Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2004-01-01

Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....

Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

Directory of Open Access Journals (Sweden)

Huiying Sun

2014-01-01

Full Text Available We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ differential games. A necessary and sufficient condition involved with the connection between stochastic Tn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic Tn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs. Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

Equation for disentangling time-ordered exponentials with arbitrary quadratic generators

International Nuclear Information System (INIS)

Budanov, V.G.

1987-01-01

In many quantum-mechanical constructions, it is necessary to disentangle an operator-valued time-ordered exponential with time-dependent generators quadratic in the creation and annihilation operators. By disentangling, one understands the finding of the matrix elements of the time-ordered exponential or, in a more general formulation. The solution of the problem can also be reduced to calculation of a matrix time-ordered exponential that solves the corresponding classical problem. However, in either case the evolution equations in their usual form do not enable one to take into account explicitly the symmetry of the system. In this paper the methods of Weyl analysis are used to find an ordinary differential equation on a matrix Lie algebra that is invariant with respect to the adjoint action of the dynamical symmetry group of a quadratic Hamiltonian and replaces the operator evolution equation for the Green's function

Lambda-lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, O.; Schultz, U.P.

2004-01-01

-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters......Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...

Burgers' turbulence problem with linear or quadratic external potential

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.

2005-01-01

We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....

Phase space eigenfunctions of multidimensional quadratic Hamiltonians

International Nuclear Information System (INIS)

Dodonov, V.V.; Man'ko, V.I.

1986-01-01

We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)

Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

International Nuclear Information System (INIS)

Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

2014-01-01

By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained

Solitary wave dynamics in time-dependent potentials

International Nuclear Information System (INIS)

Abou Salem, Walid K.

2008-01-01

The long time dynamics of solitary wave solutions of the nonlinear Schroedinger equation in time-dependent external potentials is rigorously studied. To set the stage, the well-posedness of the Cauchy problem for a generalized nonautonomous nonlinear Schroedinger equation with time-dependent nonlinearities and potential is established. Afterward, the dynamics of NLS solitary waves in time-dependent potentials is studied. It is shown that in the space-adiabatic regime where the external potential varies slowly in space compared to the size of the soliton, the dynamics of the center of the soliton is described by Hamilton's equations, plus terms due to radiation damping. Finally, two physical applications are discussed: the first is adiabatic transportation of solitons and the second is the Mathieu instability of trapped solitons due to time-periodic perturbations

Comparison between linear quadratic and early time dose models

International Nuclear Information System (INIS)

Chougule, A.A.; Supe, S.J.

1993-01-01

During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs

A linear-quadratic model of cell survival considering both sublethal and potentially lethal radiation damage

International Nuclear Information System (INIS)

Rutz, H.P.; Coucke, P.A.; Mirimanoff, R.O.

1991-01-01

The authors assessed the dose-dependence of repair of potentially lethal damage in Chinese hamster ovary cells x-irradiated in vitro. The recovery ratio (RR) by which survival (SF) of the irradiated cells was enhanced increased exponentially with a linear and a quadratic component namely ζ and ψ: RR=exp(ζD+ψD 2 ). Survival of irradiated cells can thus be expressed by a combined linear-quadratic model considering 4 variables, namely α and β for the capacity of the cells to accumulate sublethal damage, and ζ and ψ for their capacity to repair potentially lethal damage: SF=exp((ζ-α)D+ (ψ-β)D 2 ). author. 26 refs.; 1 fig.; 1 tab

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

International Nuclear Information System (INIS)

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C.; Cardoso, J.L.; Kunold, A.

2015-01-01

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a

Lie algebraic approach to the time-dependent quantum general harmonic oscillator and the bi-dimensional charged particle in time-dependent electromagnetic fields

Energy Technology Data Exchange (ETDEWEB)

Ibarra-Sierra, V.G.; Sandoval-Santana, J.C. [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, 09340 México D.F. (Mexico); Cardoso, J.L. [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico); Kunold, A., E-mail: akb@correo.azc.uam.mx [Área de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa-Tamaulipas, Azcapotzalco, 02200 México D.F. (Mexico)

2015-11-15

We discuss the one-dimensional, time-dependent general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express a quantum Hamiltonian and therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the Hamiltonian of a charged particle in electromagnetic fields exploiting the similarities between the terms of these two Hamiltonians. These results are applied to the solution of five different examples: the linear potential which is used to introduce the Lie algebraic method, a radio frequency ion trap, a Kanai–Caldirola-like forced harmonic oscillator, a charged particle in a time dependent magnetic field, and a charged particle in constant magnetic field and oscillating electric field. In particular we present exact analytical expressions that are fitting for the study of a rotating quadrupole field ion trap and magneto-transport in two-dimensional semiconductor heterostructures illuminated by microwave radiation. In these examples we show that this powerful method is suitable to treat quadratic Hamiltonians with time dependent coefficients quite efficiently yielding closed analytical expressions for the propagator and the Heisenberg picture position and momentum operators. -- Highlights: •We deal with the general quadratic Hamiltonian and a particle in electromagnetic fields. •The evolution operator is worked out through the Lie algebraic approach. •We also obtain the propagator and Heisenberg picture position and momentum operators. •Analytical expressions for a

Quadratic algebras

CERN Document Server

Polishchuk, Alexander

2005-01-01

Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.

Dynamical invariants for variable quadratic Hamiltonians

International Nuclear Information System (INIS)

Suslov, Sergei K

2010-01-01

We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.

Construction of time-dependent dynamical invariants: A new approach

International Nuclear Information System (INIS)

Bertin, M. C.; Pimentel, B. M.; Ramirez, J. A.

2012-01-01

We propose a new way to obtain polynomial dynamical invariants of the classical and quantum time-dependent harmonic oscillator from the equations of motion. We also establish relations between linear and quadratic invariants, and discuss how the quadratic invariant can be related to the Ermakov invariant.

Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

Directory of Open Access Journals (Sweden)

Minsong Zhang

2014-01-01

Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Davydov–Chaban Hamiltonian in presence of time-dependent potential

Energy Technology Data Exchange (ETDEWEB)

Sobhani, Hadi; Hassanabadi, Hassan, E-mail: h.hassanabadi@shahroodut.ac.ir

2016-09-10

In this article, we have investigated collective effects of atomic nuclei in presence of a time-dependent potential in Davydov–Chaban Hamiltonian. Since such potential has an explicit time-dependency, in order to obtain the wave function of considered system, we should face with time-dependent Schrödinger equation. Obtaining the wave function could be possible using Lewis–Riesenfeld dynamical invariant method. Appropriate dynamical invariant has been constructed after determining the wave functions and values, the wave function will obtain.

Quadratic adaptive algorithm for solving cardiac action potential models.

Science.gov (United States)

Chen, Min-Hung; Chen, Po-Yuan; Luo, Ching-Hsing

2016-10-01

An adaptive integration method is proposed for computing cardiac action potential models accurately and efficiently. Time steps are adaptively chosen by solving a quadratic formula involving the first and second derivatives of the membrane action potential. To improve the numerical accuracy, we devise an extremum-locator (el) function to predict the local extremum when approaching the peak amplitude of the action potential. In addition, the time step restriction (tsr) technique is designed to limit the increase in time steps, and thus prevent the membrane potential from changing abruptly. The performance of the proposed method is tested using the Luo-Rudy phase 1 (LR1), dynamic (LR2), and human O'Hara-Rudy dynamic (ORd) ventricular action potential models, and the Courtemanche atrial model incorporating a Markov sodium channel model. Numerical experiments demonstrate that the action potential generated using the proposed method is more accurate than that using the traditional Hybrid method, especially near the peak region. The traditional Hybrid method may choose large time steps near to the peak region, and sometimes causes the action potential to become distorted. In contrast, the proposed new method chooses very fine time steps in the peak region, but large time steps in the smooth region, and the profiles are smoother and closer to the reference solution. In the test on the stiff Markov ionic channel model, the Hybrid blows up if the allowable time step is set to be greater than 0.1ms. In contrast, our method can adjust the time step size automatically, and is stable. Overall, the proposed method is more accurate than and as efficient as the traditional Hybrid method, especially for the human ORd model. The proposed method shows improvement for action potentials with a non-smooth morphology, and it needs further investigation to determine whether the method is helpful during propagation of the action potential. Copyright © 2016 Elsevier Ltd. All rights

An EOQ model of time quadratic and inventory dependent demand for deteriorated items with partially backlogged shortages under trade credit

Science.gov (United States)

Singh, Pushpinder; Mishra, Nitin Kumar; Singh, Vikramjeet; Saxena, Seema

2017-07-01

In this paper a single buyer, single supplier inventory model with time quadratic and stock dependent demand for a finite planning horizon has been studied. Single deteriorating item which suffers shortage, with partial backlogging and some lost sales is considered. Model is divided into two scenarios, one with non permissible delay in payment and other with permissible delay in payment. Latter is called, centralized system, where supplier offers trade credit to retailer. In the centralized system cost saving is shared amongst the two. The objective is to study the difference in minimum costs borne by retailer and supplier, under two scenarios including the above mentioned parameters. To obtain optimal solution of the problem the model is solved analytically. Numerical example and a comparative study are then discussed supported by sensitivity analysis of each parameter.

Stochastic multiresonance for a fractional linear oscillator with time-delayed kernel and quadratic noise

Science.gov (United States)

Guo, Feng; Wang, Xue-Yuan; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Zhang, Zheng-Yu; Huang, Xu-Hui

2017-12-01

The stochastic resonance for a fractional oscillator with time-delayed kernel and quadratic trichotomous noise is investigated. Applying linear system theory and Laplace transform, the system output amplitude (SPA) for the fractional oscillator is obtained. It is found that the SPA is a periodical function of the kernel delayed-time. Stochastic multiplicative phenomenon appears on the SPA versus the driving frequency, versus the noise amplitude, and versus the fractional exponent. The non-monotonous dependence of the SPA on the system parameters is also discussed.

Exact time-dependent exchange-correlation potentials for strong-field electron dynamics

International Nuclear Information System (INIS)

Lein, Manfred; Kuemmel, Stephan

2005-01-01

By solving the time-dependent Schroedinger equation and inverting the time-dependent Kohn-Sham scheme we obtain the exact time-dependent exchange-correlation potential of density-functional theory for the strong-field dynamics of a correlated system. We demonstrate that essential features of the exact exchange-correlation potential can be related to derivative discontinuities in stationary density-functional theory. Incorporating the discontinuity in a time-dependent density-functional calculation greatly improves the description of the ionization process

Optimized effective potential in real time: Problems and prospects in time-dependent density-functional theory

International Nuclear Information System (INIS)

Mundt, Michael; Kuemmel, Stephan

2006-01-01

The integral equation for the time-dependent optimized effective potential (TDOEP) in time-dependent density-functional theory is transformed into a set of partial-differential equations. These equations only involve occupied Kohn-Sham orbitals and orbital shifts resulting from the difference between the exchange-correlation potential and the orbital-dependent potential. Due to the success of an analog scheme in the static case, a scheme that propagates orbitals and orbital shifts in real time is a natural candidate for an exact solution of the TDOEP equation. We investigate the numerical stability of such a scheme. An approximation beyond the Krieger-Li-Iafrate approximation for the time-dependent exchange-correlation potential is analyzed

Lambda-Lifting in Quadratic Time

DEFF Research Database (Denmark)

Danvy, Olivier; Schultz, Ulrik Pagh

2002-01-01

Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which...... is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity of lambda-lifting from O(n 3 log n)toO(n2 log n), where n is the size of the program. Since a lambda-lifter can output...

Rescuing Quadratic Inflation

CERN Document Server

Ellis, John; Sueiro, Maria

2014-01-01

Inflationary models based on a single scalar field $\\phi$ with a quadratic potential $V = \\frac{1}{2} m^2 \\phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological density perturbations, $r_T$. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on $n_s$ and $r_T$. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.

Time-dependent image potential at a metal surface

International Nuclear Information System (INIS)

Alducin, M.; Diez Muino, R.; Juaristi, J.I.

2003-01-01

Transient effects in the image potential induced by a point charge suddenly created in front of a metal surface are studied. The time evolution of the image potential is calculated using linear response theory. Two different time scales are defined: (i) the time required for the creation of the image potential and (ii) the time it takes to converge to its stationary value. Their dependence on the distance of the charge to the surface is discussed. The effect of the electron gas damping is also analyzed. For a typical metallic density, the order of magnitude of the creation time is 0.1 fs, whereas for a charge created close to the surface the convergence time is around 1-2 fs

Scheduling of head-dependent cascaded hydro systems: Mixed-integer quadratic programming approach

International Nuclear Information System (INIS)

Catalao, J.P.S.; Pousinho, H.M.I.; Mendes, V.M.F.

2010-01-01

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach.

Scheduling of head-dependent cascaded hydro systems: Mixed-integer quadratic programming approach

Energy Technology Data Exchange (ETDEWEB)

Catalao, J.P.S.; Pousinho, H.M.I. [Department of Electromechanical Engineering, University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilha (Portugal); Mendes, V.M.F. [Department of Electrical Engineering and Automation, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Emidio Navarro, 1950-062 Lisbon (Portugal)

2010-03-15

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach. (author)

Decay constants for pulsed monoenergetic neutron systems with quadratically anisotropic scattering

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1977-06-01

The eigenvalues of the time-dependent transport equation for monoenergetic neutrons have been studied numerically for various combinations of linearly and quadratically anisotropic scattering assuming a space dependence of e β . The results, presented in the form of tables and graphs, show that quadratic anisotropy leads to a more complicated eigenvalue spectrum. However, no drastic changes occur in comparison to purely linear anistropy.(author)

Coherent states of systems with quadratic Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica

2015-06-15

Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

Coherent states of systems with quadratic Hamiltonians

International Nuclear Information System (INIS)

Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.

2015-01-01

Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)

Covariant quantization of Lagrangians with quadratic dependent fields and derivative couplings

International Nuclear Information System (INIS)

Lam, C.S.; Wang, K.

1977-01-01

A covariant path-integral formula is derived for Lagrangians with quadratic dependent fields and derivative couplings. It differs from the naive one by a factor which can be viewed graphically as due to the coupling with ghost fields. These path integrals can be shown to be unitary and to satisfy equations of motion if and only if this extra factor is present. Applications of this formula to gauge and other field theories are discussed

Separable quadratic stochastic operators

International Nuclear Information System (INIS)

Rozikov, U.A.; Nazir, S.

