to harmonic excitation. By means of a combined analytical—numerical procedure, results are obtained for arbitrary values of Coulomb friction, excitation frequency, and natural frequencies of the bodies. For certain values of these parameters, multiple lockups per cycle are possible. In this respect, the problem investigated here is a natural extension of the one considered by Den Hartog, who in obtaining his closed form solution assumed a maximum of two lockups per cycle.

The L sub 1 finite element method for pure convection problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1991-01-01

The least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.

High-beta analytic equilibria in circular, elliptical, and D-shaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows

NASA Astrophysics Data System (ADS)

López, O. E.; Guazzotto, L.

2017-03-01

The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation (PDE) subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. To extend the elliptical solution to a D-shaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604-614 (2004)] is presented for relevant scenarios.

Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories

NASA Astrophysics Data System (ADS)

Alazzawi, Sabina; Lechner, Gandalf

2017-09-01

We present a solution method for the inverse scattering problem for integrable two-dimensional relativistic quantum field theories, specified in terms of a given massive single particle spectrum and a factorizing S-matrix. An arbitrary number of massive particles transforming under an arbitrary compact global gauge group is allowed, thereby generalizing previous constructions of scalar theories. The two-particle S-matrix S is assumed to be an analytic solution of the Yang-Baxter equation with standard properties, including unitarity, TCP invariance, and crossing symmetry. Using methods from operator algebras and complex analysis, we identify sufficient criteria on S that imply the solution of the inverse scattering problem. These conditions are shown to be satisfied in particular by so-called diagonal S-matrices, but presumably also in other cases such as the O( N)-invariant nonlinear {σ}-models.

Boundary states at reflective moving boundaries

NASA Astrophysics Data System (ADS)

Acosta Minoli, Cesar A.; Kopriva, David A.

2012-06-01

We derive and evaluate boundary states for Maxwell's equations, the linear, and the nonlinear Euler gas-dynamics equations to compute wave reflection from moving boundaries. In this study we use a Discontinuous Galerkin Spectral Element method (DGSEM) with Arbitrary Lagrangian-Eulerian (ALE) mapping for the spatial approximation, but the boundary states can be used with other methods, like finite volume schemes. We present four studies using Maxwell's equations, one for the linear Euler equations, and one more for the nonlinear Euler equations. These are: reflection of light from a plane mirror moving at constant velocity, reflection of light from a moving cylinder, reflection of light from a vibrating mirror, reflection of sound from a plane wall and dipole sound generation by an oscillating cylinder in an inviscid flow. The studies show that the boundary states preserve spectral convergence in the solution and in derived quantities like divergence and vorticity.

Soliton polarization rotation in fiber lasers

NASA Astrophysics Data System (ADS)

Afanasjev, V. V.

1995-02-01

I have found the approximate analytical solution in explicit form for a vector soliton with an arbitrary component ratio. My solution describes the dependence of soliton intensity on polarization angle and also nonlinear polarization rotation. The analytical results agree well with the numerical simulations.

Localized states in an arbitrarily bent quantum wire (bend-imitating approach)

NASA Astrophysics Data System (ADS)

Vakhnenko, Oleksity O.

1996-02-01

The bend-imitating matching technique is proposed to simplify the quantum mechanical treatment of singly and multiply bent 2D quantum wires of constant width, arbitrary bending angles, arbitrary bending radii and arbitrary distances between the bends. The spectrum of one-electron localized states and its dependence on the bending angle and the bending radius in a singly bent wire is explicitly calculated. Doubly bent wires are shown to possess doubly split localized states. The splitting energies as a function of the distance between the bends and the bending angles and bending radii have also been obtained. A similar description of bent 3D quantum wires and bent optical fibers is expected to be possible.

Analytic reflected light curves for exoplanets

NASA Astrophysics Data System (ADS)

Haggard, Hal M.; Cowan, Nicolas B.

2018-07-01

The disc-integrated reflected brightness of an exoplanet changes as a function of time due to orbital and rotational motions coupled with an inhomogeneous albedo map. We have previously derived analytic reflected light curves for spherical harmonic albedo maps in the special case of a synchronously rotating planet on an edge-on orbit (Cowan, Fuentes & Haggard). In this paper, we present analytic reflected light curves for the general case of a planet on an inclined orbit, with arbitrary spin period and non-zero obliquity. We do so for two different albedo basis maps: bright points (δ-maps), and spherical harmonics (Y_ l^m-maps). In particular, we use Wigner D-matrices to express an harmonic light curve for an arbitrary viewing geometry as a non-linear combination of harmonic light curves for the simpler edge-on, synchronously rotating geometry. These solutions will enable future exploration of the degeneracies and information content of reflected light curves, as well as fast calculation of light curves for mapping exoplanets based on time-resolved photometry. To these ends, we make available Exoplanet Analytic Reflected Lightcurves, a simple open-source code that allows rapid computation of reflected light curves.

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 3.0)

NASA Technical Reports Server (NTRS)

Epton, Michael A.; Magnus, Alfred E.

1990-01-01

An outline of the derivation of the differential equation governing linear subsonic and supersonic potential flow is given. The use of Green's Theorem to obtain an integral equation over the boundary surface is discussed. The engineering techniques incorporated in the Panel Aerodynamics (PAN AIR) program (a discretization method which solves the integral equation for arbitrary first order boundary conditions) are then discussed in detail. Items discussed include the construction of the compressibility transformation, splining techniques, imposition of the boundary conditions, influence coefficient computation (including the concept of the finite part of an integral), computation of pressure coefficients, and computation of forces and moments. Principal revisions to version 3.0 are the following: (1) appendices H and K more fully describe the Aerodynamic Influence Coefficient (AIC) construction; (2) appendix L now provides a complete description of the AIC solution process; (3) appendix P is new and discusses the theory for the new FDP module (which calculates streamlines and offbody points); and (4) numerous small corrections and revisions reflecting the MAG module rewrite.

Connections between Kac-Moody algebras and M-theory

NASA Astrophysics Data System (ADS)

Cook, Paul P.

2007-11-01

We investigate some of the motivations and consequences of the conjecture that the Kac-Moody algebra E11 is the symmetry algebra of M-theory, and we develop methods to aid the further investigation of this idea. The definitions required to work with abstract root systems of Lie algebras are given in review leading up to the definition of a Kac-Moody algebra. The motivations for the E11 conjecture are presented and the nonlinear realisation of gravity relevant to the conjecture is described. We give a beginner's guide to producing the algebras of E11, relevant to M-theory, and K27, relevant to the bosonic string theory, along with their l1 representations are constructed. Reference tables of low level roots are produced for both the adjoint and l1 representations of these algebras. In addition a particular group element, having a generic form for all G+++ algebras, is shown to encode all the half-BPS brane solutions of the maximally oxidised supergravities. Special analysis is given to the role of space-time signature in the context of this group element and subsequent to this analysis spacelike brane solutions are derived from the same solution generating group element. Finally the appearance of U-duality charge multiplets from E11 is reviewed. General formulae for finding the content of arbitrary brane charge multiplets are given and the content of the particle and string multiplets in dimensions 4,5,6,7 and 8 is shown to be contained in the l1 representation of E11.

Minority game with arbitrary cutoffs

NASA Astrophysics Data System (ADS)

Johnson, N. F.; Hui, P. M.; Zheng, Dafang; Tai, C. W.

1999-07-01

We study a model of a competing population of N adaptive agents, with similar capabilities, repeatedly deciding whether to attend a bar with an arbitrary cutoff L. Decisions are based upon past outcomes. The agents are only told whether the actual attendance is above or below L. For L∼ N/2, the game reproduces the main features of Challet and Zhang's minority game. As L is lowered, however, the mean attendances in different runs tend to divide into two groups. The corresponding standard deviations for these two groups are very different. This grouping effect results from the dynamical feedback governing the game's time-evolution, and is not reproduced if the agents are fed a random history.

Solution of plane cascade flow using improved surface singularity methods

NASA Technical Reports Server (NTRS)

Mcfarland, E. R.

1981-01-01

A solution method has been developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those found in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method's capabilities are presented.

Habemus superstratum! A constructive proof of the existence of superstrata

NASA Astrophysics Data System (ADS)

Bena, Iosif; Giusto, Stefano; Russo, Rodolfo; Shigemori, Masaki; Warner, Nicholas P.

2015-05-01

We construct the first example of a superstratum: a class of smooth horizonless supergravity solutions that are parameterized by arbitrary continuous functions of (at least) two variables and have the same charges as the supersymmetric D1-D5-P black hole. We work in Type IIB string theory on T 4 or K3 and our solutions involve a subset of fields that can be described by a six-dimensional supergravity with two tensor multiplets. The solutions can thus be constructed using a linear structure, and we give an explicit recipe to start from a superposition of modes specified by an arbitrary function of two variables and impose regularity to obtain the full horizonless solutions in closed form. We also give the precise CFT description of these solutions and show that they are not dual to descendants of chiral primaries. They are thus much more general than all the known solutions whose CFT dual is precisely understood. Hence our construction represents a substantial step toward the ultimate goal of constructing the fully generic superstratum that can account for a finite fraction of the entropy of the three-charge black hole in the regime of parameters where the classical black hole solution exists.

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

Dubrovsky, V. G.; Topovsky, A. V.

New exact solutions, nonstationary and stationary, of Veselov-Novikov (VN) equation in the forms of simple nonlinear and linear superpositions of arbitrary number N of exact special solutions u{sup (n)}, n= 1, Horizontal-Ellipsis , N are constructed via Zakharov and Manakov {partial_derivative}-dressing method. Simple nonlinear superpositions are represented up to a constant by the sums of solutions u{sup (n)} and calculated by {partial_derivative}-dressing on nonzero energy level of the first auxiliary linear problem, i.e., 2D stationary Schroedinger equation. It is remarkable that in the zero energy limit simple nonlinear superpositions convert to linear ones in the form of the sums ofmore » special solutions u{sup (n)}. It is shown that the sums u=u{sup (k{sub 1})}+...+u{sup (k{sub m})}, 1 Less-Than-Or-Slanted-Equal-To k{sub 1} < k{sub 2} < Horizontal-Ellipsis < k{sub m} Less-Than-Or-Slanted-Equal-To N of arbitrary subsets of these solutions are also exact solutions of VN equation. The presented exact solutions include as superpositions of special line solitons and also superpositions of plane wave type singular periodic solutions. By construction these exact solutions represent also new exact transparent potentials of 2D stationary Schroedinger equation and can serve as model potentials for electrons in planar structures of modern electronics.« less

Arbitrary unitary transformations on optical states using a quantum memory

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

Campbell, Geoff T.; Pinel, Olivier; Hosseini, Mahdi

2014-12-04

We show that optical memories arranged along an optical path can perform arbitrary unitary transformations on frequency domain optical states. The protocol offers favourable scaling and can be used with any quantum memory that uses an off-resonant Raman transition to reversibly transfer optical information to an atomic spin coherence.

Direct method for measuring and witnessing quantum entanglement of arbitrary two-qubit states through Hong-Ou-Mandel interference

NASA Astrophysics Data System (ADS)

Bartkiewicz, Karol; Chimczak, Grzegorz; Lemr, Karel

2017-02-01

We describe a direct method for experimental determination of the negativity of an arbitrary two-qubit state with 11 measurements performed on multiple copies of the two-qubit system. Our method is based on the experimentally accessible sequences of singlet projections performed on up to four qubit pairs. In particular, our method permits the application of the Peres-Horodecki separability criterion to an arbitrary two-qubit state. We explicitly demonstrate that measuring entanglement in terms of negativity requires three measurements more than detecting two-qubit entanglement. The reported minimal set of interferometric measurements provides a complete description of bipartite quantum entanglement in terms of two-photon interference. This set is smaller than the set of 15 measurements needed to perform a complete quantum state tomography of an arbitrary two-qubit system. Finally, we demonstrate that the set of nine Makhlin's invariants needed to express the negativity can be measured by performing 13 multicopy projections. We demonstrate both that these invariants are a useful theoretical concept for designing specialized quantum interferometers and that their direct measurement within the framework of linear optics does not require performing complete quantum state tomography.

Synchronization of relativistic particles in the hyperbolic Kuramoto model

NASA Astrophysics Data System (ADS)

Ritchie, Louis M.; Lohe, M. A.; Williams, Anthony G.

2018-05-01

We formulate a noncompact version of the Kuramoto model by replacing the invariance group SO(2) of the plane rotations by the noncompact group SO(1, 1). The N equations of the system are expressed in terms of hyperbolic angles αi and are similar to those of the Kuramoto model, except that the trigonometric functions are replaced by hyperbolic functions. Trajectories are generally unbounded, nevertheless synchronization occurs for any positive couplings κi, arbitrary positive multiplicative parameters λi and arbitrary exponents ωi. There are no critical values for the coupling constants. We measure the onset of synchronization by means of several order and disorder parameters. We show numerically and by means of exact solutions for N = 2 that solutions can develop singularities if the coupling constants are negative, or if the initial values are not suitably restricted. We describe a physical interpretation of the system as a cluster of interacting relativistic particles in 1 + 1 dimensions, subject to linear repulsive forces with space-time trajectories parametrized by the rapidity αi. The trajectories synchronize provided that the particle separations remain predominantly time-like, and the synchronized cluster can be viewed as a bound state of N relativistic particle constituents. We extend the defining equations of the system to higher dimensions by means of vector equations which are covariant with respect to SO(p, q).

Characterizing the hydration state of L-threonine in solution using terahertz time-domain attenuated total reflection spectroscopy

NASA Astrophysics Data System (ADS)

Huang, Huachuan; Liu, Qiao; Zhu, Liguo; Li, Zeren

2018-01-01

The hydration of biomolecules is closely related to the dynamic process of their functional expression, therefore, characterizing hydration phenomena is a subject of keen interest. However, direct measurements on the global hydration state of biomolecules couldn't have been acquired using traditional techniques such as thermodynamics, ultrasound, microwave spectroscopy or viscosity, etc. In order to realize global hydration characterization of amino acid such as L-threonine, terahertz time-domain attenuated total reflectance spectroscopy (THz-TDS-ATR) was adopted in this paper. By measuring the complex permittivity of L-threonine solutions with various concentrations in the THz region, the hydration state and its concentration dependence were obtained, indicating that the number of hydrous water decreased with the increase of concentration. The hydration number was evaluated to be 17.8 when the molar concentration of L-threonine was 0.34 mol/L, and dropped to 13.2 when the molar concentration increased to 0.84 mol/L, when global hydration was taken into account. According to the proposed direct measurements, it is believed that the THz-TDS-ATR technique is a powerful tool for studying the picosecond molecular dynamics of amino acid solutions.

Quantum Teamwork for Unconditional Multiparty Communication with Gaussian States

NASA Astrophysics Data System (ADS)

Zhang, Jing; Adesso, Gerardo; Xie, Changde; Peng, Kunchi

2009-08-01

We demonstrate the capability of continuous variable Gaussian states to communicate multipartite quantum information. A quantum teamwork protocol is presented according to which an arbitrary possibly entangled multimode state can be faithfully teleported between two teams each comprising many cooperative users. We prove that N-mode Gaussian weighted graph states exist for arbitrary N that enable unconditional quantum teamwork implementations for any arrangement of the teams. These perfect continuous variable maximally multipartite entangled resources are typical among pure Gaussian states and are unaffected by the entanglement frustration occurring in multiqubit states.

Asymptotic-preserving Lagrangian approach for modeling anisotropic transport in magnetized plasmas for arbitrary magnetic fields

NASA Astrophysics Data System (ADS)

Chacon, Luis; Del-Castillo-Negrete, Diego; Hauck, Cory

2012-10-01

Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (χ/χ˜10^10 in fusion plasmas). Recently, a Lagrangian Green's function approach, developed for the purely parallel transport case,footnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011)^,footnotetextD. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, 19, 056112 (2012) has been extended to the anisotropic transport case in the tokamak-ordering limit with constant density.footnotetextL. Chac'on, D. del-Castillo-Negrete, C. Hauck, JCP, submitted (2012) An operator-split algorithm is proposed that allows one to treat Eulerian and Lagrangian components separately. The approach is shown to feature bounded numerical errors for arbitrary χ/χ ratios, which renders it asymptotic-preserving. In this poster, we will present the generalization of the Lagrangian approach to arbitrary magnetic fields. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.

Deeper and sparser nets are optimal

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

Beiu, V.; Makaruk, H.E.

1998-03-01

The starting points of this paper are two size-optimal solutions: (1) one for implementing arbitrary Boolean functions (Home and Hush, 1994); and (2) another one for implementing certain sub-classes of Boolean functions (Red`kin, 1970). Because VLSI implementations do not cope well with highly interconnected nets--the area of a chip grows with the cube of the fan-in (Hammerstrom, 1988)--this paper will analyze the influence of limited fan-in on the size optimality for the two solutions mentioned. First, the authors will extend a result from Home and Hush (1994) valid for fan-in {Delta} = 2 to arbitrary fan-in. Second, they will provemore » that size-optimal solutions are obtained for small constant fan-in for both constructions, while relative minimum size solutions can be obtained for fan-ins strictly lower that linear. These results are in agreement with similar ones proving that for small constant fan-ins ({Delta} = 6...9) there exist VLSI-optimal (i.e., minimizing AT{sup 2}) solutions (Beiu, 1997a), while there are similar small constants relating to the capacity of processing information (Miller 1956).« less

Deeper sparsely nets are size-optimal

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

Beiu, V.; Makaruk, H.E.

1997-12-01

The starting points of this paper are two size-optimal solutions: (i) one for implementing arbitrary Boolean functions (Horne, 1994); and (ii) another one for implementing certain sub-classes of Boolean functions (Red`kin, 1970). Because VLSI implementations do not cope well with highly interconnected nets--the area of a chip grows with the cube of the fan-in (Hammerstrom, 1988)--this paper will analyze the influence of limited fan-in on the size optimality for the two solutions mentioned. First, the authors will extend a result from Horne and Hush (1994) valid for fan-in {Delta} = 2 to arbitrary fan-in. Second, they will prove that size-optimalmore » solutions are obtained for small constant fan-in for both constructions, while relative minimum size solutions can be obtained for fan-ins strictly lower than linear. These results are in agreement with similar ones proving that for small constant fan-ins ({Delta} = 6...9) there exist VLSI-optimal (i.e. minimizing AT{sup 2}) solutions (Beiu, 1997a), while there are similar small constants relating to the capacity of processing information (Miller 1956).« less

A Reconstructed Discontinuous Galerkin Method for the Compressible Euler Equations on Arbitrary Grids

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

Hong Luo; Luquing Luo; Robert Nourgaliev

2009-06-01

A reconstruction-based discontinuous Galerkin (DG) method is presented for the solution of the compressible Euler equations on arbitrary grids. By taking advantage of handily available and yet invaluable information, namely the derivatives, in the context of the discontinuous Galerkin methods, a solution polynomial of one degree higher is reconstructed using a least-squares method. The stencils used in the reconstruction involve only the van Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The resulting DG method can be regarded as an improvement of a recovery-based DG method in the sense that it shares the samemore » nice features as the recovery-based DG method, such as high accuracy and efficiency, and yet overcomes some of its shortcomings such as a lack of flexibility, compactness, and robustness. The developed DG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate the accuracy and efficiency of the method. The numerical results indicate that this reconstructed DG method is able to obtain a third-order accurate solution at a slightly higher cost than its second-order DG method and provide an increase in performance over the third order DG method in terms of computing time and storage requirement.« less

Energy spectra and wave function of trigonometric Rosen-Morse potential as an effective quantum chromodynamics potential in D-dimensions

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

Deta, U. A., E-mail: utamaalan@yahoo.co.id; Suparmi,; Cari,

2014-09-30

The Energy Spectra and Wave Function of Schrodinger equation in D-Dimensions for trigonometric Rosen-Morse potential were investigated analytically using Nikiforov-Uvarov method. This potential captures the essential traits of the quark-gluon dynamics of Quantum Chromodynamics. The approximate energy spectra are given in the close form and the corresponding approximate wave function for arbitrary l-state (l ≠ 0) in D-dimensions are formulated in the form of differential polynomials. The wave function of this potential unnormalizable for general case. The wave function of this potential unnormalizable for general case. The existence of extra dimensions (centrifugal factor) and this potential increase the energy spectramore » of system.« less

Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning.

PubMed

Gorban, A N; Mirkes, E M; Zinovyev, A

2016-12-01

Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including high sensitivity to contaminating factors and dimensionality curse. Therefore, a lot of recent applications in machine learning exploited properties of non-quadratic error functionals based on L 1 norm or even sub-linear potentials corresponding to quasinorms L p (0

Introducing a new family of short-range potentials and their numerical solutions using the asymptotic iteration method

NASA Astrophysics Data System (ADS)

Assi, I. A.; Sous, A. J.

2018-05-01

The goal of this work is to derive a new class of short-range potentials that could have a wide range of physical applications, specially in molecular physics. The tridiagonal representation approach has been developed beyond its limitations to produce new potentials by requiring the representation of the Schrödinger wave operator to be multidiagonal and symmetric. This produces a family of Hulthén potentials that has a specific structure, as mentioned in the introduction. As an example, we have solved the nonrelativistic wave equation for the new four-parameter short-range screening potential numerically using the asymptotic iteration method, where we tabulated the eigenvalues for both s -wave and arbitrary l -wave cases in tables.

An exact solution for axial flow in cylindrically symmetric, steady-state detonation in polytropic explosive with an arbitrary rate of decomposition

NASA Astrophysics Data System (ADS)

Cowperthwaite, M.

1994-03-01

Methods of differential geometry and Bernoulli's equation, written as B=0, are used to develop a new approach for constructing an exact solution for axial flow in a classical, two-dimensional, ZND detonation wave in a polytropic explosive with an arbitrary rate of decomposition. This geometric approach is fundamentally different from the traditional approaches to this axial flow problem formulated by Wood and Kirkwood (WK) and Fickett and Davis (FD), and gives equations for the axial particle velocity (u), the sound speed (c), the pressure (p), and the density (ρ), that are expressed in terms of the detonation velocity (D), the extent of decomposition (λ), the polytropic index (K), and two nonideal parameters ɛ3 and ɛ1, and reduce to the equations for steady-state, one-dimensional detonation as ɛ3 and ɛ1 approach zero. In contrast to the FD approach, the equations for u and c are obtained from first integrals of a tangent vector à on (u,c,λ) space, and the invariant condition, ÃB=aB=0, bypasses the FD eigenvalue problem by defining ɛ3 in terms of the detonation velocity deficit D/D∞ and K. In contrast to the WK approach, the equations for p and ρ are obtained from equations expressing the conservation of axial momentum and energy. Because the equations for these flow variables are derived without using the conservation of mass, the axial radial particle velocity gradient (war) associated with the flow can be obtained from the continuity equation without making approximations. The relationship between ɛ1 and ɛ3 that closes the solution is obtained from equations expressing constraints imposed on the axial flow at the shock front by the axial and radial momentum equations, the curved shock and the decomposition rate law, and a particular solution is constructed from the ɛ1-ɛ3 relationship determined by a prescribed rate law and value of K. Properties of particular solutions are presented to provide a better understanding of two-dimensional detonation, and a new axial condition for detonation failure is used to show that detonation failure can occur before the curve relating D/D∞ to the axial radius of curvature of the shock (Sa) becomes infinite.

Solution of plane cascade flow using improved surface singularity methods. [application of panel method to internal aerodynamics

NASA Technical Reports Server (NTRS)

Mcfarland, E. R.

1981-01-01

A solution method was developed for calculating compressible inviscid flow through a linear cascade of arbitrary blade shapes. The method uses advanced surface singularity formulations which were adapted from those in current external flow analyses. The resulting solution technique provides a fast flexible calculation for flows through turbomachinery blade rows. The solution method and some examples of the method's capabilities are presented.

Vacuum polarization of a quantized scalar field in the thermal state in a long throat

NASA Astrophysics Data System (ADS)

Popov, Arkady A.

2016-12-01

Vacuum polarization of scalar fields in the background of a long throat is investigated. The field is assumed to be both massive or massless, with arbitrary coupling to the scalar curvature, and in a thermal state at an arbitrary temperature. Analytical approximation for ⟨φ2⟩ren is obtained.

Optimum three-dimensional atmospheric entry from the analytical solution of Chapman's exact equations

NASA Technical Reports Server (NTRS)

Busemann, A.; Vinh, N. X.; Culp, R. D.

1974-01-01

The general solution for the optimum three-dimensional aerodynamic control of a lifting vehicle entering a planetary atmosphere is developed. A set of dimensionless variables, modified Chapman variables, is introduced. The resulting exact equations of motion, referred to as Chapman's exact equations, have the advantage that they are completely free of the physical characteristics of the vehicle. Furthermore, a completely general lift-drag relationship is used in the derivation. The results obtained apply to any type of vehicle of arbitrary weight, dimensions and shape, having an arbitrary drag polar, and entering any planetary atmosphere. The aerodynamic controls chosen are the lift coefficient and the bank angle. General optimum control laws for these controls are developed. Several earlier particular solutions are shown to be special cases of this general result. Results are valid for both free and constrained terminal position.

Induced drag ideal efficiency factor of arbitrary lateral-vertical wing forms

NASA Technical Reports Server (NTRS)

Deyoung, J.

1980-01-01

A relatively simple equation is presented for estimating the induced drag ideal efficiency factor e for arbitrary cross sectional wing forms. This equation is based on eight basic but varied wing configurations which have exact solutions. The e function which relates the basic wings is developed statistically and is a continuous function of configuration geometry. The basic wing configurations include boxwings shaped as a rectangle, ellipse, and diamond; the V-wing; end-plate wing; 90 degree cruciform; circle dumbbell; and biplane. Example applications of the e equations are made to many wing forms such as wings with struts which form partial span rectangle dumbbell wings; bowtie, cruciform, winglet, and fan wings; and multiwings. Derivations are presented in the appendices of exact closed form solutions found of e for the V-wing and 90 degree cruciform wing and for an asymptotic solution for multiwings.

Entanglement detection in the vicinity of arbitrary Dicke states.

PubMed

Duan, L-M

2011-10-28

Dicke states represent a class of multipartite entangled states that can be generated experimentally with many applications in quantum information. We propose a method to experimentally detect genuine multipartite entanglement in the vicinity of arbitrary Dicke states. The detection scheme can be used to experimentally quantify the entanglement depth of many-body systems and is easy to implement as it requires measurement of only three collective spin operators. The detection criterion is strong as it heralds multipartite entanglement even in cases where the state fidelity goes down exponentially with the number of qubits.

Permutation-symmetric three-particle hyper-spherical harmonics based on the S3 ⊗ SO(3)rot ⊂ O(2)⊗SO(3)rot ⊂ U(3)⋊S2 ⊂ O(6) subgroup chain

NASA Astrophysics Data System (ADS)

Salom, Igor; Dmitrašinović, V.

2017-07-01

We construct the three-body permutation symmetric hyperspherical harmonics to be used in the non-relativistic three-body Schrödinger equation in three spatial dimensions (3D). We label the state vectors according to the S3 ⊗ SO(3)rot ⊂ O (2) ⊗ SO(3)rot ⊂ U (3) ⋊S2 ⊂ O (6) subgroup chain, where S3 is the three-body permutation group and S2 is its two element subgroup containing transposition of first two particles, O (2) is the ;democracy transformation;, or ;kinematic rotation; group for three particles; SO(3)rot is the 3D rotation group, and U (3) , O (6) are the usual Lie groups. We discuss the good quantum numbers implied by the above chain of algebras, as well as their relation to the S3 permutation properties of the harmonics, particularly in view of the SO(3)rot ⊂ SU (3) degeneracy. We provide a definite, practically implementable algorithm for the calculation of harmonics with arbitrary finite integer values of the hyper angular momentum K, and show an explicit example of this construction in a specific case with degeneracy, as well as tables of K ≤ 6 harmonics. All harmonics are expressed as homogeneous polynomials in the Jacobi vectors (λ , ρ) with coefficients given as algebraic numbers unless the ;operator method; is chosen for the lifting of the SO(3)rot ⊂ SU (3) multiplicity and the dimension of the degenerate subspace is greater than four - in which case one must resort to numerical diagonalization; the latter condition is not met by any K ≤ 15 harmonic, or by any L ≤ 7 harmonic with arbitrary K. We also calculate a certain type of matrix elements (the Gaunt integrals of products of three harmonics) in two ways: 1) by explicit evaluation of integrals and 2) by reduction to known SU (3) Clebsch-Gordan coefficients. In this way we complete the calculation of the ingredients sufficient for the solution to the quantum-mechanical three-body bound state problem.

Optimal remote preparation of arbitrary multi-qubit real-parameter states via two-qubit entangled states

NASA Astrophysics Data System (ADS)

Wei, Jiahua; Shi, Lei; Luo, Junwen; Zhu, Yu; Kang, Qiaoyan; Yu, Longqiang; Wu, Hao; Jiang, Jun; Zhao, Boxin

2018-06-01

In this paper, we present an efficient scheme for remote state preparation of arbitrary n-qubit states with real coefficients. Quantum channel is composed of n maximally two-qubit entangled states, and several appropriate mutually orthogonal bases including the real parameters of prepared states are delicately constructed without the introduction of auxiliary particles. It is noted that the successful probability is 100% by using our proposal under the condition that the parameters of prepared states are all real. Compared to general states, the probability of our protocol is improved at the cost of the information reduction in the transmitted state.

Self-consistent approach to the solution of the light transfer problem for irradiances in marine waters with arbitrary turbidity, depth, and surface illumination. I. Case of absorption and elastic scattering.

PubMed

Haltrin, V I

1998-06-20

A self-consistent variant of the two-flow approximation that takes into account strong anisotropy of light scattering in seawater of finite depth and arbitrary turbidity is presented. To achieve an appropriate accuracy, this approach uses experimental dependencies between downward and total mean cosines. It calculates irradiances, diffuse attenuation coefficients, and diffuse reflectances in waters with arbitrary values of scattering, backscattering, and attenuation coefficients. It also takes into account arbitrary conditions of illumination and reflection from the bottom with the Lambertian albedo. This theory can be used for the calculation of apparent optical properties in both open and coastal oceanic waters, lakes, and rivers. It can also be applied to other types of absorbing and scattering medium such as paints, photographic emulsions, and biological tissues.