2009-04-01

We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)

Path integral solution for some time-dependent potential

International Nuclear Information System (INIS)

Storchak, S.N.

1989-12-01

The quantum-mechanical problem with a time-dependent potential is solved by the path integral method. The solution is obtained by the application of the previously derived general formula for rheonomic homogeneous point transformation and reparametrization in the path integral. (author). 4 refs

Tunnelling in a time dependent quartic potential: Possible implications for cosmology

International Nuclear Information System (INIS)

Kabir, R; Mukherjee, A

2014-01-01

The theory of a real scalar field with an arbitrary potential plays an important role in cosmology, particularly in the context of inflationary scenarios. However, in most applications, the potential is treated as independent of time, whereas in an evolving universe, for example, before the onset of inflation, the potential is actually likely to be changing with time. As pointed out by Berry in the context of single-particle quantum mechanics, the existence of multiple time scales can lead to results that are qualitatively different from those obtained with a static potential. The present paper reports on numerical investigations in a scalar field theory with a double-well potential that depends explicitly on time. The transition rate per unit volume for the decay of the false vacuum is found to depend strongly on time. Possible implications for old inflation are discussed

Use of Quadratic Time-Frequency Representations to Analyze Cetacean Mammal Sounds

National Research Council Canada - National Science Library

Papandreou-Suppappola, Antonia

2001-01-01

.... Analysis of the group delay structure of the mammalian vocal communication signals was matched to the appropriate quadratic time-frequency class for proper signal processing with minimal skewing of the results...

Fast, multiple optimizations of quadratic dose objective functions in IMRT

International Nuclear Information System (INIS)

Breedveld, Sebastiaan; Storchi, Pascal R M; Keijzer, Marleen; Heijmen, Ben J M

2006-01-01

Inverse treatment planning for intensity-modulated radiotherapy may include time consuming, multiple minimizations of an objective function. In this paper, methods are presented to speed up the process of (repeated) minimization of the well-known quadratic dose objective function, extended with a smoothing term that ensures generation of clinically acceptable beam profiles. In between two subsequent optimizations, the voxel-dependent importance factors of the quadratic terms will generally be adjusted, based on an intermediate plan evaluation. The objective function has been written in matrix-vector format, facilitating the use of a recently published, fast quadratic minimization algorithm, instead of commonly applied gradient-based methods. This format also reduces the calculation time in between subsequent minimizations, related to adjustment of the voxel-dependent importance factors. Sparse matrices are used to limit the required amount of computer memory. For three patients, comparisons have been made with a gradient method. Mean speed improvements of up to a factor of 37 have been achieved

Accurate nonlocal theory for cascaded quadratic soliton compression

DEFF Research Database (Denmark)

Bache, Morten; Bang, Ole; Moses, Jeffrey

2007-01-01

We study soliton compression in bulk quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....

Coherent states of general time-dependent harmonic oscillator

Indian Academy of Sciences (India)

Abstract. By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator. The coherent states, both in x- and p-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger than Η/2 and is equal to the minimum of the ...

The evolution of streams in a time-dependent potential

NARCIS (Netherlands)

Buist, Hans J. T.; Helmi, Amina

2015-01-01

We study the evolution of streams in a time-dependent spherical gravitational potential. Our goal is to establish what are the imprints of this time evolution on the properties of streams as well as their observability. To this end, we have performed a suite of test-particle experiments for a host

The Harmonic Potential Theorem for a Quantum System with Time-Dependent Effective Mass

International Nuclear Information System (INIS)

Lai Meng-Yun; Xiao Duan-Liang; Pan Xiao-Yin

2015-01-01

We investigate the many-body wave function of a quantum system with time-dependent effective mass, confined by a harmonic potential with time-dependent frequency, and perturbed by a time-dependent spatially homogeneous electric field. It is found that the wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the harmonic potential theorem wave function when both the effective mass and frequency are static. An example of application is also given. (paper)

Zhang neural network for online solution of time-varying convex quadratic program subject to time-varying linear-equality constraints

International Nuclear Information System (INIS)

Zhang Yunong; Li Zhan

2009-01-01

In this Letter, by following Zhang et al.'s method, a recurrent neural network (termed as Zhang neural network, ZNN) is developed and analyzed for solving online the time-varying convex quadratic-programming problem subject to time-varying linear-equality constraints. Different from conventional gradient-based neural networks (GNN), such a ZNN model makes full use of the time-derivative information of time-varying coefficient. The resultant ZNN model is theoretically proved to have global exponential convergence to the time-varying theoretical optimal solution of the investigated time-varying convex quadratic program. Computer-simulation results further substantiate the effectiveness, efficiency and novelty of such ZNN model and method.

Quadratic dependence of the spin-induced Hall voltage on longitudinal electric field

International Nuclear Information System (INIS)

Miah, M. Idrish

2008-01-01

The effect of optically induced spins in semiconductors in the low electric field is investigated. Here we report an experiment which investigates the effect of a longitudinal electric field (E) on the spin-polarized carriers generated by a circularly polarized light in semiconductors. Our experiment observes the effect as a spin-induced anomalous Hall voltage (V AH ) resulting from spin-carrier electrons accumulating at the transverse edges of the sample. Unlike the ordinary Hall effect, a quadratic dependence of V AH on E is observed, which agrees with the results of the recent theoretical investigations. It is also found that V AH depends on the doping density. The results are discussed

Nonlinear dynamics of quadratically cubic systems

International Nuclear Information System (INIS)

Rudenko, O V

2013-01-01

We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)

Quadratic Boost A-Source Impedance Network

DEFF Research Database (Denmark)

Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii

2016-01-01

A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance...

Quadratic dependence of the spin-induced Hall voltage on longitudinal electric field

Energy Technology Data Exchange (ETDEWEB)

Miah, M. Idrish [Nanoscale Science and Technology Centre, Griffith University, Nathan, Brisbane, QLD 4111 (Australia); School of Biomolecular and Physical Sciences, Griffith University, Nathan, Brisbane, QLD 4111 (Australia); Department of Physics, University of Chittagong, Chittagong 4331 (Bangladesh)], E-mail: m.miah@griffith.edu.au

2008-10-15

The effect of optically induced spins in semiconductors in the low electric field is investigated. Here we report an experiment which investigates the effect of a longitudinal electric field (E) on the spin-polarized carriers generated by a circularly polarized light in semiconductors. Our experiment observes the effect as a spin-induced anomalous Hall voltage (V{sub AH}) resulting from spin-carrier electrons accumulating at the transverse edges of the sample. Unlike the ordinary Hall effect, a quadratic dependence of V{sub AH} on E is observed, which agrees with the results of the recent theoretical investigations. It is also found that V{sub AH} depends on the doping density. The results are discussed.

Quadratic theory and feedback controllers for linear time delay systems

International Nuclear Information System (INIS)

Lee, E.B.

1976-01-01

Recent research on the design of controllers for systems having time delays is discussed. Results for the ''open loop'' and ''closed loop'' designs will be presented. In both cases results for minimizing a quadratic cost functional are given. The usefulness of these results is not known, but similar results for the non-delay case are being routinely applied. (author)

Quadratic spatial soliton interactions

Science.gov (United States)

Jankovic, Ladislav

Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30

Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems

NARCIS (Netherlands)

Opmeer, MR; Curtain, RF

2004-01-01

In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show

Berry phases for 3D Hartree-type equations with a quadratic potential and a uniform magnetic field

International Nuclear Information System (INIS)

Litvinets, F N; Shapovalov, A V; Trifonov, A Yu

2007-01-01

A countable set of asymptotic space-localized solutions is constructed for a 3D Hartree-type equation with a quadratic potential by the complex germ method in the adiabatic approximation. The asymptotic parameter is 1/T, where T >> 1 is the adiabatic evolution time. A generalization of the Berry phase of the linear Schroedinger equation is formulated for the Hartree-type equation. For the solutions constructed, the Berry phases are found in an explicit form

Geometric Approaches to Quadratic Equations from Other Times and Places.

Science.gov (United States)

Allaire, Patricia R.; Bradley, Robert E.

2001-01-01

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Exact wavefunctions for a time-dependent Coulomb potential

International Nuclear Information System (INIS)

Menouar, S; Maamache, M; Saadi, Y; Choi, J R

2008-01-01

The one-dimensional Schroedinger equation associated with a time-dependent Coulomb potential is studied. The invariant operator method (Lewis and Riesenfeld) and unitary transformation approach are employed to derive quantum solutions of the system. We obtain an ordinary second-order differential equation whose analytical exact solution has been unknown. It is confirmed that the form of this equation is similar to the radial Schroedinger equation for the hydrogen atom in a (arbitrary) strong magnetic field. The qualitative properties for the eigenstates spectrum are described separately for the different values of the parameter ω 0 appearing in the x 2 term, x being the position, i.e., ω 0 > 0, ω 0 0 = 0. For the ω 0 = 0 case, the eigenvalue equation of invariant operator reduces to a solvable form and, consequently, we have provided exact eigenstates of the time-dependent Hamiltonian system

Fitting timeseries by continuous-time Markov chains: A quadratic programming approach

International Nuclear Information System (INIS)

Crommelin, D.T.; Vanden-Eijnden, E.

2006-01-01

Construction of stochastic models that describe the effective dynamics of observables of interest is an useful instrument in various fields of application, such as physics, climate science, and finance. We present a new technique for the construction of such models. From the timeseries of an observable, we construct a discrete-in-time Markov chain and calculate the eigenspectrum of its transition probability (or stochastic) matrix. As a next step we aim to find the generator of a continuous-time Markov chain whose eigenspectrum resembles the observed eigenspectrum as closely as possible, using an appropriate norm. The generator is found by solving a minimization problem: the norm is chosen such that the object function is quadratic and convex, so that the minimization problem can be solved using quadratic programming techniques. The technique is illustrated on various toy problems as well as on datasets stemming from simulations of molecular dynamics and of atmospheric flows

Newton equation for canonical, Lie-algebraic, and quadratic deformation of classical space

International Nuclear Information System (INIS)

Daszkiewicz, Marcin; Walczyk, Cezary J.

2008-01-01

The Newton equation describing particle motion in a constant external field force on canonical, Lie-algebraic, and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent, while in the case of Lie-algebraic noncommutativity, when spatial coordinates commute to the time variable, the additional acceleration of the particle is generated. We also indicate that in the case of spatial coordinates commuting in a Lie-algebraic way, as well as for quadratic deformation, there appear additional velocity and position-dependent forces

Robustness analysis of the Zhang neural network for online time-varying quadratic optimization

International Nuclear Information System (INIS)

Zhang Yunong; Ruan Gongqin; Li Kene; Yang Yiwen

2010-01-01

A general type of recurrent neural network (termed as Zhang neural network, ZNN) has recently been proposed by Zhang et al for the online solution of time-varying quadratic-minimization (QM) and quadratic-programming (QP) problems. Global exponential convergence of the ZNN could be achieved theoretically in an ideal error-free situation. In this paper, with the normal differentiation and dynamics-implementation errors considered, the robustness properties of the ZNN model are investigated for solving these time-varying problems. In addition, linear activation functions and power-sigmoid activation functions could be applied to such a perturbed ZNN model. Both theoretical-analysis and computer-simulation results demonstrate the good ZNN robustness and superior performance for online time-varying QM and QP problem solving, especially when using power-sigmoid activation functions.

New results for time reversed symplectic dynamic systems and quadratic functionals

Directory of Open Access Journals (Sweden)

Roman Simon Hilscher

2012-05-01

Full Text Available In this paper, we examine time scale symplectic (or Hamiltonian systems and the associated quadratic functionals which contain a forward shift in the time variable. Such systems and functionals have a close connection to Jacobi systems for calculus of variations and optimal control problems on time scales. Our results, among which we consider the Reid roundabout theorem, generalize the corresponding classical theory for time reversed discrete symplectic systems, as well as they complete the recently developed theory of time scale symplectic systems.

Lagrangian finite element method for 3D time-dependent non-isothermal flow of K-BKZ fluids

DEFF Research Database (Denmark)

Román Marín, José Manuel; Rasmussen, Henrik K.

2009-01-01

equation is replaced with a temperature dependent pseudo time. The spatial coordinate system attached to the particles is discretized by 10-node quadratic tetrahedral elements using Cartesian coordinates. The temperature and the pressure are discretized by 10-node quadratic and linear interpolation...... utilizing an implicit variable step backwards differencing (BDF2) scheme, obtaining second order convergence of the temperature in time. A quadratic interpolation in time is applied to approximate the time integral in the K-BKZ equation. This type of scheme ensures third order accuracy with respect......, respectively, in the tetrahedral particle elements. The spatial discretization of the governing equations follows a mixed Galerkin finite element method. This type of scheme ensures third order accuracy with respect to the discretization of spatial dimension. The temperature equation is solved in time...

Initial post dynamic buckling of a quadratic-cubic column ...

African Journals Online (AJOL)

In this investigation, we determine the dynamic buckling load of an imperfect finite column resting on a mixed quadratic-cubic nonlinear elastic foundation trapped by an explicitly time dependent sinusoidally slowly varying dynamic load .The resultant coefficients are dynamically slowly varying and the formulation contains ...

Learning of Precise Spike Times with Homeostatic Membrane Potential Dependent Synaptic Plasticity.

Directory of Open Access Journals (Sweden)

Christian Albers

Full Text Available Precise spatio-temporal patterns of neuronal action potentials underly e.g. sensory representations and control of muscle activities. However, it is not known how the synaptic efficacies in the neuronal networks of the brain adapt such that they can reliably generate spikes at specific points in time. Existing activity-dependent plasticity rules like Spike-Timing-Dependent Plasticity are agnostic to the goal of learning spike times. On the other hand, the existing formal and supervised learning algorithms perform a temporally precise comparison of projected activity with the target, but there is no known biologically plausible implementation of this comparison. Here, we propose a simple and local unsupervised synaptic plasticity mechanism that is derived from the requirement of a balanced membrane potential. Since the relevant signal for synaptic change is the postsynaptic voltage rather than spike times, we call the plasticity rule Membrane Potential Dependent Plasticity (MPDP. Combining our plasticity mechanism with spike after-hyperpolarization causes a sensitivity of synaptic change to pre- and postsynaptic spike times which can reproduce Hebbian spike timing dependent plasticity for inhibitory synapses as was found in experiments. In addition, the sensitivity of MPDP to the time course of the voltage when generating a spike allows MPDP to distinguish between weak (spurious and strong (teacher spikes, which therefore provides a neuronal basis for the comparison of actual and target activity. For spatio-temporal input spike patterns our conceptually simple plasticity rule achieves a surprisingly high storage capacity for spike associations. The sensitivity of the MPDP to the subthreshold membrane potential during training allows robust memory retrieval after learning even in the presence of activity corrupted by noise. We propose that MPDP represents a biophysically plausible mechanism to learn temporal target activity patterns.