Transient Thermoelectric Solution Employing Green's Functions

NASA Technical Reports Server (NTRS)

Mackey, Jon; Sehirlioglu, Alp; Dynys, Fred

2014-01-01

The study works to formulate convenient solutions to the problem of a thermoelectric couple operating under a time varying condition. Transient operation of a thermoelectric will become increasingly common as thermoelectric technology permits applications in an increasing number of uses. A number of terrestrial applications, in contrast to steady-state space applications, can subject devices to time varying conditions. For instance thermoelectrics can be exposed to transient conditions in the automotive industry depending on engine system dynamics along with factors like driving style. In an effort to generalize the thermoelectric solution a Greens function method is used, so that arbitrary time varying boundary and initial conditions may be applied to the system without reformulation. The solution demonstrates that in thermoelectric applications of a transient nature additional factors must be taken into account and optimized. For instance, the materials specific heat and density become critical parameters in addition to the thermal mass of a heat sink or the details of the thermal profile, such as oscillating frequency. The calculations can yield the optimum operating conditions to maximize power output andor efficiency for a given type of device.

Teleportation with a mixed state of four qubits and the generalized singlet fraction

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

Yeo, Ye

2006-11-15

Recently, an explicit protocol E{sub 0} for faithfully teleporting arbitrary two-qubit states using genuine four-qubit entangled states was presented by us [Phys. Rev. Lett. 96, 060502 (2006)]. Here, we show that E{sub 0} with an arbitrary four-qubit mixed-state resource {xi} is equivalent to a generalized depolarizing bichannel with probabilities given by the maximally entangled components of the resource. These are defined in terms of our four-qubit entangled states. We define the generalized singlet fraction G[{xi}] and illustrate its physical significance with several examples. We argue that in order to teleport arbitrary two-qubit states with average fidelity better than is classicallymore » possible, we have to demand that G[{xi}]>1/2. In addition, we conjecture that when G[{xi}]<1/4, then no entanglement could be teleported. It is shown that to determine the usefulness of {xi} for E{sub 0}, it is necessary to analyze G[{xi}].« less

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy.

PubMed

Haas, Fernando; Mahmood, Shahzad

2015-11-01

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy

NASA Astrophysics Data System (ADS)

Haas, Fernando; Mahmood, Shahzad

2015-11-01

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

Classical heat transport in anharmonic molecular junctions: exact solutions.

PubMed

Liu, Sha; Agarwalla, Bijay Kumar; Wang, Jian-Sheng; Li, Baowen

2013-02-01

We study full counting statistics for classical heat transport through anharmonic or nonlinear molecular junctions formed by interacting oscillators. An analytical result of the steady-state heat flux for an overdamped anharmonic junction with arbitrary temperature bias is obtained. It is found that the thermal conductance can be expressed in terms of a temperature-dependent effective force constant. The role of anharmonicity is identified. We also give the general formula for the second cumulant of heat in steady state, as well as the average geometric heat flux when two system parameters are modulated adiabatically. We present an anharmonic example for which all cumulants for heat can be obtained exactly. For a bounded single oscillator model with mass we found that the cumulants are independent of the nonlinear potential.

Calcium Chloride in Neonatal Parenteral Nutrition Solutions with and without Added Cysteine: Compatibility Studies Using Laser and Micro-Flow Imaging Methodology.

PubMed

Huston, Robert K; Christensen, J Mark; Alshahrani, Sultan M; Mohamed, Sumeia M; Clark, Sara M; Nason, Jeffrey A; Wu, Ying Xing

2015-01-01

Previous studies of compatibility of calcium chloride (CaCl2) and phosphates have not included particle counts in the range specified by the United States Pharmacopeia. Micro-flow imaging techniques have been shown to be comparable to light obscuration when determining particle count and size in pharmaceutical solutions. The purpose of this study was to do compatibility testing for parenteral nutrition (PN) solutions containing CaCl2 using dynamic light scattering and micro-flow imaging techniques. Solutions containing TrophAmine (Braun Medical Inc, Irvine, CA), CaCl2, and sodium phosphate (NaPhos) were compounded with and without cysteine. All solutions contained standard additives to neonatal PN solutions including dextrose, trace metals, and electrolytes. Control solutions contained no calcium or phosphate. Solutions were analyzed for particle size and particle count. Means of Z-average particle size and particle counts of controls were determined. Study solutions were compared to controls and United States Pharmacopeia (USP) Chapter 788 guidelines. The maximum amount of Phos that was compatible in solutions that contained at least 10 mmol/L of Ca in 2.5% amino acids (AA) was determined. Compatibility of these solutions was verified by performing analyses of 5 repeats of these solutions. Microscopic analyses of the repeats were also performed. Amounts of CaCl2 and NaPhos that were compatible in solutions containing 1.5%, 2%, 2.5%, and 3% AA were determined. The maximum amount of NaPhos that could be added to TrophAmine solutions of > = 2.5% AA containing at least 10 mmol/L of CaCl2 was 7.5 mmol/L. Adding 50 mg/dL of cysteine increased the amount of NaPhos that could be added to solutions containing 10 mmol/L of CaCl2 to 10 mmol/L. Calcium chloride can be added to neonatal PN solutions containing NaPhos in concentrations that can potentially provide an intravenous intake of adequate amounts of calcium and phosphorus.

Graphical Solution of Polynomial Equations

ERIC Educational Resources Information Center

Grishin, Anatole

2009-01-01

Graphing utilities, such as the ubiquitous graphing calculator, are often used in finding the approximate real roots of polynomial equations. In this paper the author offers a simple graphing technique that allows one to find all solutions of a polynomial equation (1) of arbitrary degree; (2) with real or complex coefficients; and (3) possessing…

Method of preparing mercury with an arbitrary isotopic distribution

DOEpatents

Grossman, Mark W.; George, William A.

1986-01-01

This invention provides for a process for preparing mercury with a predetermined, arbitrary, isotopic distribution. In one embodiment, different isotopic types of Hg.sub.2 Cl.sub.2, corresponding to the predetermined isotopic distribution of Hg desired, are placed in an electrolyte solution of HCl and H.sub.2 O. The resulting mercurous ions are then electrolytically plated onto a cathode wire producing mercury containing the predetermined isotopic distribution. In a similar fashion, Hg with a predetermined isotopic distribution is obtained from different isotopic types of HgO. In this embodiment, the HgO is dissolved in an electrolytic solution of glacial acetic acid and H.sub.2 O. The isotopic specific Hg is then electrolytically plated onto a cathode and then recovered.

Rapid calculation of acoustic fields from arbitrary continuous-wave sources.

PubMed

Treeby, Bradley E; Budisky, Jakub; Wise, Elliott S; Jaros, Jiri; Cox, B T

2018-01-01

A Green's function solution is derived for calculating the acoustic field generated by phased array transducers of arbitrary shape when driven by a single frequency continuous wave excitation with spatially varying amplitude and phase. The solution is based on the Green's function for the homogeneous wave equation expressed in the spatial frequency domain or k-space. The temporal convolution integral is solved analytically, and the remaining integrals are expressed in the form of the spatial Fourier transform. This allows the acoustic pressure for all spatial positions to be calculated in a single step using two fast Fourier transforms. The model is demonstrated through several numerical examples, including single element rectangular and spherically focused bowl transducers, and multi-element linear and hemispherical arrays.

Method of preparing mercury with an arbitrary isotopic distribution

DOEpatents

Grossman, M.W.; George, W.A.

1986-12-16

This invention provides for a process for preparing mercury with a predetermined, arbitrary, isotopic distribution. In one embodiment, different isotopic types of Hg[sub 2]Cl[sub 2], corresponding to the predetermined isotopic distribution of Hg desired, are placed in an electrolyte solution of HCl and H[sub 2]O. The resulting mercurous ions are then electrolytically plated onto a cathode wire producing mercury containing the predetermined isotopic distribution. In a similar fashion, Hg with a predetermined isotopic distribution is obtained from different isotopic types of HgO. In this embodiment, the HgO is dissolved in an electrolytic solution of glacial acetic acid and H[sub 2]O. The isotopic specific Hg is then electrolytically plated onto a cathode and then recovered. 1 fig.

Entanglement Concentration for Arbitrary Four-Photon Cluster State Assisted with Single Photons

NASA Astrophysics Data System (ADS)

Zhao, Sheng-Yang; Cai, Chun; Liu, Jiong; Zhou, Lan; Sheng, Yu-Bo

2016-02-01

We present an entanglement concentration protocol (ECP) to concentrate arbitrary four-photon less-entangled cluster state into maximally entangled cluster state. Different from other ECPs for cluster state, we only exploit the single photon as auxiliary, which makes this protocol feasible and economic. In our ECP, the concentrated maximally entangled state can be retained for further application and the discarded state can be reused for a higher success probability. This ECP works with the help of cross-Kerr nonlinearity and conventional photon detectors. This ECP may be useful in future one-way quantum computation.

Rotaxane liquid crystals with variable length: The effect of switching efficiency on the isotropic-nematic transition

NASA Astrophysics Data System (ADS)

He, Hao; Sevick, Edith M.; Williams, David R. M.

2018-04-01

We examine a solution of non-adaptive two-state rotaxane molecules which can switch from a short state of length L to a long state of length qL, using statistical thermodynamics. This molecular switching is externally driven and can result in an isotropic-nematic phase transition without altering temperature and concentration. Here we concentrate on the limitation imposed by switching inefficiency, i.e., on the case where molecular switching is not quantitative, leading to a solution of rotaxanes in different states. We present switching diagrams that can guide in the design of rotaxanes which affect a macroscopic phase change.

A General Computational Approach for Magnetohydrodynamic Flows Using the CFX Code: Buoyant Flow Through a Vertical Square Channel

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

Di Piazza, Ivan; Buehler, Leo

2000-09-15

The buoyancy-driven magnetoconvection in the cross section of an infinitely long vertical square duct is investigated numerically using the CFX code package. The implementation of a magnetohydrodynamic (MHD) problem in CFX is discussed, with particular reference to the Lorentz forces and the electric potential boundary conditions for arbitrary electrical conductivity of the walls. The method proposed is general and applies to arbitrary geometries with an arbitrary orientation of the magnetic field. Results for fully developed flow under various thermal boundary conditions are compared with asymptotic analytical solutions. The comparison shows that the asymptotic analysis is confirmed for highly conducting wallsmore » as high velocity jets occur at the side walls. For weakly conducting walls, the side layers become more conducting than the side walls, and strong electric currents flow within these layers parallel to the magnetic field. As a consequence, the velocity jets are suppressed, and the core solution is only corrected by the viscous forces near the wall. The implementation of MHD in CFX is achieved.« less

Universal scheme for finite-probability perfect transfer of arbitrary multispin states through spin chains

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

Man, Zhong-Xiao, E-mail: zxman@mail.qfnu.edu.cn; An, Nguyen Ba, E-mail: nban@iop.vast.ac.vn; Xia, Yun-Jie, E-mail: yjxia@mail.qfnu.edu.cn

In combination with the theories of open system and quantum recovering measurement, we propose a quantum state transfer scheme using spin chains by performing two sequential operations: a projective measurement on the spins of ‘environment’ followed by suitably designed quantum recovering measurements on the spins of interest. The scheme allows perfect transfer of arbitrary multispin states through multiple parallel spin chains with finite probability. Our scheme is universal in the sense that it is state-independent and applicable to any model possessing spin–spin interactions. We also present possible methods to implement the required measurements taking into account the current experimental technologies.more » As applications, we consider two typical models for which the probabilities of perfect state transfer are found to be reasonably high at optimally chosen moments during the time evolution. - Highlights: • Scheme that can achieve perfect quantum state transfer is devised. • The scheme is state-independent and applicable to any spin-interaction models. • The scheme allows perfect transfer of arbitrary multispin states. • Applications to two typical models are considered in detail.« less

Long-time predictions in nonlinear dynamics

NASA Technical Reports Server (NTRS)

Szebehely, V.

1980-01-01

It is known that nonintegrable dynamical systems do not allow precise predictions concerning their behavior for arbitrary long times. The available series solutions are not uniformly convergent according to Poincare's theorem and numerical integrations lose their meaningfulness after the elapse of arbitrary long times. Two approaches are the use of existing global integrals and statistical methods. This paper presents a generalized method along the first approach. As examples long-time predictions in the classical gravitational satellite and planetary problems are treated.

Dynamics of the Rydberg state population of slow highly charged ions impinging a solid surface at arbitrary collision geometry

NASA Astrophysics Data System (ADS)

Nedeljković, N. N.; Majkić, M. D.; Božanić, D. K.; Dojčilović, R. J.

2016-06-01

We consider the population dynamics of the intermediate Rydberg states of highly charged ions (core charge Z\\gg 1, principal quantum number {n}{{A}}\\gg 1) interacting with solid surfaces at arbitrary collision geometry. The recently developed resonant two-state vector model for the grazing incidence (2012 J. Phys. B: At. Mol. Opt. Phys. 45 215202) is extended to the quasi-resonant case and arbitrary angle of incidence. According to the model, the population probabilities depend both on the projectile parallel and perpendicular velocity components, in a complementary way. A cascade neutralization process for {{{Xe}}}Z+ ions, for Z=15{--}45, interacting with a conductive-surface is considered by taking into account the population dynamics. For an arbitrary collision geometry and given range of ionic velocities, a micro-staircase model for the simultaneous calculation of the kinetic energy gain and the charge state of the ion in front of the surface is proposed. The relevance of the obtained results for the explanation of the formation of nanostructures on solid surfaces by slow highly charged ions for normal incidence geometry is briefly discussed.

Habemus superstratum! A constructive proof of the existence of superstrata

DOE PAGES

Bena, Iosif; Giusto, Stefano; Russo, Rodolfo; ...

2015-05-21

Here, we construct the first example of a superstratum: a class of smooth horizonless supergravity solutions that are parameterized by arbitrary continuous functions of (at least) two variables and have the same charges as the supersymmetric D1-D5-P black hole. We work in Type IIB string theory on T 4 or K 3 and our solutions involve a subset of fields that can be described by a six-dimensional supergravity with two tensor multiplets. The solutions can thus be constructed using a linear structure, and we give an explicit recipe to start from a superposition of modes specified by an arbitrary functionmore » of two variables and impose regularity to obtain the full horizonless solutions in closed form. We also give the precise CFT description of these solutions and show that they are not dual to descendants of chiral primaries. They are thus much more general than all the known solutions whose CFT dual is precisely understood. Hence our construction represents a substantial step toward the ultimate goal of constructing the fully generic superstratum that can account for a finite fraction of the entropy of the three-charge black hole in the regime of parameters where the classical black hole solution exists.« less

Cosmological rotating black holes in five-dimensional fake supergravity

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

Nozawa, Masato; Maeda, Kei-ichi; Waseda Research Institute for Science and Engineering, Okubo 3-4-1, Shinjuku, Tokyo 169-8555

2011-01-15

In recent series of papers, we found an arbitrary dimensional, time-evolving, and spatially inhomogeneous solution in Einstein-Maxwell-dilaton gravity with particular couplings. Similar to the supersymmetric case, the solution can be arbitrarily superposed in spite of nontrivial time-dependence, since the metric is specified by a set of harmonic functions. When each harmonic has a single point source at the center, the solution describes a spherically symmetric black hole with regular Killing horizons and the spacetime approaches asymptotically to the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology. We discuss in this paper that in 5 dimensions, this equilibrium condition traces back to the first-order 'Killing spinor'more » equation in 'fake supergravity' coupled to arbitrary U(1) gauge fields and scalars. We present a five-dimensional, asymptotically FLRW, rotating black-hole solution admitting a nontrivial 'Killing spinor', which is a spinning generalization of our previous solution. We argue that the solution admits nondegenerate and rotating Killing horizons in contrast with the supersymmetric solutions. It is shown that the present pseudo-supersymmetric solution admits closed timelike curves around the central singularities. When only one harmonic is time-dependent, the solution oxidizes to 11 dimensions and realizes the dynamically intersecting M2/M2/M2-branes in a rotating Kasner universe. The Kaluza-Klein-type black holes are also discussed.« less

Propagating Qualitative Values Through Quantitative Equations

NASA Technical Reports Server (NTRS)

Kulkarni, Deepak

1992-01-01

In most practical problems where traditional numeric simulation is not adequate, one need to reason about a system with both qualitative and quantitative equations. In this paper, we address the problem of propagating qualitative values represented as interval values through quantitative equations. Previous research has produced exponential-time algorithms for approximate solution of the problem. These may not meet the stringent requirements of many real time applications. This paper advances the state of art by producing a linear-time algorithm that can propagate a qualitative value through a class of complex quantitative equations exactly and through arbitrary algebraic expressions approximately. The algorithm was found applicable to Space Shuttle Reaction Control System model.

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

Erol, V.; Netas Telecommunication Inc., Istanbul

Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known monotones for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. The study on these monotones has been a hot topic in quantum information [1-7] in order to understand the role of entanglement in this discipline. It can be observed that from any arbitrary quantum pure state a mixed state can obtained. A natural generalization of this observation would be to consider local operations classical communication (LOCC)more » transformations between general pure states of two parties. Although this question is a little more difficult, a complete solution has been developed using the mathematical framework of the majorization theory [8]. In this work, we analyze the relation between entanglement monotones concurrence and negativity with respect to majorization for general two-level quantum systems of two particles.« less

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

Larsen, E.W.

A class of Projected Discrete-Ordinates (PDO) methods is described for obtaining iterative solutions of discrete-ordinates problems with convergence rates comparable to those observed using Diffusion Synthetic Acceleration (DSA). The spatially discretized PDO solutions are generally not equal to the DSA solutions, but unlike DSA, which requires great care in the use of spatial discretizations to preserve stability, the PDO solutions remain stable and rapidly convergent with essentially arbitrary spatial discretizations. Numerical results are presented which illustrate the rapid convergence and the accuracy of solutions obtained using PDO methods with commonplace differencing methods.

Exact traveling soliton solutions for the generalized Benjamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Boudoue Hubert, Malwe; Kudryashov, Nikolai A.; Justin, Mibaile; Abbagari, Souleymanou; Betchewe, Gambo; Doka, Serge Y.

2018-03-01

In this paper, we investigate the generalized Benjamin-Bona-Mahony equation which better describes long waves with arbitrary power-law nonlinearity. As a result, we obtain exact travelling wave soliton solutions, such as anti-kink soliton solution, bright soliton solution, dark soliton solution and periodic solution. These solutions have many free parameters such that they may be used to simulate many experimental situations. The main contribution, in this work, is to not apply the computer codes for construction of exact solutions and not consider the integration constants as zero, because they give all variants for solutions.

An isotherm-based thermodynamic model of multicomponent aqueous solutions, applicable over the entire concentration range.

PubMed

Dutcher, Cari S; Ge, Xinlei; Wexler, Anthony S; Clegg, Simon L

2013-04-18

In previous studies (Dutcher et al. J. Phys. Chem. C 2011, 115, 16474-16487; 2012, 116, 1850-1864), we derived equations for the Gibbs energy, solvent and solute activities, and solute concentrations in multicomponent liquid mixtures, based upon expressions for adsorption isotherms that include arbitrary numbers of hydration layers on each solute. In this work, the long-range electrostatic interactions that dominate in dilute solutions are added to the Gibbs energy expression, thus extending the range of concentrations for which the model can be used from pure liquid solute(s) to infinite dilution in the solvent, water. An equation for the conversion of the reference state for solute activity coefficients to infinite dilution in water has been derived. A number of simplifications are identified, notably the equivalence of the sorption site parameters r and the stoichiometric coefficients of the solutes, resulting in a reduction in the number of model parameters. Solute concentrations in mixtures conform to a modified Zdanovskii-Stokes-Robinson mixing rule, and solute activity coefficients to a modified McKay-Perring relation, when the effects of the long-range (Debye-Hückel) term in the equations are taken into account. Practical applications of the equations to osmotic and activity coefficients of pure aqueous electrolyte solutions and mixtures show both satisfactory accuracy from low to high concentrations, together with a thermodynamically reasonable extrapolation (beyond the range of measurements) to extreme concentration and to the pure liquid solute(s).

General Lagrangian formulation for higher spin fields with arbitrary index symmetry. 2. Fermionic fields

NASA Astrophysics Data System (ADS)

Reshetnyak, A.

2013-04-01

We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having k rows, on a basis of the BRST-BFV approach suggested for bosonic fields in our first article [I.L. Buchbinder, A. Reshetnyak, Nucl. Phys. B 862 (2012) 270, arXiv:1110.5044 [hep-th

Two-Step Deterministic Remote Preparation of an Arbitrary Quantum State

NASA Astrophysics Data System (ADS)

Wang, Mei-Yu; Yan, Feng-Li

2010-11-01

We present a two-step deterministic remote state preparation protocol for an arbitrary quhit with the aid of a three-particle Greenberger—Horne—Zeilinger state. Generalization of this protocol for higher-dimensional Hilbert space systems among three parties is also given. We show that only single-particle von Neumann measurements, local operations, and classical communication are necessary. Moreover, since the overall information of the quantum state can be divided into two different pieces, which may be at different locations, this protocol may be useful in the quantum information field.

Application of modern control theory to the design of optimum aircraft controllers

NASA Technical Reports Server (NTRS)

Power, L. J.

1973-01-01

The synthesis procedure presented is based on the solution of the output regulator problem of linear optimal control theory for time-invariant systems. By this technique, solution of the matrix Riccati equation leads to a constant linear feedback control law for an output regulator which will maintain a plant in a particular equilibrium condition in the presence of impulse disturbances. Two simple algorithms are presented that can be used in an automatic synthesis procedure for the design of maneuverable output regulators requiring only selected state variables for feedback. The first algorithm is for the construction of optimal feedforward control laws that can be superimposed upon a Kalman output regulator and that will drive the output of a plant to a desired constant value on command. The second algorithm is for the construction of optimal Luenberger observers that can be used to obtain feedback control laws for the output regulator requiring measurement of only part of the state vector. This algorithm constructs observers which have minimum response time under the constraint that the magnitude of the gains in the observer filter be less than some arbitrary limit.

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

PubMed

Otevrel, Marek; Klepárník, Karel

2002-10-01

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

Late time acceleration of the 3-space in a higher dimensional steady state universe in dilaton gravity

NASA Astrophysics Data System (ADS)

Akarsu, Özgür; Dereli, Tekin

2013-02-01

We present cosmological solutions for (1+3+n)-dimensional steady state universe in dilaton gravity with an arbitrary dilaton coupling constant w and exponential dilaton self-interaction potentials in the string frame. We focus particularly on the class in which the 3-space expands with a time varying deceleration parameter. We discuss the number of the internal dimensions and the value of the dilaton coupling constant to determine the cases that are consistent with the observed universe and the primordial nucleosynthesis. The 3-space starts with a decelerated expansion rate and evolves into accelerated expansion phase subject to the values of w and n, but ends with a Big Rip in all cases. We discuss the cosmological evolution in further detail for the cases w = 1 and w = ½ that permit exact solutions. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the internal dimensions and thinks that the conventional general relativity is valid at cosmological scales.

Dynamics of cosmic strings with higher-dimensional windings

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

Yamauchi, Daisuke; Lake, Matthew J.; Thailand Center of Excellence in Physics, Ministry of Education,Bangkok 10400

2015-06-11

We consider F-strings with arbitrary configurations in the Minkowski directions of a higher-dimensional spacetime, which also wrap and spin around S{sup 1} subcycles of constant radius in an arbitrary internal manifold, and determine the relation between the higher-dimensional and the effective four-dimensional quantities that govern the string dynamics. We show that, for any such configuration, the motion of the windings in the compact space may render the string effectively tensionless from a four-dimensional perspective, so that it remains static with respect to the large dimensions. Such a critical configuration occurs when (locally) exactly half the square of the string lengthmore » lies in the large dimensions and half lies in the compact space. The critical solution is then seen to arise as a special case, in which the wavelength of the windings is equal to their circumference. As examples, long straight strings and circular loops are considered in detail, and the solutions to the equations of motion that satisfy the tensionless condition are presented. These solutions are then generalized to planar loops and arbitrary three-dimensional configurations. Under the process of dimensional reduction, in which higher-dimensional motion is equivalent to an effective worldsheet current (giving rise to a conserved charge), this phenomenon may be seen as the analogue of the tensionless condition which arises for superconducting and chiral-current carrying cosmic strings.« less

Dynamics of cosmic strings with higher-dimensional windings

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

Yamauchi, Daisuke; Lake, Matthew J., E-mail: yamauchi@resceu.s.u-tokyo.ac.jp, E-mail: matthewj@nu.ac.th

2015-06-01

We consider F-strings with arbitrary configurations in the Minkowski directions of a higher-dimensional spacetime, which also wrap and spin around S{sup 1} subcycles of constant radius in an arbitrary internal manifold, and determine the relation between the higher-dimensional and the effective four-dimensional quantities that govern the string dynamics. We show that, for any such configuration, the motion of the windings in the compact space may render the string effectively tensionless from a four-dimensional perspective, so that it remains static with respect to the large dimensions. Such a critical configuration occurs when (locally) exactly half the square of the string lengthmore » lies in the large dimensions and half lies in the compact space. The critical solution is then seen to arise as a special case, in which the wavelength of the windings is equal to their circumference. As examples, long straight strings and circular loops are considered in detail, and the solutions to the equations of motion that satisfy the tensionless condition are presented. These solutions are then generalized to planar loops and arbitrary three-dimensional configurations. Under the process of dimensional reduction, in which higher-dimensional motion is equivalent to an effective worldsheet current (giving rise to a conserved charge), this phenomenon may be seen as the analogue of the tensionless condition which arises for superconducting and chiral-current carrying cosmic strings.« less

Phases of higher spin black holes: Hawking-Page, transitions between black holes, and a critical point

NASA Astrophysics Data System (ADS)

Bañados, Máximo; Düring, Gustavo; Faraggi, Alberto; Reyes, Ignacio A.

2017-08-01

We study the thermodynamic phase diagram of three-dimensional s l (N ;R ) higher spin black holes. By analyzing the semiclassical partition function we uncover a rich structure that includes Hawking-Page transitions to the AdS3 vacuum, first order phase transitions among black hole states, and a second order critical point. Our analysis is explicit for N =4 but we extrapolate some of our conclusions to arbitrary N . In particular, we argue that even N is stable in the ensemble under consideration but odd N is not.

Analysis of high-aspect-ratio jet-flap wings of arbitrary geometry

NASA Technical Reports Server (NTRS)

Lissaman, P. B. S.

1973-01-01

An analytical technique to compute the performance of an arbitrary jet-flapped wing is developed. The solution technique is based on the method of Maskell and Spence in which the well-known lifting-line approach is coupled with an auxiliary equation providing the extra function needed in jet-flap theory. The present method is generalized to handle straight, uncambered wings of arbitrary planform, twist, and blowing (including unsymmetrical cases). An analytical procedure is developed for continuous variations in the above geometric data with special functions to exactly treat discontinuities in any of the geometric and blowing data. A rational theory for the effect of finite wing thickness is introduced as well as simplified concepts of effective aspect ratio for rapid estimation of performance.

Discriminatory Solutions for (n,n-2)-Games.

DTIC Science & Technology

An ( n ,m)-game is an n -person game in which all coalitions with less than m players are not vital. A p-discriminatory solution to a game is a von...for an arbitrary ( n , n -2)-game to have a k-discriminatory solution. These conditions are used to characterize all 2-discriminatory solutions for 4...person games, and for the simple ( n , n -2)-games in which all coalitions with at least n -2 players are winning coalitions. (Author)

New solutions for steady bubbles in a Hele-Shaw cell

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

Tanveer, S.

1987-03-01

Exact solutions are presented for steadily moving bubbles in a Hele--Shaw cell when the effect of surface tension is neglected. These solutions form a three-parameter family. For specified area, both the speed of the bubble and the distance of its centroid from the channel centerline remain arbitrary when surface tension is ignored. However, numerical evidence suggests that this twofold arbitrariness is removed by the effect of surface tension, i.e., for given bubble area and surface tension, solutions exist only when the bubble velocity and the centroid distance from the channel centerline attain one or more isolated values. From a limitedmore » numerical search, no nonsymmetric solutions could be found; however, a branch of symmetric bubble solutions that was not found in earlier work was found. This branch corresponds to one of the Romero-Vanden-Broeck branch of finger solutions when the bubble size is large. A new procedure for numerical calculations of bubble solutions in the presence of surface tension is presented and is found to work very well for reasonably large bubbles, unlike the previous method of Tanveer (Phys. Fluids 29, 3537 (1986)). The precise power law dependence of bubble velocity on surface tension for small surface tension is explored for bubbles of different area. Agreement is noted with recent analytical results for a finger.« less

TranAir: A full-potential, solution-adaptive, rectangular grid code for predicting subsonic, transonic, and supersonic flows about arbitrary configurations. User's manual

NASA Technical Reports Server (NTRS)

Johnson, F. T.; Samant, S. S.; Bieterman, M. B.; Melvin, R. G.; Young, D. P.; Bussoletti, J. E.; Hilmes, C. L.

1992-01-01

The TranAir computer program calculates transonic flow about arbitrary configurations at subsonic, transonic, and supersonic freestream Mach numbers. TranAir solves the nonlinear full potential equations subject to a variety of boundary conditions modeling wakes, inlets, exhausts, porous walls, and impermeable surfaces. Regions with different total temperature and pressure can be represented. The user's manual describes how to run the TranAir program and its graphical support programs.

Numerical and experimental study of curved and planar frequency selective surfaces with arbitrary illumination. M.S. Thesis - Maryland Univ., 1989

NASA Technical Reports Server (NTRS)

Caroglanian, Armen

1991-01-01

A frequency selective surface (FSS) composed of apertures in a metallic sheet is known as the inductive FSS. The infinite inductive FSS theory is derived and the aperture fields are solved by a spectral domain formulation with method of moments solution. Both full domain and subsectional basis functions are studied. A locally planar technique (LPT) is used to determine the forward scattered field from a generally shaped inductive FSS with arbitrary illumination.

A cylindrical shell with an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1982-01-01

The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system of five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented.

Improved algorithms and methods for room sound-field prediction by acoustical radiosity in arbitrary polyhedral rooms.

PubMed

Nosal, Eva-Marie; Hodgson, Murray; Ashdown, Ian

2004-08-01

This paper explores acoustical (or time-dependent) radiosity--a geometrical-acoustics sound-field prediction method that assumes diffuse surface reflection. The literature of acoustical radiosity is briefly reviewed and the advantages and disadvantages of the method are discussed. A discrete form of the integral equation that results from meshing the enclosure boundaries into patches is presented and used in a discrete-time algorithm. Furthermore, an averaging technique is used to reduce computational requirements. To generalize to nonrectangular rooms, a spherical-triangle method is proposed as a means of evaluating the integrals over solid angles that appear in the discrete form of the integral equation. The evaluation of form factors, which also appear in the numerical solution, is discussed for rectangular and nonrectangular rooms. This algorithm and associated methods are validated by comparison of the steady-state predictions for a spherical enclosure to analytical solutions.

Improved algorithms and methods for room sound-field prediction by acoustical radiosity in arbitrary polyhedral rooms

NASA Astrophysics Data System (ADS)

Nosal, Eva-Marie; Hodgson, Murray; Ashdown, Ian

2004-08-01

This paper explores acoustical (or time-dependent) radiosity-a geometrical-acoustics sound-field prediction method that assumes diffuse surface reflection. The literature of acoustical radiosity is briefly reviewed and the advantages and disadvantages of the method are discussed. A discrete form of the integral equation that results from meshing the enclosure boundaries into patches is presented and used in a discrete-time algorithm. Furthermore, an averaging technique is used to reduce computational requirements. To generalize to nonrectangular rooms, a spherical-triangle method is proposed as a means of evaluating the integrals over solid angles that appear in the discrete form of the integral equation. The evaluation of form factors, which also appear in the numerical solution, is discussed for rectangular and nonrectangular rooms. This algorithm and associated methods are validated by comparison of the steady-state predictions for a spherical enclosure to analytical solutions.

Exact PDF equations and closure approximations for advective-reactive transport

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

Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.

2013-06-01

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recentlymore » proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.« less

Quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation.

PubMed

D'Ariano, G M; Lo Presti, P

2001-05-07

Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. We present a general method based on quantum tomography for measuring experimentally the matrix elements of an arbitrary quantum operation. As input the method needs only a single entangled state. The feasibility of the technique for the electromagnetic field is shown, and the experimental setup is illustrated based on homodyne tomography of a twin beam.

Exact solutions in oscillating airfoil theory

NASA Technical Reports Server (NTRS)

Williams, M. H.

1977-01-01

A result obtained by Williams (1977) for two-dimensional airfoils oscillating in an arbitrary subsonic parallel flowfield is reformulated to show that the pressure distribution induced by any deformation can be construed from the particular solutions for heaving and pitching motions. Specific formulas are presented for an oscillating control surface with a sealed gap.

Propagation of a Toroidal Magnetic Cloud through the Inner Heliosphere

NASA Astrophysics Data System (ADS)

Romashets, Eugene; Vandas, Marek

2003-09-01

An analytical solution for a potential magnetic field with arbitrary intensity around a toroidal magnetic cloud has been found. The background external field may have a gradient. The solution is used for calculation of magnetic cloud propagation. Obtained velocity profiles show a good agreement with in situ observations near the Earth's orbit.

Testing subleading multiple soft graviton theorem for CHY prescription

NASA Astrophysics Data System (ADS)

Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay

2018-01-01

In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.

Permeability Sensitivity Functions and Rapid Simulation of Hydraulic-Testing Measurements Using Perturbation Theory

NASA Astrophysics Data System (ADS)

Escobar Gómez, J. D.; Torres-Verdín, C.

2018-03-01

Single-well pressure-diffusion simulators enable improved quantitative understanding of hydraulic-testing measurements in the presence of arbitrary spatial variations of rock properties. Simulators of this type implement robust numerical algorithms which are often computationally expensive, thereby making the solution of the forward modeling problem onerous and inefficient. We introduce a time-domain perturbation theory for anisotropic permeable media to efficiently and accurately approximate the transient pressure response of spatially complex aquifers. Although theoretically valid for any spatially dependent rock/fluid property, our single-phase flow study emphasizes arbitrary spatial variations of permeability and anisotropy, which constitute key objectives of hydraulic-testing operations. Contrary to time-honored techniques, the perturbation method invokes pressure-flow deconvolution to compute the background medium's permeability sensitivity function (PSF) with a single numerical simulation run. Subsequently, the first-order term of the perturbed solution is obtained by solving an integral equation that weighs the spatial variations of permeability with the spatial-dependent and time-dependent PSF. Finally, discrete convolution transforms the constant-flow approximation to arbitrary multirate conditions. Multidimensional numerical simulation studies for a wide range of single-well field conditions indicate that perturbed solutions can be computed in less than a few CPU seconds with relative errors in pressure of <5%, corresponding to perturbations in background permeability of up to two orders of magnitude. Our work confirms that the proposed joint perturbation-convolution (JPC) method is an efficient alternative to analytical and numerical solutions for accurate modeling of pressure-diffusion phenomena induced by Neumann or Dirichlet boundary conditions.

Experimental solution for scattered imaging of the interference of plasmonic and photonic mode waves launched by metal nano-slits.

PubMed

Li, Xing; Gao, Yaru; Jiang, Shuna; Ma, Li; Liu, Chunxiang; Cheng, Chuanfu

2015-02-09

Using an L-shaped metal nanoslit to generate waves of the pure photonic and plasmonic modes simultaneously, we perform an experimental solution for the scattered imaging of the interference of the two waves. From the fringe data of interference, the amplitudes and the wavevector components of the two waves are obtained. The initial phases of the two waves are obtained from the phase map reconstructed with the interference of the scattered image and the reference wave in the interferometer. The difference in the wavevector components gives rise to an additional phase delay. We introduce the scattering theory under Kirchhoff's approximation to metal slit regime and explain the wavevector difference reasonably. The solution of the quantities is a comprehensive reflection of excitation, scattering and interference of the two waves. By decomposing the polarized incident field with respect to the slit element, the scattered image produced by slit of arbitrary shape can be solved with the nanoscale Huygens-Fresnel principle. This is demonstrated by the experimental intensity pattern and phase map produced by a ring-slit and its consistency with the calculated results.

Criterion and flexibility of operation difficulty for perfect teleportation of arbitrary n-qutrit state with ( n: n)-qutrit pure state

NASA Astrophysics Data System (ADS)

Zhang, ZiYun; Liu, YiMin; Zhang, Wen; Zhang, ZhanJun

2011-08-01

Under the preconditions that a ( n: n)-qutrit pure state is taken as the quantum channel to teleport an arbitrary n-qutrit state and the sender is able to perform generalized-Bell-state measurements and publish the results, the necessary transformation operation in the receiver's site is worked out in terms of the technique of swapping states. A criterion on whether such quantum channel can be utilized for perfect teleportation is derived by virtue of the unitarity of the resultant transformation operator. Moreover, the flexibility between the measurement difficulty and the reconstruction difficulty is shown and discussed.

Dust ring formation due to sublimation of dust grains drifting radially inward by the Poynting-Robertson drag: An analytical model

NASA Astrophysics Data System (ADS)

Kobayashi, Hiroshi; Watanabe, Sei-ichiro; Kimura, Hiroshi; Yamamoto, Tetsuo

2009-05-01

Dust particles exposed to the stellar radiation and wind drift radially inward by the Poynting-Robertson (P-R) drag and pile up at the zone where they begin to sublime substantially. The reason they pile up or form a ring is that their inward drifts due to the P-R drag are suppressed by stellar radiation pressure when the ratio of radiation pressure to stellar gravity on them increases during their sublimation phases. We present analytic solutions to the orbital and mass evolution of such subliming dust particles, and find their drift velocities at the pileup zone are almost independent of their initial semimajor axes and masses. We derive analytically an enhancement factor of the number density of the particles at the outer edge of the sublimation zone from the solutions. We show that the formula of the enhancement factor reproduces well numerical simulations in the previous studies. The enhancement factor for spherical dust particles of silicate and carbon extends from 3 to more than 20 at stellar luminosities L=0.8-500L, where L is solar luminosity. Although the enhancement factor for fluffy dust particles is smaller than that for spherical particles, sublimating particles inevitably form a dust ring as long as their masses decrease faster than their surface areas during sublimation. The formulation is applicable to dust ring formation for arbitrary shape and material of dust in dust-debris disks as well as in the Solar System.

Stable and Spectrally Accurate Schemes for the Navier-Stokes Equations

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

Jia, Jun; Liu, Jie

2011-01-01

In this paper, we present an accurate, efficient and stable numerical method for the incompressible Navier-Stokes equations (NSEs). The method is based on (1) an equivalent pressure Poisson equation formulation of the NSE with proper pressure boundary conditions, which facilitates the design of high-order and stable numerical methods, and (2) the Krylov deferred correction (KDC) accelerated method of lines transpose (mbox MoL{sup T}), which is very stable, efficient, and of arbitrary order in time. Numerical tests with known exact solutions in three dimensions show that the new method is spectrally accurate in time, and a numerical order of convergence 9more » was observed. Two-dimensional computational results of flow past a cylinder and flow in a bifurcated tube are also reported.« less

Thermal Analysis of Antenna Structures. Part 2: Panel Temperature Distribution

NASA Technical Reports Server (NTRS)

Schonfeld, D.; Lansing, F. L.

1983-01-01

This article is the second in a series that analyzes the temperature distribution in microwave antennas. An analytical solution in a series form is obtained for the temperature distribution in a flat plate analogous to an antenna surface panel under arbitrary temperature and boundary conditions. The solution includes the effects of radiation and air convection from the plate. Good agreement is obtained between the numerical and analytical solutions.

Convergence analysis of sliding mode trajectories in multi-objective neural networks learning.

PubMed

Costa, Marcelo Azevedo; Braga, Antonio Padua; de Menezes, Benjamin Rodrigues

2012-09-01

The Pareto-optimality concept is used in this paper in order to represent a constrained set of solutions that are able to trade-off the two main objective functions involved in neural networks supervised learning: data-set error and network complexity. The neural network is described as a dynamic system having error and complexity as its state variables and learning is presented as a process of controlling a learning trajectory in the resulting state space. In order to control the trajectories, sliding mode dynamics is imposed to the network. It is shown that arbitrary learning trajectories can be achieved by maintaining the sliding mode gains within their convergence intervals. Formal proofs of convergence conditions are therefore presented. The concept of trajectory learning presented in this paper goes further beyond the selection of a final state in the Pareto set, since it can be reached through different trajectories and states in the trajectory can be assessed individually against an additional objective function. Copyright © 2012 Elsevier Ltd. All rights reserved.

Non-neutral plasma diode in the presence of a transverse magnetic field

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

Pramanik, Sourav; Chakrabarti, Nikhil; Kuznetsov, V. I.

An analytical study of the plasma states in non-neutral plasma diodes in the presence of an external transverse magnetic field is presented for an arbitrary neutralization parameter γ. Considerations are restricted to the regime where no electrons are turned around by the magnetic field. The emitter electric field strength E{sub 0} is used as a characteristic function to investigate the existence of solutions depending on the diode length, the applied voltage, the neutralization parameter, and the magnetic field strength. The potential distribution has a wave form for small magnitudes of the external magnetic field, as well as for the casemore » when magnetic field is absent. A new family of solutions appears along with the Bursian ones. On the other hand, as the Larmor radius becomes comparable with the beam Debye length, oscillations in the potential disappear, and only the Bursian branches remain. Unlike the vacuum diode, there are steady state solutions for the negative values of the emitter field strength. As the neutralization parameter (γ) increases, the emitter field strength relating to the SCL (space charge limit) bifurcation point diminishes, and at γ > 1, the value of the emitter's electric field strength at the space charge limit (E{sub 0,SCL}) turns out to be negative.« less

An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks.

PubMed

Salis, Howard; Kaznessis, Yiannis N

2005-12-01

Stochastic chemical kinetics more accurately describes the dynamics of "small" chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.

Analysis of energy states in modulation doped multiquantum well heterostructures

NASA Technical Reports Server (NTRS)

Ji, G.; Henderson, T.; Peng, C. K.; Huang, D.; Morkoc, H.

1990-01-01

A precise and effective numerical procedure to model the band diagram of modulation doped multiquantum well heterostructures is presented. This method is based on a self-consistent iterative solution of the Schroedinger equation and the Poisson equation. It can be used rather easily in any arbitrary modulation-doped structure. In addition to confined energy subbands, the unconfined states can be calculated as well. Examples on realistic device structures are given to demonstrate capabilities of this procedure. The numerical results are in good agreement with experiments. With the aid of this method the transitions involving both the confined and unconfined conduction subbands in a modulation doped AlGaAs/GaAs superlattice, and in a strained layer InGaAs/GaAs superlattice are identified. These results represent the first observation of unconfined transitions in modulation doped multiquantum well structures.

Quantum lattice model solver HΦ

NASA Astrophysics Data System (ADS)

Kawamura, Mitsuaki; Yoshimi, Kazuyoshi; Misawa, Takahiro; Yamaji, Youhei; Todo, Synge; Kawashima, Naoki

2017-08-01

HΦ [aitch-phi ] is a program package based on the Lanczos-type eigenvalue solution applicable to a broad range of quantum lattice models, i.e., arbitrary quantum lattice models with two-body interactions, including the Heisenberg model, the Kitaev model, the Hubbard model and the Kondo-lattice model. While it works well on PCs and PC-clusters, HΦ also runs efficiently on massively parallel computers, which considerably extends the tractable range of the system size. In addition, unlike most existing packages, HΦ supports finite-temperature calculations through the method of thermal pure quantum (TPQ) states. In this paper, we explain theoretical background and user-interface of HΦ. We also show the benchmark results of HΦ on supercomputers such as the K computer at RIKEN Advanced Institute for Computational Science (AICS) and SGI ICE XA (Sekirei) at the Institute for the Solid State Physics (ISSP).

Quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi4 model

NASA Astrophysics Data System (ADS)

Kwiatkowski, G.; Leble, S.

2014-03-01

Analytical form of quantum corrections to quasi-periodic solution of Sine-Gordon model and periodic solution of phi4 model is obtained through zeta function regularisation with account of all rest variables of a d-dimensional theory. Qualitative dependence of quantum corrections on parameters of the classical systems is also evaluated for a much broader class of potentials u(x) = b2f(bx) + C with b and C as arbitrary real constants.

Two-step entanglement concentration for arbitrary electronic cluster state

NASA Astrophysics Data System (ADS)

Zhao, Sheng-Yang; Liu, Jiong; Zhou, Lan; Sheng, Yu-Bo

2013-12-01

We present an efficient protocol for concentrating an arbitrary four-electron less-entangled cluster state into a maximally entangled cluster state. As a two-step entanglement concentration protocol (ECP), it only needs one pair of less-entangled cluster state, which makes this ECP more economical. With the help of electronic polarization beam splitter (PBS) and the charge detection, the whole concentration process is essentially the quantum nondemolition (QND) measurement. Therefore, the concentrated maximally entangled state can be remained for further application. Moreover, the discarded terms in some traditional ECPs can be reused to obtain a high success probability. It is feasible and useful in current one-way quantum computation.

'Footballs', conical singularities, and the Liouville equation

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

Redi, Michele

We generalize the football shaped extra dimensions scenario to an arbitrary number of branes. The problem is related to the solution of the Liouville equation with singularities, and explicit solutions are presented for the case of three branes. The tensions of the branes do not need to be tuned with each other but only satisfy mild global constraints.

Approach to solution of coupled heat transfer problem on the surface of hypersonic vehicle of arbitrary shape

NASA Astrophysics Data System (ADS)

Bocharov, A. N.; Bityurin, V. A.; Golovin, N. N.; Evstigneev, N. M.; Petrovskiy, V. P.; Ryabkov, O. I.; Teplyakov, I. O.; Shustov, A. A.; Solomonov, Yu S.; Fortov, V. E.

2016-11-01

In this paper, an approach to solve conjugate heat- and mass-transfer problems is considered to be applied to hypersonic vehicle surface of arbitrary shape. The approach under developing should satisfy the following demands. (i) The surface of the body of interest may have arbitrary geometrical shape. (ii) The shape of the body can change during calculation. (iii) The flight characteristics may vary in a wide range, specifically flight altitude, free-stream Mach number, angle-of-attack, etc. (iv) The approach should be realized with using the high-performance-computing (HPC) technologies. The approach is based on coupled solution of 3D unsteady hypersonic flow equations and 3D unsteady heat conductance problem for the thick wall. Iterative process is applied to account for ablation of wall material and, consequently, mass injection from the surface and changes in the surface shape. While iterations, unstructured computational grids both in the flow region and within the wall interior are adapted to the current geometry and flow conditions. The flow computations are done on HPC platform and are most time-consuming part of the whole problem, while heat conductance problem can be solved on many kinds of computers.

Estimation of Image Sensor Fill Factor Using a Single Arbitrary Image

PubMed Central

Wen, Wei; Khatibi, Siamak

2017-01-01

Achieving a high fill factor is a bottleneck problem for capturing high-quality images. There are hardware and software solutions to overcome this problem. In the solutions, the fill factor is known. However, this is an industrial secrecy by most image sensor manufacturers due to its direct effect on the assessment of the sensor quality. In this paper, we propose a method to estimate the fill factor of a camera sensor from an arbitrary single image. The virtual response function of the imaging process and sensor irradiance are estimated from the generation of virtual images. Then the global intensity values of the virtual images are obtained, which are the result of fusing the virtual images into a single, high dynamic range radiance map. A non-linear function is inferred from the original and global intensity values of the virtual images. The fill factor is estimated by the conditional minimum of the inferred function. The method is verified using images of two datasets. The results show that our method estimates the fill factor correctly with significant stability and accuracy from one single arbitrary image according to the low standard deviation of the estimated fill factors from each of images and for each camera. PMID:28335459

Exact Local Correlations and Full Counting Statistics for Arbitrary States of the One-Dimensional Interacting Bose Gas

NASA Astrophysics Data System (ADS)

Bastianello, Alvise; Piroli, Lorenzo; Calabrese, Pasquale

2018-05-01

We derive exact analytic expressions for the n -body local correlations in the one-dimensional Bose gas with contact repulsive interactions (Lieb-Liniger model) in the thermodynamic limit. Our results are valid for arbitrary states of the model, including ground and thermal states, stationary states after a quantum quench, and nonequilibrium steady states arising in transport settings. Calculations for these states are explicitly presented and physical consequences are critically discussed. We also show that the n -body local correlations are directly related to the full counting statistics for the particle-number fluctuations in a short interval, for which we provide an explicit analytic result.

An optical fusion gate for W-states

NASA Astrophysics Data System (ADS)

Özdemir, Ş. K.; Matsunaga, E.; Tashima, T.; Yamamoto, T.; Koashi, M.; Imoto, N.

2011-10-01

We introduce a simple optical gate to fuse arbitrary-size polarization entangled W-states to prepare larger W-states. The gate requires a polarizing beam splitter (PBS), a half-wave plate (HWP) and two photon detectors. We study, numerically and analytically, the necessary resource consumption for preparing larger W-states by fusing smaller ones with the proposed fusion gate. We show analytically that resource requirement scales at most sub-exponentially with the increasing size of the state to be prepared. We numerically determine the resource cost for fusion without recycling where W-states of arbitrary size can be optimally prepared. Moreover, we introduce another strategy that is based on recycling and outperforms the optimal strategy for the non-recycling case.

General Potential Theory of Arbitrary Wing Sections

NASA Technical Reports Server (NTRS)

Theodorsen, T.; Garrick, I. E.

1979-01-01

The problem of determining the two dimensional potential flow around wing sections of any shape is examined. The problem is condensed into the compact form of an integral equation capable of yielding numerical solutions by a direct process. An attempt is made to analyze and coordinate the results of earlier studies relating to properties of wing sections. The existing approximate theory of thin wing sections and the Joukowski theory with its numerous generalizations are reduced to special cases of the general theory of arbitrary sections, permitting a clearer perspective of the entire field. The method which permits the determination of the velocity at any point of an arbitrary section and the associated lift and moments is described. The method is also discussed in terms for developing new shapes of preassigned aerodynamical properties.

Monogamy relations of concurrence for any dimensional quantum systems

NASA Astrophysics Data System (ADS)

Zhu, Xue-Na; Li-Jost, Xianqing; Fei, Shao-Ming

2017-11-01

We study monogamy relations for arbitrary dimensional multipartite systems. Monogamy relations based on concurrence and concurrence of assistance for any dimensional m_1⊗ m_2⊗ \\cdots ⊗ mN quantum states are derived, which give rise to the restrictions on the entanglement distributions among the subsystems. Besides, we give the lower bound of concurrence for four-partite mixed states. The approach can be readily generalized to arbitrary multipartite systems.

Analytical solution for a class of network dynamics with mechanical and financial applications

NASA Astrophysics Data System (ADS)

Krejčí, P.; Lamba, H.; Melnik, S.; Rachinskii, D.

2014-09-01

We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set of states and there is no limit on the complexity of the network. The results provide both an efficient numerical method and the potential for accurate analytic approximation of the dynamics on such networks. As illustrative applications, we introduce a quasistatic mechanical model with objects interacting via frictional forces and a financial market model with avalanches and critical behavior that are generated by momentum trading strategies.

Contribution to the optimal shape design of two-dimensional internal flows with embedded shocks

NASA Technical Reports Server (NTRS)

Iollo, Angelo; Salas, Manuel D.

1995-01-01

We explore the practicability of optimal shape design for flows modeled by the Euler equations. We define a functional whose minimum represents the optimality condition. The gradient of the functional with respect to the geometry is calculated with the Lagrange multipliers, which are determined by solving a co-state equation. The optimization problem is then examined by comparing the performance of several gradient-based optimization algorithms. In this formulation, the flow field can be computed to an arbitrary order of accuracy. Finally, some results for internal flows with embedded shocks are presented, including a case for which the solution to the inverse problem does not belong to the design space.

Surface curvature singularities of polytropic spheres in Palatini f (R ,T ) gravity

NASA Astrophysics Data System (ADS)

Barrientos O., José; Rubilar, Guillermo F.

2016-01-01

We consider Palatini f (R ,T ) gravity models, similar to those introduced by Harko et al. (2012), where the gravitational Lagrangian is given by an arbitrary function of the curvature scalar R and of the trace of the energy-momentum tensor T . Interior spherical static solutions are studied considering the model of matter given by a perfect fluid configuration and a polytropic equation of state. We analyze the curvature singularities found previously for Palatini f (R ) gravity and discuss the possibility to remove them in some particular f (R ,T ) models. We show that it is possible to construct a restricted family of models for which these singularities are not present.

Stability of the Nagaoka-type ferromagnetic state in a t2 g orbital system on a cubic lattice

NASA Astrophysics Data System (ADS)

Bobrow, Eric; Li, Yi

2018-04-01

We generalize the previous exact results of the Nagaoka-type itinerant ferromagnetic states in a three-dimensional t2 g orbital system to allow for multiple holes. The system is a simple cubic lattice with each site possessing dx y,dy z, and dx z orbitals, which allow two-dimensional hopping within each orbital plane. In the strong-coupling limit of U →∞ , the orbital-generalized Nagaoka ferromagnetic states are proved to be degenerate with the ground state in the thermodynamic limit when the hole number per orbital layer scales slower than L1/2. This result is valid for arbitrary values of the ferromagnetic Hund's coupling J >0 and interorbital repulsion V ≥0 . The stability of the Nagaoka-type state at finite electron densities with respect to a single spin flip is investigated. These results provide helpful guidance for studying the mechanism of itinerant ferromagnetism for the t2 g orbital materials.

Wave propagation in elastic and damped structures with stabilized negative-stiffness components

NASA Astrophysics Data System (ADS)

Drugan, W. J.

2017-09-01

Effects on wave propagation achievable by introduction of a negative-stiffness component are investigated via perhaps the simplest discrete repeating element that can remain stable in the component's presence. When the system is elastic, appropriate tuning of the stabilized component's negative stiffness introduces a no-pass zone theoretically extending from zero to an arbitrarily high frequency, tunable by a mass ratio adjustment. When the negative-stiffness component is tuned to the system's stability limit and a mass ratio is sufficiently small, the system restricts propagation to waves of approximately a single arbitrary frequency, adjustable by tuning the stiffness ratio of the positive-stiffness components. The elastic system's general solutions are closed-form and transparent. When damping is added, the general solutions are still closed-form, but so complex that they do not clearly display how the negative stiffness component affects the system's response and how it should best be tuned to achieve desired effects. Approximate solutions having these features are obtained via four perturbation analyses: one for long wavelengths; one for small damping; and two for small mass ratios. The long-wavelengths solution shows that appropriate tuning of the negative-stiffness component can prevent propagation of long-wavelength waves. The small damping solution shows that the zero-damping low-frequency no-pass zone remains, while waves that do propagate are highly damped when a mass ratio is made small. Finally, very interesting effects are achievable at the full system's stability limit. For small mass ratios, the wavelength range of waves prohibited from propagation can be adjusted, from all to none, by tuning the system's damping: When one mass ratio is small, all waves with wavelengths larger than an arbitrary damping-adjusted value can be prohibited from propagation, while when the inverse of this mass ratio is small, all waves with wavelengths outside an arbitrary single adjustable value or range of values can be prohibited from propagation. All of the approximate solutions' analytically-transparent predictions are confirmed by the exact solution. The conclusions are that a stabilized tuned negative-stiffness component greatly enhances control of wave propagation in a purely elastic system, and when adjustable damping is added, even further control is facilitated.

Asymptotically and exactly energy balanced augmented flux-ADER schemes with application to hyperbolic conservation laws with geometric source terms

NASA Astrophysics Data System (ADS)

Navas-Montilla, A.; Murillo, J.

2016-07-01

In this work, an arbitrary order HLL-type numerical scheme is constructed using the flux-ADER methodology. The proposed scheme is based on an augmented Derivative Riemann solver that was used for the first time in Navas-Montilla and Murillo (2015) [1]. Such solver, hereafter referred to as Flux-Source (FS) solver, was conceived as a high order extension of the augmented Roe solver and led to the generation of a novel numerical scheme called AR-ADER scheme. Here, we provide a general definition of the FS solver independently of the Riemann solver used in it. Moreover, a simplified version of the solver, referred to as Linearized-Flux-Source (LFS) solver, is presented. This novel version of the FS solver allows to compute the solution without requiring reconstruction of derivatives of the fluxes, nevertheless some drawbacks are evidenced. In contrast to other previously defined Derivative Riemann solvers, the proposed FS and LFS solvers take into account the presence of the source term in the resolution of the Derivative Riemann Problem (DRP), which is of particular interest when dealing with geometric source terms. When applied to the shallow water equations, the proposed HLLS-ADER and AR-ADER schemes can be constructed to fulfill the exactly well-balanced property, showing that an arbitrary quadrature of the integral of the source inside the cell does not ensure energy balanced solutions. As a result of this work, energy balanced flux-ADER schemes that provide the exact solution for steady cases and that converge to the exact solution with arbitrary order for transient cases are constructed.

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

Bozza, V.; Postiglione, A., E-mail: valboz@sa.infn.it, E-mail: postiglione@fis.uniroma3.it

The metric outside an isolated object made up of ordinary matter is bound to be the classical Schwarzschild vacuum solution of General Relativity. Nevertheless, some solutions are known (e.g. Morris-Thorne wormholes) that do not match Schwarzschild asymptotically. On a phenomenological point of view, gravitational lensing in metrics falling as 1/r{sup q} has recently attracted great interest. In this work, we explore the conditions on the source matter for constructing static spherically symmetric metrics exhibiting an arbitrary power-law as Newtonian limit. For such space-times we also derive the expressions of gravitational redshift and force on probe masses, which, together with lightmore » deflection, can be used in astrophysical searches of non-Schwarzschild objects made up of exotic matter. Interestingly, we prove that even a minimally coupled scalar field with a power-law potential can support non-Schwarzschild metrics with arbitrary asymptotic behaviour.« less

Computer program for calculating laminar, transitional, and turbulent boundary layers for a compressible axisymmetric flow

NASA Technical Reports Server (NTRS)

Albers, J. A.; Gregg, J. L.

1974-01-01

A finite-difference program is described for calculating the viscous compressible boundary layer flow over either planar or axisymmetric surfaces. The flow may be initially laminar and progress through a transitional zone to fully turbulent flow, or it may remain laminar, depending on the imposed boundary conditions, laws of viscosity, and numerical solution of the momentum and energy equations. The flow may also be forced into a turbulent flow at a chosen spot by the data input. The input may contain the factors of arbitrary Reynolds number, free-stream Mach number, free-stream turbulence, wall heating or cooling, longitudinal wall curvature, wall suction or blowing, and wall roughness. The solution may start from an initial Falkner-Skan similarity profile, an approximate equilibrium turbulent profile, or an initial arbitrary input profile.

Unidirectional Quantum Remote Control: Teleportation of Control-State

NASA Astrophysics Data System (ADS)

Zheng, Yi-Zhuang; Gu, Yong-Jian; Wu, Gui-Chu; Guo, Guang-Can

2003-08-01

We investigate the problem of teleportation of unitary operations by unidirectional control-state teleportation and propose a scheme called unidirectional quantum remote control. The scheme is based on the isomorphism between operation and state. It allows us to store a unitary operation in a control state, thereby teleportation of the unitary operation can be implemented by unidirectional teleportation of the control-state. We find that the probability of success for implementing an arbitrary unitary operation on arbitrary M-qubit state by unidirectional control-state teleportation is 4-M, and 2M ebits and 4M cbits are consumed in each teleportation. The project supported by the National Fundamental Research Programme (2001CB309300) and the Zhejiang Provincial Natural Science Foundation of China under Grant No. 102068

Numerical solutions of Navier-Stokes equations for a Butler wing

NASA Technical Reports Server (NTRS)

Abolhassani, J. S.; Tiwari, S. N.