Learning of Precise Spike Times with Homeostatic Membrane Potential Dependent Synaptic Plasticity.

Science.gov (United States)

Albers, Christian; Westkott, Maren; Pawelzik, Klaus

2016-01-01

Precise spatio-temporal patterns of neuronal action potentials underly e.g. sensory representations and control of muscle activities. However, it is not known how the synaptic efficacies in the neuronal networks of the brain adapt such that they can reliably generate spikes at specific points in time. Existing activity-dependent plasticity rules like Spike-Timing-Dependent Plasticity are agnostic to the goal of learning spike times. On the other hand, the existing formal and supervised learning algorithms perform a temporally precise comparison of projected activity with the target, but there is no known biologically plausible implementation of this comparison. Here, we propose a simple and local unsupervised synaptic plasticity mechanism that is derived from the requirement of a balanced membrane potential. Since the relevant signal for synaptic change is the postsynaptic voltage rather than spike times, we call the plasticity rule Membrane Potential Dependent Plasticity (MPDP). Combining our plasticity mechanism with spike after-hyperpolarization causes a sensitivity of synaptic change to pre- and postsynaptic spike times which can reproduce Hebbian spike timing dependent plasticity for inhibitory synapses as was found in experiments. In addition, the sensitivity of MPDP to the time course of the voltage when generating a spike allows MPDP to distinguish between weak (spurious) and strong (teacher) spikes, which therefore provides a neuronal basis for the comparison of actual and target activity. For spatio-temporal input spike patterns our conceptually simple plasticity rule achieves a surprisingly high storage capacity for spike associations. The sensitivity of the MPDP to the subthreshold membrane potential during training allows robust memory retrieval after learning even in the presence of activity corrupted by noise. We propose that MPDP represents a biophysically plausible mechanism to learn temporal target activity patterns.

Temperature dependence of Kerr coefficient and quadratic polarized optical coefficient of a paraelectric Mn:Fe:KTN crystal

Directory of Open Access Journals (Sweden)

Qieni Lu

2015-08-01

Full Text Available We measure temperature dependence on Kerr coefficient and quadratic polarized optical coefficient of a paraelectric Mn:Fe:KTN crystal simultaneously in this work, based on digital holographic interferometry (DHI. And the spatial distribution of the field-induced refractive index change can also be visualized and estimated by numerically retrieving sequential phase maps of Mn:Fe:KTN crystal from recording digital holograms in different states. The refractive indices decrease with increasing temperature and quadratic polarized optical coefficient is insensitive to temperature. The experimental results suggest that the DHI method presented here is highly applicable in both visualizing the temporal and spatial behavior of the internal electric field and accurately measuring electro-optic coefficient for electrooptical media.

Binary classification posed as a quadratically constrained quadratic ...

Indian Academy of Sciences (India)

Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or ...

Parametrization of complex absorbing potentials for time-dependent quantum dynamics

International Nuclear Information System (INIS)

Vibok, A.; Balint-Kurti, G.G.

1992-01-01

Five different forms of complex absorbing potentials are examined and compared. Such potentials are needed to absorb wavepackets near the edges of grids in time-dependent quantum dynamical calculations. The extent to which the different potentials transmit or reflect an incident wavepacket is quantified, and optimal potential parameters to minimize both the reflection and transmission for each type of potential are derived. A rigorously derived scaling procedure, which permits the derivation of optimal potential parameters for use with any chosen mass or kinetic energy from those optimized for different conditions, is described. Tables are also presented which permit the immediate selection of the parameters for an absorbing potential of a particular form so as to allow a preselected (very small) degree of transmitted plus reflected probability to be attained. It is always desirable to devote a minimal region to the absorbing potential, while at the same time effectively absorbing all of the wavepacket and neither transmitting nor reflecting any of it. The tables presented here enable the use to easily select the potential parameters he will require to attain these goals. 23 refs., 7 figs., 4 tabs

Wave function for time-dependent harmonically confined electrons in a time-dependent electric field.

Science.gov (United States)

Li, Yu-Qi; Pan, Xiao-Yin; Sahni, Viraht

2013-09-21

The many-body wave function of a system of interacting particles confined by a time-dependent harmonic potential and perturbed by a time-dependent spatially homogeneous electric field is derived via the Feynman path-integral method. The wave function is comprised of a phase factor times the solution to the unperturbed time-dependent Schrödinger equation with the latter being translated by a time-dependent value that satisfies the classical driven equation of motion. The wave function reduces to that of the Harmonic Potential Theorem wave function for the case of the time-independent harmonic confining potential.

The quantum cosmological wavefunction at very early times for a quadratic gravity theory

International Nuclear Information System (INIS)

Davis, Simon

2003-01-01

The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, the wavefunction would satisfy a third-order differential equation near the inflationary epoch which has a solution that is singular in the scale factor limit a(t) → 0. When scalar field derivatives are included, a sixth-order differential equation is obtained for the wavefunction and the solution by Mellin transform is regular in the a → 0 limit. It follows that inclusion of the scalar field in the quadratic gravity action is necessary for consistency of the quantum cosmology of the theory at very early times

Learning quadratic receptive fields from neural responses to natural stimuli.

Science.gov (United States)

Rajan, Kanaka; Marre, Olivier; Tkačik, Gašper

2013-07-01

Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are selective for only a small number of linear projections of a potentially high-dimensional input. In this review, we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g., naturalistic) stimulus distribution, we review several inference methods, focusing in particular on two information theory-based approaches (maximization of stimulus energy and of noise entropy) and two likelihood-based approaches (Bayesian spike-triggered covariance and extensions of generalized linear models). We analyze the formal relationship between the likelihood-based and information-based approaches to demonstrate how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.

A time-domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems

Science.gov (United States)

Heinkenschloss, Matthias

2005-01-01

We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.

On using the linear-quadratic model in daily clinical practice

International Nuclear Information System (INIS)

Yaes, R.J.; Patel, P.; Maruyama, Y.

1991-01-01

To facilitate its use in the clinic, Barendsen's formulation of the Linear-Quadratic (LQ) model is modified by expressing isoeffect doses in terms of the Standard Effective Dose, Ds, the isoeffective dose for the standard fractionation schedule of 2 Gy fractions given once per day, 5 days per week. For any arbitrary fractionation schedule, where total dose D is given in N fractions of size d in a total time T, the corresponding Standard Effective Dose, Ds, will be proportional to the total dose D and the proportionality constant will be called the Standard Relative Effectiveness, SRE, to distinguish it from Barendsen's Relative Effectiveness, RE. Thus, Ds = SRE.D. The constant SRE depends on the parameters of the fractionation schedule, and on the tumor or normal tissue being irradiated. For the simple LQ model with no time dependence, which is applicable to late reacting tissue, SRE = [(d + delta)/(2 + delta)], where d is the fraction size and delta = alpha/beta is the alpha/beta ratio for the tissue of interest, with both d and delta expressed in units of Gy. Application of this method to the Linear Quadratic model with a time dependence, the LQ + time model, and to low dose rate brachytherapy will be discussed. To clarify the method of calculation, and to demonstrate its simplicity, examples from the clinical literature will be used

Josephson-like currents in graphene for arbitrary time-dependent potential barriers

OpenAIRE

Savel'ev, Sergey E.; Hausler, Wolfgang; Hanggi, Peter

2011-01-01

From the exact solution of the Dirac-Weyl equation we find unusual currents j_y running in y-direction parallel to a time-dependent scalar potential barrier W(x,t) placed upon a monolayer of graphene, even for vanishing momentum component p_y. In their sine-like dependence on the phase difference of wave functions, describing left and right moving Dirac fermions, these currents resemble Josephson currents in superconductors, including the occurance of Shapiro steps at certain frequencies of p...

Hidden conic quadratic representation of some nonconvex quadratic optimization problems

NARCIS (Netherlands)

Ben-Tal, A.; den Hertog, D.

The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated

Measurement of quadratic electrogyration effect in castor oil

Science.gov (United States)

Izdebski, Marek; Ledzion, Rafał; Górski, Piotr

2015-07-01

This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.

Some aspects of the description of relativistic particles in external fields. [Time dependent and time independent potentials

Energy Technology Data Exchange (ETDEWEB)

Labonte, G

1973-01-01

We study the time description of the motion of relativistic particles in both the dependent and time independent potentials. The differential equations of motion considered are the standard linear spin zero and one half equations. They are always meaningful in the sense that, at all times, unique well defined operator valued distributions in the three space variables are determined. We discuss the problem of determining which set of creation and annihilation operators is relevant in a given problem. We examine the implementation of certain simple requirements which seem to be necessary in order for the mathematical formalism to be able to describe a physical system. We show that whenever the equation of motion is homogeneous, the study of all physical requirements reduces to studying Bogoliubov transformations between creation and annihilation operators. We study such transformations where we obtain some new important results concerning their general properties. We examine in detail a quantized field in presence of an external source, electrons and positrons acted upon by a plane electromagnetic wave, Dirac fields acted upon by potentials of the form A(x) delta (t) and A(x) THETA (t-t/sub 0/). We study Dirac fields in presence of potentials which have time dependences which can be represented by sequences of step functions. We then discuss the limiting case where the time dependence is continuous. We prove that the requirements that there exists a unitary evolution operator or that physical particles can be described are exactly equivalent. (auth)

Time-dependent local potential in a Tomonaga-Luttinger liquid

Science.gov (United States)

Kamar, Naushad Ahmad; Giamarchi, Thierry

2017-12-01

We study the energy deposition in a one-dimensional interacting quantum system with a pointlike potential modulated in amplitude. The pointlike potential at position x =0 has a constant part and a small oscillation in time with a frequency ω . We use bosonization, renormalization group, and linear response theory to calculate the corresponding energy deposition. It exhibits a power law behavior as a function of the frequency that reflects the Tomonaga-Luttinger liquid (TLL) nature of the system. Depending on the interactions in the system, characterized by the TLL parameter K of the system, a crossover between weak and strong coupling for the backscattering due to the potential is possible. We compute the frequency scale ω*, at which such crossover exists. We find that the energy deposition due to the backscattering shows different exponents for K >1 and K <1 . We discuss possible experimental consequences, in the context of cold atomic gases, of our theoretical results.

Quadratic third-order tensor optimization problem with quadratic constraints

Directory of Open Access Journals (Sweden)

Lixing Yang

2014-05-01

Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.

From interatomic interaction potentials via Einstein field equation techniques to time dependent contact mechanics

International Nuclear Information System (INIS)

Schwarzer, N

2014-01-01

In order to understand the principle differences between rheological or simple stress tests like the uniaxial tensile test to contact mechanical tests and the differences between quasistatic contact experiments and oscillatory ones, this study resorts to effective first principles. This study will show how relatively simple models simulating bond interactions in solids using effective potentials like Lennard-Jones and Morse can be used to investigate the effect of time dependent stress-induced softening or stiffening of these solids. The usefulness of the current study is in the possibility of deriving relatively simple dependences of the bulk-modulus B on time, shear and pressure P with time t. In cases where it is possible to describe, or at least partially describe a material by Lennard-Jones potential approaches, the above- mentioned dependences are even completely free of microscopic material parameters. Instead of bond energies and length, only specific integral parameters like Young’s modulus and Poisson’s ratio are required. However, in the case of time dependent (viscose) material behavior the parameters are not constants anymore. They themselves depend on time and the actual stress field, especially the shear field. A body completely consisting of so called standard linear solid interacting particles will then phenomenologically show a completely different and usually much more complicated mechanical behavior. The influence of the time dependent pressure-shear-induced Young’s modulus change is discussed with respect to mechanical contact experiments and their analysis in the case of viscose materials. (papers)

Time-dependent embedding

OpenAIRE

Inglesfield, J. E.

2007-01-01

A method of solving the time-dependent Schr\\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an embedding term added on to the Hamiltonian. This time-dependent embedding term is derived from the Fourier transform of the energy-dependent embedding potential, which embeds the time-independent Schr\\"odinger equation. Results are presented for a one-dimensi...

Exact Time-Dependent Exchange-Correlation Potential in Electron Scattering Processes

Science.gov (United States)

Suzuki, Yasumitsu; Lacombe, Lionel; Watanabe, Kazuyuki; Maitra, Neepa T.

2017-12-01

We identify peak and valley structures in the exact exchange-correlation potential of time-dependent density functional theory that are crucial for time-resolved electron scattering in a model one-dimensional system. These structures are completely missed by adiabatic approximations that, consequently, significantly underestimate the scattering probability. A recently proposed nonadiabatic approximation is shown to correctly capture the approach of the electron to the target when the initial Kohn-Sham state is chosen judiciously, and it is more accurate than standard adiabatic functionals but ultimately fails to accurately capture reflection. These results may explain the underestimation of scattering probabilities in some recent studies on molecules and surfaces.

Construction of exact invariants of time-dependent linear nonholonomic dynamical systems

International Nuclear Information System (INIS)

Fu Jingli; Jimenez, Salvador; Tang Yifa; Vazquez, Luis

2008-01-01

In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out

Construction of exact invariants of time-dependent linear nonholonomic dynamical systems

Energy Technology Data Exchange (ETDEWEB)

Fu Jingli [Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018 (China)], E-mail: sqfujingli@163.com; Jimenez, Salvador [Departamento de Matematica Aplicada TTII, E.T.S.I. Telecomunicacion, Universidad Politecnica de Madrid, 28040 Madrid (Spain); Tang Yifa [State Key Laboratory of Scientific and Engineering Computing, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, PO Box 2719, Beijing 100080 (China); Vazquez, Luis [Departamento de Matematica Aplicada Facultad de Informatica, Universidad Complutense de Madrid, 28040 Madrid (Spain); Centro de Astrobiologia (CSIC-INTA), Torrejon de Ardoz, 28850 Madrid (Spain)

2008-03-03

In this work, we build exact dynamical invariants for time-dependent, linear, nonholonomic Hamiltonian systems in two dimensions. Our aim is to obtain an additional insight into the theoretical understanding of generalized Hamilton canonical equations. In particular, we investigate systems represented by a quadratic Hamiltonian subject to linear nonholonomic constraints. We use a Lie algebraic method on the systems to build the invariants. The role and scope of these invariants is pointed out.