1985-01-01

The flow field is simulated on the surface of a given delta wing (Butler wing) at zero incident in a uniform stream. The simulation is done by integrating a set of flow field equations. This set of equations governs the unsteady, viscous, compressible, heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. These equations are solved by the finite difference method, and results obtained for high-speed freestream conditions are compared with theoretical and experimental results. In this study, the Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallel-piped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDC VPS 32 computer.

Shallow-water sloshing in a moving vessel with variable cross-section and wetting-drying using an extension of George's well-balanced finite volume solver

NASA Astrophysics Data System (ADS)

Alemi Ardakani, Hamid; Bridges, Thomas J.; Turner, Matthew R.

2016-06-01

A class of augmented approximate Riemann solvers due to George (2008) [12] is extended to solve the shallow-water equations in a moving vessel with variable bottom topography and variable cross-section with wetting and drying. A class of Roe-type upwind solvers for the system of balance laws is derived which respects the steady-state solutions. The numerical solutions of the new adapted augmented f-wave solvers are validated against the Roe-type solvers. The theory is extended to solve the shallow-water flows in moving vessels with arbitrary cross-section with influx-efflux boundary conditions motivated by the shallow-water sloshing in the ocean wave energy converter (WEC) proposed by Offshore Wave Energy Ltd. (OWEL) [1]. A fractional step approach is used to handle the time-dependent forcing functions. The numerical solutions are compared to an extended new Roe-type solver for the system of balance laws with a time-dependent source function. The shallow-water sloshing finite volume solver can be coupled to a Runge-Kutta integrator for the vessel motion.

Volume integral equation for electromagnetic scattering: Rigorous derivation and analysis for a set of multilayered particles with piecewise-smooth boundaries in a passive host medium

NASA Astrophysics Data System (ADS)

Yurkin, Maxim A.; Mishchenko, Michael I.

2018-04-01

We present a general derivation of the frequency-domain volume integral equation (VIE) for the electric field inside a nonmagnetic scattering object from the differential Maxwell equations, transmission boundary conditions, radiation condition at infinity, and locally-finite-energy condition. The derivation applies to an arbitrary spatially finite group of particles made of isotropic materials and embedded in a passive host medium, including those with edges, corners, and intersecting internal interfaces. This is a substantially more general type of scatterer than in all previous derivations. We explicitly treat the strong singularity of the integral kernel, but keep the entire discussion accessible to the applied scattering community. We also consider the known results on the existence and uniqueness of VIE solution and conjecture a general sufficient condition for that. Finally, we discuss an alternative way of deriving the VIE for an arbitrary object by means of a continuous transformation of the everywhere smooth refractive-index function into a discontinuous one. Overall, the paper examines and pushes forward the state-of-the-art understanding of various analytical aspects of the VIE.

Subleading soft theorem for multiple soft gravitons

NASA Astrophysics Data System (ADS)

Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay

2017-12-01

We derive the subleading soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. Our results are valid to all orders in perturbation theory when the number of non-compact space-time dimensions is six or more, but only for tree amplitudes for five or less non-compact space-time dimensions due to enhanced contribution to loop amplitudes from the infrared region.

Flow-induced gelation of living (micellar) polymers

NASA Technical Reports Server (NTRS)

Bruinsma, Robijn; Gelbart, William M.; Ben-Shaul, Avinoam

1992-01-01

The effect of shear velocity gradients on the size (L) of rodlike micelles in dilute and semidilute solution is considered. A kinetic equation is introduced for the time-dependent concentration of aggregates of length L, consisting of 'bimolecular' combination processes L + L-prime yield (L + L-prime) and unimolecular fragmentations L yield L + (L - L-prime). The former are described by a generalization (from spheres to rods) of the Smoluchowski mechanism for shear-induced coalesence of emulsions, and the latter by incorporating the tension-deformation effects due to flow. Steady-state solutions to the kinetic equation are obtained, with the corresponding mean micellar size evaluated as a function of the Peclet number P (i.e., the dimensionless ratio of the flow rate and the rotational diffusion coefficient). For sufficiently dilute solutions, only a weak dependence of the micellar size on P is found. In the semidilute regime, however, an apparent divergence in the micellar size at P of about 1 suggests a flow-induced first-order gelation phenomenon.

A high-order staggered meshless method for elliptic problems

DOE PAGES

Trask, Nathaniel; Perego, Mauro; Bochev, Pavel Blagoveston

2017-03-21

Here, we present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that specification of the dual metric attributes is implicit in the method's construction. Our method combines a topological gradient operator on the local primal grid with a generalized moving least squares approximation of the divergence on the local dual grid. We show that the resulting approximation of the div-grad operator maintains polynomial reproduction to arbitrary orders and yields a meshless method, which attainsmore » $$O(h^{m})$$ convergence in both $L^2$- and $H^1$-norms, similar to mixed finite element methods. We demonstrate this convergence on curvilinear domains using manufactured solutions in two and three dimensions. Application of the new method to problems with discontinuous coefficients reveals solutions that are qualitatively similar to those of compatible mesh-based discretizations.« less

The inner zone electron model AE-5

NASA Technical Reports Server (NTRS)

Teague, M. J.; Vette, J. I.

1972-01-01

A description is given of the work performed in the development of the inner radiation zone electron model, AE-5. A complete description of the omnidirectional flux model is given for energy thresholds E sub T in the range 4.0 E sub T/(MeV) 0.04 and for L values in the range 2.8 L 1.2 for an epoch of October 1967. Confidence codes for certain regions of B-L space and certain energies are given based on data coverage and the assumptions made in the analysis. The electron model programs that can be supplied to a user are referred to. One of these, a program for accessing the model flux at arbitrary points in B-L space and arbitrary energies, includes the latest outer zone electron model and proton model. The model AE-5, is based on data from five satellites, OGO 1, OGO 3, 1963-38C, OV3-3, and Explorer 26, spanning the period December 1964 to December 1967.

General minimal surface solution for gravitational instantons

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Kalaycı, J.; Nutku, Y.

1997-07-01

We construct the general instanton metric obtained from Weierstrass' general local solution for minimal surfaces using the correspondence between minimal surfaces in three-dimensional Euclidean space and gravitational instantons admitting two Killing vectors. The resulting metric contains one arbitrary analytic function and we show that it can be transformed to the Gibbons-Hawking form of an instanton metric that was reported earlier.

On the Complexity of the Asymmetric VPN Problem

NASA Astrophysics Data System (ADS)

Rothvoß, Thomas; Sanità, Laura

We give the first constant factor approximation algorithm for the asymmetric Virtual Private Network (textsc{Vpn}) problem with arbitrary concave costs. We even show the stronger result, that there is always a tree solution of cost at most 2·OPT and that a tree solution of (expected) cost at most 49.84·OPT can be determined in polynomial time.

Efficient molecular density functional theory using generalized spherical harmonics expansions.

PubMed

Ding, Lu; Levesque, Maximilien; Borgis, Daniel; Belloni, Luc

2017-09-07

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r≡(x,y,z) and of the three Euler angles Ω≡(θ,ϕ,ψ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.

Direct solution for thermal stresses in a nose cap under an arbitrary axisymmetric temperature distribution

NASA Technical Reports Server (NTRS)

Davis, Randall C.

1988-01-01

The design of a nose cap for a hypersonic vehicle is an iterative process requiring a rapid, easy to use and accurate stress analysis. The objective of this paper is to develop such a stress analysis technique from a direct solution of the thermal stress equations for a spherical shell. The nose cap structure is treated as a thin spherical shell with an axisymmetric temperature distribution. The governing differential equations are solved by expressing the stress solution to the thermoelastic equations in terms of a series of derivatives of the Legendre polynomials. The process of finding the coefficients for the series solution in terms of the temperature distribution is generalized by expressing the temperature along the shell and through the thickness as a polynomial in the spherical angle coordinate. Under this generalization the orthogonality property of the Legendre polynomials leads to a sequence of integrals involving powers of the spherical shell coordinate times the derivative of the Legendre polynomials. The coefficients of the temperature polynomial appear outside of these integrals. Thus, the integrals are evaluated only once and their values tabulated for use with any arbitrary polynomial temperature distribution.

Faithful Remote Information Concentration Based on the Optimal Universal 1→2 Telecloning of Arbitrary Two-Qubit States

NASA Astrophysics Data System (ADS)

Peng, Jia-Yin; Lei, Hong-Xuan; Mo, Zhi-Wen

2014-05-01

The previous protocols of remote quantum information concentration were focused on the reverse process of quantum telecloning of single-qubit states. We here investigate the reverse process of optimal universal 1→2 telecloning of arbitrary two-qubit states. The aim of this telecloning is to distribute respectively the quantum information to two groups of spatially separated receivers from a group of two senders situated at two different locations. Our scheme shows that the distributed quantum information can be remotely concentrated back to a group of two different receivers with 1 of probability by utilizing maximally four-particle cluster state and four-particle GHZ state as quantum channel.

Electron transfer in proton-hydrogen collisions under dense quantum plasma

NASA Astrophysics Data System (ADS)

Nayek, Sujay; Bhattacharya, Arka; Kamali, Mohd Zahurin Mohamed; Ghoshal, Arijit; Ratnavelu, Kurunathan

2017-09-01

The effects of dense quantum plasma on 1 s → nlm charge transfer, for arbitrary n,l,m, in proton-hydrogen collisions have been studied by employing a distorted wave approximation. The interactions among the charged particles in the plasma have been represented by modified Debye-Huckel potentials. A detailed study has been made to explore the effects of background plasma environment on the differential and total cross sections for electron capture into different angular momentum states for the incident energy in the range 10-1000 keV. For the unscreened case, our results agree well with some of the most accurate results available in the literature.

Probabilistic Teleportation of an Arbitrary Two-Qubit State via Positive Operator-Valued Measurement with Multi Parties

NASA Astrophysics Data System (ADS)

Shi, Lei; Wei, Jia-Hua; Li, Yun-Xia; Ma, Li-Hua; Xue, Yang; Luo, Jun-Wen

2017-04-01

We propose a novel scheme to probabilistically transmit an arbitrary unknown two-qubit quantum state via Positive Operator-Valued Measurement with the help of two partially entangled states. In this scheme, the teleportation with two senders and two receives can be realized when the information of non-maximally entangled states is only available for the senders. Furthermore, the concrete implementation processes of this proposal are presented, meanwhile the classical communication cost and the successful probability of our scheme are calculated. Supported by the National Natural Science Foundation of China under Grant Nos. 60974037, 61134008, 11074307, and 61273202

Controlled quantum perfect teleportation of multiple arbitrary multi-qubit states

NASA Astrophysics Data System (ADS)

Shi, Runhua; Huang, Liusheng; Yang, Wei; Zhong, Hong

2011-12-01

We present an efficient controlled quantum perfect teleportation scheme. In our scheme, multiple senders can teleport multiple arbitrary unknown multi-qubit states to a single receiver via a previously shared entanglement state with the help of one or more controllers. Furthermore, our scheme has a very good performance in the measurement and operation complexity, since it only needs to perform Bell state and single-particle measurements and to apply Controlled-Not gate and other single-particle unitary operations. In addition, compared with traditional schemes, our scheme needs less qubits as the quantum resources and exchanges less classical information, and thus obtains higher communication efficiency.

Computing arbitrary defect structures on arbitrary lattices on arbitrary geometries from arbitrary energies

NASA Astrophysics Data System (ADS)

Allen, Brian; Travesset, Alex

2004-03-01

Dislocations and disclinations play a fundamental role in the properties of two dimensional crystals. In this talk, it will be shown that a general computational framework can be developed by combining previous work of Seung and Nelson* and modern advances in objected oriented design. This allows separating the problem into independent classes such as: geometry (sphere, plane, torus..), lattice (triangular, square, etc..), type of defect (dislocation, disclinations, etc..), boundary conditions, type of order (crystalline, hexatic) or energy functional. As applications, the ground state of crystals in several geometries will be discussed. Experimental examples with colloidal particles will be shown. *S. Seung and D. Nelson, Phys. Rev. A 38, 1005 (1988)

Faithful teleportation with arbitrary pure or mixed resource states

NASA Astrophysics Data System (ADS)

Zhao, Ming-Jing; Li, Zong-Guo; Fei, Shao-Ming; Wang, Zhi-Xi; Li-Jost, Xianqing

2011-05-01

We study faithful teleportation systematically with arbitrary entangled states as resources. The necessary conditions of mixed states to complete perfect teleportation are proved. Based on these results, the necessary and sufficient conditions of faithful teleportation of an unknown state |phirang in { C}^d with an entangled resource ρ in { C}^m \\otimes { C}^d and { C}^d \\otimes { C}^n are derived. It is shown that for ρ in { C}^m \\otimes { C}^d, ρ must be a maximally entangled state, while for ρ in { C}^d \\otimes { C}^n, ρ must be a pure maximally entangled state. Moreover, we show that the sender's measurements must be all projectors of maximally entangled pure states. The relations between the entanglement of the formation of the resource states and faithful teleportation are also discussed.

Optimal four-impulse rendezvous between coplanar elliptical orbits

NASA Astrophysics Data System (ADS)

Wang, JianXia; Baoyin, HeXi; Li, JunFeng; Sun, FuChun

2011-04-01

Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden's primer vector theory is favored by many researchers with its clear physical concept and simplicity in solution. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital rendezvous in a near circular orbit and achieved great success. Extending Prussing's work, this paper will employ the primer vector theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit (referred to as T-H equations), the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large eccentricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden's necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentricity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution. If the initial values are taken randomly, it is difficult to converge to the optimal solution.

Solid-solution aqueous-solution equilibria: thermodynamic theory and representation

USGS Publications Warehouse

Glynn, P.D.; Reardon, E.J.

1990-01-01

Thorstenson and Plummer's (1977) "stoichiometric saturation' model is reviewed, and a general relation between stoichiometric saturation Kss constants and excess free energies of mixing is derived for a binary solid-solution B1-xCxA: GE = RT[ln Kss - xln(xKCA) - (l-x)ln((l-x)KBA)]. This equation allows a suitable excess free energy function, such as Guggenheim's (1937) sub-regular function, to be fitted from experimentally determined Kss constants. Solid-phase free energies and component activity-coefficients can then be determined from one or two fitted parameters and from the endmember solubility products KBA and KCA. A general form of Lippmann's (1977,1980) "solutus equation is derived from an examination of Lippmann's (1977,1980) "total solubility product' model. Lippmann's ??II or "total solubility product' variable is used to represent graphically not only thermodynamic equilibrium states and primary saturation states but also stoichiometric saturation and pure phase saturation states. -from Authors

Multistable orientation in a nematic liquid crystal cell induced by external field and interfacial interaction

NASA Astrophysics Data System (ADS)

Ong, Hiap Liew; Meyer, Robert B.; Hurd, Alan J.

1984-04-01

The effects of a short-range, arbitrary strength interfacial potential on the magnetic field, electric field, and optical field induced Freedericksz transition in a nematic liquid crystal cell are examined and the exact solution is obtained. By generalizing the criterion for the existence of a first-order optical field induced Freedericksz transition that was obtained previously [H. L. Ong, Phys. Rev. A 28, 2393 (1983)], the general criterion for the transition to be first order is obtained. Based on the existing experimental results, the possibility of surface induced first-order transitions is discussed and three simple empirical approaches are suggested for observing multistable orientation. The early results on the magnetic and electric fields induced Freedericksz transition and the inadequacy of the usual experimental observation methods (phase shift and capacitance measurements) are also discussed.

Conservation Laws and Symmetry Properties of a Class of Higher Order Theories of Gravity

NASA Astrophysics Data System (ADS)

Barraco, D.; Dominguez, E.; Guibert, R.; Hamity, V.

1998-04-01

We consider a class of fourth order theories of gravity with arbitrary matter fields arising from a diffeomorphism invariant Lagrangian density mathcal{L}_T = mathcal{L}_G + mathcal{L}_M, with mathcal{L}_G = sqrt { - g} left[ {R + hleft( R right)} right]and mathcal{L}_Mthe phenomenological representation of the nongravitational fields. We derive first the generalization of the Einstein pseudotensor and the von Freud superpotential. We then show, using the arbitrariness that is always present in the choice of pseudotensor and superpotential, that we can choose these superpotentials to have the same form as those for the Hilbert Lagrangian of general relativity (GR). In particular we may introduce the Moller superpotential of GR as associated with a double-index differential conservation law. Similarly, using the Moller superpotential we prove that we can choose the Komar vector of GR to construct a conserved quantity for isolated asymptotically flat systems. For the example R + R2theory we prove then, that the active mass is equal to the total energy (or inertial mass) of the system.

Ionization state of L-phenylalanine at the air-water interface.

PubMed

Griffith, Elizabeth C; Vaida, Veronica

2013-01-16

The ionization state of organic molecules at the air-water interface and the related problem of the surface pH of water have significant consequences on the catalytic role of the surface in chemical reactions and are currently areas of intense research and controversy. In this work, infrared reflection-absorption spectroscopy (IRRAS) is used to identify changes in the ionization state of L-phenylalanine in the surface region versus the bulk aqueous solution. L-phenylalanine has the unique advantage of possessing two different hydrophilic groups, a carboxylic acid and an amine base, which can deprotonate and protonate respectively depending on the ionic environment they experience at the water surface. In this work, the polar group vibrations in the surface region are identified spectroscopically in varying bulk pH solutions, and are subsequently compared with the ionization state of the polar groups of molecules residing in the bulk environment. The polar groups of L-phenylalanine at the surface transition to their deprotonated state at bulk pH values lower than the molecules residing in the bulk, indicating a decrease in their pK(a) at the surface, and implying an enhanced hydroxide ion concentration in the surface region relative to the bulk.

Two-particle multichannel systems in a finite volume with arbitrary spin

DOE PAGES

Briceno, Raul A.

2014-04-08

The quantization condition for two-particle systems with arbitrary number of two-body open coupled channels, spin and masses in a finite cubic volume with either periodic or twisted boundary conditions is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is relativistic, holds for all momenta below the three- and four-particle thresholds, and is exact up to exponential volume corrections that are governed by L/r, where L is the spatial extent of the volume and r is the range of the interactions between the particles. With hadronic systems the rangemore » of the interaction is set by the inverse of the pion mass, m π, and as a result the formalism presented is suitable for m πL>>1. Implications of the formalism for the studies of multichannel baryon-baryon systems are discussed.« less

Color correction strategies in optical design

NASA Astrophysics Data System (ADS)

Pfisterer, Richard N.; Vorndran, Shelby D.

2014-12-01

An overview of color correction strategies is presented. Starting with basic first-order aberration theory, we identify known color corrected solutions for doublets and triplets. Reviewing the modern approaches of Robb-Mercado, Rayces-Aguilar, and C. de Albuquerque et al, we find that they confirm the existence of glass combinations for doublets and triplets that yield color corrected solutions that we already know exist. Finally we explore the use of the y, ӯ diagram in conjunction with aberration theory to identify the solution space of glasses capable of leading to color corrected solutions in arbitrary optical systems.

Conservative DEC Discretization of Incompressible Navier-Stokes Equations on Arbitrary Surface Simplicial Meshes

NASA Astrophysics Data System (ADS)

Mohamed, Mamdouh; Hirani, Anil; Samtaney, Ravi

2017-11-01

A conservative discretization of incompressible Navier-Stokes equations over surfaces is developed using discrete exterior calculus (DEC). The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of signed diagonal Hodge star operators, while using the circumcentric dual defined on arbitrary meshes, is shown to produce correct solutions even when many non-Delaunay triangles pairs exist. This allows the DEC discretization to admit arbitrary surface simplicial meshes, in contrast to the previously held notion that DEC was limited only to Delaunay meshes. The discretization scheme is presented along with several numerical test cases demonstrating its numerical convergence and conservation properties. Recent developments regarding the extension to conservative higher order methods are also presented. KAUST Baseline Research Funds of R. Samtaney.

Nonequilibrium Steady State Generated by a Moving Defect: The Supersonic Threshold

NASA Astrophysics Data System (ADS)

Bastianello, Alvise; De Luca, Andrea

2018-02-01

We consider the dynamics of a system of free fermions on a 1D lattice in the presence of a defect moving at constant velocity. The defect has the form of a localized time-dependent variation of the chemical potential and induces at long times a nonequilibrium steady state (NESS), which spreads around the defect. We present a general formulation that allows recasting the time-dependent protocol in a scattering problem on a static potential. We obtain a complete characterization of the NESS. In particular, we show a strong dependence on the defect velocity and the existence of a sharp threshold when such velocity exceeds the speed of sound. Beyond this value, the NESS is not produced and, remarkably, the defect travels without significantly perturbing the system. We present an exact solution for a δ -like defect traveling with an arbitrary velocity and we develop a semiclassical approximation that provides accurate results for smooth defects.

Origins and optimization of entanglement in plasmonically coupled quantum dots

DOE PAGES

Otten, Matthew; Larson, Jeffrey; Min, Misun; ...

2016-08-11

In this paper, a system of two or more quantum dots interacting with a dissipative plasmonic nanostructure is investigated in detail by using a cavity quantum electrodynamics approach with a model Hamiltonian. We focus on determining and understanding system configurations that generate multiple bipartite quantum entanglements between the occupation states of the quantum dots. These configurations include allowing for the quantum dots to be asymmetrically coupled to the plasmonic system. Analytical solution of a simplified limit for an arbitrary number of quantum dots and numerical simulations and optimization for the two- and three-dot cases are used to develop guidelines formore » maximizing the bipartite entanglements. For any number of quantum dots, we show that through simple starting states and parameter guidelines, one quantum dot can be made to share a strong amount of bipartite entanglement with all other quantum dots in the system, while entangling all other pairs to a lesser degree.« less

Tree-level correlations in the strong field regime

NASA Astrophysics Data System (ADS)

Gelis, François

2017-09-01

We consider the correlation function of an arbitrary number of local observables in quantum field theory, in situations where the field amplitude is large. Using a quasi-classical approximation (valid for a highly occupied initial mixed state, or for a coherent initial state if the classical dynamics has instabilities), we show that at tree level these correlations are dominated by fluctuations at the initial time. We obtain a general expression of the correlation functions in terms of the classical solution of the field equation of motion and its derivatives with respect to its initial conditions, that can be arranged graphically as the sum of labeled trees where the nodes are the individual observables, and the links are pairs of derivatives acting on them. For 3-point (and higher) correlation functions, there are additional tree-level terms beyond the quasi-classical approximation, generated by fluctuations in the bulk.

Subleading soft graviton theorem for loop amplitudes

NASA Astrophysics Data System (ADS)

Sen, Ashoke

2017-11-01

Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.

Multi Objective Controller Design for Linear System via Optimal Interpolation

NASA Technical Reports Server (NTRS)

Ozbay, Hitay

1996-01-01

We propose a methodology for the design of a controller which satisfies a set of closed-loop objectives simultaneously. The set of objectives consists of: (1) pole placement, (2) decoupled command tracking of step inputs at steady-state, and (3) minimization of step response transients with respect to envelope specifications. We first obtain a characterization of all controllers placing the closed-loop poles in a prescribed region of the complex plane. In this characterization, the free parameter matrix Q(s) is to be determined to attain objectives (2) and (3). Objective (2) is expressed as determining a Pareto optimal solution to a vector valued optimization problem. The solution of this problem is obtained by transforming it to a scalar convex optimization problem. This solution determines Q(O) and the remaining freedom in choosing Q(s) is used to satisfy objective (3). We write Q(s) = (l/v(s))bar-Q(s) for a prescribed polynomial v(s). Bar-Q(s) is a polynomial matrix which is arbitrary except that Q(O) and the order of bar-Q(s) are fixed. Obeying these constraints bar-Q(s) is now to be 'shaped' to minimize the step response characteristics of specific input/output pairs according to the maximum envelope violations. This problem is expressed as a vector valued optimization problem using the concept of Pareto optimality. We then investigate a scalar optimization problem associated with this vector valued problem and show that it is convex. The organization of the report is as follows. The next section includes some definitions and preliminary lemmas. We then give the problem statement which is followed by a section including a detailed development of the design procedure. We then consider an aircraft control example. The last section gives some concluding remarks. The Appendix includes the proofs of technical lemmas, printouts of computer programs, and figures.

Accidental Peccei-Quinn Symmetry Protected to Arbitrary Order

NASA Astrophysics Data System (ADS)

Di Luzio, Luca; Nardi, Enrico; Ubaldi, Lorenzo

2017-07-01

A S U (N )L×S U (N )R gauge theory for a scalar multiplet Y transforming in the bifundamental representation (N ,N ¯) preserves, for N >4 , an accidental U (1 ) symmetry first broken at operator dimension N . A vacuum expectation value for Y can break the symmetry to Hs=S U (N )L+R or to Hh=S U (N -1 )L×S U (N -1 )R×U (1 )L +R . In the first case the accidental U (1 ) gets also broken, yielding a pseudo-Nambu-Goldstone boson with mass suppression controlled by N . In the second case a global U (1 ) remains unbroken. The strong C P problem is solved by coupling Y to new fermions carrying color. The first case allows for a Peccei-Quinn solution with U (1 )PQ protected by the gauge symmetry up to order N . In the second case U (1 ) can get broken by condensates of the new strong dynamics, resulting in a composite axion. By coupling Y to fermions carrying only weak isospin, models for axionlike particles can be constructed.

78 FR 18370 - Investigations Regarding Eligibility To Apply for Worker Adjustment Assistance

Federal Register 2010, 2011, 2012, 2013, 2014

2013-03-26

... (State/One-Stop) 82538 Zebra Technologies (Company) Lincoln, RI 03/08/13 03/07/13 82539 Elster Solutions... Semiconductor, Clarksville, TN....... 03/08/13 03/07/13 L.L.C. (Company) 82543 Zebra Technologies (Company... NewPage Duluth Paper Mill Duluth, MN 03/04/13 03/01/13 (State/One-Stop) 82522 United Technologies...

Counterrotating prop-fan simulations which feature a relative-motion multiblock grid decomposition enabling arbitrary time-steps

NASA Technical Reports Server (NTRS)

Janus, J. Mark; Whitfield, David L.

1990-01-01

Improvements are presented of a computer algorithm developed for the time-accurate flow analysis of rotating machines. The flow model is a finite volume method utilizing a high-resolution approximate Riemann solver for interface flux definitions. The numerical scheme is a block LU implicit iterative-refinement method which possesses apparent unconditional stability. Multiblock composite gridding is used to orderly partition the field into a specified arrangement of blocks exhibiting varying degrees of similarity. Block-block relative motion is achieved using local grid distortion to reduce grid skewness and accommodate arbitrary time step selection. A general high-order numerical scheme is applied to satisfy the geometric conservation law. An even-blade-count counterrotating unducted fan configuration is chosen for a computational study comparing solutions resulting from altering parameters such as time step size and iteration count. The solutions are compared with measured data.

Arbitrary Lagrangian-Eulerian Method with Local Structured Adaptive Mesh Refinement for Modeling Shock Hydrodynamics

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

Anderson, R W; Pember, R B; Elliott, N S

2001-10-22

A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. This method facilitates the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required through dynamic adaption. Many of the core issues involved in the development of the combined ALEAMR method hinge upon the integration of AMR with a staggered grid Lagrangian integration method. The novel components of the method are mainly driven by the need to reconcile traditionalmore » AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.« less

Entanglement evolution across a conformal interface

NASA Astrophysics Data System (ADS)

Wen, Xueda; Wang, Yuxuan; Ryu, Shinsei

2018-05-01

For two-dimensional conformal field theories (CFTs) in the ground state, it is known that a conformal interface along the entanglement cut can suppress the entanglement entropy from to , where L is the length of the subsystem A, and is the effective central charge which depends on the transmission property of the conformal interface. In this work, by making use of conformal mappings, we show that a conformal interface has the same effect on entanglement evolution in non-equilibrium cases, including global, local and certain inhomogeneous quantum quenches. I.e. a conformal interface suppresses the time evolution of entanglement entropy by effectively replacing the central charge c with , where is exactly the same as that in the ground state case. We confirm this conclusion by a numerical study on a critical fermion chain. Furthermore, based on the quasi-particle picture, we conjecture that this conclusion holds for an arbitrary quantum quench in CFTs, as long as the initial state can be described by a regularized conformal boundary state.

Nonlinear flap-lag-axial equations of a rotating beam with arbitrary precone angle

NASA Technical Reports Server (NTRS)

Kvaternik, R. G.; White, W. F., Jr.; Kaza, K. R. V.

1978-01-01

In an attempt both to unify and extend the analytical basis of several aspects of the dynamic behavior of flexible rotating beams, the second-degree nonlinear equations of motion for the coupled flapwise bending, lagwise bending, and axial extension of an untwisted, torsionally rigid, nonuniform, rotating beam having an arbitrary angle of precone with the plane perpendicular to the axis of rotation are derived using Hamilton's principle. The derivation of the equations is based on the geometric nonlinear theory of elasticity and the resulting equations are consistent with the assumption that the strains are negligible compared to unity. No restrictions are imposed on the relative displacements or angular rotations of the cross sections of the beam other than those implied by the assumption of small strains. Illustrative numerical results, obtained by using an integrating matrix as the basis for the method of solution, are presented both for the purpose of validating the present method of solution and indicating the range of applicability of the equations of motion and the method of solution.

Solute transport in a single fracture involving an arbitrary length decay chain with rock matrix comprising different geological layers.

PubMed

Mahmoudzadeh, Batoul; Liu, Longcheng; Moreno, Luis; Neretnieks, Ivars

2014-08-01

A model is developed to describe solute transport and retention in fractured rocks. It accounts for advection along the fracture, molecular diffusion from the fracture to the rock matrix composed of several geological layers, adsorption on the fracture surface, adsorption in the rock matrix layers and radioactive decay-chains. The analytical solution, obtained for the Laplace-transformed concentration at the outlet of the flowing channel, can conveniently be transformed back to the time domain by the use of the de Hoog algorithm. This allows one to readily include it into a fracture network model or a channel network model to predict nuclide transport through channels in heterogeneous fractured media consisting of an arbitrary number of rock units with piecewise constant properties. More importantly, the simulations made in this study recommend that it is necessary to account for decay-chains and also rock matrix comprising at least two different geological layers, if justified, in safety and performance assessment of the repositories for spent nuclear fuel. Copyright © 2014 Elsevier B.V. All rights reserved.