Self-Replicating Quadratics

Science.gov (United States)

Withers, Christopher S.; Nadarajah, Saralees

2012-01-01

We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

Exact solutions to the supply chain equations for arbitrary, time-dependent demands

DEFF Research Database (Denmark)

Warburton, Roger D.H.; Hodgson, J.P.E.; Nielsen, Erland Hejn

2014-01-01

, so users can determine the inventory behavior to any desired precision. To illustrate, we solve the equations for a non-linear, quadratic time-dependence in the demand. For practical use, only a few terms in the series are required, a proposition illustrated by the For All Practical Purposes (FAPP......We study the impact on inventory of an unexpected, non-linear, time-dependent demand and present the exact solutions over time to the supply chain equations without requiring any approximations. We begin by imposing a boundary condition of stability at infinity, from which we derive expressions...... for the estimated demand and the target work in progress when the demand is time-dependent. The resulting inventory equation is solved in terms of the Lambert modes with all of the demand non-linearities confined to the pre-shape function. The series solution is exact, and all terms are reasonably easy to calculate...

Complex eigenvalues for neutron transport equation with quadratically anisotropic scattering

International Nuclear Information System (INIS)

Sjoestrand, N.G.

1981-01-01

Complex eigenvalues for the monoenergetic neutron transport equation in the buckling approximation have been calculated for various combinations of linearly and quadratically anisotropic scattering. The results are discussed in terms of the time-dependent case. Tables are given of complex bucklings for real decay constants and of complex decay constants for real bucklings. The results fit nicely into the pattern of real and purely imaginary eigenvalues obtained earlier. (author)

A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions

International Nuclear Information System (INIS)

Jian Jinbao; Hu Qingjie; Tang Chunming; Zheng Haiyan

2007-01-01

In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported

Quadratic Damping

Science.gov (United States)

Fay, Temple H.

2012-01-01

Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

Quadratic tracer dynamical models tobacco growth

International Nuclear Information System (INIS)

Qiang Jiyi; Hua Cuncai; Wang Shaohua

2011-01-01

In order to study the non-uniformly transferring process of some tracer dosages, we assume that the absorption of some tracer by tobacco is a quadratic function of the tracer quantity of the tracer in the case of fast absorption, whereas the exclusion of the tracer from tobacco is a linear function of the tracer quantity in the case of slow exclusion, after the tracer is introduced into tobacco once at zero time. A single-compartment quadratic dynamical model of Logistic type is established for the leaves of tobacco. Then, a two-compartment quadratic dynamical model is established for leaves and calms of the tobacco. Qualitative analysis of the models shows that the tracer applied to the leaves of the tobacco is excluded finally; however, the tracer stays at the tobacco for finite time. Two methods are also given for computing the parameters in the models. Finally, the results of the models are verified by the 32 P experiment for the absorption of tobacco. (authors)

Linear quadratic optimization for positive LTI system

Science.gov (United States)

Muhafzan, Yenti, Syafrida Wirma; Zulakmal

2017-05-01

Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

International Nuclear Information System (INIS)

Zhang Hong; Li Guo-Hua

2016-01-01

Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier–Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation. (paper)

Quadratic soliton self-reflection at a quadratically nonlinear interface

Science.gov (United States)

Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai

2003-11-01

The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.

A Realization of a Quasi-Random Walk for Atoms in Time-Dependent Optical Potentials

Directory of Open Access Journals (Sweden)

Torsten Hinkel

2015-09-01

Full Text Available We consider the time dependent dynamics of an atom in a two-color pumped cavity, longitudinally through a side mirror and transversally via direct driving of the atomic dipole. The beating of the two driving frequencies leads to a time dependent effective optical potential that forces the atom into a non-trivial motion, strongly resembling a discrete random walk behavior between lattice sites. We provide both numerical and analytical analysis of such a quasi-random walk behavior.

Quadratic reactivity fuel cycle model

International Nuclear Information System (INIS)

Lewins, J.D.

1985-01-01

For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau 2 as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau 2 in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper

Optimal Quadratic Programming Algorithms

CERN Document Server

Dostal, Zdenek

2009-01-01

Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This title presents various algorithms for solving large QP problems. It is suitable as an introductory text on quadratic programming for graduate students and researchers

Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian.

Science.gov (United States)

Ginzburg, D; Mann, A

2014-03-10

A Lie algebraic method for propagation of the Wigner quasi-distribution function (QDF) under quadratic Hamiltonian was presented by Zoubi and Ben-Aryeh. We show that the same method can be used in order to propagate a rather general class of QDFs, which we call the "Gaussian class." This class contains as special cases the well-known Wigner, Husimi, Glauber, and Kirkwood-Rihaczek QDFs. We present some examples of the calculation of the time evolution of those functions.

Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

Science.gov (United States)

Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.

2018-04-01

We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.

Linear-quadratic control and quadratic differential forms for multidimensional behaviors

NARCIS (Netherlands)

Napp, D.; Trentelman, H.L.

2011-01-01

This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look

Exact solution of the time-dependent harmonic plus an inverse harmonic potential with a time-dependent electromagnetic field

International Nuclear Information System (INIS)

Yuece, Cem

2003-01-01

In this paper, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic oscillator with time-independent parameters and the exact wave function is obtained

Delay-Dependent Stability Criteria of Uncertain Periodic Switched Recurrent Neural Networks with Time-Varying Delays

Directory of Open Access Journals (Sweden)

Xing Yin

2011-01-01

uncertain periodic switched recurrent neural networks with time-varying delays. When uncertain discrete-time recurrent neural network is a periodic system, it is expressed as switched neural network for the finite switching state. Based on the switched quadratic Lyapunov functional approach (SQLF and free-weighting matrix approach (FWM, some linear matrix inequality criteria are found to guarantee the delay-dependent asymptotical stability of these systems. Two examples illustrate the exactness of the proposed criteria.

Temporal quadratic expansion nodal Green's function method

International Nuclear Information System (INIS)

Liu Cong; Jing Xingqing; Xu Xiaolin

2000-01-01

A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method

Dynamical properties of a particle in a time-dependent double-well potential

International Nuclear Information System (INIS)

Leonel, Edson D; McClintock, P V E

2004-01-01

Some chaotic properties of a classical particle interacting with a time-dependent double-square-well potential are studied. The dynamics of the system is characterized using a two-dimensional nonlinear area-preserving map. Scaling arguments are used to study the chaotic sea in the low-energy domain. It is shown that the distributions of successive reflections and of corresponding successive reflection times obey power laws with the same exponent. If one or both wells move randomly, the particle experiences the phenomenon of Fermi acceleration in the sense that it has unlimited energy growth

Modified Emden-type equation with dissipative term quadratic in velocity

International Nuclear Information System (INIS)

Ghosh, Subrata; Talukdar, B; Das, Umapada; Saha, Aparna

2012-01-01

Based on some physical observation we introduce a generalized modified Emden-type equation (MEE) with a position-dependent dissipative term which is quadratic in velocity. Unlike the usual MEE, the first integral of the proposed generalized MEE is such that one can express the velocity of the system as a function of coordinate for all values of the parameters of the system. This permits us to study the dynamical properties of the system using straightforward analytical methods. The results presented in the phase diagram and plots of vector fields clearly delineate how does the presence of quadratic damping affect the motion of our nonlinear oscillator. From the differential equation provided by the first integral of the generalized MEE, we have found an approximate analytical solution of the equation which reproduces the time variation of the corresponding numerical solution to a fair degree of accuracy. (paper)

On the time-dependent Aharonov–Bohm effect

Directory of Open Access Journals (Sweden)

Jian Jing

2017-11-01

Full Text Available The Aharonov–Bohm effect in the background of a time-dependent vector potential is re-examined for both non-relativistic and relativistic cases. Based on the solutions to the Schrodinger and Dirac equations which contain the time-dependent magnetic vector potential, we find that contrary to the conclusions in a recent paper (Singleton and Vagenas 2013 [4], the interference pattern will be altered with respect to time because of the time-dependent vector potential.

Spatial statistics of pitting corrosion patterning: Quadrat counts and the non-homogeneous Poisson process

International Nuclear Information System (INIS)

Lopez de la Cruz, J.; Gutierrez, M.A.

2008-01-01

This paper presents a stochastic analysis of spatial point patterns as effect of localized pitting corrosion. The Quadrat Counts method is studied with two empirical pit patterns. The results are dependent on the quadrat size and bias is introduced when empty quadrats are accounted for the analysis. The spatially inhomogeneous Poisson process is used to improve the performance of the Quadrat Counts method. The latter combines Quadrat Counts with distance-based statistics in the analysis of pit patterns. The Inter-Event and the Nearest-Neighbour statistics are here implemented in order to compare their results. Further, the treatment of patterns in irregular domains is discussed

Faithfully quadratic rings

CERN Document Server

Dickmann, M

2015-01-01

In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A^2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in

Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems

International Nuclear Information System (INIS)

Marquette, Ian

2011-01-01

There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

Exact invariants in the form of momentum resonances for particle motion in one-dimensional, time-dependent potentials

International Nuclear Information System (INIS)

Goedert, J.; Lewis, H.R.

1984-01-01

A momentum-resonance ansatz of Lewis and Leach was used to study exact invariants for time-dependent, one-dimensional potentials. This ansatz provides a framework for finding invariants admitted by a larger class of time-dependent potentials that was known previously. For a potential that admits an exact invariant in this resonance form, we have shown how to construct the invariant as a functional of the potential in terms of the solution of a definite linear algebraic system of equations. We have found a necessary and sufficient condition on the potential for the existence of an invariant with a given number of resonances. There exist more potentials that admit invariants with two resonances than were previously known and we have found an example in parametric form of such a potential. We have also found examples of potentials that admit invariants with three resonances

Molecular wave function and effective adiabatic potentials calculated by extended multi-configuration time-dependent Hartree-Fock method

Energy Technology Data Exchange (ETDEWEB)

Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru [Department of Chemistry, School of Science, The University of Tokyo, 7-3-1, Hongo Bunkyo-ku, Tokyo, 113-0033 (Japan)

2015-12-31

We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understand dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.

Gravitation and quadratic forms

International Nuclear Information System (INIS)

Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta; Mali, Mahendra; Shah, Nabha

2017-01-01

The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

Gravitation and quadratic forms

Energy Technology Data Exchange (ETDEWEB)

Ananth, Sudarshan [Indian Institute of Science Education and Research,Pune 411008 (India); Brink, Lars [Department of Physics, Chalmers University of Technology,S-41296 Göteborg (Sweden); Institute of Advanced Studies and Department of Physics & Applied Physics,Nanyang Technological University,Singapore 637371 (Singapore); Majumdar, Sucheta [Indian Institute of Science Education and Research,Pune 411008 (India); Mali, Mahendra [School of Physics, Indian Institute of Science Education and Research,Thiruvananthapuram, Trivandrum 695016 (India); Shah, Nabha [Indian Institute of Science Education and Research,Pune 411008 (India)

2017-03-31

The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

Quadratic obstructions to small-time local controllability for scalar-input systems

Science.gov (United States)

Beauchard, Karine; Marbach, Frédéric

2018-03-01

We consider nonlinear finite-dimensional scalar-input control systems in the vicinity of an equilibrium. When the linearized system is controllable, the nonlinear system is smoothly small-time locally controllable: whatever m > 0 and T > 0, the state can reach a whole neighborhood of the equilibrium at time T with controls arbitrary small in Cm-norm. When the linearized system is not controllable, we prove that: either the state is constrained to live within a smooth strict manifold, up to a cubic residual, or the quadratic order adds a signed drift with respect to it. This drift holds along a Lie bracket of length (2 k + 1), is quantified in terms of an H-k-norm of the control, holds for controls small in W 2 k , ∞-norm and these spaces are optimal. Our proof requires only C3 regularity of the vector field. This work underlines the importance of the norm used in the smallness assumption on the control, even in finite dimension.

Double Dissociation of Spike Timing-Dependent Potentiation and Depression by Subunit-Preferring NMDA Receptor Antagonists in Mouse Barrel Cortex

NARCIS (Netherlands)

Banerjee, A.; Meredith, R.M.; Rodriguez-Moreno, A.; Mierau, S.B.; Auberson, Y.P.; Paulsen, O.

2009-01-01

Spike timing-dependent plasticity (STDP) is a strong candidate for an N-methyl-D-aspartate (NMDA) receptor-dependent form of synaptic plasticity that could underlie the development of receptive field properties in sensory neocortices. Whilst induction of timing-dependent long-term potentiation

On orthogonality preserving quadratic stochastic operators

Energy Technology Data Exchange (ETDEWEB)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)

2015-05-15

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

On orthogonality preserving quadratic stochastic operators

International Nuclear Information System (INIS)

Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

2015-01-01

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too

Quadratic Lagrangians and Legendre transformation

International Nuclear Information System (INIS)

Magnano, G.

1988-01-01

In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor

Time-dependent friction and solvation time correlation function

International Nuclear Information System (INIS)

Samanta, Alok; Ali, Sk Musharaf; Ghosh, Swapan K

2005-01-01

We have derived a new relation between the time-dependent friction and solvation time correlation function (STCF) for non-polar fluids. The friction values calculated using this relation and simulation results on STCF for a Lennard-Jones fluid are shown to have excellent agreement with the same obtained through mode-coupling theory. Also derived is a relation between the time-dependent dielectric friction and STCF for polar fluids. Routes are thus provided to obtain the time-dependent friction (non-polar as well as dielectric) from an experimentally measured quantity like STCF, even if the interparticle interaction potential is not known

Time-dependent problems in quantum-mechanical state reconstruction

International Nuclear Information System (INIS)

Leonhardt, U.; Bardroff, P. J.

1997-01-01

We study the state reconstruction of wave packets that travel in time-dependent potentials. We solve the problem for explicitly time-dependent potentials. We solve the problem for explicitly time-dependent harmonic oscillators and sketch a general adaptive technique for finding the wave function that matches and observed evolution. (authors)

Quadratic measurement and conditional state preparation in an optomechanical system

DEFF Research Database (Denmark)

A. Brawley, George; Vanner, Michael A.; Bowen, Warwick P.

2014-01-01

We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator.......We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator....

Approximative analytic eigenvalues for orbital excitations in the case of a coulomb potential plus linear and quadratic radial terms

International Nuclear Information System (INIS)

Rekab, S.; Zenine, N.

2006-01-01

We consider the three dimensional non relativistic eigenvalue problem in the case of a Coulomb potential plus linear and quadratic radial terms. In the framework of the Rayleigh-Schrodinger Perturbation Theory, using a specific choice of the unperturbed Hamiltonian, we obtain approximate analytic expressions for the eigenvalues of orbital excitations. The implications and the range of validity of the obtained analytic expression are discussed

Aspects of Quadratic Gravity

CERN Document Server

Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio

2016-01-01

We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...

Anomalous transport in fluid field with random waiting time depending on the preceding jump length

Science.gov (United States)

Zhang, Hong; Li, Guo-Hua

2016-11-01

Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation. Project supported by the Foundation for Young Key Teachers of Chengdu University of Technology, China (Grant No. KYGG201414) and the Opening Foundation of Geomathematics Key Laboratory of Sichuan Province, China (Grant No. scsxdz2013009).

The excitation of an independent-particle gas - classical or quantal - by a time-dependent potential well

International Nuclear Information System (INIS)

Blocki, J.; Skalski, J.; Swiatecki, W.J.

1995-01-01

A systematic numerical investigation of the excitation of a classical or quantal gas of non-interacting particles in a time-dependent potential well is described. The excitation energy was followed in time for one oscillation around the sphere for six types of deformation: spheroidal shapes and Legendre polynomial ripples P 2 , P 3 , P 4 , P 5 , P 6 , with relative rms amplitudes of 0.2. Ten different speeds of deformation and eleven different values of the diffuseness of the potential well were studied, making altogether 660 quantal and 660 classical time-dependent calculations. In the upper range of deformation speeds the quantal results for the non-integrable shapes P 3 -P 6 agree approximately with the wall formula for dissipation, the deviations being largely accounted for by the wave-mechanical suppression factor of Koonin et al. For low deformation speeds the dissipation becomes dominated by one or two avoided level crossings. (orig.)

On Characterization of Quadratic Splines

DEFF Research Database (Denmark)

Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong

2005-01-01

that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general....

Evolution of universes in quadratic theories of gravity

International Nuclear Information System (INIS)

Barrow, John D.; Hervik, Sigbjoern

2006-01-01

We use a dynamical systems approach to investigate Bianchi type I and II universes in quadratic theories of gravity. Because of the complicated nature of the equations of motion we focus on the stability of exact solutions and find that there exists an isotropic Friedmann-Robertson-Walker (FRW) universe acting as a past attractor. This may indicate that there is an isotropization mechanism at early times for these kind of theories. We also discuss the Kasner universes, elucidate the associated center manifold structure, and show that there exists a set of nonzero measure which has the Kasner solutions as a past attractor. Regarding the late-time behavior, the stability shows a dependence of the parameters of the theory. We give the conditions under which the de Sitter solution is stable and also show that for certain values of the parameters there is a possible late-time behavior with phantomlike behavior. New types of anisotropic inflationary behavior are found which do not have counterparts in general relativity

Energy shift and conduction-to-valence band transition mediated by a time-dependent potential barrier in graphene

Science.gov (United States)

Chaves, Andrey; da Costa, D. R.; de Sousa, G. O.; Pereira, J. M.; Farias, G. A.

2015-09-01

We investigate the scattering of a wave packet describing low-energy electrons in graphene by a time-dependent finite-step potential barrier. Our results demonstrate that, after Klein tunneling through the barrier, the electron acquires an extra energy which depends on the rate of change of the barrier height with time. If this rate is negative, the electron loses energy and ends up as a valence band state after leaving the barrier, which effectively behaves as a positively charged quasiparticle.

The bounds of feasible space on constrained nonconvex quadratic programming

Science.gov (United States)

Zhu, Jinghao

2008-03-01

This paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmingsE Results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a P-problem [N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395]. It is proposed that one applies this method for using the canonical dual transformation [D.Y. Gao, Canonical duality theory and solutions to constrained nonconvex quadratic programming, J. Global Optimization 29 (2004) 377-399] for solving a standard quadratic programming problem.

Optimal control linear quadratic methods

CERN Document Server

Anderson, Brian D O

2007-01-01

This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the

Simulation of resonance hyper-Rayleigh scattering of molecules and metal clusters using a time-dependent density functional theory approach.

Science.gov (United States)

Hu, Zhongwei; Autschbach, Jochen; Jensen, Lasse

2014-09-28

Resonance hyper-Rayleigh scattering (HRS) of molecules and metal clusters have been simulated based on a time-dependent density functional theory approach. The resonance first-order hyperpolarizability (β) is obtained by implementing damped quadratic response theory using the (2n + 1) rule. To test this implementation, the prototypical dipolar molecule para-nitroaniline (p-NA) and the octupolar molecule crystal violet are used as benchmark systems. Moreover, small silver clusters Ag 8 and Ag 20 are tested with a focus on determining the two-photon resonant enhancement arising from the strong metal transition. Our results show that, on a per atom basis, the small silver clusters possess two-photon enhanced HRS comparable to that of larger nanoparticles. This finding indicates the potential interest of using small metal clusters for designing new nonlinear optical materials.

Inhibition of chaotic escape from a potential well using small parametric modulations

International Nuclear Information System (INIS)

Chacon, R.; Balibrea, F.; Lopez, M.A.

1996-01-01

It is shown theoretically for the first time that, depending on its period, amplitude, and initial phase, a periodic parametric modulation can suppress a chaotic escape from a potential well. The instance of the Helmholtz oscillator is used to demonstrate, by means of Melnikov close-quote s method, that parametric modulations of the linear or quadratic potential terms inhibit chaotic escape when certain resonance conditions are met. copyright 1996 American Institute of Physics

Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials

Science.gov (United States)

Antonelli, Paolo; Michelangeli, Alessandro; Scandone, Raffaele

2018-04-01

We prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.

Extending the Scope of Robust Quadratic Optimization

NARCIS (Netherlands)

Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand

In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in

Simulation of time-dependent Heisenberg models in one dimension

DEFF Research Database (Denmark)

Volosniev, A. G.; Hammer, H. -W.; Zinner, N. T.

2016-01-01

In this Letter, we provide a theoretical analysis of strongly interacting quantum systems confined by a time-dependent external potential in one spatial dimension. We show that such systems can be used to simulate spin chains described by Heisenberg Hamiltonians in which the exchange coupling...... constants can be manipulated by time-dependent driving of the shape of the external confinement. As illustrative examples, we consider a harmonic trapping potential with a variable frequency and an infinite square well potential with a time-dependent barrier in the middle....

Existence of time-dependent density-functional theory for open electronic systems: time-dependent holographic electron density theorem.

Science.gov (United States)

Zheng, Xiao; Yam, ChiYung; Wang, Fan; Chen, GuanHua

2011-08-28

We present the time-dependent holographic electron density theorem (TD-HEDT), which lays the foundation of time-dependent density-functional theory (TDDFT) for open electronic systems. For any finite electronic system, the TD-HEDT formally establishes a one-to-one correspondence between the electron density inside any finite subsystem and the time-dependent external potential. As a result, any electronic property of an open system in principle can be determined uniquely by the electron density function inside the open region. Implications of the TD-HEDT on the practicality of TDDFT are also discussed.

Self-consistent RPA and the time-dependent density matrix approach

Energy Technology Data Exchange (ETDEWEB)

Schuck, P. [Institut de Physique Nucleaire, Orsay (France); CNRS et Universite Joseph Fourier, Laboratoire de Physique et Modelisation des Milieux Condenses, Grenoble (France); Tohyama, M. [Kyorin University School of Medicine, Mitaka, Tokyo (Japan)

2016-10-15

The time-dependent density matrix (TDDM) or BBGKY (Bogoliubov, Born, Green, Kirkwood, Yvon) approach is decoupled and closed at the three-body level in finding a natural representation of the latter in terms of a quadratic form of two-body correlation functions. In the small amplitude limit an extended RPA coupled to an also extended second RPA is obtained. Since including two-body correlations means that the ground state cannot be a Hartree-Fock state, naturally the corresponding RPA is upgraded to Self-Consistent RPA (SCRPA) which was introduced independently earlier and which is built on a correlated ground state. SCRPA conserves all the properties of standard RPA. Applications to the exactly solvable Lipkin and the 1D Hubbard models show good performances of SCRPA and TDDM. (orig.)

Quadratic residues and non-residues selected topics

CERN Document Server

Wright, Steve

2016-01-01

This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.

Students' Understanding of Quadratic Equations

Science.gov (United States)

López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

2016-01-01

Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

Tailoring of motional states in double-well potentials by time-dependent processes

International Nuclear Information System (INIS)

Haerkoenen, Kari; Kaerki, Ollijuhani; Suominen, Kalle-Antti

2006-01-01

We show that the vibrational state tailoring method developed for molecular systems can be applied for cold atoms in optical lattices. The original method is based on a three-level model interacting with two strong laser pulses in a counterintuitive sequence [M. Rodriguez et al., Phys. Rev. A 62, 053413 (2000)]. Here we outline the conditions for achieving similar dynamics with single time-dependent potential surfaces. It is shown that guided switching between diabatic and adiabatic evolution has an essential role in this system. We also show that efficient and precise tailoring of motional states in optical lattices can be achieved, for instance, simply by superimposing two lattices and moving them with respect to each other

Quadratic forms for Feynman-Kac semigroups

International Nuclear Information System (INIS)

Hibey, Joseph L.; Charalambous, Charalambos D.

2006-01-01

Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions

Integrable Hamiltonian systems and interactions through quadratic constraints

International Nuclear Information System (INIS)

Pohlmeyer, K.

1975-08-01

Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de

Wave Functions for Time-Dependent Dirac Equation under GUP

Science.gov (United States)

Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen

2018-04-01

In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009

Orthogonality preserving infinite dimensional quadratic stochastic operators

International Nuclear Information System (INIS)

Akın, Hasan; Mukhamedov, Farrukh

2015-01-01

In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators

Polyhedral combinatorics of the cardinality constrained quadratic knapsack problem and the quadratic selective travelling salesman problem

DEFF Research Database (Denmark)

Mak, Vicky; Thomadsen, Tommy

2006-01-01

This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...

Quadratically convergent MCSCF scheme using Fock operators

International Nuclear Information System (INIS)

Das, G.

1981-01-01

A quadratically convergent formulation of the MCSCF method using Fock operators is presented. Among its advantages the present formulation is quadratically convergent unlike the earlier ones based on Fock operators. In contrast to other quadratically convergent schemes as well as the one based on generalized Brillouin's theorem, this method leads easily to a hybrid scheme where the weakly coupled orbitals (such as the core) are handled purely by Fock equations, while the rest of the orbitals are treated by a quadratically convergent approach with a truncated virtual space obtained by the use of the corresponding Fock equations

Quadratic brackets from symplectic forms

International Nuclear Information System (INIS)

Alekseev, Anton Yu.; Todorov, Ivan T.

1994-01-01

We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))

Quadratic Stabilization of LPV System by an LTI Controller Based on ILMI Algorithm

Directory of Open Access Journals (Sweden)

Wei Xie

2007-01-01

Full Text Available A linear time-invariant (LTI output feedback controller is designed for a linear parameter-varying (LPV control system to achieve quadratic stability. The LPV system includes immeasurable dependent parameters that are assumed to vary in a polytopic space. To solve this control problem, a heuristic algorithm is proposed in the form of an iterative linear matrix inequality (ILMI formulation. Furthermore, an effective method of setting an initial value of the ILMI algorithm is also proposed to increase the probability of getting an admissible solution for the controller design problem.

Experiences with the quadratic Korringa-Kohn-Rostoker band theory method

International Nuclear Information System (INIS)

Faulkner, J.S.

1992-01-01

This paper reports on the Quadratic Korriga-Kohn-Rostoker method which is a fast band theory method in the sense that all eigenvalues for a given k are obtained from one matrix diagonalization, but it differs from other fast band theory methods in that it is derived entirely from multiple-scattering theory, without the introduction of a Rayleigh-Ritz variations step. In this theory, the atomic potentials are shifted by Δσ(r) with Δ equal to E-E 0 and σ(r) equal to one when r is inside the Wigner-Seitz cell and zero otherwise, and it turns out that the matrix of coefficients is an entire function of Δ. This matrix can be terminated to give a linear KKR, quadratic KKR, cubic KKR,..., or not terminated at all to give the pivoted multiple-scattering equations. Full potential are no harder to deal with than potentials with a shape approximation

The grounds for time dependent market potentials from dealers' dynamics

Science.gov (United States)

Yamada, K.; Takayasu, H.; Takayasu, M.

2008-06-01

We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers’ feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market’s potential force. When markets are dominated by dealers with positive feedback the resulting potential force is repulsive, while the effect of negative feedback enhances the attractive potential force.

A revisit to quadratic programming with fuzzy parameters

International Nuclear Information System (INIS)

Liu, S.-T.

2009-01-01

Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons and Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.

QUADrATiC: scalable gene expression connectivity mapping for repurposing FDA-approved therapeutics.