Analytic solution and pulse area theorem for three-level atoms

NASA Astrophysics Data System (ADS)

Shchedrin, Gavriil; O'Brien, Chris; Rostovtsev, Yuri; Scully, Marlan O.

2015-12-01

We report an analytic solution for a three-level atom driven by arbitrary time-dependent electromagnetic pulses. In particular, we consider far-detuned driving pulses and show an excellent match between our analytic result and the numerical simulations. We use our solution to derive a pulse area theorem for three-level V and Λ systems without making the rotating wave approximation. Formulated as an energy conservation law, this pulse area theorem can be used to understand pulse propagation through three-level media.

Development of a time-dependent incompressible Navier-Stokes solver based on a fractional-step method

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe

1990-01-01

The main goals are the development, validation, and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems. A solution method that combines a finite volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.

Optical communication with two-photon coherent states. II - Photoemissive detection and structured receiver performance

NASA Technical Reports Server (NTRS)

Shapiro, J. H.; Yuen, H. P.; Machado Mata, J. A.

1979-01-01

In a previous paper (1978), the authors developed a method of analyzing the performance of two-photon coherent state (TCS) systems for free-space optical communications. General theorems permitting application of classical point process results to detection and estimation of signals in arbitrary quantum states were derived. The present paper examines the general problem of photoemissive detection statistics. On the basis of the photocounting theory of Kelley and Kleiner (1964) it is shown that for arbitrary pure state illumination, the resulting photocurrent is in general a self-exciting point process. The photocount statistics for first-order coherent fields reduce to those of a special class of Markov birth processes, which the authors term single-mode birth processes. These general results are applied to the structure of TCS radiation, and it is shown that the use of TCS radiation with direct or heterodyne detection results in minimal performance increments over comparable coherent-state systems. However, significant performance advantages are offered by use of TCS radiation with homodyne detection. The abstract quantum descriptions of homodyne and heterodyne detection are derived and a synthesis procedure for obtaining quantum measurements described by arbitrary TCS is given.

Dynamic mapping of conical intersection seams: A general method for incorporating the geometric phase in adiabatic dynamics in polyatomic systems

NASA Astrophysics Data System (ADS)

Xie, Changjian; Malbon, Christopher L.; Yarkony, David R.; Guo, Hua

2017-07-01

The incorporation of the geometric phase in single-state adiabatic dynamics near a conical intersection (CI) seam has so far been restricted to molecular systems with high symmetry or simple model Hamiltonians. This is due to the fact that the ab initio determined derivative coupling (DC) in a multi-dimensional space is not curl-free, thus making its line integral path dependent. In a recent work [C. L. Malbon et al., J. Chem. Phys. 145, 234111 (2016)], we proposed a new and general approach based on an ab initio determined diabatic representation consisting of only two electronic states, in which the DC is completely removable, so that its line integral is path independent in the simply connected domains that exclude the CI seam. Then with the CIs included, the line integral of the single-valued DC can be used to construct the complex geometry-dependent phase needed to exactly eliminate the double-valued character of the real-valued adiabatic electronic wavefunction. This geometry-dependent phase gives rise to a vector potential which, when included in the adiabatic representation, rigorously accounts for the geometric phase in a system with an arbitrary locus of the CI seam and an arbitrary number of internal coordinates. In this work, we demonstrate this approach in a three-dimensional treatment of the tunneling facilitated dissociation of the S1 state of phenol, which is affected by a Cs symmetry allowed but otherwise accidental seam of CI. Here, since the space is three-dimensional rather than two-dimensional, the seam is a curve rather than a point. The nodal structure of the ground state vibronic wavefunction is shown to map out the seam of CI.

Efficient transfer of an arbitrary qutrit state in circuit quantum electrodynamics.

PubMed

Liu, Tong; Xiong, Shao-Jie; Cao, Xiao-Zhi; Su, Qi-Ping; Yang, Chui-Ping

2015-12-01

Compared with a qubit, a qutrit (i.e., three-level quantum system) has a larger Hilbert space and thus can be used to encode more information in quantum information processing and communication. Here, we propose a method to transfer an arbitrary quantum state between two flux qutrits coupled to two resonators. This scheme is simple because it only requires two basic operations. The state-transfer operation can be performed fast because only resonant interactions are used. Numerical simulations show that the high-fidelity transfer of quantum states between the two qutrits is feasible with current circuit-QED technology. This scheme is quite general and can be applied to accomplish the same task for other solid-state qutrits coupled to resonators.

Warped AdS3 black holes

NASA Astrophysics Data System (ADS)

Anninos, Dionysios; Li, Wei; Padi, Megha; Song, Wei; Strominger, Andrew

2009-03-01

Three dimensional topologically massive gravity (TMG) with a negative cosmological constant -l-2 and positive Newton constant G admits an AdS3 vacuum solution for any value of the graviton mass μ. These are all known to be perturbatively unstable except at the recently explored chiral point μl = 1. However we show herein that for every value of μl ≠ 3 there are two other (potentially stable) vacuum solutions given by SL(2,Bbb R) × U(1)-invariant warped AdS3 geometries, with a timelike or spacelike U(1) isometry. Critical behavior occurs at μl = 3, where the warping transitions from a stretching to a squashing, and there are a pair of warped solutions with a null U(1) isometry. For μl > 3, there are known warped black hole solutions which are asymptotic to warped AdS3. We show that these black holes are discrete quotients of warped AdS3 just as BTZ black holes are discrete quotients of ordinary AdS3. Moreover new solutions of this type, relevant to any theory with warped AdS3 solutions, are exhibited. Finally we note that the black hole thermodynamics is consistent with the hypothesis that, for μl > 3, the warped AdS3 ground state of TMG is holographically dual to a 2D boundary CFT with central charges c_R-formula and c_L-formula.

Theoretical antisymmetric span loading for wings of arbitrary plan form at subsonic speeds

NASA Technical Reports Server (NTRS)

Deyoung, John

1951-01-01

A simplified lifting-surface theory that includes effects of compressibility and spanwise variation of section lift-curve slope is used to provide charts with which antisymmetric loading due to arbitrary antisymmetric angle of attack can be found for wings having symmetric plan forms with a constant spanwise sweep angle of the quarter-chord line. Consideration is given to the flexible wing in roll. Aerodynamic characteristics due to rolling, deflected ailerons, and sideslip of wings with dihedral are considered. Solutions are presented for straight-tapered wings for a range of swept plan forms.

The mechanical problems on additive manufacturing of viscoelastic solids with integral conditions on a surface increasing in the growth process

NASA Astrophysics Data System (ADS)

Parshin, D. A.; Manzhirov, A. V.

2018-04-01

Quasistatic mechanical problems on additive manufacturing aging viscoelastic solids are investigated. The processes of piecewise-continuous accretion of such solids are considered. The consideration is carried out in the framework of linear mechanics of growing solids. A theorem about commutativity of the integration over an arbitrary surface increasing in the solid growing process and the time-derived integral operator of viscoelasticity with a limit depending on the solid point is proved. This theorem provides an efficient way to construct on the basis of Saint-Venant principle solutions of nonclassical boundary-value problems for describing the mechanical behaviour of additively formed solids with integral satisfaction of boundary conditions on the surfaces expanding due to the additional material influx to the formed solid. The constructed solutions will retrace the evolution of the stress-strain state of the solids under consideration during and after the processes of their additive formation. An example of applying the proved theorem is given.

A perfect spin filtering device through Mach-Zehnder interferometry in a GaAs/AlGaAs electron gas

NASA Astrophysics Data System (ADS)

López, Alexander; Medina, Ernesto; Bolívar, Nelson; Berche, Bertrand

2010-03-01

A spin filtering device based on quantum spin interference is addressed, for use with a two-dimensional GaAs/AlGaAs electron gas that has both Rashba and Dresselhaus spin-orbit (SO) couplings and an applied external magnetic field. We propose an experimentally feasible electronic Mach-Zehnder interferometer and derive a map, in parameter space, that determines perfect spin filtering conditions. We find two broad spin filtering regimes: one where filtering is achieved in the original incoming quantization basis, that takes advantage of the purely non-Abelian nature of the spin rotations; and another where one needs a tilted preferential axis in order to observe the polarized output spinor. Both solutions apply for arbitrary incoming electron polarization and energy, and are only limited in output amplitude by the randomness of the incoming spinor state. Including a full account of the beam splitter and mirror effects on spin yields solutions only for the tilted basis, but encompasses a broad range of filtering conditions.

A perfect spin filtering device through Mach-Zehnder interferometry in a GaAs/AlGaAs electron gas.

PubMed

López, Alexander; Medina, Ernesto; Bolívar, Nelson; Berche, Bertrand

2010-03-24

A spin filtering device based on quantum spin interference is addressed, for use with a two-dimensional GaAs/AlGaAs electron gas that has both Rashba and Dresselhaus spin-orbit (SO) couplings and an applied external magnetic field. We propose an experimentally feasible electronic Mach-Zehnder interferometer and derive a map, in parameter space, that determines perfect spin filtering conditions. We find two broad spin filtering regimes: one where filtering is achieved in the original incoming quantization basis, that takes advantage of the purely non-Abelian nature of the spin rotations; and another where one needs a tilted preferential axis in order to observe the polarized output spinor. Both solutions apply for arbitrary incoming electron polarization and energy, and are only limited in output amplitude by the randomness of the incoming spinor state. Including a full account of the beam splitter and mirror effects on spin yields solutions only for the tilted basis, but encompasses a broad range of filtering conditions.

A cylindrical shell with an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

Yahsi, O. S.; Erdogan, F.

1983-01-01

The general problem of a shallow shell with constant curvatures is considered. It is assumed that the shell contains an arbitrarily oriented through crack and the material is specially orthotropic. The nonsymmetric problem is solved for arbitrary self equilibrating crack surface tractions, which, added to an appropriate solution for an uncracked shell, would give the result for a cracked shell under most general loading conditions. The problem is reduced to a system to five singular integral equations in a set of unknown functions representing relative displacements and rotations on the crack surfaces. The stress state around the crack tip is asymptotically analyzed and it is shown that the results are identical to those obtained from the two dimensional in plane and antiplane elasticity solutions. The numerical results are given for a cylindrical shell containing an arbitrarily oriented through crack. Some sample results showing the effect of the Poisson's ratio and the material orthotropy are also presented. Previously annunced in STAR as N83-16783

Scheme for implementing perfect quantum teleportation with four-qubit entangled states in cavity quantum electrodynamics

NASA Astrophysics Data System (ADS)

Tang, Jing-Wu; Zhao, Guan-Xiang; He, Xiong-Hui

2011-05-01

Recently, Peng et al. [2010 Eur. Phys. J. D 58 403] proposed to teleport an arbitrary two-qubit state with a family of four-qubit entangled states, which simultaneously include the tensor product of two Bell states, linear cluster state and Dicke-class state. This paper proposes to implement their scheme in cavity quantum electrodynamics and then presents a new family of four-qubit entangled state |Ω4>1234. It simultaneously includes all the well-known four-qubit entangled states which can be used to teleport an arbitrary two-qubit state. The distinct advantage of the scheme is that it only needs a single setup to prepare the whole family of four-qubit entangled states, which will be very convenient for experimental realization. After discussing the experimental condition in detail, we show the scheme may be feasible based on present technology in cavity quantum electrodynamics.

Further Evidence in Support of the Universal Nilpotent Grammatical Computational Paradigm of Quantum Physics

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

Marcer, Peter J.; Rowlands, Peter

2010-12-22

Further evidence is presented in favour of the computational paradigm, conceived and constructed by Rowlands and Diaz, as detailed in Rowlands' book Zero to Infinity (2007), and in particular the authors' paper 'The Grammatical Universe: the Laws of Thermodynamics and Quantum Entanglement'. The paradigm, which has isomorphic group and algebraic quantum mechanical language interpretations, not only predicts the well-established facts of quantum physics, the periodic table, chemistry / valence and of molecular biology, whose understanding it extends; it also provides an elegant, simple solution to the unresolved quantum measurement problem. In this fundamental paradigm, all the computational constructs / predictionsmore » that emerge, follow from the simple fact, that, as in quantum mechanics, the wave function is defined only up to an arbitrary fixed phase. This fixed phase provides a simple physical understanding of the quantum vacuum in quantum field theory, where only relative phases, known to be able to encode 3+1 relativistic space-time geometries, can be measured. It is the arbitrary fixed measurement standard, against which everything that follows is to be measured, even though the standard itself cannot be, since nothing exists against which to measure it. The standard, as an arbitrary fixed reference phase, functions as the holographic basis for a self-organized universal quantum process of emergent novel fermion states of matter where, following each emergence, the arbitrary standard is re-fixed anew so as to provide a complete history / holographic record or hologram of the current fixed past, advancing an unending irreversible evolution, such as is the evidence of our senses. The fermion states, in accord with the Pauli exclusion principle, each correspond to a unique nilpotent symbol in the infinite alphabet (which specifies the grammar in this nilpotent universal computational rewrite system (NUCRS) paradigm); and the alphabet, as Hill and Rowlands hypothesize on substantial evidence [26], includes that of the RNA / DNA genetic code and, as holographic phase encodings / holograms, the 4D geometries of all living systems as self-organised grammatical computational rewrite machines / machinery. Human brains, natural grammatical (written symbol) languages, 4D geometric self-awareness and a totally new emergent property of matter, human consciousness, can thus with some measure of confidence be postulated as further genetic consequences which follow from this self-organizing fundamental rewrite NUCRS construction. For it, like natural language, possesses a semantics and not just a syntax, where the initial symbol, i.e. the arbitrary fixed phase measurement standard, is able to function as the template for the blueprints of the emergent 4D relativistic real and virtual geometries to come, in a 'from the Self Creation to the creation of the human self' computational rewrite process evolution.« less

Further Evidence in Support of the Universal Nilpotent Grammatical Computational Paradigm of Quantum Physics

NASA Astrophysics Data System (ADS)

Marcer, Peter J.; Rowlands, Peter

2010-12-01

Further evidence is presented in favour of the computational paradigm, conceived and constructed by Rowlands and Diaz, as detailed in Rowlands' book Zero to Infinity (2007) [2], and in particular the authors' paper `The Grammatical Universe: the Laws of Thermodynamics and Quantum Entanglement' [1]. The paradigm, which has isomorphic group and algebraic quantum mechanical language interpretations, not only predicts the well-established facts of quantum physics, the periodic table, chemistry / valence and of molecular biology, whose understanding it extends; it also provides an elegant, simple solution to the unresolved quantum measurement problem. In this fundamental paradigm, all the computational constructs / predictions that emerge, follow from the simple fact, that, as in quantum mechanics, the wave function is defined only up to an arbitrary fixed phase. This fixed phase provides a simple physical understanding of the quantum vacuum in quantum field theory, where only relative phases, known to be able to encode 3+1 relativistic space-time geometries, can be measured. It is the arbitrary fixed measurement standard, against which everything that follows is to be measured, even though the standard itself cannot be, since nothing exists against which to measure it. The standard, as an arbitrary fixed reference phase, functions as the holographic basis for a self-organized universal quantum process of emergent novel fermion states of matter where, following each emergence, the arbitrary standard is re-fixed anew so as to provide a complete history / holographic record or hologram of the current fixed past, advancing an unending irreversible evolution, such as is the evidence of our senses. The fermion states, in accord with the Pauli exclusion principle, each correspond to a unique nilpotent symbol in the infinite alphabet (which specifies the grammar in this nilpotent universal computational rewrite system (NUCRS) paradigm); and the alphabet, as Hill and Rowlands hypothesize on substantial evidence [26], includes that of the RNA / DNA genetic code and, as holographic phase encodings / holograms, the 4D geometries of all living systems as self-organised grammatical computational rewrite machines / machinery. Human brains, natural grammatical (written symbol) languages, 4D geometric self-awareness and a totally new emergent property of matter, human consciousness, can thus with some measure of confidence be postulated as further genetic consequences which follow from this self-organizing fundamental rewrite NUCRS construction. For it, like natural language, possesses a semantics and not just a syntax, where the initial symbol, i.e. the arbitrary fixed phase measurement standard, is able to function as the template for the blueprints of the emergent 4D relativistic real and virtual geometries to come, in a `from the Self Creation to the creation of the human self' computational rewrite process evolution.

Arbitrary spin-to-orbital angular momentum conversion of light

NASA Astrophysics Data System (ADS)

Devlin, Robert C.; Ambrosio, Antonio; Rubin, Noah A.; Mueller, J. P. Balthasar; Capasso, Federico

2017-11-01

Optical elements that convert the spin angular momentum (SAM) of light into vortex beams have found applications in classical and quantum optics. These elements—SAM-to-orbital angular momentum (OAM) converters—are based on the geometric phase and only permit the conversion of left- and right-circular polarizations (spin states) into states with opposite OAM. We present a method for converting arbitrary SAM states into total angular momentum states characterized by a superposition of independent OAM. We designed a metasurface that converts left- and right-circular polarizations into states with independent values of OAM and designed another device that performs this operation for elliptically polarized states. These results illustrate a general material-mediated connection between SAM and OAM of light and may find applications in producing complex structured light and in optical communication.

Dynamics and thermodynamics of linear quantum open systems.

PubMed

Martinez, Esteban A; Paz, Juan Pablo

2013-03-29

We analyze the evolution of the quantum state of networks of quantum oscillators coupled with arbitrary external environments. We show that the reduced density matrix of the network always obeys a local master equation with a simple analytical solution. We use this to study the emergence of thermodynamical laws in the long time regime demonstrating two main results: First, we show that it is impossible to build a quantum absorption refrigerator using linear networks (thus, nonlinearity is an essential resource for such refrigerators recently studied by Levy and Kosloff [Phys. Rev. Lett. 108, 070604 (2012)] and Levy et al. [Phys. Rev. B 85, 061126 (2012)]). Then, we show that the third law imposes constraints on the low frequency behavior of the environmental spectral densities.

Modeling of the charge-state separation at ITEP experimental facility for material science based on a Bernas ion source.

PubMed

Barminova, H Y; Saratovskyh, M S

2016-02-01

The experiment automation system is supposed to be developed for experimental facility for material science at ITEP, based on a Bernas ion source. The program CAMFT is assumed to be involved into the program of the experiment automation. CAMFT is developed to simulate the intense charged particle bunch motion in the external magnetic fields with arbitrary geometry by means of the accurate solution of the particle motion equation. Program allows the consideration of the bunch intensity up to 10(10) ppb. Preliminary calculations are performed at ITEP supercomputer. The results of the simulation of the beam pre-acceleration and following turn in magnetic field are presented for different initial conditions.

Can observations look back to the beginning of inflation?

NASA Astrophysics Data System (ADS)

Wetterich, C.

2016-03-01

The cosmic microwave background can measure the inflaton potential only if inflation lasts sufficiently long before the time of horizon crossing of observable fluctuations, such that non-linear effects in the time evolution of Green's functions lead to a loss of memory of initial conditions for the ultraviolet tail of the spectrum. Within a derivative expansion of the quantum effective action for an interacting scalar field we discuss the most general solution for the correlation function, including arbitrary pure and mixed quantum states. In this approximation no loss of memory occurs - cosmic microwave observations see the initial spectrum at the beginning of inflation, processed only mildly by the scale-violating effects at horizon crossing induced by the inflaton potential.

Optimal phase estimation with arbitrary a priori knowledge

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

Demkowicz-Dobrzanski, Rafal

2011-06-15

The optimal-phase estimation strategy is derived when partial a priori knowledge on the estimated phase is available. The solution is found with the help of the most famous result from the entanglement theory: the positive partial transpose criterion. The structure of the optimal measurements, estimators, and the optimal probe states is analyzed. This Rapid Communication provides a unified framework bridging the gap in the literature on the subject which until now dealt almost exclusively with two extreme cases: almost perfect knowledge (local approach based on Fisher information) and no a priori knowledge (global approach based on covariant measurements). Special attentionmore » is paid to a natural a priori probability distribution arising from a diffusion process.« less

Analytic drain current model for III-V cylindrical nanowire transistors

NASA Astrophysics Data System (ADS)

Marin, E. G.; Ruiz, F. G.; Schmidt, V.; Godoy, A.; Riel, H.; Gámiz, F.

2015-07-01

An analytical model is proposed to determine the drain current of III-V cylindrical nanowires (NWs). The model uses the gradual channel approximation and takes into account the complete analytical solution of the Poisson and Schrödinger equations for the Γ-valley and for an arbitrary number of subbands. Fermi-Dirac statistics are considered to describe the 1D electron gas in the NWs, being the resulting recursive Fermi-Dirac integral of order -1/2 successfully integrated under reasonable assumptions. The model has been validated against numerical simulations showing excellent agreement for different semiconductor materials, diameters up to 40 nm, gate overdrive biases up to 0.7 V, and densities of interface states up to 1013eV-1cm-2 .

Modeling of the charge-state separation at ITEP experimental facility for material science based on a Bernas ion source

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

Barminova, H. Y., E-mail: barminova@bk.ru; Saratovskyh, M. S.

2016-02-15

The experiment automation system is supposed to be developed for experimental facility for material science at ITEP, based on a Bernas ion source. The program CAMFT is assumed to be involved into the program of the experiment automation. CAMFT is developed to simulate the intense charged particle bunch motion in the external magnetic fields with arbitrary geometry by means of the accurate solution of the particle motion equation. Program allows the consideration of the bunch intensity up to 10{sup 10} ppb. Preliminary calculations are performed at ITEP supercomputer. The results of the simulation of the beam pre-acceleration and following turnmore » in magnetic field are presented for different initial conditions.« less

Spin and pseudospin symmetric Dirac particles in the field of Tietz—Hua potential including Coulomb tensor interaction

NASA Astrophysics Data System (ADS)

Sameer, M. Ikhdair; Majid, Hamzavi

2013-09-01

Approximate analytical solutions of the Dirac equation for Tietz—Hua (TH) potential including Coulomb-like tensor (CLT) potential with arbitrary spin—orbit quantum number κ are obtained within the Pekeris approximation scheme to deal with the spin—orbit coupling terms κ(κ ± 1)r-2. Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov—Uvarov (NU) method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated.

Vortex lattices in binary mixtures of repulsive superfluids

NASA Astrophysics Data System (ADS)

Mingarelli, Luca; Keaveny, Eric E.; Barnett, Ryan

2018-04-01

We present an extension of the framework introduced in previous work [L. Mingarelli, E. E. Keaveny, and R. Barnett, J. Phys.: Condens. Matter 28, 285201 (2016), 10.1088/0953-8984/28/28/285201] to treat multicomponent systems, showing that new degrees of freedom are necessary in order to obtain the desired boundary conditions. We then apply this extended framework to the coupled Gross-Pitaevskii equations to investigate the ground states of two-component systems with equal masses, thereby extending previous work in the lowest Landau limit [E. J. Mueller and T.-L. Ho, Phys. Rev. Lett. 88, 180403 (2002), 10.1103/PhysRevLett.88.180403] to arbitrary interactions within Gross-Pitaevskii theory. We show that away from the lowest Landau level limit, the predominant vortex lattice consists of two interlaced triangular lattices. Finally, we derive a linear relation which accurately describes the phase boundaries in the strong interacting regimes.

Aluminum and Phthalates in Calcium Gluconate: Contribution From Glass and Plastic Packaging.

PubMed

Yokel, Robert A; Unrine, Jason M

2017-01-01

Aluminum contamination of parenteral nutrition solutions has been documented for 3 decades. It can result in elevated blood, bone, and whole body aluminum levels associated with neurotoxicity, reduced bone mass and mineral content, and perhaps hepatotoxicity. The primary aluminum source among parenteral nutrition components is glass-packaged calcium gluconate, in which aluminum concentration in the past 3 decades has averaged approximately 4000 μg/L, compared with <200 μg/L in plastic container-packaged calcium gluconate. A concern about plastic packaging is leaching of plasticizers, including phthalates, which have the potential to cause endocrine (male reproductive system) disruption and neurotoxicity. Aluminum was quantified in samples collected periodically for more than 2 years from 3 calcium gluconate sources used to prepare parenteral nutrition solutions; 2 packaged in glass (from France and the United States) and 1 in plastic (from Germany); in a recently released plastic-packaged solution (from the United States); and in the 2 glass containers. Phthalate concentration was determined in selected samples of each product and leachate of the plastic containers. The initial aluminum concentration was approximately 5000 μg/L in the 2 glass-packaged products and approximately 20 μg/L in the plastic-packaged product, and increased approximately 30%, 50%, and 100% in 2 years, respectively. The aluminum concentration in a recently released Calcium Gluconate Injection USP was approximately 320 μg/L. Phthalates were not detected in any calcium gluconate solutions or leachates. Plastic packaging greatly reduces the contribution of aluminum to parenteral nutrition solutions from calcium gluconate compared with the glass-packaged product.

Computer Solution of the Schrodinger Equation--Two Useful Programs.

ERIC Educational Resources Information Center

Evans, D. E.

1980-01-01

Describes a general purpose algorithm which enables one to calculate the allowed energy eigenvalues for an arbitrary potential. Results of a calculation where a centrifugal potential is added to the hydrogenic Coulomb potential are discussed. (Author/HM)

Multi-normed spaces based on non-discrete measures and their tensor products

NASA Astrophysics Data System (ADS)

Helemskii, A. Ya.

2018-04-01

Lambert discovered a new type of structures situated, in a sense, between normed spaces and abstract operator spaces. His definition was based on the notion of amplifying a normed space by means of the spaces \\ell_2^n. Later, several mathematicians studied more general structures (`p-multi- normed spaces') introduced by means of the spaces \\ell_p^n, 1≤ p≤∞. We pass from \\ell_p to L_p(X,μ) with an arbitrary measure. This becomes possible in the framework of the non- coordinate approach to the notion of amplification. In the case of a discrete counting measure, this approach is equivalent to the approach in the papers mentioned. Two categories arise. One consists of amplifications by means of an arbitrary normed space, and the other consists of p-convex amplifications by means of L_p(X,μ). Each of them has its own tensor product of objects (the existence of each product is proved by a separate explicit construction). As a final result, we show that the `p-convex' tensor product has an especially transparent form for the minimal L_p-amplifications of L_q-spaces, where q is conjugate to p. Namely, tensoring L_q(Y,ν) and L_q(Z,λ), we obtain L_q(Y× Z, ν×λ).

Hierarchically controlled remote preparation of an arbitrary single-qubit state by using a four-qubit |χ > entangled state

NASA Astrophysics Data System (ADS)

Ma, Peng-Cheng; Chen, Gui-Bin; Li, Xiao-Wei; Zhan, You-Bang

2018-05-01

In this paper, we present a scheme for Hierarchically controlled remote preparation of an arbitrary single-qubit state via a four-qubit |χ > state as the quantum channel. In this scheme, a sender wishes to help three agents to remotely prepare a quantum state, respectively. The three agents are divided into two grades, that is, an agent is in the upper grade and other two agents are in the lower grade. It is shown that the agent of the upper grade only needs the assistance of any one of the other two agents for recovering the sender's original state, while an agent of the lower grade needs the collaboration of all the other two agents. In other words, the agents of two grades have different authorities to recover sender's original state.

Deterministic Joint Remote Preparation of an Arbitrary Sevenqubit Cluster-type State

NASA Astrophysics Data System (ADS)

Ding, MengXiao; Jiang, Min

2017-06-01

In this paper, we propose a scheme for joint remotely preparing an arbitrary seven-qubit cluster-type state by using several GHZ entangled states as the quantum channel. The coefficients of the prepared states can be not only real, but also complex. Firstly, Alice performs a three-qubit projective measurement according to the amplitude coefficients of the target state, and then Bob carries out another three-qubit projective measurement based on its phase coefficients. Next, one three-qubit state containing all information of the target state is prepared with suitable operation. Finally, the target seven-qubit cluster-type state can be prepared by introducing four auxiliary qubits and performing appropriate local unitary operations based on the prepared three-qubit state in a deterministic way. The receiver's all recovery operations are summarized into a concise formula. Furthermore, it's worth noting that our scheme is more novel and feasible with the present technologies than most other previous schemes.

Lubin-Tate extensions, an elementary approach

NASA Astrophysics Data System (ADS)

Ershov, Yu L.

2007-12-01

We give an elementary proof of the assertion that the Lubin-Tate extension L\\ge K is an Abelian extension whose Galois group is isomorphic to U_K/N_{L/K}(U_L) for arbitrary fields K that have Henselian discrete valuation rings with finite residue fields. The term `elementary' only means that the proofs are algebraic (that is, no transcedental methods are used [1], pp. 327, 332).

On the consistency of the Oppenheimer-Snyder solution for a dust star. Reply to Marshall's criticism

NASA Astrophysics Data System (ADS)

Zakir, Zahid

2018-02-01

The recent alternative to the Oppenheimer-Snyder (OS) solution for a dust star proposed by Marshall in the paper "Gravitational collapse without black holes" (Astrophys. Space Sci. 342:329, 2012) is analyzed. It is shown that this proposal leads to a non-diagonal metric, with which the Einstein equations become practically unsolvable. Any ansatz proposed as their exact solution turns out to be arbitrary and may be unlimited number of the such solutions. This is due to the fact that an auxiliary function y(R,r), introduced by OS as t=M(y), is unambiguously fixed by the diagonality condition and the matching on the surface, and thus in the non-diagonal case it remains arbitrary. It is also shown that the OS solution, as a description in terms of the Schwarzschild coordinates, leads to a frozen star (or frozar) picture not only for the surface, asymptotically freezing outside the gravitational radius, but for interior layers too which also freeze near their own asymptotes. At most of the inner region these asymptotes are located almost equidistantly and only for layers initially close to the surface they become denser. The reason for the such densifying is not "a gravitational repulsion", but their later freezing and higher spatial contractions, while they remain be uniform and free falling in the comoving frames.