Science.gov (United States)

O'Reilly, Paul G; Wen, Qing; Bankhead, Peter; Dunne, Philip D; McArt, Darragh G; McPherson, Suzanne; Hamilton, Peter W; Mills, Ken I; Zhang, Shu-Dong

2016-05-04

Gene expression connectivity mapping has proven to be a powerful and flexible tool for research. Its application has been shown in a broad range of research topics, most commonly as a means of identifying potential small molecule compounds, which may be further investigated as candidates for repurposing to treat diseases. The public release of voluminous data from the Library of Integrated Cellular Signatures (LINCS) programme further enhanced the utilities and potentials of gene expression connectivity mapping in biomedicine. We describe QUADrATiC ( http://go.qub.ac.uk/QUADrATiC ), a user-friendly tool for the exploration of gene expression connectivity on the subset of the LINCS data set corresponding to FDA-approved small molecule compounds. It enables the identification of compounds for repurposing therapeutic potentials. The software is designed to cope with the increased volume of data over existing tools, by taking advantage of multicore computing architectures to provide a scalable solution, which may be installed and operated on a range of computers, from laptops to servers. This scalability is provided by the use of the modern concurrent programming paradigm provided by the Akka framework. The QUADrATiC Graphical User Interface (GUI) has been developed using advanced Javascript frameworks, providing novel visualization capabilities for further analysis of connections. There is also a web services interface, allowing integration with other programs or scripts. QUADrATiC has been shown to provide an improvement over existing connectivity map software, in terms of scope (based on the LINCS data set), applicability (using FDA-approved compounds), usability and speed. It offers potential to biological researchers to analyze transcriptional data and generate potential therapeutics for focussed study in the lab. QUADrATiC represents a step change in the process of investigating gene expression connectivity and provides more biologically-relevant results than

Detection of density dependence requires density manipulations and calculation of lambda.

Science.gov (United States)

Fowler, N L; Overath, R Deborah; Pease, Craig M

2006-03-01

To investigate density-dependent population regulation in the perennial bunchgrass Bouteloua rigidiseta, we experimentally manipulated density by removing adults or adding seeds to replicate quadrats in a natural population for three annual intervals. We monitored the adjacent control quadrats for 14 annual intervals. We constructed a population projection matrix for each quadrat in each interval, calculated lambda, and did a life table response experiment (LTRE) analysis. We tested the effects of density upon lambda by comparing experimental and control quadrats, and by an analysis of the 15-year observational data set. As measured by effects on lambda and on N(t+1/Nt in the experimental treatments, negative density dependence was strong: the population was being effectively regulated. The relative contributions of different matrix elements to treatment effect on lambda differed among years and treatments; overall the pattern was one of small contributions by many different life cycle stages. In contrast, density dependence could not be detected using only the observational (control quadrats) data, even though this data set covered a much longer time span. Nor did experimental effects on separate matrix elements reach statistical significance. These results suggest that ecologists may fail to detect density dependence when it is present if they have only descriptive, not experimental, data, do not have data for the entire life cycle, or analyze life cycle components separately.

The Electromagnetic Field of Elementary Time-Dependent Toroidal Sources

International Nuclear Information System (INIS)

Afanas'ev, G.N.; Stepanovskij, Yu.P.

1994-01-01

The radiation field of toroidal-like time-dependent current configurations is investigated. Time-dependent charge-current sources are found outside which the electromagnetic strengths disappear but the potentials survive. This can be used to carry out time-dependent Aharonov-Bohm-like experiments and the information transfer. Using the Neumann-Helmholtz parametrization of the current density we present the time-dependent electromagnetic field in a form convenient for applications. 17 refs

Generation of matter-wave solitons of the Gross-Pitaevskii equation with a time-dependent complicated potential

Energy Technology Data Exchange (ETDEWEB)

Mohamadou, Alidou [Condensed Matter Laboratory, Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala (Cameroon); Abdus Salam International Centre for Theoretical Physics, P.O. Box 538, Strada Costiera 11, I-34014 Trieste (Italy); Wamba, Etienne; Kofane, Timoleon C. [Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon); Doka, Serge Y. [Higher Teacher Training College, University of Maroua, P.O. Box 55, Maroua (Cameroon); Ekogo, Thierry B. [Departement de Physique, Universite des Sciences et Techniques de Masuku, B.P. 943, Franceville (Gabonese Republic)

2011-08-15

We examine the generation of bright matter-wave solitons in the Gross-Pitaevskii equation describing Bose-Einstein condensates with a time-dependent complex potential, which is composed of a repulsive parabolic background potential and a gravitational field. By performing a modified lens-type transformation, an explicit expression for the growth rate of a purely growing modulational instability is presented and analyzed. We point out the effects of the gravitational field, as well as of the parameter related to the feeding or loss of atoms in the condensate, on the instability growth rate. It is evident from numerical simulations that the feeding with atoms and the magnetic trap have opposite effects on the dynamics of the system. It is shown that the feeding or loss parameter can be well used to control the instability domain. Our study shows that the gravitational field changes the condensate trail of the soliton trains during the propagation. We also perform a numerical analysis to solve the Gross-Pitaevskii equation with a time-dependent complicated potential. The numerical results on the effect of both the gravitational field and the parameter of feeding or loss of atoms in the condensate agree well with predictions of the linear stability analysis. Another result of the present work is the modification of the background wave function in the Thomas-Fermi approximation during the numerical simulations.

Chaos in Time-Dependent Space-Charge Potentials

CERN Document Server

Betzel, Gregory T; Sideris, Ioannis V

2005-01-01

We consider a spherically symmetric, homologously breathing, space-charge-dominated beam bunch in the spirit of the particle-core model. The question we ask is: How does the time dependence influence the population of chaotic orbits? The static beam has zero chaotic orbits; the equation of particle motion is integrable up to quadrature. This is generally not true once the bunch is set into oscillation. We quantify the population of chaotic orbits as a function of space charge and oscillation amplitude (mismatch). We also apply a newly developed measure of chaos, one that distinguishes between regular, sticky, and wildly chaotic orbits, to characterize the phase space in detail. We then introduce colored noise into the system and show how its presence modifies the dynamics. One finding is that, despite the presence of a sizeable population of chaotic orbits, halo formation in the homologously breathing beam is much less prevalent than in an envelope-matched counterpart wherein an internal collective mode is ex...

Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

International Nuclear Information System (INIS)

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2002-01-01

For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied

Quadratic Diophantine equations

CERN Document Server

Andreescu, Titu

2015-01-01

This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

Exponential integrators in time-dependent density-functional calculations

Science.gov (United States)

Kidd, Daniel; Covington, Cody; Varga, Kálmán

2017-12-01

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

Hartree--Fock time-dependent problem

Energy Technology Data Exchange (ETDEWEB)

Bove, A; Fano, G [Bologna Univ. (Italy). Istituto di Fisica; Istituto Nazionale di Fisica Nucleare, Bologna (Italy)); Da Prato, G [Rome Univ. (Italy). Istituto di Matematica

1976-06-01

A previous result is generalized. An existence and uniqueness theorem is proved for the Hartree--Fock time-dependent problem in the case of a finite Fermi system interacting via a two body potential which is supposed to be dominated by the kinetic energy part of the one-particle Hamiltonian.

Computational complexity of time-dependent density functional theory

International Nuclear Information System (INIS)

Whitfield, J D; Yung, M-H; Tempel, D G; Aspuru-Guzik, A; Boixo, S

2014-01-01

Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence of a fictitious non-interacting system (known as the Kohn–Sham system), which can reproduce the one-electron reduced probability density of the actual system. We build upon these works and show that on the interior of the domain of existence, the Kohn–Sham system can be efficiently obtained given the time-dependent density. We introduce a V-representability parameter which diverges at the boundary of the existence domain and serves to quantify the numerical difficulty of constructing the Kohn-Sham potential. For bounded values of V-representability, we present a polynomial time quantum algorithm to generate the time-dependent Kohn–Sham potential with controllable error bounds. (paper)

Existence for stationary mean-field games with congestion and quadratic Hamiltonians

KAUST Repository

Gomes, Diogo A.; Mitake, Hiroyoshi

2015-01-01

Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular

Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients

Directory of Open Access Journals (Sweden)

Xue-Gang Zhou

2014-01-01

Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.

Wave propagation in elastic medium with heterogeneous quadratic nonlinearity

International Nuclear Information System (INIS)

Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin

2011-01-01

This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.

Time-dependent massless Dirac fermions in graphene

Energy Technology Data Exchange (ETDEWEB)

Khantoul, Boubakeur, E-mail: bobphys@gmail.com [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom); Department of Physics, University of Jijel, BP 98, Ouled Aissa, 18000 Jijel (Algeria); Fring, Andreas, E-mail: a.fring@city.ac.uk [Department of Mathematics, City University London, Northampton Square, London EC1V 0HB (United Kingdom)

2015-10-30

Using the Lewis–Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent vector potential. The eigenvalue equations for the two spinor components of the Lewis–Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians. - Highlights: • An explicit analytical solution for a massless 2+1 dimensional time-dependent Dirac equation is found. • All steps of the Lewis–Riesenfeld method have been carried out.

Exactly solvable energy-dependent potentials

International Nuclear Information System (INIS)

Garcia-Martinez, J.; Garcia-Ravelo, J.; Pena, J.J.; Schulze-Halberg, A.

2009-01-01

We introduce a method for constructing exactly-solvable Schroedinger equations with energy-dependent potentials. Our method is based on converting a general linear differential equation of second order into a Schroedinger equation with energy-dependent potential. Particular examples presented here include harmonic oscillator, Coulomb and Morse potentials with various types of energy dependence.

Quantum Many-Body System in Presence of Time-Dependent Potential and Electric Field

Energy Technology Data Exchange (ETDEWEB)

Sobhani, Hadi; Hassanabadi, Hassan [Shahrood University of Technology, Shahrood (Iran, Islamic Republic of)

2017-07-15

In this article, a quantum many-body system is considered. Then two time-dependent interactions have been added to the system. Changing of them is assumed in general form. After that, by using algebraic method, time evolution of this many-body system has been investigated. In order to study the time evolution, Lewis-Riesenfeld dynamical invariant and time evolution operator method have been used. Appropriate dynamical invariants are constructed and their Eigenvalues are derived as well as appropriate time evolution operators are constructed. These calculations have been done in general form so there are no limiting assumptions on changing of time-dependent functions.

Induced motion of domain walls in multiferroics with quadratic interaction

Energy Technology Data Exchange (ETDEWEB)

Gerasimchuk, Victor S., E-mail: viktor.gera@gmail.com [National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremohy Avenue 37, 03056 Kiev (Ukraine); Shitov, Anatoliy A., E-mail: shitov@mail.ru [Donbass National Academy of Civil Engineering, Derzhavina Street 2, 86123 Makeevka, Donetsk Region (Ukraine)

2013-10-15

We theoretically study the dynamics of 180-degree domain wall of the ab-type in magnetic materials with quadratic magnetoelectric interaction in external alternating magnetic and electric fields. The features of the oscillatory and translational motions of the domain walls and stripe structures depending on the parameters of external fields and characteristics of the multiferroics are discussed. The possibility of the domain walls drift in a purely electric field is established. - Highlights: • We study DW and stripe DS in multiferroics with quadratic magnetoelectric interaction. • We build up the theory of oscillatory and translational (drift) DW and DS motion. • DW motion can be caused by crossed alternating electric and magnetic fields. • DW motion can be caused by alternating “pure” electric field. • DW drift velocity is formed by the AFM and Dzyaloshinskii interaction terms.

On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity

Directory of Open Access Journals (Sweden)

Koh Kim Jie

2017-01-01

Full Text Available Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution.

An adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems

International Nuclear Information System (INIS)

Baranger, M.; Veneroni, M.

1977-11-01

It is shown how to derive the parameters of a phenomenological collective model from a microscopic theory. The microscopic theory is Hartree-Fock, and one starts from the time-dependent Hartree-Fock equation. To this, the adiabatic approximation is added, and the energy in powers of an adiabatic parameter is expanded, which results in a collective kinetic energy quadratic in the velocities, with coefficients depending on the coordinates, as in the phenomenological models. The adiabatic equations of motion are derived in different ways and their analogy with classical mechanics is stressed. The role of the adiabatic hypothesis and its range of validity, are analyzed in detail. It assumes slow motion, but not small amplitude, and is therefore suitable for large-amplitude collective motion. The RPA is obtained as the limiting case where the amplitude is also small. The translational mass is correctly given and the moment of inertia under rotation is that of Thouless and Valatin

Short-time existence of solutions for mean-field games with congestion

KAUST Repository

Gomes, Diogo A.

2015-11-20

We consider time-dependent mean-field games with congestion that are given by a Hamilton–Jacobi equation coupled with a Fokker–Planck equation. These models are motivated by crowd dynamics in which agents have difficulty moving in high-density areas. The congestion effects make the Hamilton–Jacobi equation singular. The uniqueness of solutions for this problem is well understood; however, the existence of classical solutions was only known in very special cases, stationary problems with quadratic Hamiltonians and some time-dependent explicit examples. Here, we demonstrate the short-time existence of C∞ solutions for sub-quadratic Hamiltonians.

A Finite Continuation Algorithm for Bound Constrained Quadratic Programming

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.

1999-01-01

The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...

SPARSE: quadratic time simultaneous alignment and folding of RNAs without sequence-based heuristics.

Science.gov (United States)

Will, Sebastian; Otto, Christina; Miladi, Milad; Möhl, Mathias; Backofen, Rolf

2015-08-01

RNA-Seq experiments have revealed a multitude of novel ncRNAs. The gold standard for their analysis based on simultaneous alignment and folding suffers from extreme time complexity of [Formula: see text]. Subsequently, numerous faster 'Sankoff-style' approaches have been suggested. Commonly, the performance of such methods relies on sequence-based heuristics that restrict the search space to optimal or near-optimal sequence alignments; however, the accuracy of sequence-based methods breaks down for RNAs with sequence identities below 60%. Alignment approaches like LocARNA that do not require sequence-based heuristics, have been limited to high complexity ([Formula: see text] quartic time). Breaking this barrier, we introduce the novel Sankoff-style algorithm 'sparsified prediction and alignment of RNAs based on their structure ensembles (SPARSE)', which runs in quadratic time without sequence-based heuristics. To achieve this low complexity, on par with sequence alignment algorithms, SPARSE features strong sparsification based on structural properties of the RNA ensembles. Following PMcomp, SPARSE gains further speed-up from lightweight energy computation. Although all existing lightweight Sankoff-style methods restrict Sankoff's original model by disallowing loop deletions and insertions, SPARSE transfers the Sankoff algorithm to the lightweight energy model completely for the first time. Compared with LocARNA, SPARSE achieves similar alignment and better folding quality in significantly less time (speedup: 3.7). At similar run-time, it aligns low sequence identity instances substantially more accurate than RAF, which uses sequence-based heuristics. © The Author 2015. Published by Oxford University Press.