Radially separated classical lumps in non-Abelian gauge models

NASA Astrophysics Data System (ADS)

Burzlaff, Jürgen

1985-04-01

We search for smooth and time-independent finite-energy solutions to Yang-Mills-Higgs theory with an arbitrary compact gauge group. Excluding the monopole solutions which have been studied before, we concentrate on configurations with no long-range fields, which include the saddle points corresponding to noncontractible (hyper-) loops. It is shown that if the radial dependence of the fields is factorized, only one solution satisfies all these conditions. This solution is the one which has been studied before by Dashen, Hasslacher, and Neveu and by Boguta, and whose existence has recently been proved rigorously. Formulas for the asymptotic behavior of this solution are given.

Numerical solution of potential flow about arbitrary 2-dimensional multiple bodies

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Thames, F. C.

1982-01-01

A procedure for the finite-difference numerical solution of the lifting potential flow about any number of arbitrarily shaped bodies is given. The solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having coordinate lines coincident with the contours of all bodies in the field, regardless of their shapes and number. The effects of all numerical parameters involved are analyzed and appropriate values are recommended. Comparisons with analytic solutions for single Karman-Trefftz airfoils and a circular cylinder pair show excellent agreement. The technique of application of the boundary-fitted coordinate systems to the numerical solution of partial differential equations is illustrated.

Some Investigations Relating to the Elastostatics of a Tapered Tube

DTIC Science & Technology

1978-03-01

regularity of the solution on the Z axis. Indeed the assumption of such’regularity is stated explicitly by Heins (p. 789) and the problems solved (e.g. a... assumptions , becomes where t h e integrand is evaluated a t ( + i ,O). This i s a form P a of t he i n t e g r a l representa t ion of t h e...solut ion. Now l e t us look a t t h e assumptions on Q. F i r s t of a l l , i n order t o be sure t h a t our operations a r e l eg i

Breaking of scale invariance in the time dependence of correlation functions in isotropic and homogeneous turbulence

NASA Astrophysics Data System (ADS)

Tarpin, Malo; Canet, Léonie; Wschebor, Nicolás

2018-05-01

In this paper, we present theoretical results on the statistical properties of stationary, homogeneous, and isotropic turbulence in incompressible flows in three dimensions. Within the framework of the non-perturbative renormalization group, we derive a closed renormalization flow equation for a generic n-point correlation (and response) function for large wave-numbers with respect to the inverse integral scale. The closure is obtained from a controlled expansion and relies on extended symmetries of the Navier-Stokes field theory. It yields the exact leading behavior of the flow equation at large wave-numbers |p→ i| and for arbitrary time differences ti in the stationary state. Furthermore, we obtain the form of the general solution of the corresponding fixed point equation, which yields the analytical form of the leading wave-number and time dependence of n-point correlation functions, for large wave-numbers and both for small ti and in the limit ti → ∞. At small ti, the leading contribution at large wave-numbers is logarithmically equivalent to -α (ɛL ) 2 /3|∑tip→ i|2, where α is a non-universal constant, L is the integral scale, and ɛ is the mean energy injection rate. For the 2-point function, the (tp)2 dependence is known to originate from the sweeping effect. The derived formula embodies the generalization of the effect of sweeping to n-point correlation functions. At large wave-numbers and large ti, we show that the ti2 dependence in the leading order contribution crosses over to a |ti| dependence. The expression of the correlation functions in this regime was not derived before, even for the 2-point function. Both predictions can be tested in direct numerical simulations and in experiments.

Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

NASA Astrophysics Data System (ADS)

Elwakil, S. A.; El-Labany, S. K.; Zahran, M. A.; Sabry, R.

2004-04-01

The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D( u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K( u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m>1 is the power of the nonlinear convection term).

Exact traveling-wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional Schrödinger equation with polynomial nonlinearity of arbitrary order.

PubMed

Petrović, Nikola Z; Belić, Milivoj; Zhong, Wei-Ping

2011-02-01

We obtain exact traveling wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with variable coefficients and polynomial Kerr nonlinearity of an arbitrarily high order. Exact solutions, given in terms of Jacobi elliptic functions, are presented for the special cases of cubic-quintic and septic models. We demonstrate that the widely used method for finding exact solutions in terms of Jacobi elliptic functions is not applicable to the nonlinear Schrödinger equation with saturable nonlinearity. ©2011 American Physical Society

Development of a time-dependent incompressible Navier-Stokes solver based on a fractional-step method

NASA Technical Reports Server (NTRS)

Rosenfeld, Moshe

1990-01-01

The development, validation and application of a fractional step solution method of the time-dependent incompressible Navier-Stokes equations in generalized coordinate systems are discussed. A solution method that combines a finite-volume discretization with a novel choice of the dependent variables and a fractional step splitting to obtain accurate solutions in arbitrary geometries was previously developed for fixed-grids. In the present research effort, this solution method is extended to include more general situations, including cases with moving grids. The numerical techniques are enhanced to gain efficiency and generality.

Liquid Annular Seal Research

NASA Technical Reports Server (NTRS)

Palazzolo, Alan B.; Venkataraman, Balaji; Padavala, Sathya S.; Ryan, Steve; Vallely, Pat; Funston, Kerry

1996-01-01

This paper highlights the accomplishments on a joint effort between NASA - Marshall Space Flight Center and Texas A and M University to develop accurate seal analysis software for use in rocket turbopump design, design audits and trouble shooting. Results for arbitrary clearance profile, transient simulation, thermal effects solution and flexible seal wall model are presented. A new solution for eccentric seals based on cubic spline interpolation and ordinary differential equation integration is also presented.

Electromagnetic van Kampen waves

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

Ignatov, A. M., E-mail: aign@fpl.gpi.ru

2017-01-15

The theory of van Kampen waves in plasma with an arbitrary anisotropic distribution function is developed. The obtained solutions are explicitly expressed in terms of the permittivity tensor. There are three types of perturbations, one of which is characterized by the frequency dependence on the wave vector, while for the other two, the dispersion relation is lacking. Solutions to the conjugate equations allowing one to solve the initial value problem are analyzed.

Transverse vibration of a simply supported beam with symmetric overhang of arbitrary length

Treesearch

J. F. Murphy

1997-01-01

The numerical solution to the frequency equation for the transverse vibration of a simple beam with symmetric overhang is found. The numerical results converge to the analytical solutions for the two limiting cases of a beam with no overhang and a beam with no span and agree with the case in which the supports are at the nodal points of a freely vibrating beam. An...

Electromagnetic scattering from two-dimensional thick material junctions

NASA Technical Reports Server (NTRS)

Ricoy, M. A.; Volakis, John L.

1990-01-01

The problem of the plane wave diffraction is examined by an arbitrary symmetric two dimensional junction, where Generalized Impedance Boundary Conditions (GIBCs) and Generalized Sheet Transition Conditions (GSTCs) are employed to simulate the slabs. GIBCs and GSTCs are constructed for multilayer planar slabs of arbitrary thickness and the resulting GIBC/GSTC reflection coefficients are compared with exact counterparts to evaluate the GIBCs/GSTCs. The plane wave diffraction by a multilayer material slab recessed in a perfectly conducting ground plane is formulated and solved via the Generalized Scattering Matrix Formulation (GDMF) in conjunction with the dual integral equation approach. Various scattering patterns are computed and validated with exact results where possible. The diffraction by a material discontinuity in a thick dielectric/ferrite slab is considered by modelling the constituent slabs with GSTCs. A non-unique solution in terms of unknown constants is obtained, and these constants are evaluated for the recessed slab geometry by comparison with the solution obtained therein. Several other simplified cases are also presented and discussed. An eigenfunction expansion method is introduced to determine the unknown solution constants in the general case. This procedure is applied to the non-unique solution in terms of unknown constants; and scattering patterns are presented for various slab junctions and compared with alternative results where possible.

Displaying CFD Solution Parameters on Arbitrary Cut Planes

NASA Technical Reports Server (NTRS)

Pao, S. Paul

2008-01-01

USMC6 is a Fortran 90 computer program for post-processing in support of visualization of flows simulated by computational fluid dynamics (CFD). The name "USMC6" is partly an abbreviation of "TetrUSS - USM3D Solution Cutter," reflecting its origin as a post-processor for use with USM3D - a CFD program that is a component of the Tetrahedral Unstructured Software System and that solves the Navier-Stokes equations on tetrahedral unstructured grids. "Cutter" here refers to a capability to acquire and process solution data on (1) arbitrary planes that cut through grid volumes, or (2) user-selected spheroidal, conical, cylindrical, and/or prismatic domains cut from within grids. Cutting saves time by enabling concentration of post-processing and visualization efforts on smaller solution domains of interest. The user can select from among more than 40 flow functions. The cut planes can be trimmed to circular or rectangular shape. The user specifies cuts and functions in a free-format input file using simple and easy-to-remember keywords. The USMC6 command line is simple enough that the slicing process can readily be embedded in a shell script for assembly-line post-processing. The output of USMC6 is a data file ready for plotting.

Asymptotic behavior for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions

NASA Astrophysics Data System (ADS)

Katayama, Soichiro

We consider the Cauchy problem for systems of nonlinear wave equations with multiple propagation speeds in three space dimensions. Under the null condition for such systems, the global existence of small amplitude solutions is known. In this paper, we will show that the global solution is asymptotically free in the energy sense, by obtaining the asymptotic pointwise behavior of the derivatives of the solution. Nonetheless we can also show that the pointwise behavior of the solution itself may be quite different from that of the free solution. In connection with the above results, a theorem is also developed to characterize asymptotically free solutions for wave equations in arbitrary space dimensions.

A fluorescent chemosensor for Zn(II). Exciplex formation in solution and the solid state.

PubMed

Bencini, Andrea; Berni, Emanuela; Bianchi, Antonio; Fornasari, Patrizia; Giorgi, Claudia; Lima, Joao C; Lodeiro, Carlos; Melo, Maria J; de Melo, J Seixas; Parola, Antonio Jorge; Pina, Fernando; Pina, Joao; Valtancoli, Barbara

2004-07-21

The macrocyclic phenanthrolinophane 2,9-[2,5,8-triaza-5-(N-anthracene-9-methylamino)ethyl]-[9]-1,10-phenanthrolinophane (L) bearing a pendant arm containing a coordinating amine and an anthracene group forms stable complexes with Zn(II), Cd(II) and Hg(II) in solution. Stability constants of these complexes were determined in 0.10 mol dm(-3) NMe(4)Cl H(2)O-MeCN (1:1, v/v) solution at 298.1 +/- 0.1 K by means of potentiometric (pH metric) titration. The fluorescence emission properties of these complexes were studied in this solvent. For the Zn(II) complex, steady-state and time-resolved fluorescence studies were performed in ethanol solution and in the solid state. In solution, intramolecular pi-stacking interaction between phenanthroline and anthracene in the ground state and exciplex emission in the excited state were observed. From the temperature dependence of the photostationary ratio (I(Exc)/I(M)), the activation energy for the exciplex formation (E(a)) and the binding energy of the exciplex (-DeltaH) were determined. The crystal structure of the [ZnLBr](ClO(4)).H(2)O compound was resolved, showing that in the solid state both intra- and inter-molecular pi-stacking interactions are present. Such interactions were also evidenced by UV-vis absorption and emission spectra in the solid state. The absorption spectrum of a thin film of the solid complex is red-shifted compared with the solution spectra, whereas its emission spectrum reveals the unique featureless exciplex band, blue shifted compared with the solution. In conjunction with X-ray data the solid-state data was interpreted as being due to a new exciplex where no pi-stacking (full overlap of the pi-electron cloud of the two chromophores - anthracene and phenanthroline) is observed. L is a fluorescent chemosensor able to signal Zn(II) in presence of Cd(II) and Hg(II), since the last two metal ions do not give rise either to the formation of pi-stacking complexes or to exciplex emission in solution.

On Pythagoras Theorem for Products of Spectral Triples

NASA Astrophysics Data System (ADS)

D'Andrea, Francesco; Martinetti, Pierre

2013-05-01

We discuss a version of Pythagoras theorem in noncommutative geometry. Usual Pythagoras theorem can be formulated in terms of Connes' distance, between pure states, in the product of commutative spectral triples. We investigate the generalization to both non-pure states and arbitrary spectral triples. We show that Pythagoras theorem is replaced by some Pythagoras inequalities, that we prove for the product of arbitrary (i.e. non-necessarily commutative) spectral triples, assuming only some unitality condition. We show that these inequalities are optimal, and we provide non-unital counter-examples inspired by K-homology.

Wide-band polarization controller for Si photonic integrated circuits.

PubMed

Velha, P; Sorianello, V; Preite, M V; De Angelis, G; Cassese, T; Bianchi, A; Testa, F; Romagnoli, M

2016-12-15

A circuit for the management of any arbitrary polarization state of light is demonstrated on an integrated silicon (Si) photonics platform. This circuit allows us to adapt any polarization into the standard fundamental TE mode of a Si waveguide and, conversely, to control the polarization and set it to any arbitrary polarization state. In addition, the integrated thermal tuning allows kilohertz speed which can be used to perform a polarization scrambler. The circuit was used in a WDM link and successfully used to adapt four channels into a standard Si photonic integrated circuit.

Generalized Born-Oppenheimer treatment of Jahn-Teller systems in Hilbert spaces of arbitrary dimension: theory and application to a three-state model potential.

PubMed

Varandas, A J C; Sarkar, B

2011-05-14

Generalized Born-Oppenheimer equations including the geometrical phase effect are derived for three- and four-fold electronic manifolds in Jahn-Teller systems near the degeneracy seam. The method is readily extendable to N-fold systems of arbitrary dimension. An application is reported for a model threefold system, and the results are compared with Born-Oppenheimer (geometrical phase ignored), extended Born-Oppenheimer, and coupled three-state calculations. The theory shows unprecedented simplicity while depicting all features of more elaborated ones.

Energy as a witness of multipartite entanglement in chains of arbitrary spins

NASA Astrophysics Data System (ADS)

Troiani, F.; Siloi, I.

2012-09-01

We develop a general approach for deriving the energy minima of biseparable states in chains of arbitrary spins s, and we report numerical results for spin values s≤5/2 (with N≤8). The minima provide a set of threshold values for exchange energy that allow us to detect different degrees of multipartite entanglement in one-dimensional spin systems. We finally demonstrate that the Heisenberg exchange Hamiltonian of N spins has a nondegenerate N-partite entangled ground state, and it can thus witness such correlations in all finite spin chains.

Transferring arbitrary d-dimensional quantum states of a superconducting transmon qudit in circuit QED.

PubMed

Liu, Tong; Su, Qi-Ping; Yang, Jin-Hu; Zhang, Yu; Xiong, Shao-Jie; Liu, Jin-Ming; Yang, Chui-Ping

2017-08-01

A qudit (d-level quantum system) has a large Hilbert space and thus can be used to achieve many quantum information and communication tasks. Here, we propose a method to transfer arbitrary d-dimensional quantum states (known or unknown) between two superconducting transmon qudits coupled to a single cavity. The state transfer can be performed by employing resonant interactions only. In addition, quantum states can be deterministically transferred without measurement. Numerical simulations show that high-fidelity transfer of quantum states between two superconducting transmon qudits (d ≤ 5) is feasible with current circuit QED technology. This proposal is quite general and can be applied to accomplish the same task with natural or artificial atoms of a ladder-type level structure coupled to a cavity or resonator.

Self-assembly of PEGylated tetra-phenylalanine derivatives: structural insights from solution and solid state studies

PubMed Central

Diaferia, Carlo; Mercurio, Flavia Anna; Giannini, Cinzia; Sibillano, Teresa; Morelli, Giancarlo; Leone, Marilisa; Accardo, Antonella

2016-01-01

Water soluble fibers of PEGylated tetra-phenylalanine (F4), chemically modified at the N-terminus with the DOTA chelating agent, have been proposed as innovative contrast agent (CA) in Magnetic Resonance Imaging (MRI) upon complexation of the gadolinium ion. An in-depth structural characterization of PEGylated F4-fibers, in presence (DOTA-L6-F4) and in absence of DOTA (L6-F4), is reported in solution and at the solid state, by a multiplicity of techniques including CD, FTIR, NMR, DLS, WAXS and SAXS. This study aims to better understand how the aggregation process influences the performance of nanostructures as MRI CAs. Critical aggregation concentrations for L6-F4 (43 μM) and DOTA-L6-F4 (75 μM) indicate that self-aggregation process occurs in the same concentration range, independently of the presence of the CA. The driving force for the aggregation is the π-stacking between the side chains of the aromatic framework. CD, FTIR and WAXS measurements indicate an antiparallel β-sheet organization of the monomers in the resulting fibers. Moreover, WAXS and FTIR experiments point out that in solution the nanomaterials retain the same morphology and monomer organizations of the solid state, although the addition of the DOTA chelating agent affects the size and the degree of order of the fibers. PMID:27220817

A new equilibrium torus solution and GRMHD initial conditions

NASA Astrophysics Data System (ADS)

Penna, Robert F.; Kulkarni, Akshay; Narayan, Ramesh

2013-11-01

Context. General relativistic magnetohydrodynamic (GRMHD) simulations are providing influential models for black hole spin measurements, gamma ray bursts, and supermassive black hole feedback. Many of these simulations use the same initial condition: a rotating torus of fluid in hydrostatic equilibrium. A persistent concern is that simulation results sometimes depend on arbitrary features of the initial torus. For example, the Bernoulli parameter (which is related to outflows), appears to be controlled by the Bernoulli parameter of the initial torus. Aims: In this paper, we give a new equilibrium torus solution and describe two applications for the future. First, it can be used as a more physical initial condition for GRMHD simulations than earlier torus solutions. Second, it can be used in conjunction with earlier torus solutions to isolate the simulation results that depend on initial conditions. Methods: We assume axisymmetry, an ideal gas equation of state, constant entropy, and ignore self-gravity. We fix an angular momentum distribution and solve the relativistic Euler equations in the Kerr metric. Results: The Bernoulli parameter, rotation rate, and geometrical thickness of the torus can be adjusted independently. Our torus tends to be more bound and have a larger radial extent than earlier torus solutions. Conclusions: While this paper was in preparation, several GRMHD simulations appeared based on our equilibrium torus. We believe it will continue to provide a more realistic starting point for future simulations.

Infrared and Raman spectra of N-acetyl- L-amino acid methylamides with aromatic side groups

NASA Astrophysics Data System (ADS)

Matsuura, Hiroatsu; Hasegawa, Kodo; Miyazawa, Tatsuo

Infrared and Raman spectra of N-acetyl- L-phenylalanine methylamide, N-acetyl- L-tyrosine methylamide and N-acetyl- L-tryptophan methylamide, as model compounds of aromatic amino acid residues in proteins, were measured in the solid state and in methanol solutions. Vibrational assignments of the spectra were made by utilizing the deuteration effect and by comparison with the spectra of related compounds which include toluene, p-cresol and 3-methylindole. The amide I, III and IV bands were strong in Raman scattering, but other characteristic amide bands were ill-defined. In the Raman spectra of methanol solutions, only the bands due to the aromatic side group vibrations were markedly observed, but those due to the peptide backbone vibrations were very weak, suggesting the coexistence of various molecular conformations in solution.

Faithful Transfer Arbitrary Pure States with Mixed Resources

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing; Li, Lin; Ma, Song-Ya; Chen, Xiu-Bo; Yang, Yi-Xian

2013-09-01

In this paper, we show that some special mixed quantum resource experience the same property of pure entanglement such as Bell state for quantum teleportation. It is shown that one mixed state and three bits of classical communication cost can be used to teleport one unknown qubit compared with two bits via pure resources. The schemes are easily implement with model physical techniques. Moreover, these resources are also optimal and typical for faithfully remotely prepare an arbitrary qubit, two-qubit and three-qubit states with mixed quantum resources. Our schemes are completed as same as those with pure quantum entanglement resources except only 1 bit additional classical communication cost required. The success probability is independent of the form of the mixed resources.

Efficient and faithful remote preparation of arbitrary three- and four-particle -class entangled states

NASA Astrophysics Data System (ADS)

Wang, Dong; Hu, You-Di; Wang, Zhe-Qiang; Ye, Liu

2015-06-01

We develop two efficient measurement-based schemes for remotely preparing arbitrary three- and four-particle W-class entangled states by utilizing genuine tripartite Greenberg-Horn-Zeilinger-type states as quantum channels, respectively. Through appropriate local operations and classical communication, the desired states can be faithfully retrieved at the receiver's place with certain probability. Compared with the previously existing schemes, the success probability in current schemes is greatly increased. Moreover, the required classical communication cost is calculated as well. Further, several attractive discussions on the properties of the presented schemes, including the success probability and reducibility, are made. Remarkably, the proposed schemes can be faithfully achieved with unity total success probability when the employed channels are reduced into maximally entangled ones.

Q-plates as higher order polarization controllers for orbital angular momentum modes of fiber.

PubMed

Gregg, P; Mirhosseini, M; Rubano, A; Marrucci, L; Karimi, E; Boyd, R W; Ramachandran, S

2015-04-15

We demonstrate that a |q|=1/2 plate, in conjunction with appropriate polarization optics, can selectively and switchably excite all linear combinations of the first radial mode order |l|=1 orbital angular momentum (OAM) fiber modes. This enables full mapping of free-space polarization states onto fiber vector modes, including the radially (TM) and azimuthally polarized (TE) modes. The setup requires few optical components and can yield mode purities as high as ∼30  dB. Additionally, just as a conventional fiber polarization controller creates arbitrary elliptical polarization states to counteract fiber birefringence and yield desired polarizations at the output of a single-mode fiber, q-plates disentangle degenerate state mixing effects between fiber OAM states to yield pure states, even after long-length fiber propagation. We thus demonstrate the ability to switch dynamically, potentially at ∼GHz rates, between OAM modes, or create desired linear combinations of them. We envision applications in fiber-based lasers employing vector or OAM mode outputs, as well as communications networking schemes exploiting spatial modes for higher dimensional encoding.

Special solutions to Chazy equation

NASA Astrophysics Data System (ADS)

Varin, V. P.

2017-02-01

We consider the classical Chazy equation, which is known to be integrable in hypergeometric functions. But this solution has remained purely existential and was never used numerically. We give explicit formulas for hypergeometric solutions in terms of initial data. A special solution was found in the upper half plane H with the same tessellation of H as that of the modular group. This allowed us to derive some new identities for the Eisenstein series. We constructed a special solution in the unit disk and gave an explicit description of singularities on its natural boundary. A global solution to Chazy equation in elliptic and theta functions was found that allows parametrization of an arbitrary solution to Chazy equation. The results have applications to analytic number theory.

CHEMKIN2. General Gas-Phase Chemical Kinetics

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

Rupley, F.M.

1992-01-24

CHEMKIN is a high-level tool for chemists to use to describe arbitrary gas-phase chemical reaction mechanisms and systems of governing equations. It remains, however, for the user to select and implement a solution method; this is not provided. It consists of two major components: the Interpreter and the Gas-phase Subroutine Library. The Interpreter reads a symbolic description of an arbitrary, user-specified chemical reaction mechanism. A data file is generated which forms a link to the Gas-phase Subroutine Library, a collection of about 200 modular subroutines which may be called to return thermodynamic properties, chemical production rates, derivatives of thermodynamic properties,more » derivatives of chemical production rates, or sensitivity parameters. Both single and double precision versions of CHEMKIN are included. Also provided is a set of FORTRAN subroutines for evaluating gas-phase transport properties such as thermal conductivities, viscosities, and diffusion coefficients. These properties are an important part of any computational simulation of a chemically reacting flow. The transport properties subroutines are designed to be used in conjunction with the CHEMKIN Subroutine Library. The transport properties depend on the state of the gas and on certain molecular parameters. The parameters considered are the Lennard-Jones potential well depth and collision diameter, the dipole moment, the polarizability, and the rotational relaxation collision number.« less

Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion

NASA Astrophysics Data System (ADS)

Olšina, Jan; Kramer, Tobias; Kreisbeck, Christoph; Mančal, Tomáš

2014-10-01

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.

Quantum spin dynamics with pairwise-tunable, long-range interactions

PubMed Central

Hung, C.-L.; González-Tudela, Alejandro; Cirac, J. Ignacio; Kimble, H. J.

2016-01-01

We present a platform for the simulation of quantum magnetism with full control of interactions between pairs of spins at arbitrary distances in 1D and 2D lattices. In our scheme, two internal atomic states represent a pseudospin for atoms trapped within a photonic crystal waveguide (PCW). With the atomic transition frequency aligned inside a band gap of the PCW, virtual photons mediate coherent spin–spin interactions between lattice sites. To obtain full control of interaction coefficients at arbitrary atom–atom separations, ground-state energy shifts are introduced as a function of distance across the PCW. In conjunction with auxiliary pump fields, spin-exchange versus atom–atom separation can be engineered with arbitrary magnitude and phase, and arranged to introduce nontrivial Berry phases in the spin lattice, thus opening new avenues for realizing topological spin models. We illustrate the broad applicability of our scheme by explicit construction for several well-known spin models. PMID:27496329

Universal instability of hairy black holes in Lovelock-Galileon theories in D dimensions

NASA Astrophysics Data System (ADS)

Takahashi, Kazufumi; Suyama, Teruaki; Kobayashi, Tsutomu

2016-03-01

We analyze spherically symmetric black hole solutions with time-dependent scalar hair in a class of Lovelock-Galileon theories, which are the scalar-tensor theories with second-order field equations in arbitrary dimensions. We first show that known black hole solutions in five dimensions are always plagued by the ghost/gradient instability in the vicinity of the horizon. We then generalize such black hole solutions to higher dimensions and show that the same instability found in five dimensions appears universally in any number of dimensions.

Analytical solution for wave propagation through a graded index interface between a right-handed and a left-handed material.

PubMed

Dalarsson, Mariana; Tassin, Philippe

2009-04-13

We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index structure, and we show excellent agreement between the analytical solution and the corresponding results obtained by accurate numerical simulations. Our model straightforwardly allows for arbitrary spectral dispersion.

Quantum State Transmission in a Superconducting Charge Qubit-Atom Hybrid

PubMed Central

Yu, Deshui; Valado, María Martínez; Hufnagel, Christoph; Kwek, Leong Chuan; Amico, Luigi; Dumke, Rainer

2016-01-01

Hybrids consisting of macroscopic superconducting circuits and microscopic components, such as atoms and spins, have the potential of transmitting an arbitrary state between different quantum species, leading to the prospective of high-speed operation and long-time storage of quantum information. Here we propose a novel hybrid structure, where a neutral-atom qubit directly interfaces with a superconducting charge qubit, to implement the qubit-state transmission. The highly-excited Rydberg atom located inside the gate capacitor strongly affects the behavior of Cooper pairs in the box while the atom in the ground state hardly interferes with the superconducting device. In addition, the DC Stark shift of the atomic states significantly depends on the charge-qubit states. By means of the standard spectroscopic techniques and sweeping the gate voltage bias, we show how to transfer an arbitrary quantum state from the superconducting device to the atom and vice versa. PMID:27922087

Chemical equilibrium of ablation materials including condensed species

NASA Technical Reports Server (NTRS)

Stroud, C. W.; Brinkley, K. L.

1975-01-01

Equilibrium is determined by finding chemical composition with minimum free energy. Method of steepest descent is applied to quadratic representation of free-energy surface. Solution is initiated by selecting arbitrary set of mole fractions, from which point on free-energy surface is computed.

Two-point resistance of an m × n resistor network with an arbitrary boundary and its application in RLC network

NASA Astrophysics Data System (ADS)

Zhi-Zhong, Tan

2016-05-01

A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform (RT) method, a problem that has never been resolved before, for the Green’s function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h 1 = 1 - cos ϕ i - sin ϕ i cot n ϕ i . This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits. Project supported by the Prophase Preparatory Project of Natural Science Foundation of Nantong University, China (Grant No. 15ZY16).

General kinetic solution for the Biermann battery with an associated pressure anisotropy generation

NASA Astrophysics Data System (ADS)

Schoeffler, K. M.; Silva, L. O.

2018-01-01

Fully kinetic analytic calculations of an initially Maxwellian distribution with arbitrary density and temperature gradients exhibit the development of temperature anisotropies and magnetic field growth associated with the Biermann battery. The calculation, performed by taking a small order expansion of the ratio of the Debye length to the gradient scale, predicts anisotropies and magnetic fields as a function of space given an arbitrary temperature and density profile. These predictions are shown to qualitatively match the values measured from particle-in-cell simulations, where the development of the Weibel instability occurs at the same location and with a wavenumber aligned with the predicted temperature anisotropy.

Open Group Transformations

NASA Astrophysics Data System (ADS)

Batalin, Igor; Marnelius, Robert

Open groups whose generators are in arbitrary involutions may be quantized within a ghost extended framework in terms of a nilpotent BFV-BRST charge operator. Previously we have shown that generalized quantum Maurer-Cartan equations for arbitrary open groups may be extracted from the quantum connection operators and that they also follow from a simple quantum master equation involving an extended nilpotent BFV-BRST charge and a master charge. Here we give further details of these results. In addition we establish the general structure of the solutions of the quantum master equation. We also construct an extended formulation whose properties are determined by the extended BRST charge in the master equation.

Visualizing the Zero-Potential Line of Bipolar Electrodes with Arbitrary Geometry.

PubMed

Li, Meng; Liu, Shasha; Jiang, Yingyan; Wang, Wei

2018-06-05

In a typical bipolar electrochemistry (BPE) configuration, voltage applied between the two driving electrodes induced a potential drop through solution filled in the microchannel, resulting in an interfacial potential difference between solution and BPE varied along the BPE. In the present work, we employed a recently developed plasmonic imaging technique to map the distribution of surface potential of bipolar electrodes with various geometries including round, triangle, hexagon, star, and rhombus shapes under the nonfaradaic charging process, from which the line of zero potential (LZP) was visualized and determined. We further investigated the dependence of LZP on electrode geometry and the distribution of external electric field and explained the experimental results with a charge balance mechanism. The triangular and star-shaped BPEs show quite different LZP features from the other ones with symmetrical geometry. These experimentally obtained potential distributions are all in good agreement with electromagnetic simulations. Finally, the line of zero overpotential (LZO) of the triangular-shaped BPE under faradaic reactions were investigated. The results confirm the shift of LZO when faradaic reactions occurred at the corresponding ends of BPE. The present work demonstrates the first experimental capability to map the potential distribution of BPE with arbitrary geometry under an arbitrary driving field. It is anticipated to help the design and optimization on the geometry of electrodes and microchannels with implications for boosting their applications in chemical sensing and materials synthesis.

Modeling the effects of pH and ionic strength on swelling of anionic polyelectrolyte gels

NASA Astrophysics Data System (ADS)

Drozdov, A. D.; deClaville Christiansen, J.

2015-07-01

A constitutive model is developed for the elastic response of an anionic polyelectrolyte gel under swelling in water with an arbitrary pH and an arbitrary molar fraction of dissolved monovalent salt. A gel is treated as a three-phase medium consisting of a solid phase (polymer network), solvent (water), and solute (mobile ions). Transport of solvent and solute is thought of as their diffusion through the polymer network accelerated by an electric field formed by mobile and fixed ions and accompanied by chemical reactions (dissociation of functional groups attached to polymer chains and formation of ion pairs between bound charges and mobile counter-ions). Constitutive equations are derived by means of the free energy imbalance inequality for an arbitrary three-dimensional deformation with finite strains. These relations are applied to analyze equilibrium swelling diagrams on poly(acrylic acid) gel, poly(methacrylic acid) gel, and three composite hydrogels under water uptake in a bath (i) with a fixed molar fraction of salt and varied pH, and (ii) with a fixed pH and varied molar fraction of salt. To validate the ability of the model to predict observations quantitatively, material constants are found by matching swelling curves under one type of experimental conditions and results of simulation are compared with experimental data in the other type of tests.

Clinical ethics consultation's dilemma, and a solution.

PubMed

Rasmussen, Lisa M

2011-01-01

Clinical ethics consultation is on the horns of a dilemma. One horn skewers the field for its lack of standards, while the other horn skewers it for proposing arbitrary or deeply contested foundations. I articulate the dilemma by discussing several critiques of the field and the challenge of formulating standards and suggest that the solution lies, at least until a robust consensus emerges, with establishing a list of proscriptive standards to guide the field.

Studying the validity of relativistic hydrodynamics with a new exact solution of the Boltzmann equation

NASA Astrophysics Data System (ADS)

Denicol, Gabriel; Heinz, Ulrich; Martinez, Mauricio; Noronha, Jorge; Strickland, Michael

2014-12-01

We present an exact solution to the Boltzmann equation which describes a system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion for arbitrary shear viscosity to entropy density ratio. This new solution is constructed by considering the conformal map between Minkowski space and the direct product of three-dimensional de Sitter space with a line. The resulting solution respects S O (3 )q⊗S O (1 ,1 )⊗Z2 symmetry. We compare the exact kinetic solution with exact solutions of the corresponding macroscopic equations that were obtained from the kinetic theory in ideal and second-order viscous hydrodynamic approximations. The macroscopic solutions are obtained in de Sitter space and are subject to the same symmetries used to obtain the exact kinetic solution.

A general method of aquitard control of flow for arbitrary orientation of wells in Aquitard- Aquifer-Aquitard System (AAA)

NASA Astrophysics Data System (ADS)

Zhan, H.; Sun, D.

2006-12-01

Aquitards are low permeable sedimentary layers that often serve as interfaces through which recharge, contaminants, and nutrients from the vadose zone enter aquifers. Aquitards are capable of storing water, yet lack of ability to transmit water. Hydrologists have recognized the importance of aquitards on subsurface flow and transport for many decades. However, for various reasons, studies of aquitards have received much less attention than that of the aquifers for many years. In this study, we have investigated the effects of aquitard on drawdown caused by arbitrary orientation of well pumping in an aquitard-aquifer-aquitard system. Pumping well could be partial penetrating vertical well, horizontal well or slanted well at arbitrary angles to horizontal plane. We have derived the solutions for six cases with various combinations of water table, aquitard, aquifer, aquitard, and bedrocks. Previous study treated the leakage from aquitard-aquifer mass flux as a volumetric source/sink term in the governing equation of flow in the aquifer. In this study, new semi-analytical solutions are acquired for the aquitard-aquifer-aquitard system via rigorous mass conservation laws. Flows in aquitard and aquifer are treated as separate systems which are linked through the continuity of flux and head at the aquitard-aquifer boundary. This general solution is applicable to both water table aquifer and leaky-confined aquifer. Examples illustrate the effect of aquitard properties at different well configurations. The results will be used to generate type curves for various situations. The results of this paper are useful for parameter identification and water resource management. Keywords: Aquitard-Aquifer-Aquitard; Pumping Well, Slanted Well, Horizontal well, Type curves.

[Computer modeling the hydrostatic pressure characteristics of the membrane potential for polymeric membrane, separated non-homogeneous electrolyte solutions].

PubMed

Slezak, Izabella H; Jasik-Slezak, Jolanta; Rogal, Mirosława; Slezak, Andrzej

2006-01-01

On the basis of model equation depending the membrane potential deltapsis, on mechanical pressure difference (deltaP), concentration polarization coefficient (zetas), concentration Rayleigh number (RC) and ratio concentration of solutions separated by membrane (Ch/Cl), the characteristics deltapsis = f(deltaP)zetas,RC,Ch/Cl for steady values of zetas, RC and Ch/Cl in single-membrane system were calculated. In this system neutral and isotropic polymeric membrane oriented in horizontal plane, the non-homogeneous binary electrolytic solutions of various concentrations were separated. Nonhomogeneity of solutions is results from creations of the concentration boundary layers on both sides of the membrane. Calculations were made for the case where on a one side of the membrane aqueous solution of NaCl at steady concentration 10(-3) mol x l(-1) (Cl) was placed and on the other aqueous solutions of NaCl at concentrations from 10(-3) mol x l(-1) to 2 x 10(-2) mol x l(-1) (Ch). Their densities were greater than NaCl solution's at 10(-3) mol x l(-1). It was shown that membrane potential depends on hydrodynamic state of a complex concentration boundary layer-membrane-concentration boundary layer, what is controlled by deltaP, Ch/Cl, RC and zetas.

Control quantum evolution speed of a single dephasing qubit for arbitrary initial states via periodic dynamical decoupling pulses.

PubMed

Song, Ya-Ju; Tan, Qing-Shou; Kuang, Le-Man

2017-03-08

We investigate the possibility to control quantum evolution speed of a single dephasing qubit for arbitrary initial states by the use of periodic dynamical decoupling (PDD) pulses. It is indicated that the quantum speed limit time (QSLT) is determined by initial and final quantum coherence of the qubit, as well as the non-Markovianity of the system under consideration during the evolution when the qubit is subjected to a zero-temperature Ohmic-like dephasing reservoir. It is shown that final quantum coherence of the qubit and the non-Markovianity of the system can be modulated by PDD pulses. Our results show that for arbitrary initial states of the dephasing qubit with non-vanishing quantum coherence, PDD pulses can be used to induce potential acceleration of the quantum evolution in the short-time regime, while PDD pulses can lead to potential speedup and slow down in the long-time regime. We demonstrate that the effect of PDD on the QSLT for the Ohmic or sub-Ohmic spectrum (Markovian reservoir) is much different from that for the super-Ohmic spectrum (non-Markovian reservoir).

Single-copy entanglement in critical quantum spin chains

NASA Astrophysics Data System (ADS)

Eisert, J.; Cramer, M.

2005-10-01

We consider the single-copy entanglement as a quantity to assess quantum correlations in the ground state in quantum many-body systems. We show for a large class of models that already on the level of single specimens of spin chains, criticality is accompanied with the possibility of distilling a maximally entangled state of arbitrary dimension from a sufficiently large block deterministically, with local operations and classical communication. These analytical results—which refine previous results on the divergence of block entropy as the rate at which maximally entangled pairs can be distilled from many identically prepared chains—are made quantitative for general isotropic translationally invariant spin chains that can be mapped onto a quasifree fermionic system, and for the anisotropic XY model. For the XX model, we provide the asymptotic scaling of ˜(1/6)log2(L) , and contrast it with the block entropy.

TranAir: A full-potential, solution-adaptive, rectangular grid code for predicting subsonic, transonic, and supersonic flows about arbitrary configurations. Theory document

NASA Technical Reports Server (NTRS)

Johnson, F. T.; Samant, S. S.; Bieterman, M. B.; Melvin, R. G.; Young, D. P.; Bussoletti, J. E.; Hilmes, C. L.

1992-01-01

A new computer program, called TranAir, for analyzing complex configurations in transonic flow (with subsonic or supersonic freestream) was developed. This program provides accurate and efficient simulations of nonlinear aerodynamic flows about arbitrary geometries with the ease and flexibility of a typical panel method program. The numerical method implemented in TranAir is described. The method solves the full potential equation subject to a set of general boundary conditions and can handle regions with differing total pressure and temperature. The boundary value problem is discretized using the finite element method on a locally refined rectangular grid. The grid is automatically constructed by the code and is superimposed on the boundary described by networks of panels; thus no surface fitted grid generation is required. The nonlinear discrete system arising from the finite element method is solved using a preconditioned Krylov subspace method embedded in an inexact Newton method. The solution is obtained on a sequence of successively refined grids which are either constructed adaptively based on estimated solution errors or are predetermined based on user inputs. Many results obtained by using TranAir to analyze aerodynamic configurations are presented.

Extended phase graphs with anisotropic diffusion

NASA Astrophysics Data System (ADS)

Weigel, M.; Schwenk, S.; Kiselev, V. G.; Scheffler, K.; Hennig, J.

2010-08-01

The extended phase graph (EPG) calculus gives an elegant pictorial description of magnetization response in multi-pulse MR sequences. The use of the EPG calculus enables a high computational efficiency for the quantitation of echo intensities even for complex sequences with multiple refocusing pulses with arbitrary flip angles. In this work, the EPG concept dealing with RF pulses with arbitrary flip angles and phases is extended to account for anisotropic diffusion in the presence of arbitrary varying gradients. The diffusion effect can be expressed by specific diffusion weightings of individual magnetization pathways. This can be represented as an action of a linear operator on the magnetization state. The algorithm allows easy integration of diffusion anisotropy effects. The formalism is validated on known examples from literature and used to calculate the effective diffusion weighting in multi-echo sequences with arbitrary refocusing flip angles.

Quantum state engineering using one-dimensional discrete-time quantum walks

NASA Astrophysics Data System (ADS)

Innocenti, Luca; Majury, Helena; Giordani, Taira; Spagnolo, Nicolò; Sciarrino, Fabio; Paternostro, Mauro; Ferraro, Alessandro

2017-12-01

Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform chosen for implementation, and a general framework is still missing. Here we show that coined quantum walks on a line, which represent a framework general enough to encompass a variety of different platforms, can be used for quantum state engineering of arbitrary superpositions of the walker's sites. We achieve this goal by identifying a set of conditions that fully characterize the reachable states in the space comprising walker and coin and providing a method to efficiently compute the corresponding set of coin parameters. We assess the feasibility of our proposal by identifying a linear optics experiment based on photonic orbital angular momentum technology.

Consistent multiphase-field theory for interface driven multidomain dynamics

NASA Astrophysics Data System (ADS)

Tóth, Gyula I.; Pusztai, Tamás; Gránásy, László

2015-11-01

We present a multiphase-field theory for describing pattern formation in multidomain and/or multicomponent systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical and physical consistency. We first analyze previous multiphase-field theories and identify their advantageous and disadvantageous features. On the basis of this analysis, we introduce a way of constructing the free energy surface and derive a generalized multiphase description for arbitrary number of phases (or domains). The presented approach retains the variational formalism, reduces (or extends) naturally to lower (or higher) number of fields on the level of both the free energy functional and the dynamic equations, enables the use of arbitrary pairwise equilibrium interfacial properties, penalizes multiple junctions increasingly with the number of phases, ensures non-negative entropy production and the convergence of the dynamic solutions to the equilibrium solutions, and avoids the appearance of spurious phases on binary interfaces. The approach is tested for multicomponent phase separation and grain coarsening.

Schemes for deterministic joint remote preparation of an arbitrary tripartite four-qubit entangled state

NASA Astrophysics Data System (ADS)

Ma, Peng-Cheng; Chen, Gui-Bin; Li, Xiao-Wei; Zhan, You-Bang

2016-10-01

We present two schemes for the joint remote state preparation (JRSP) of an arbitrary tripartite four-qubit entangled state with complex coefficients via four and two three-qubit GHZ states as the quantum channel, respectively. In these schemes, the two senders share the original state which they wish to help the receiver remotely prepare. To complete the JRSP schemes, some novel sets of mutually orthogonal basis vectors are introduced. It is shown that, only if the two senders collaborate with each other, and perform projective measurements under a suitable measuring basis on their own qubits respectively, can the receiver reconstruct the original state by means of some appropriate unitary operations. We demonstrate, in our both schemes, the total success probability of the JRSP can reach 1. Moreover, compared with the first scheme in this paper, the advantage of the second scheme is that the entanglement resource can be reduced.

Arbitrary spin-to-orbital angular momentum conversion of light.

PubMed

Devlin, Robert C; Ambrosio, Antonio; Rubin, Noah A; Mueller, J P Balthasar; Capasso, Federico

2017-11-17

Optical elements that convert the spin angular momentum (SAM) of light into vortex beams have found applications in classical and quantum optics. These elements-SAM-to-orbital angular momentum (OAM) converters-are based on the geometric phase and only permit the conversion of left- and right-circular polarizations (spin states) into states with opposite OAM. We present a method for converting arbitrary SAM states into total angular momentum states characterized by a superposition of independent OAM. We designed a metasurface that converts left- and right-circular polarizations into states with independent values of OAM and designed another device that performs this operation for elliptically polarized states. These results illustrate a general material-mediated connection between SAM and OAM of light and may find applications in producing complex structured light and in optical communication. Copyright © 2017, American Association for the Advancement of Science.

Nonparaxial wave beams and packets with general astigmatism

NASA Astrophysics Data System (ADS)

Kiselev, A. P.; Plachenov, A. B.; Chamorro-Posada, P.

2012-04-01

We present exact solutions of the wave equation involving an arbitrary wave form with a phase closely similar to the general astigmatic phase of paraxial wave optics. Special choices of the wave form allow general astigmatic beamlike and pulselike waves with a Gaussian-type unrestricted localization in space and time. These solutions are generalizations of the known Bateman-type waves obtained from the connection existing between beamlike solutions of the paraxial parabolic equation and relatively undistorted wave solutions of the wave equation. As a technical tool, we present a full description of parametrizations of 2×2 symmetric matrices with positive imaginary part, which arise in the theory of Gaussian beams.

On the existence of the field line solutions of the Einstein-Maxwell equations

NASA Astrophysics Data System (ADS)

Vancea, Ion V.

The main result of this paper is the proof that there are local electric and magnetic field configurations expressed in terms of field lines on an arbitrary hyperbolic manifold. This electromagnetic field is described by (dual) solutions of the Maxwell’s equations of the Einstein-Maxwell theory. These solutions have the following important properties: (i) they are general, in the sense that the knot solutions are particular cases of them and (ii) they reduce to the electromagnetic fields in the field line representation in the flat space-time. Also, we discuss briefly the real representation of these electromagnetic configurations and write down the corresponding Einstein equations.

Computational approach to Thornley's problem by bivariate operational calculus

NASA Astrophysics Data System (ADS)

Bazhlekova, E.; Dimovski, I.

2012-10-01

Thornley's problem is an initial-boundary value problem with a nonlocal boundary condition for linear onedimensional reaction-diffusion equation, used as a mathematical model of spiral phyllotaxis in botany. Applying a bivariate operational calculus we find explicit representation of the solution, containing two convolution products of special solutions and the arbitrary initial and boundary functions. We use a non-classical convolution with respect to the space variable, extending in this way the classical Duhamel principle. The special solutions involved are represented in the form of fast convergent series. Numerical examples are considered to show the application of the present technique and to analyze the character of the solution.

Some operational tools for solving fractional and higher integer order differential equations: A survey on their mutual relations

NASA Astrophysics Data System (ADS)

Kiryakova, Virginia S.

2012-11-01

The Laplace Transform (LT) serves as a basis of the Operational Calculus (OC), widely explored by engineers and applied scientists in solving mathematical models for their practical needs. This transform is closely related to the exponential and trigonometric functions (exp, cos, sin) and to the classical differentiation and integration operators, reducing them to simple algebraic operations. Thus, the classical LT and the OC give useful tool to handle differential equations and systems with constant coefficients. Several generalizations of the LT have been introduced to allow solving, in a similar way, of differential equations with variable coefficients and of higher integer orders, as well as of fractional (arbitrary non-integer) orders. Note that fractional order mathematical models are recently widely used to describe better various systems and phenomena of the real world. This paper surveys briefly some of our results on classes of such integral transforms, that can be obtained from the LT by means of "transmutations" which are operators of the generalized fractional calculus (GFC). On the list of these Laplace-type integral transforms, we consider the Borel-Dzrbashjan, Meijer, Krätzel, Obrechkoff, generalized Obrechkoff (multi-index Borel-Dzrbashjan) transforms, etc. All of them are G- and H-integral transforms of convolutional type, having as kernels Meijer's G- or Fox's H-functions. Besides, some special functions (also being G- and H-functions), among them - the generalized Bessel-type and Mittag-Leffler (M-L) type functions, are generating Gel'fond-Leontiev (G-L) operators of generalized differentiation and integration, which happen to be also operators of GFC. Our integral transforms have operational properties analogous to those of the LT - they do algebrize the G-L generalized integrations and differentiations, and thus can serve for solving wide classes of differential equations with variable coefficients of arbitrary, including non-integer order. Throughout the survey, we illustrate the parallels in the relationships: Laplace type integral transforms - special functions as kernels - operators of generalized integration and differentiation generated by special functions - special functions as solutions of related differential equations. The role of the so-called Special Functions of Fractional Calculus is emphasized.

Open-ended formulation of self-consistent field response theory with the polarizable continuum model for solvation.

PubMed

Di Remigio, Roberto; Beerepoot, Maarten T P; Cornaton, Yann; Ringholm, Magnus; Steindal, Arnfinn Hykkerud; Ruud, Kenneth; Frediani, Luca

2016-12-21

The study of high-order absorption properties of molecules is a field of growing importance. Quantum-chemical studies can help design chromophores with desirable characteristics. Given that most experiments are performed in solution, it is important to devise a cost-effective strategy to include solvation effects in quantum-chemical studies of these properties. We here present an open-ended formulation of self-consistent field (SCF) response theory for a molecular solute coupled to a polarizable continuum model (PCM) description of the solvent. Our formulation relies on the open-ended, density matrix-based quasienergy formulation of SCF response theory of Thorvaldsen, et al., [J. Chem. Phys., 2008, 129, 214108] and the variational formulation of the PCM, as presented by Lipparini et al., [J. Chem. Phys., 2010, 133, 014106]. Within the PCM approach to solvation, the mutual solute-solvent polarization is represented by means of an apparent surface charge (ASC) spread over the molecular cavity defining the solute-solvent boundary. In the variational formulation, the ASC is an independent, variational degree of freedom. This allows us to formulate response theory for molecular solutes in the fixed-cavity approximation up to arbitrary order and with arbitrary perturbation operators. For electric dipole perturbations, pole and residue analyses of the response functions naturally lead to the identification of excitation energies and transition moments. We document the implementation of this approach in the Dalton program package using a recently developed open-ended response code and the PCMSolver libraries and present results for one-, two-, three-, four- and five-photon absorption processes of three small molecules in solution.

Adaptive Fuzzy Control Design for Stochastic Nonlinear Switched Systems With Arbitrary Switchings and Unmodeled Dynamics.

PubMed

Li, Yongming; Sui, Shuai; Tong, Shaocheng

2017-02-01

This paper deals with the problem of adaptive fuzzy output feedback control for a class of stochastic nonlinear switched systems. The controlled system in this paper possesses unmeasured states, completely unknown nonlinear system functions, unmodeled dynamics, and arbitrary switchings. A state observer which does not depend on the switching signal is constructed to tackle the unmeasured states. Fuzzy logic systems are employed to identify the completely unknown nonlinear system functions. Based on the common Lyapunov stability theory and stochastic small-gain theorem, a new robust adaptive fuzzy backstepping stabilization control strategy is developed. The stability of the closed-loop system on input-state-practically stable in probability is proved. The simulation results are given to verify the efficiency of the proposed fuzzy adaptive control scheme.

Dynamic non-reciprocal meta-surfaces with arbitrary phase reconfigurability based on photonic transition in meta-atoms

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

Shi, Yu; Fan, Shanhui, E-mail: shanhui@stanford.edu

2016-01-11

We introduce a distinct class of dynamic non-reciprocal meta-surfaces with arbitrary phase-reconfigurability. This meta-surface consists of an array of meta-atoms, each of which is subject to temporal refractive index modulation, which induces photonic transitions between the states of the meta-atom. We show that arbitrary phase profile for the outgoing wave can be achieved by controlling the phase of the modulation at each meta-atom. Moreover, such dynamic meta-surfaces exhibit non-reciprocal response without the need for magneto-optical effects. The use of photonic transition significantly enhances the tunability and the possible functionalities of meta-surfaces.

Evaluation of Proteins' Rotational Diffusion Coefficients from Simulations of Their Free Brownian Motion in Volume-Occupied Environments.

PubMed

Długosz, Maciej; Antosiewicz, Jan M

2014-01-14

We have investigated the rotational dynamics of hen egg white lysozyme in monodisperse aqueous solutions of concentrations up to 250 mg/mL, using a rigid-body Brownian dynamics method that accurately accounts for anisotropies of diffusing objects. We have examined the validity of the free diffusion concept in the analysis of computer simulations of volume-occupied molecular solutions. We have found that, when as the only intermolecular interaction, the excluded volume effect is considered, rotational diffusion of molecules adheres to the free diffusion model. Further, we present a method based on the exact (in the case of the free diffusion) analytic forms of autocorrelation functions of particular vectors rigidly attached to diffusing objects, which allows one to obtain from results of molecular simulations the three principal rotational diffusion coefficients characterizing rotational Brownian motion of an arbitrarily shaped rigid particle for an arbitrary concentration of crowders. We have applied this approach to trajectories resulting from Brownian dynamics simulations of hen egg white lysozyme solutions. We show that the apparent anisotropy of proteins' rotational motions increases with an increasing degree of crowding. Finally, we demonstrate that even if the hydrodynamic anisotropy of molecules is neglected and molecules are simulated using their average translational and rotational diffusion coefficients, excluded volume effects still lead to their anisotropic rotational dynamics.

Linked-List-Based Multibody Dynamics (MBDyn) Engine

NASA Technical Reports Server (NTRS)

MacLean, John; Brain, Thomas; Wuiocho, Leslie; Huynh, An; Ghosh, Tushar

2012-01-01

This new release of MBDyn is a software engine that calculates the dynamics states of kinematic, rigid, or flexible multibody systems. An MBDyn multibody system may consist of multiple groups of articulated chains, trees, or closed-loop topologies. Transient topologies are handled through conservation of energy and momentum. The solution for rigid-body systems is exact, and several configurable levels of nonlinear term fidelity are available for flexible dynamics systems. The algorithms have been optimized for efficiency and can be used for both non-real-time (NRT) and real-time (RT) simulations. Interfaces are currently compatible with NASA's Trick Simulation Environment. This new release represents a significant advance in capability and ease of use. The two most significant new additions are an application programming interface (API) that clarifies and simplifies use of MBDyn, and a link-list infrastructure that allows a single MBDyn instance to propagate an arbitrary number of interacting groups of multibody top ologies. MBDyn calculates state and state derivative vectors for integration using an external integration routine. A Trickcompatible interface is provided for initialization, data logging, integration, and input/output.

An overview of medical malpractice litigation and the perceived crisis.

PubMed

Litvin, S Gerald

2005-04-01

In this overview of medical malpractice litigation in the United States, practical and philosophic aspects of the so-called malpractice litigation crisis are addressed. After reviewing the historical, legal rationale for compensating victims of negligent conduct by others, attention is focused on the plight of physicians who are charged with medical negligence and the oppressive insurance premiums that impose a heavy burden on all health care providers, particularly those in the surgical fields. A variety of political solutions advanced to "correct" the problem is reviewed. A historical prospective of malpractice litigation in the United States is presented together with an analysis of various legislative proposals--many of which have already been enacted in various states that will ostensibly "cure" the problems that concern clinicians. Consideration of the various legislative proposals includes: arbitrary limits on pain and suffering awards (caps); elimination of joint and several liability; regulation of attorneys fees; elimination of the collateral source rule; abrogation of punitive damages; proposals for periodic payments; and statutes of repose. Various procedural changes in the processing of malpractice claims are reviewed and analyzed from the perspective of both fairness and efficacy.

Cubic Equations and the Ideal Trisection of the Arbitrary Angle

ERIC Educational Resources Information Center

Farnsworth, Marion B.

2006-01-01

In the year 1837 mathematical proof was set forth authoritatively stating that it is impossible to trisect an arbitrary angle with a compass and an unmarked straightedge in the classical sense. The famous proof depends on an incompatible cubic equation having the cosine of an angle of 60 and the cube of the cosine of one-third of an angle of 60 as…

Matrix elements of explicitly correlated Gaussian basis functions with arbitrary angular momentum

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

Joyce, Tennesse; Varga, Kálmán

2016-05-14

A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with arbitrary angular momentum is presented. The calculations are checked on several excited states of three and four electron systems. The presented formalism can be used as unified framework for high accuracy calculations of properties of small atoms and molecules.

On the Debye-Hückel effect of electric screening

NASA Astrophysics Data System (ADS)

Campos, L. M. B. C.; Lau, F. J. P.

2014-07-01

The paper considers non-linear self-consistent electric potential equation (Sec. I), due to a cloud made of a single species of electric charges, satisfying a Boltzmann distribution law (Sec. II). Exact solutions are obtained in a simple logarithmic form, in three cases: (Sec. III) spherical radial symmetry; (Sec. IV) plane parallel symmetry; (Sec. V) a special case of azimuthal-cylindrical symmetry. All these solutions, and their transformations (Sec. VI), involve the Debye-Hückel radius; the latter was originally defined from a solution of the linearized self-consistent potential equation. Using an exact solution of the self-consistent potential equation, the distance at which the potential vanishes differs from the Debye-Hückel radius by a factor of √2 . The preceding (Secs. II-VI) simple logarithmic exact solutions of the self-consistent potential equations involve no arbitrary constants, and thus are special or singular integrals not the general integral. The general solution of the self-consistent potential equation is obtained in the plane parallel case (Sec. VII), and it involves two arbitrary constants that can be reduced to one via a translation (Sec. VIII). The plots of dimensionless potential (Figure 1), electric field (Figure 2), charge density (Figure 3), and total charge between ζ and infinity (Figure 4), versus distance normalized to Debye-Hückel radius ζ ≡ z/a, show that (Sec. IX) there is a continuum of solutions, ranging from a charge distribution concentrated inside the Debye-Hückel radius to one spread-out beyond it. The latter case leads to the limiting case of logarithmic potential, and stronger electric field; the former case, of very concentrated charge distribution, leads to a fratricide effect and weaker electric field.

On the Debye–Hückel effect of electric screening

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

Campos, L. M. B. C.; Lau, F. J. P.

2014-07-15

The paper considers non-linear self-consistent electric potential equation (Sec. I), due to a cloud made of a single species of electric charges, satisfying a Boltzmann distribution law (Sec. II). Exact solutions are obtained in a simple logarithmic form, in three cases: (Sec. III) spherical radial symmetry; (Sec. IV) plane parallel symmetry; (Sec. V) a special case of azimuthal-cylindrical symmetry. All these solutions, and their transformations (Sec. VI), involve the Debye-Hückel radius; the latter was originally defined from a solution of the linearized self-consistent potential equation. Using an exact solution of the self-consistent potential equation, the distance at which the potentialmore » vanishes differs from the Debye-Hückel radius by a factor of √(2). The preceding (Secs. II–VI) simple logarithmic exact solutions of the self-consistent potential equations involve no arbitrary constants, and thus are special or singular integrals not the general integral. The general solution of the self-consistent potential equation is obtained in the plane parallel case (Sec. VII), and it involves two arbitrary constants that can be reduced to one via a translation (Sec. VIII). The plots of dimensionless potential (Figure 1), electric field (Figure 2), charge density (Figure 3), and total charge between ζ and infinity (Figure 4), versus distance normalized to Debye-Hückel radius ζ ≡ z/a, show that (Sec. IX) there is a continuum of solutions, ranging from a charge distribution concentrated inside the Debye-Hückel radius to one spread-out beyond it. The latter case leads to the limiting case of logarithmic potential, and stronger electric field; the former case, of very concentrated charge distribution, leads to a fratricide effect and weaker electric field.« less

Quantum spectral curve for arbitrary state/operator in AdS5/CFT4

NASA Astrophysics Data System (ADS)

Gromov, Nikolay; Kazakov, Vladimir; Leurent, Sébastien; Volin, Dmytro

2015-09-01

We give a derivation of quantum spectral curve (QSC) — a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys. Rev. Lett. 112 (2014). We also generalize this construction to all local single trace operators of the theory, in contrast to the TBA-like approaches worked out only for a limited class of states. We reveal a rich algebraic and analytic structure of the QSC in terms of a so called Q-system — a finite set of Baxter-like Q-functions. This new point of view on the finite size spectral problem is shown to be completely compatible, though in a far from trivial way, with already known exact equations (analytic Y-system/TBA, or FiNLIE). We use the knowledge of this underlying Q-system to demonstrate how the classical finite gap solutions and the asymptotic Bethe ansatz emerge from our formalism in appropriate limits.