Time-dependent mass of cosmological perturbations in the hybrid and dressed metric approaches to loop quantum cosmology

Science.gov (United States)

Elizaga Navascués, Beatriz; Martín de Blas, Daniel; Mena Marugán, Guillermo A.

2018-02-01

Loop quantum cosmology has recently been applied in order to extend the analysis of primordial perturbations to the Planck era and discuss the possible effects of quantum geometry on the cosmic microwave background. Two approaches to loop quantum cosmology with admissible ultraviolet behavior leading to predictions that are compatible with observations are the so-called hybrid and dressed metric approaches. In spite of their similarities and relations, we show in this work that the effective equations that they provide for the evolution of the tensor and scalar perturbations are somewhat different. When backreaction is neglected, the discrepancy appears only in the time-dependent mass term of the corresponding field equations. We explain the origin of this difference, arising from the distinct quantization procedures. Besides, given the privileged role that the big bounce plays in loop quantum cosmology, e.g. as a natural instant of time to set initial conditions for the perturbations, we also analyze the positivity of the time-dependent mass when this bounce occurs. We prove that the mass of the tensor perturbations is positive in the hybrid approach when the kinetic contribution to the energy density of the inflaton dominates over its potential, as well as for a considerably large sector of backgrounds around that situation, while this mass is always nonpositive in the dressed metric approach. Similar results are demonstrated for the scalar perturbations in a sector of background solutions that includes the kinetically dominated ones; namely, the mass then is positive for the hybrid approach, whereas it typically becomes negative in the dressed metric case. More precisely, this last statement is strictly valid when the potential is quadratic for values of the inflaton mass that are phenomenologically favored.

Quadratic programming with fuzzy parameters: A membership function approach

International Nuclear Information System (INIS)

Liu, S.-T.

2009-01-01

Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the fuzzy quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides are represented by convex fuzzy numbers. Since the parameters in the program are fuzzy numbers, the derived objective value is a fuzzy number as well. Using Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. An example illustrates method proposed in this paper.

Propagators for the time-dependent Kohn-Sham equations

International Nuclear Information System (INIS)

Castro, Alberto; Marques, Miguel A. L.; Rubio, Angel

2004-01-01

In this paper we address the problem of the numerical integration of the time-dependent Schroedinger equation i∂ t φ=Hφ. In particular, we are concerned with the important case where H is the self-consistent Kohn-Sham Hamiltonian that stems from time-dependent functional theory. As the Kohn-Sham potential depends parametrically on the time-dependent density, H is in general time dependent, even in the absence of an external time-dependent field. The present analysis also holds for the description of the excited state dynamics of a many-electron system under the influence of arbitrary external time-dependent electromagnetic fields. Our discussion is separated in two parts: (i) First, we look at several algorithms to approximate exp(A), where A is a time-independent operator [e.g., A=-iΔtH(τ) for some given time τ]. In particular, polynomial expansions, projection in Krylov subspaces, and split-operator methods are investigated. (ii) We then discuss different approximations for the time-evolution operator, such as the midpoint and implicit rules, and Magnus expansions. Split-operator techniques can also be modified to approximate the full time-dependent propagator. As the Hamiltonian is time dependent, problem (ii) is not equivalent to (i). All these techniques have been implemented and tested in our computer code OCTOPUS, but can be of general use in other frameworks and implementations

Stability in quadratic torsion theories

Energy Technology Data Exchange (ETDEWEB)

Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)

2017-11-15

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

Stability in quadratic torsion theories

International Nuclear Information System (INIS)

Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado

2017-01-01

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

Non-chaotic behaviour for a class of quadratic jerk equations

International Nuclear Information System (INIS)

Malasoma, J.-M.

2009-01-01

It is shown that a class constituted by 27 different types of non-linear third-order differential equations of the form x - =j(x,x . ,x), where j is a quadratic polynomial with only one or two terms, and for which ∂j(x,y,z)/∂z is not a constant function of time, does not exhibit chaos. The three-dimensional dynamical systems associated to these equations are not necessarily dissipative everywhere nor conservative everywhere in the corresponding phase spaces. Our results include and improve some recent results obtained by Yang and Chen who only considered the case where j was a homogeneous quadratic polynomial with two terms.

Application of the linear-quadratic model to myelotoxicity associated with radioimmunotherapy

International Nuclear Information System (INIS)

Wilder, R.B.; DeNardo, G.L.; Sheri, S.; Fowler, J.F.; Wessels, B.W.; DeNardo, S.J.

1996-01-01

The purposes of this study were: To use the linear-quadratic model to determine time-dependent biologically effective doses (BEDs) that were delivered to the bone marrow by multiple infusions of radiolabeled antibodies, and (2) to determine whether granulocyte and platelet counts correlate better with BED than administered radioactivity. Twenty patients with B-cell malignancies that had progressed despite intensive chemotherapy and who had a significant number of malignant cells in their bone marrow were treated with multiple 0.7-3.7 GBq/m 2 intravenous infusions of Lym-1, a murine monoclonal antibody that binds to a tumour-associated antigen, labeled with iodine-131. Granulocyte and platelet counts were measured in order to assess bone marrow toxicity. The cumulative 131 I-Lym-1 radioactivity administered to each patient was calculated. BEDs from multiple 131 I-Lym-1 infusions were summated in order to arrive at a total BED for each patient. There was a weak association between granulocyte and platelet counts and radioactivity. Likewise, there was a weak association between granulocyte and platelet counts and BED. The attempt to take bone marrow absorbed doses and overall treatment time into consideration with the linear-quadratic model did not produce a stronger association than was observed between peripheral blood counts and administered radioactivity. The association between granulocyte and platelet counts and BED may have been weakened by several factors, including variable bone marrow reserve at the start of 131 I-Lym-1 therapy and the delivery of heterogeneous, absorbed doses of radiation to the bone marrow. (orig./MG)

An example in linear quadratic optimal control

NARCIS (Netherlands)

Weiss, George; Zwart, Heiko J.

1998-01-01

We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme

Fermionic particles with position-dependent mass in the presence of ...

Indian Academy of Sciences (India)

Approximate solutions of the Dirac equation with position-dependent mass are presented for the inversely quadratic Yukawa potential and Coulomb-like tensor interaction by using the asymptotic iteration method. The energy eigenvalues and the corresponding normalized eigenfunctions are obtained in the case of ...

Time-dependent Hartree approximation and time-dependent harmonic oscillator model

International Nuclear Information System (INIS)

Blaizot, J.P.

1982-01-01

We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schroedinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory. (orig.)

Radiotherapy treatment planning linear-quadratic radiobiology

CERN Document Server

Chapman, J Donald

2015-01-01

Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil

Maitra-Burke example of initial-state dependence in time-dependent density-functional theory

International Nuclear Information System (INIS)

Holas, A.; Balawender, R.

2002-01-01

In a recent paper, Maitra and Burke [Phys. Rev. A 63, 042501 (2001); 64, 039901(E) (2001)] have given an interesting and instructive example that illustrates a specific feature of the time-dependent density-functional theory--the dependence of the reconstructed time-dependent potential not only on the electron density, but also on the initial state of the system. However, a concise form of its presentation by these authors is insufficient to reveal all its peculiarities. Our paper represents a very detailed study of this valuable example, intended to facilitate a better understanding and appreciation

Estimating factors influencing the detection probability of semiaquatic freshwater snails using quadrat survey methods

Science.gov (United States)

Roesler, Elizabeth L.; Grabowski, Timothy B.

2018-01-01

Developing effective monitoring methods for elusive, rare, or patchily distributed species requires extra considerations, such as imperfect detection. Although detection is frequently modeled, the opportunity to assess it empirically is rare, particularly for imperiled species. We used Pecos assiminea (Assiminea pecos), an endangered semiaquatic snail, as a case study to test detection and accuracy issues surrounding quadrat searches. Quadrats (9 × 20 cm; n = 12) were placed in suitable Pecos assiminea habitat and randomly assigned a treatment, defined as the number of empty snail shells (0, 3, 6, or 9). Ten observers rotated through each quadrat, conducting 5-min visual searches for shells. The probability of detecting a shell when present was 67.4 ± 3.0%, but it decreased with the increasing litter depth and fewer number of shells present. The mean (± SE) observer accuracy was 25.5 ± 4.3%. Accuracy was positively correlated to the number of shells in the quadrat and negatively correlated to the number of times a quadrat was searched. The results indicate quadrat surveys likely underrepresent true abundance, but accurately determine the presence or absence. Understanding detection and accuracy of elusive, rare, or imperiled species improves density estimates and aids in monitoring and conservation efforts.

Finite element method with quadratic quadrilateral unit for solving two dimensional incompressible N-S equation

International Nuclear Information System (INIS)

Tao Ganqiang; Yu Qing; Xiao Xiao

2011-01-01

Viscous and incompressible fluid flow is important for numerous engineering mechanics problems. Because of high non linear and incompressibility for Navier-Stokes equation, it is very difficult to solve Navier-Stokes equation by numerical method. According to its characters of Navier-Stokes equation, quartic derivation controlling equation of the two dimensional incompressible Navier-Stokes equation is set up firstly. The method solves the problem for dealing with vorticity boundary and automatically meets incompressibility condition. Then Finite Element equation for Navier-Stokes equation is proposed by using quadratic quadrilateral unit with 8 nodes in which the unit function is quadratic and non linear.-Based on it, the Finite Element program of quadratic quadrilateral unit with 8 nodes is developed. Lastly, numerical experiment proves the accuracy and dependability of the method and also shows the method has good application prospect in computational fluid mechanics. (authors)

SPARSE: quadratic time simultaneous alignment and folding of RNAs without sequence-based heuristics

Science.gov (United States)

Will, Sebastian; Otto, Christina; Miladi, Milad; Möhl, Mathias; Backofen, Rolf

2015-01-01

Motivation: RNA-Seq experiments have revealed a multitude of novel ncRNAs. The gold standard for their analysis based on simultaneous alignment and folding suffers from extreme time complexity of O(n6). Subsequently, numerous faster ‘Sankoff-style’ approaches have been suggested. Commonly, the performance of such methods relies on sequence-based heuristics that restrict the search space to optimal or near-optimal sequence alignments; however, the accuracy of sequence-based methods breaks down for RNAs with sequence identities below 60%. Alignment approaches like LocARNA that do not require sequence-based heuristics, have been limited to high complexity (≥ quartic time). Results: Breaking this barrier, we introduce the novel Sankoff-style algorithm ‘sparsified prediction and alignment of RNAs based on their structure ensembles (SPARSE)’, which runs in quadratic time without sequence-based heuristics. To achieve this low complexity, on par with sequence alignment algorithms, SPARSE features strong sparsification based on structural properties of the RNA ensembles. Following PMcomp, SPARSE gains further speed-up from lightweight energy computation. Although all existing lightweight Sankoff-style methods restrict Sankoff’s original model by disallowing loop deletions and insertions, SPARSE transfers the Sankoff algorithm to the lightweight energy model completely for the first time. Compared with LocARNA, SPARSE achieves similar alignment and better folding quality in significantly less time (speedup: 3.7). At similar run-time, it aligns low sequence identity instances substantially more accurate than RAF, which uses sequence-based heuristics. Availability and implementation: SPARSE is freely available at http://www.bioinf.uni-freiburg.de/Software/SPARSE. Contact: backofen@informatik.uni-freiburg.de Supplementary information: Supplementary data are available at Bioinformatics online. PMID:25838465

Quadratic and coulomb terms for the spectrum of a three-electron quantum dot

International Nuclear Information System (INIS)

Hassanabadi, H.; Hamzavi, M.; Zarrinkamar, S.; Rajabi, A.A.

2010-01-01

We consider the Hamiltonian of a three-electron quantum dot composed of quadratic plus Coulomb terms and calculate the system's spectra. We next apply the hyperradius to reduce the three-body Schroedinger equation into a one-variable differential equation that is solvable. To avoid the complexity, the Taylor expansion of the effective potential is enters the problem and thereby a solution is found for the eigenvalues of the corresponding three-body Schroedinger equation in terms of the Wigner parameter. Using a quasi-analytical approach, we have calculated the energy eigenvalues of the Schroedinger equation corresponding to a three-electron quantum dot. In addition to the hyperspherical coordinates, much of mathematical complexity has been avoided using the idea of Taylor expansion for the potential. For the potential, we have considered quadratic plus Coulomb terms. The obtained energy eigenvalues in terms of the Wigner parameter are given in tabular form. (author)

Quadratic independence of coordinate functions of certain ...

Indian Academy of Sciences (India)

... are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C ( M ) such that the action leaves invariant the linear span of the above coordinate functions.

Double dissociation of spike timing-dependent potentiation and depression by subunit-preferring NMDA receptor antagonists in mouse barrel cortex.

Science.gov (United States)

Banerjee, Abhishek; Meredith, Rhiannon M; Rodríguez-Moreno, Antonio; Mierau, Susanna B; Auberson, Yves P; Paulsen, Ole

2009-12-01

Spike timing-dependent plasticity (STDP) is a strong candidate for an N-methyl-D-aspartate (NMDA) receptor-dependent form of synaptic plasticity that could underlie the development of receptive field properties in sensory neocortices. Whilst induction of timing-dependent long-term potentiation (t-LTP) requires postsynaptic NMDA receptors, timing-dependent long-term depression (t-LTD) requires the activation of presynaptic NMDA receptors at layer 4-to-layer 2/3 synapses in barrel cortex. Here we investigated the developmental profile of t-LTD at layer 4-to-layer 2/3 synapses of mouse barrel cortex and studied their NMDA receptor subunit dependence. Timing-dependent LTD emerged in the first postnatal week, was present during the second week and disappeared in the adult, whereas t-LTP persisted in adulthood. An antagonist at GluN2C/D subunit-containing NMDA receptors blocked t-LTD but not t-LTP. Conversely, a GluN2A subunit-preferring antagonist blocked t-LTP but not t-LTD. The GluN2C/D subunit requirement for t-LTD appears to be synapse specific, as GluN2C/D antagonists did not block t-LTD at horizontal cross-columnar layer 2/3-to-layer 2/3 synapses, which was blocked by a GluN2B antagonist instead. These data demonstrate an NMDA receptor subunit-dependent double dissociation of t-LTD and t-LTP mechanisms at layer 4-to-layer 2/3 synapses, and suggest that t-LTD is mediated by distinct molecular mechanisms at different synapses on the same postsynaptic neuron.