Implications of Network Topology on Stability

PubMed Central

Kinkhabwala, Ali

2015-01-01

In analogy to chemical reaction networks, I demonstrate the utility of expressing the governing equations of an arbitrary dynamical system (interaction network) as sums of real functions (generalized reactions) multiplied by real scalars (generalized stoichiometries) for analysis of its stability. The reaction stoichiometries and first derivatives define the network’s “influence topology”, a signed directed bipartite graph. Parameter reduction of the influence topology permits simplified expression of the principal minors (sums of products of non-overlapping bipartite cycles) and Hurwitz determinants (sums of products of the principal minors or the bipartite cycles directly) for assessing the network’s steady state stability. Visualization of the Hurwitz determinants over the reduced parameters defines the network’s stability phase space, delimiting the range of its dynamics (specifically, the possible numbers of unstable roots at each steady state solution). Any further explicit algebraic specification of the network will project onto this stability phase space. Stability analysis via this hierarchical approach is demonstrated on classical networks from multiple fields. PMID:25826219

DNN-state identification of 2D distributed parameter systems

NASA Astrophysics Data System (ADS)

Chairez, I.; Fuentes, R.; Poznyak, A.; Poznyak, T.; Escudero, M.; Viana, L.

2012-02-01

There are many examples in science and engineering which are reduced to a set of partial differential equations (PDEs) through a process of mathematical modelling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. Moreover, to find exact solutions of those PDEs is not a trivial task especially if the PDE is described in two or more dimensions. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary accuracy. In this article, a strategy based on the differential neural network (DNN) for the non-parametric identification of a mathematical model described by a class of two-dimensional (2D) PDEs is proposed. The adaptive laws for weights ensure the 'practical stability' of the DNN-trajectories to the parabolic 2D-PDE states. To verify the qualitative behaviour of the suggested methodology, here a non-parametric modelling problem for a distributed parameter plant is analysed.

A multi-species reactive transport model to estimate biogeochemical rates based on single-well push-pull test data

NASA Astrophysics Data System (ADS)

Phanikumar, Mantha S.; McGuire, Jennifer T.

2010-08-01

Push-pull tests are a popular technique to investigate various aquifer properties and microbial reaction kinetics in situ. Most previous studies have interpreted push-pull test data using approximate analytical solutions to estimate (generally first-order) reaction rate coefficients. Though useful, these analytical solutions may not be able to describe important complexities in rate data. This paper reports the development of a multi-species, radial coordinate numerical model (PPTEST) that includes the effects of sorption, reaction lag time and arbitrary reaction order kinetics to estimate rates in the presence of mixing interfaces such as those created between injected "push" water and native aquifer water. The model has the ability to describe an arbitrary number of species and user-defined reaction rate expressions including Monod/Michelis-Menten kinetics. The FORTRAN code uses a finite-difference numerical model based on the advection-dispersion-reaction equation and was developed to describe the radial flow and transport during a push-pull test. The accuracy of the numerical solutions was assessed by comparing numerical results with analytical solutions and field data available in the literature. The model described the observed breakthrough data for tracers (chloride and iodide-131) and reactive components (sulfate and strontium-85) well and was found to be useful for testing hypotheses related to the complex set of processes operating near mixing interfaces.

The One-Dimensional Damped Forced Harmonic Oscillator Revisited

ERIC Educational Resources Information Center

Flores-Hidalgo, G.; Barone, F. A.

2011-01-01

In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate students and professors in an introductory course of mechanics.

A general strategy for hybrid thin film fabrication and transfer onto arbitrary substrates.

PubMed

Zhang, Yong; Magan, John J; Blau, Werner J

2014-04-28

The development of thin film-based structures/devices often requires thin films to be transferred onto arbitrary substrates/surfaces. Controllable and non-destructive transfer method, although highly desired, remains quite challenging. Here we report a general method for fabrication and transfer of hybrid (ultra)thin films. The proposed solution-based in-situ transfer method shows not only its robust ability for thin film transfer onto arbitrary substrates but also its highly controlled and non-destructive characteristic. With a hole structure as the support, fully-stretched free-standing thin film is prepared. The successful transfer to a curved surface demonstrates the possibility for production of thin film-coated complex optical components. Ultrathin (35 nm) hybrid film transferred onto PET (50 μm thick) shows high transparency (>90% in visible range), conductivity (1.54 × 10(4) S/m), and flexibility (radius of curvature down to mm scale). The reported transfer method would provide a powerful route towards complex thin film-based structures/devices.

Acoustic scattering by arbitrary distributions of disjoint, homogeneous cylinders or spheres.

PubMed

Hesford, Andrew J; Astheimer, Jeffrey P; Waag, Robert C

2010-05-01

A T-matrix formulation is presented to compute acoustic scattering from arbitrary, disjoint distributions of cylinders or spheres, each with arbitrary, uniform acoustic properties. The generalized approach exploits the similarities in these scattering problems to present a single system of equations that is easily specialized to cylindrical or spherical scatterers. By employing field expansions based on orthogonal harmonic functions, continuity of pressure and normal particle velocity are directly enforced at each scatterer using diagonal, analytic expressions to eliminate the need for integral equations. The effect of a cylinder or sphere that encloses all other scatterers is simulated with an outer iterative procedure that decouples the inner-object solution from the effect of the enclosing object to improve computational efficiency when interactions among the interior objects are significant. Numerical results establish the validity and efficiency of the outer iteration procedure for nested objects. Two- and three-dimensional methods that employ this outer iteration are used to measure and characterize the accuracy of two-dimensional approximations to three-dimensional scattering of elevation-focused beams.

A General Strategy for Hybrid Thin Film Fabrication and Transfer onto Arbitrary Substrates

PubMed Central

Zhang, Yong; Magan, John J.; Blau, Werner J.

2014-01-01

The development of thin film-based structures/devices often requires thin films to be transferred onto arbitrary substrates/surfaces. Controllable and non-destructive transfer method, although highly desired, remains quite challenging. Here we report a general method for fabrication and transfer of hybrid (ultra)thin films. The proposed solution-based in-situ transfer method shows not only its robust ability for thin film transfer onto arbitrary substrates but also its highly controlled and non-destructive characteristic. With a hole structure as the support, fully-stretched free-standing thin film is prepared. The successful transfer to a curved surface demonstrates the possibility for production of thin film-coated complex optical components. Ultrathin (35 nm) hybrid film transferred onto PET (50 μm thick) shows high transparency (>90% in visible range), conductivity (1.54 × 104 S/m), and flexibility (radius of curvature down to mm scale). The reported transfer method would provide a powerful route towards complex thin film-based structures/devices. PMID:24769689

Variational extension of the mean spherical approximation to arbitrary dimensions

NASA Astrophysics Data System (ADS)

Velázquez, Esov S.; Blum, Lesser; Frisch, Harry L.

1997-10-01

We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager limit T ΔS MSA / ΔE MSA → 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while for d=2 this limit is 1.

Top-quark decay at next-to-next-to-leading order in QCD.

PubMed

Gao, Jun; Li, Chong Sheng; Zhu, Hua Xing

2013-01-25

We present the complete calculation of the top-quark decay width at next-to-next-to-leading order in QCD, including next-to-leading electroweak corrections as well as finite bottom quark mass and W boson width effects. In particular, we also show the first results of the fully differential decay rates for the top-quark semileptonic decay t → W(+)(l(+)ν)b at next-to-next-to-leading order in QCD. Our method is based on the understanding of the invariant mass distribution of the final-state jet in the singular limit from effective field theory. Our result can be used to study arbitrary infrared-safe observables of top-quark decay with the highest perturbative accuracy.

Bounds on the number of hidden neurons in three-layer binary neural networks.

PubMed

Zhang, Zhaozhi; Ma, Xiaomin; Yang, Yixian

2003-09-01

This paper investigates an important problem concerning the complexity of three-layer binary neural networks (BNNs) with one hidden layer. The neuron in the studied BNNs employs a hard limiter activation function with only integer weights and an integer threshold. The studies are focused on implementations of arbitrary Boolean functions which map from [0, 1]n into [0, 1]. A deterministic algorithm called set covering algorithm (SCA) is proposed for the construction of a three-layer BNN to implement an arbitrary Boolean function. The SCA is based on a unit sphere covering (USC) of the Hamming space (HS) which is chosen in advance. It is proved that for the implementation of an arbitrary Boolean function of n-variables (n > or = 3) by using SCA, [3L/2] hidden neurons are necessary and sufficient, where L is the number of unit spheres contained in the chosen USC of the n-dimensional HS. It is shown that by using SCA, the number of hidden neurons required is much less than that by using a two-parallel hyperplane method. In order to indicate the potential ability of three-layer BNNs, a lower bound on the required number of hidden neurons which is derived by using the method of estimating the Vapnik-Chervonenkis (VC) dimension is also given.

Universality of Generalized Bunching and Efficient Assessment of Boson Sampling.

PubMed

Shchesnovich, V S

2016-03-25

It is found that identical bosons (fermions) show a generalized bunching (antibunching) property in linear networks: the absolute maximum (minimum) of the probability that all N input particles are detected in a subset of K output modes of any nontrivial linear M-mode network is attained only by completely indistinguishable bosons (fermions). For fermions K is arbitrary; for bosons it is either (i) arbitrary for only classically correlated bosons or (ii) satisfies K≥N (or K=1) for arbitrary input states of N particles. The generalized bunching allows us to certify in a polynomial in N number of runs that a physical device realizing boson sampling with an arbitrary network operates in the regime of full quantum coherence compatible only with completely indistinguishable bosons. The protocol needs only polynomial classical computations for the standard boson sampling, whereas an analytic formula is available for the scattershot version.

Extended phase graphs with anisotropic diffusion.

PubMed

Weigel, M; Schwenk, S; Kiselev, V G; Scheffler, K; Hennig, J

2010-08-01

The extended phase graph (EPG) calculus gives an elegant pictorial description of magnetization response in multi-pulse MR sequences. The use of the EPG calculus enables a high computational efficiency for the quantitation of echo intensities even for complex sequences with multiple refocusing pulses with arbitrary flip angles. In this work, the EPG concept dealing with RF pulses with arbitrary flip angles and phases is extended to account for anisotropic diffusion in the presence of arbitrary varying gradients. The diffusion effect can be expressed by specific diffusion weightings of individual magnetization pathways. This can be represented as an action of a linear operator on the magnetization state. The algorithm allows easy integration of diffusion anisotropy effects. The formalism is validated on known examples from literature and used to calculate the effective diffusion weighting in multi-echo sequences with arbitrary refocusing flip angles. Copyright 2010 Elsevier Inc. All rights reserved.

Space-time derivative estimates of the Koch-Tataru solutions to the nematic liquid crystal system in Besov spaces

NASA Astrophysics Data System (ADS)

Liu, Qiao

2015-06-01

In recent paper [7], Y. Du and K. Wang (2013) proved that the global-in-time Koch-Tataru type solution (u, d) to the n-dimensional incompressible nematic liquid crystal flow with small initial data (u0, d0) in BMO-1 × BMO has arbitrary space-time derivative estimates in the so-called Koch-Tataru space norms. The purpose of this paper is to show that the Koch-Tataru type solution satisfies the decay estimates for any space-time derivative involving some borderline Besov space norms.

General Wahlquist metrics in all dimensions

NASA Astrophysics Data System (ADS)

Hinoue, Kazuki; Houri, Tsuyoshi; Rugina, Christina; Yasui, Yukinori

2014-07-01

It is shown that the Wahlquist metric, which is a stationary, axially symmetric perfect fluid solution with ρ +3p=const, admits a rank-2 generalized closed conformal Killing-Yano tensor with a skew-symmetric torsion. Taking advantage of the presence of such a tensor, we obtain a higher-dimensional generalization of the Wahlquist metric in arbitrary dimensions, including a family of vacuum black hole solutions with spherical horizon topology such as Schwarzschild-Tangherlini, Myers-Perry and higher-dimensional Kerr-NUT-(A)dS metrics and a family of static, spherically symmetric perfect fluid solutions in higher dimensions.

Global Dynamics of Certain Homogeneous Second-Order Quadratic Fractional Difference Equation

PubMed Central

Garić-Demirović, M.; Kulenović, M. R. S.; Nurkanović, M.

2013-01-01

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x n+1 = x n−1 2/(ax n 2 + bx n x n−1 + cx n−1 2), n = 0,1, 2,…, where the parameters a,  b, and  c are positive numbers and the initial conditions x −1 and x 0 are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal period-two solution both of which are locally asymptotically stable. PMID:24369451

Landau-Zener extension of the Tavis-Cummings model: Structure of the solution

DOE PAGES

Sun, Chen; Sinitsyn, Nikolai A.

2016-09-07

We explore the recently discovered solution of the driven Tavis-Cummings model (DTCM). It describes interaction of an arbitrary number of two-level systems with a bosonic mode that has linearly time-dependent frequency. We derive compact and tractable expressions for transition probabilities in terms of the well-known special functions. In this form, our formulas are suitable for fast numerical calculations and analytical approximations. As an application, we obtain the semiclassical limit of the exact solution and compare it to prior approximations. Furthermore, we also reveal connection between DTCM and q-deformed binomial statistics.

Exact time-dependent nonlinear dispersive wave solutions in compressible magnetized plasmas exhibiting collapse.

PubMed

Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans

2011-04-08

Compressional waves in a magnetized plasma of arbitrary resistivity are treated with the lagrangian fluid approach. An exact nonlinear solution with a nontrivial space and time dependence is obtained with boundary conditions as in Harris' current sheet. The solution shows competition among hydrodynamic convection, magnetic field diffusion, and dispersion. This results in a collapse of density and the magnetic field in the absence of dispersion. The dispersion effects arrest the collapse of density but not of the magnetic field. A possible application is in the early stage of magnetic star formation.

Edge effects in angle-ply composite laminates

NASA Technical Reports Server (NTRS)

Hsu, P. W.; Herakovich, C. T.

1977-01-01

This paper presents the results of a zeroth-order solution for edge effects in angle-ply composite laminates obtained using perturbation techniques and a limiting free body approach. The general solution for edge effects in laminates of arbitrary angle ply is applied to the special case of a (+ or - 45)s graphite/epoxy laminate. Interlaminar stress distributions are obtained as a function of the laminate thickness-to-width ratio and compared to finite difference results. The solution predicts stable, continuous stress distributions, determines finite maximum tensile interlaminar normal stress and provides mathematical evidence for singular interlaminar shear stresses in (+ or - 45) graphite/epoxy laminates.

Asymptotically exact parabolic solutions of the generalized nonlinear Schrödinger equation with varying parameters

NASA Astrophysics Data System (ADS)

Kruglov, Vladimir I.; Harvey, John D.

2006-12-01

We present exact asymptotic similariton solutions of the generalized nonlinear Schrödinger equation (NLSE) with gain or loss terms for a normal-dispersion fiber amplifier with dispersion, nonlinearity, and gain profiles that depend on the propagation distance. Our treatment is based on the mapping of the NLSE with varying parameters to the NLSE with constant dispersion and nonlinearity coefficients and an arbitrary varying gain function. We formulate an effective procedure that leads directly, under appropriate conditions, to a wide range of exact asymptotic similariton solutions of NLSE demonstrating self-similar propagating regimes with linear chirp.

Controlled Teleportation of a Qudit State by Partially Entangled GHZ States

NASA Astrophysics Data System (ADS)

Wang, Jin-wei; Shu, Lan; Mo, Zhi-wen; Zhang, Zhi-hua

2014-08-01

In this paper, we propose a controlled teleportation scheme which communicates an arbitrary ququart state via two sets of partially entangled GHZ state. The necessary measurements and operations are given detailedly. Furthmore the scheme is generalized to teleport a qudit state via s sets of partially entangled GHZ state.

Optimal Conclusive Teleportation of an Arbitrary d-Dimensional N-Particle Unknown State via a Partially Entangled Quantum Channel

NASA Astrophysics Data System (ADS)

Hao, San-Ru; Hou, Bo-Yu; Xi, Xiao-Qiang; Yue, Rui-Hong

2003-02-01

In this paper we generalize the standard teleportation to the conclusive teleportation case which can teleport an arbitrary d-dimensional N-particle unknown state via the partially entangled quantum channel. We show that only if the quantum channel satisfies a constraint condition can the most general d-dimensional N-particle unknown state be perfect conclusively teleported. We also present a method for optimal conclusively teleportation of the N-particle states and for constructing the joint POVM which can discern the quantum states on the sender's (Alice's) side. Two typical examples are given so that one can see how our method works. The project supported in part by National Natural Science Foundation of China under Grant No. 19975036 and the Foundation of Science and Technology Committee of Hunan Province of China under Grant No. 21000205

Controlled teleportation with the control of two groups of agents via entanglement

NASA Astrophysics Data System (ADS)

He, Xiao-Ling; Liu, Man; Yang, Chui-Ping

2015-03-01

We present a way for implementing controlled teleportation of an arbitrary unknown pure state of a qutrit with the control of two groups of agents via entanglement. In our proposal, the sender can successfully teleport the qutrit state to a distant receiver with the help of all agents. However, if one agent in each group does not cooperate, the receiver cannot gain any information (including amplitude information or phase information or both) about the qutrit state to be teleported. Since a qubit is a special case of a qutrit when the state lies in a fixed two-dimensional subspace of the qutrit, the present proposal can be also applied in the implementation of controlled teleportation of an arbitrary unknown pure state of a qubit with many control agents in two groups. We note that our proposal is the first one to use two groups of agents to achieve controlled teleportation.

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle

PubMed Central

Brzezicki, Samuel J.

2017-01-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function. PMID:28690412

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle.

PubMed

Crowdy, Darren G; Brzezicki, Samuel J

2017-06-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function.

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.

A 3D finite element ALE method using an approximate Riemann solution

DOE PAGES

Chiravalle, V. P.; Morgan, N. R.

2016-08-09

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

A 3D finite element ALE method using an approximate Riemann solution

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

Chiravalle, V. P.; Morgan, N. R.

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less

Reciprocity relationships in vector acoustics and their application to vector field calculations.

PubMed

Deal, Thomas J; Smith, Kevin B

2017-08-01

The reciprocity equation commonly stated in underwater acoustics relates pressure fields and monopole sources. It is often used to predict the pressure measured by a hydrophone for multiple source locations by placing a source at the hydrophone location and calculating the field everywhere for that source. A similar equation that governs the orthogonal components of the particle velocity field is needed to enable this computational method to be used for acoustic vector sensors. This paper derives a general reciprocity equation that accounts for both monopole and dipole sources. This vector-scalar reciprocity equation can be used to calculate individual components of the received vector field by altering the source type used in the propagation calculation. This enables a propagation model to calculate the received vector field components for an arbitrary number of source locations with a single model run for each vector field component instead of requiring one model run for each source location. Application of the vector-scalar reciprocity principle is demonstrated with analytic solutions for a range-independent environment and with numerical solutions for a range-dependent environment using a parabolic equation model.

Specular reflection treatment for the 3D radiative transfer equation solved with the discrete ordinates method

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

Le Hardy, D.; Favennec, Y., E-mail: yann.favennec@univ-nantes.fr; Rousseau, B.

The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken intomore » account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.« less

Approximate labeling via graph cuts based on linear programming.

PubMed

Komodakis, Nikos; Tziritas, Georgios

2007-08-01

A new framework is presented for both understanding and developing graph-cut-based combinatorial algorithms suitable for the approximate optimization of a very wide class of Markov Random Fields (MRFs) that are frequently encountered in computer vision. The proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state-of-the-art techniques like the \\alpha-expansion algorithm, which is included merely as a special case. Moreover, contrary to \\alpha-expansion, the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems, for example, even for MRFs with nonmetric potentials. In addition, they are capable of providing per-instance suboptimality bounds in all occasions, including discrete MRFs with an arbitrary potential function. These bounds prove to be very tight in practice (that is, very close to 1), which means that the resulting solutions are almost optimal. Our algorithms' effectiveness is demonstrated by presenting experimental results on a variety of low-level vision tasks, such as stereo matching, image restoration, image completion, and optical flow estimation, as well as on synthetic problems.

The focusing effect of P-wave in the Moon's and Earth's low-velocity core. Analytical solution

NASA Astrophysics Data System (ADS)

Fatyanov, A. G.; Burmin, V. Yu

2018-04-01

The important aspect in the study of the structure of the interiors of planets is the question of the presence and state of core inside them. While for the Earth this task was solved long ago, the question of whether the core of the Moon is in a liquid or solid state up to the present is debatable up to present. If the core of the Moon is liquid, then the velocity of longitudinal waves in it should be lower than in the surrounding mantle. If the core is solid, then most likely, the velocity of longitudinal waves in it is higher than in the mantle. Numerical calculations of the wave field allow us to identify the criteria for drawing conclusions about the state of the lunar core. In this paper we consider the problem of constructing an analytical solution for wave fields in a layered sphere of arbitrary radius. A stable analytic solution is obtained for the wave fields of longitudinal waves in a three-layer sphere. Calculations of the total wave fields and rays for simplified models of the Earth and the Moon with real parameters are presented. The analytical solution and the ray pattern showed that the low-velocity cores of the Earth and the Moon possess the properties of a collecting lens. This leads to the emergence of a wave field focusing area. As a result, focused waves of considerable amplitude appear on the surface of the Earth and the Moon. In the Earth case, they appear before the first PKP-wave arrival. These are so-called "precursors", which continue in the subsequent arrivals of waves. At the same time, for the simplified model of the Earth, the maximum amplitude growth is observed in the 147-degree region. For the Moon model, the maximum amplitude growth is around 180°.

[Computer modeling the dependences of the membrane potential for polymeric membrane separated non-homogeneous electrolyte solutions on concentration Rayleigh number].

PubMed

Slezak, Izabella H; Jasik-Slezak, Jolanta; Bilewicz-Wyrozumska, Teresa; Slezak, Andrzej

2006-01-01

On the basis of model equation describing the membrane potential delta psi(s) on concentration Rayleigh number (R(C)), mechanical pressure difference (deltaP), concentration polarization coefficient (zeta s) and ratio concentration of solutions separated by membrane (Ch/Cl), the characteristics delta psi(s) = f(Rc)(delta P, zeta s, Ch/Cl) for steady values of zeta s, R(C) and Ch/Cl in single-membrane system were calculated. In this system neutral and isotropic polymeric membrane oriented in horizontal plane, the non-homogeneous binary electrolytic solutions of various concentrations were separated. Nonhomogeneity of solutions is results from creations of the concentration boundary layers on both sides of the membrane. Calculations were made for the case where on a one side of the membrane aqueous solution of NaCl at steady concentration 10(-3) mol x l(-1) (Cl) was placed and on the other aqueous solutions of NaCl at concentrations from 10(-3) mol x l(-1) to 2 x 10(-2) mol x l(-1) (Ch). Their densities were greater than NaCl solution's at 10(-3) mol x l(-1). It was shown that membrane potential depends on hydrodynamic state of a complex concentration boundary layer-membrane-concentration boundary layer, what is controlled by deltaP, Ch/Cl, Rc and Zeta(s).

The boundary integral theory for slow and rapid curved solid/liquid interfaces propagating into binary systems

NASA Astrophysics Data System (ADS)

Galenko, Peter K.; Alexandrov, Dmitri V.; Titova, Ekaterina A.

2018-01-01

The boundary integral method for propagating solid/liquid interfaces is detailed with allowance for the thermo-solutal Stefan-type models. Two types of mass transfer mechanisms corresponding to the local equilibrium (parabolic-type equation) and local non-equilibrium (hyperbolic-type equation) solidification conditions are considered. A unified integro-differential equation for the curved interface is derived. This equation contains the steady-state conditions of solidification as a special case. The boundary integral analysis demonstrates how to derive the quasi-stationary Ivantsov and Horvay-Cahn solutions that, respectively, define the paraboloidal and elliptical crystal shapes. In the limit of highest Péclet numbers, these quasi-stationary solutions describe the shape of the area around the dendritic tip in the form of a smooth sphere in the isotropic case and a deformed sphere along the directions of anisotropy strength in the anisotropic case. A thermo-solutal selection criterion of the quasi-stationary growth mode of dendrites which includes arbitrary Péclet numbers is obtained. To demonstrate the selection of patterns, computational modelling of the quasi-stationary growth of crystals in a binary mixture is carried out. The modelling makes it possible to obtain selected structures in the form of dendritic, fractal or planar crystals. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.

Disappearance kinetics of solutes from synovial fluid after intra-articular injection.

PubMed Central

Owen, S G; Francis, H W; Roberts, M S

1994-01-01

1. Five rheumatoid patients with a knee joint effusion participated in the study. An aqueous solution (0.1 to 0.2 ml) containing paracetamol, salicylate, diclofenac and [125I]-albumin was injected into a given joint to yield target concentrations of approximately 20 micrograms ml-1 for diclofenac, salicylate and paracetamol and 10(8) counts ml-1 for [125I]-albumin. 2. Paracetamol, salicylate and diclofenac were analysed in synovial fluid by h.p.l.c. [125I]-albumin was analysed using gamma counting. 3. The clearances (+/- s.d.) obtained for the solutes were [125I]-albumin (0.0053 +/- 0.0019 l h-1), diclofenac (0.0096 +/- 0.0061 l h-1), salicylate (0.024 +/- 0.022 l h-1) and paracetamol (0.055 +/- 0.041 l h-1). The corresponding fractions unbound of these solutes in synovial fluid were 0.0, < or = 0.01, 0.34 +/- 0.09 and 0.85 +/- 0.10, respectively. 4. Diffusion of unbound solute through the synovium is estimated to account for (+/- s.d.) 0.52 +/- 0.08, 0.87 +/- 0.06 and 0.99 +/- 0.01 of the total clearance of diclofenac, salicylate and paracetamol from the joint space, respectively. The remaining proportion of clearance is accounted for by efflux of solute bound to albumin. 5. An expression for the ratio of synovial fluid to total plasma concentrations after systemic administration was developed to include both diffusion of unbound solute and albumin flux. Most solutes appear to satisfy the conditions in which this expression reduces to the limiting case where the unbound concentration of the solute is identical in the synovial fluid and plasma under steady state conditions. PMID:7833225

Comparison of low- and high-carbohydrate diets for type 2 diabetes management: a randomized trial.

PubMed

Tay, Jeannie; Luscombe-Marsh, Natalie D; Thompson, Campbell H; Noakes, Manny; Buckley, Jonathan D; Wittert, Gary A; Yancy, William S; Brinkworth, Grant D

2015-10-01

Few well-controlled studies have comprehensively examined the effects of very-low-carbohydrate diets on type 2 diabetes (T2D). We compared the effects of a very-low-carbohydrate, high-unsaturated fat, low-saturated fat (LC) diet with a high-carbohydrate, low-fat (HC) diet on glycemic control and cardiovascular disease risk factors in T2D after 52 wk. In this randomized controlled trial that was conducted in an outpatient research clinic, 115 obese adults with T2D [mean ± SD age: 58 ± 7 y; body mass index (in kg/m(2)): 34.6 ± 4.3; glycated hemoglobin (HbA1c): 7.3 ± 1.1%; duration of diabetes: 8 ± 6 y] were randomly assigned to consume either a hypocaloric LC diet [14% of energy as carbohydrate (carbohydrate <50 g/d), 28% of energy as protein, and 58% of energy as fat (<10% saturated fat)] or an energy-matched HC diet [53% of energy as carbohydrate, 17% of energy as protein, and 30% of energy as fat (<10% saturated fat)] combined with supervised aerobic and resistance exercise (60 min; 3 d/wk). Outcomes were glycemic control assessed with use of measurements of HbA1c, fasting blood glucose, glycemic variability assessed with use of 48-h continuous glucose monitoring, diabetes medication, weight, blood pressure, and lipids assessed at baseline, 24, and 52 wk. Both groups achieved similar completion rates (LC diet: 71%; HC diet: 65%) and mean (95% CI) reductions in weight [LC diet: -9.8 kg (-11.7, -7.9 kg); HC diet: -10.1 kg (-12.0, -8.2 kg)], blood pressure [LC diet: -7.1 (-10.6, -3.7)/-6.2 (-8.2, -4.1) mm Hg; HC diet: -5.8 (-9.4, -2.2)/-6.4 (-8.4, -4.3) mm Hg], HbA1c [LC diet: -1.0% (-1.2%, -0.7%); HC diet: -1.0% (-1.3%, -0.8%)], fasting glucose [LC diet: -0.7 mmol/L (-1.3, -0.1 mmol/L); HC diet: -1.5 mmol/L (-2.1, -0.8 mmol/L)], and LDL cholesterol [LC diet: -0.1 mmol/L (-0.3, 0.1 mmol/L); HC diet: -0.2 mmol/L (-0.4, 0.03 mmol/L)] (P-diet effect ≥ 0.10). Compared with the HC-diet group, the LC-diet group achieved greater mean (95% CI) reductions in the diabetes medication score [LC diet: -0.5 arbitrary units (-0.7, -0.4 arbitrary units); HC diet: -0.2 arbitrary units (-0.4, -0.06 arbitrary units); P = 0.02], glycemic variability assessed by measuring the continuous overall net glycemic action-1 [LC diet: -0.5 mmol/L (-0.6, -0.3 mmol/L); HC diet: -0.05 mmol/L (-0.2, -0.1 mmol/L); P = 0.003], and triglycerides [LC diet: -0.4 mmol/L (-0.5, -0.2 mmol/L); HC diet: -0.01 mmol/L (-0.2, 0.2 mmol/L); P = 0.001] and greater mean (95% CI) increases in HDL cholesterol [LC diet: 0.1 mmol/L (0.1, 0.2 mmol/L); HC diet: 0.06 mmol/L (-0.01, 0.1 mmol/L); P = 0.002]. Both diets achieved substantial weight loss and reduced HbA1c and fasting glucose. The LC diet, which was high in unsaturated fat and low in saturated fat, achieved greater improvements in the lipid profile, blood glucose stability, and reductions in diabetes medication requirements, suggesting an effective strategy for the optimization of T2D management. This trial was registered at www.anzctr.org.au as ACTRN12612000369820. © 2015 American Society for Nutrition.