A Comparative Analysis of Quadratics Unit in Singaporean, Turkish and IBDP Mathematics Textbooks

Directory of Open Access Journals (Sweden)

Reyhan Sağlam

2012-12-01

Full Text Available The purpose of this study was to analyze and compare the contents of the chapters on quadratics in three mathematics textbooks selected from Turkey, Singapore, and the International Baccalaureate Diploma Program (IBDP through content analysis. The analysis of mathematical content showed that the three textbooks have different approaches and priorities in terms of the positions of chapters and weights of the quadratics units, and the time allocated to them within the respective curricular programs. It was also found that the Turkish textbook covers a greater number of learning outcomes targeted for quadratics among the three mathematics syllabi, showing a detailed treatment of the topic compared to the other two textbooks.Key Words: Content analysis, international comparative studies, mathematics textbooks

Angle-dependent strong-field molecular ionization rates with tuned range-separated time-dependent density functional theory

Energy Technology Data Exchange (ETDEWEB)

Sissay, Adonay [Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Abanador, Paul; Mauger, François; Gaarde, Mette; Schafer, Kenneth J. [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Lopata, Kenneth, E-mail: klopata@lsu.edu [Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)

2016-09-07

Strong-field ionization and the resulting electronic dynamics are important for a range of processes such as high harmonic generation, photodamage, charge resonance enhanced ionization, and ionization-triggered charge migration. Modeling ionization dynamics in molecular systems from first-principles can be challenging due to the large spatial extent of the wavefunction which stresses the accuracy of basis sets, and the intense fields which require non-perturbative time-dependent electronic structure methods. In this paper, we develop a time-dependent density functional theory approach which uses a Gaussian-type orbital (GTO) basis set to capture strong-field ionization rates and dynamics in atoms and small molecules. This involves propagating the electronic density matrix in time with a time-dependent laser potential and a spatial non-Hermitian complex absorbing potential which is projected onto an atom-centered basis set to remove ionized charge from the simulation. For the density functional theory (DFT) functional we use a tuned range-separated functional LC-PBE*, which has the correct asymptotic 1/r form of the potential and a reduced delocalization error compared to traditional DFT functionals. Ionization rates are computed for hydrogen, molecular nitrogen, and iodoacetylene under various field frequencies, intensities, and polarizations (angle-dependent ionization), and the results are shown to quantitatively agree with time-dependent Schrödinger equation and strong-field approximation calculations. This tuned DFT with GTO method opens the door to predictive all-electron time-dependent density functional theory simulations of ionization and ionization-triggered dynamics in molecular systems using tuned range-separated hybrid functionals.

Angle-dependent strong-field molecular ionization rates with tuned range-separated time-dependent density functional theory

International Nuclear Information System (INIS)

Sissay, Adonay; Abanador, Paul; Mauger, François; Gaarde, Mette; Schafer, Kenneth J.; Lopata, Kenneth

2016-01-01

Strong-field ionization and the resulting electronic dynamics are important for a range of processes such as high harmonic generation, photodamage, charge resonance enhanced ionization, and ionization-triggered charge migration. Modeling ionization dynamics in molecular systems from first-principles can be challenging due to the large spatial extent of the wavefunction which stresses the accuracy of basis sets, and the intense fields which require non-perturbative time-dependent electronic structure methods. In this paper, we develop a time-dependent density functional theory approach which uses a Gaussian-type orbital (GTO) basis set to capture strong-field ionization rates and dynamics in atoms and small molecules. This involves propagating the electronic density matrix in time with a time-dependent laser potential and a spatial non-Hermitian complex absorbing potential which is projected onto an atom-centered basis set to remove ionized charge from the simulation. For the density functional theory (DFT) functional we use a tuned range-separated functional LC-PBE*, which has the correct asymptotic 1/r form of the potential and a reduced delocalization error compared to traditional DFT functionals. Ionization rates are computed for hydrogen, molecular nitrogen, and iodoacetylene under various field frequencies, intensities, and polarizations (angle-dependent ionization), and the results are shown to quantitatively agree with time-dependent Schrödinger equation and strong-field approximation calculations. This tuned DFT with GTO method opens the door to predictive all-electron time-dependent density functional theory simulations of ionization and ionization-triggered dynamics in molecular systems using tuned range-separated hybrid functionals.

Decay of hollow states in time-dependent density functional theory

Energy Technology Data Exchange (ETDEWEB)

Kapoor, Varun; Bauer, Dieter [Institut fuer Physik, Wismarsche Str. 43-45, Universitaet Rostock, Rostock-18051 (Germany)

2012-07-01

Hollow or multiply excited states are inaccessible in time dependent density functional theory (TDDFT) using adiabatic Kohn-Sham potentials. We determine the exact Kohn Sham (KS) potential for doubly excited states in an exactly solvable model Helium atom. The exact single-particle density corresponds to the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose origin is traced back to phase of the exact KS orbital. The potential controls the barrier height and width in order for the density to tunnel out and decay with the same rate as the doubly excited state in the ab initio time-dependent Schroedinger calculation. Instead, adiabatic KS potentials only show direct photoionization but no autoionization. A frequency-dependent linear response kernel would be necessary in order to capture the decay of autoionizing states.

State-dependent classical potentials

International Nuclear Information System (INIS)

D'Amico, M.

2001-01-01

As alternative treatment to the potential operators of standard quantum mechanics is presented. The method is derived from Bohm's mechanics. The operator scalar (V) and vector (A) potential functions are replaced by a quantum potential. It is argued that the classical potential is a special limiting case of a more general quantum potential. The theory is illustrated by deriving an equivalent single-particle equation for the i-th particle of an n-body Bohmian system. The resulting effective state-dependent potential holds the interaction between the single-particle self-wave ψ s and the environment wave ψ e of the n - 1 remaining particles. The effective state-dependent potential is offered as a resolution to the Aharonov-Bohm effect where the phase difference is shown to result from the presence of ψ e . Finally, the interaction between ψ s and ψ e is illustrated graphically

Exact cancellation of quadratic divergences in top condensation models

International Nuclear Information System (INIS)

Blumhofer, A.

1995-01-01

We discuss the hierarchy problem and the corresponding quadratic divergences in the top mode Standard Model. Quadratic divergences appear at each order 1/N c since fermionic and bosonic contributions are of different order 1/N c . It is shown that the full dynamical system to all orders in 1/N c admits a solution, where the sum of all quadratic divergent contributions disappears. ((orig.))

Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...

African Journals Online (AJOL)

Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...

Underprediction of human skin erythema at low doses per fraction by the linear quadratic model

International Nuclear Information System (INIS)

Hamilton, Christopher S.; Denham, James W.; O'Brien, Maree; Ostwald, Patricia; Kron, Tomas; Wright, Suzanne; Doerr, Wolfgang

1996-01-01

Background and purpose. The erythematous response of human skin to radiotherapy has proven useful for testing the predictions of the linear quadratic (LQ) model in terms of fractionation sensitivity and repair half time. No formal investigation of the response of human skin to doses less than 2 Gy per fraction has occurred. This study aims to test the validity of the LQ model for human skin at doses ranging from 0.4 to 5.2 Gy per fraction. Materials and methods. Complete erythema reaction profiles were obtained using reflectance spectrophotometry in two patient populations: 65 patients treated palliatively with 5, 10, 12 and 20 daily treatment fractions (varying thicknesses of bolus, various body sites) and 52 patients undergoing prostatic irradiation for localised carcinoma of the prostate (no bolus, 30-32 fractions). Results and conclusions. Gender, age, site and prior sun exposure influence pre- and post-treatment erythema values independently of dose administered. Out-of-field effects were also noted. The linear quadratic model significantly underpredicted peak erythema values at doses less than 1.5 Gy per fraction. This suggests that either the conventional linear quadratic model does not apply for low doses per fraction in human skin or that erythema is not exclusively initiated by radiation damage to the basal layer. The data are potentially explained by an induced repair model

Numerical solution of quadratic matrix equations for free vibration analysis of structures

Science.gov (United States)

Gupta, K. K.

1975-01-01

This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

An efficient and accurate method to obtain the energy-dependent Green function for general potentials

International Nuclear Information System (INIS)

Kramer, T; Heller, E J; Parrott, R E

2008-01-01

Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results and a variety of numerical methods have been developed to solve the time-dependent Schroedinger equation. The time-dependent methods work for nearly arbitrarily shaped potentials, including sources and sinks via complex-valued potentials. Many quantities are measured at fixed energy, which is seemingly not well suited for a time-dependent formulation. Very few methods exist to obtain the energy-dependent Green function for complicated potentials without resorting to ensemble averages or using certain lead-in arrangements. Here, we demonstrate in detail a time-dependent approach, which can accurately and effectively construct the energy-dependent Green function for very general potentials. The applications of the method are numerous, including chemical, mesoscopic, and atomic physics

A contiguous-quadrat sampling exercise in a shrub-invaded ...

African Journals Online (AJOL)

In each quadrat, we recorded the species present and counted the number of woody alien plants. Chromolaena diminished under annual burning. Species richness and turnover increased in all transects over time. The 25m transect was as efficient as the 30m transect; however, the latter was influenced by an edge effect, ...

Solitons in quadratic nonlinear photonic crystals

DEFF Research Database (Denmark)

Corney, Joel Frederick; Bang, Ole

2001-01-01

We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....

Simulating transient dynamics of the time-dependent time fractional Fokker–Planck systems

Energy Technology Data Exchange (ETDEWEB)

Kang, Yan-Mei, E-mail: ymkang@mail.xjtu.edu.cn

2016-09-16

For a physically realistic type of time-dependent time fractional Fokker–Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker–Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed. - Highlights: • An iteration method is proposed for the transient dynamics of time-dependent time fractional Fokker–Planck equations. • The method is based on Fourier Series solution and the multi-step transition probability formula. • With the time-modulated subdiffusion on finite interval as example, the polarized motion orientation is disclosed. • With the time-modulated subdiffusion within a confined potential as example, the death of dynamic response is observed.

Simulating transient dynamics of the time-dependent time fractional Fokker–Planck systems

International Nuclear Information System (INIS)

Kang, Yan-Mei

2016-01-01

For a physically realistic type of time-dependent time fractional Fokker–Planck (FP) equation, derived as the continuous limit of the continuous time random walk with time-modulated Boltzmann jumping weight, a semi-analytic iteration scheme based on the truncated (generalized) Fourier series is presented to simulate the resultant transient dynamics when the external time modulation is a piece-wise constant signal. At first, the iteration scheme is demonstrated with a simple time-dependent time fractional FP equation on finite interval with two absorbing boundaries, and then it is generalized to the more general time-dependent Smoluchowski-type time fractional Fokker–Planck equation. The numerical examples verify the efficiency and accuracy of the iteration method, and some novel dynamical phenomena including polarized motion orientations and periodic response death are discussed. - Highlights: • An iteration method is proposed for the transient dynamics of time-dependent time fractional Fokker–Planck equations. • The method is based on Fourier Series solution and the multi-step transition probability formula. • With the time-modulated subdiffusion on finite interval as example, the polarized motion orientation is disclosed. • With the time-modulated subdiffusion within a confined potential as example, the death of dynamic response is observed.

General time-dependent formulation of quantum scattering theory

International Nuclear Information System (INIS)

Althorpe, Stuart C.

2004-01-01

We derive and explain the key ideas behind a time-dependent formulation of quantum scattering theory, applicable generally to systems with a finite-range scattering potential. The scattering is initiated and probed by plane wave packets, which are localized just outside the range of the potential. The asymptotic limits of conventional scattering theory (initiation in the remote past; detection in the remote future) are not taken. Instead, the differential cross section (DCS) is obtained by projecting the scattered wave packet onto the probe plane wave packets. The projection also yields a time-dependent version of the DCS. Cuts through the wave packet, just as it exits the scattering potential, yield time-dependent and time-independent angular distributions that give a close-up picture of the scattering which complements the DCS. We have previously applied the theory to interpret experimental cross sections of chemical reactions [e.g., S. C. Althorpe, F. Fernandez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, and E. Wrede, Nature (London) 416, 67 (2002)]. This paper gives the derivation of the theory, and explains its relation to conventional scattering theory. For clarity, the derivation is restricted to spherical-particle scattering, though it may readily be extended to general multichannel systems. We illustrate the theory using a simple application to hard-sphere scattering

Entanglement in a model for Hawking radiation: An application of quadratic algebras

International Nuclear Information System (INIS)

Bambah, Bindu A.; Mukku, C.; Shreecharan, T.; Siva Prasad, K.

2013-01-01

Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: ► We examine a toy model for Hawking radiation with quantized black hole modes. ► We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. ► We study the “Dicke Superradiance” in black hole radiation using quadratically deformed su(2) algebras. ► We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.

Classification of ξ(s)-Quadratic Stochastic Operators on 2D simplex

International Nuclear Information System (INIS)

Mukhamedov, Farrukh; Saburov, Mansoor; Qaralleh, Izzat

2013-01-01

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some QSO has been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for the quadratic stochastic operators. To study this problem it was investigated several classes of such QSO. In this paper we study ξ (s) -QSO class of operators. We study such kind of operators on 2D simplex. We first classify these ξ (s) -QSO into 20 classes. Further, we investigate the dynamics of one class of such operators.

Non normal and non quadratic anisotropic plasticity coupled with ductile damage in sheet metal forming: Application to the hydro bulging test

International Nuclear Information System (INIS)

Badreddine, Houssem; Saanouni, Khemaies; Dogui, Abdelwaheb

2007-01-01

In this work an improved material model is proposed that shows good agreement with experimental data for both hardening curves and plastic strain ratios in uniaxial and equibiaxial proportional loading paths for steel metal until the final fracture. This model is based on non associative and non normal flow rule using two different orthotropic equivalent stresses in both yield criterion and plastic potential functions. For the plastic potential the classical Hill 1948 quadratic equivalent stress is considered while for the yield criterion the Karafillis and Boyce 1993 non quadratic equivalent stress is used taking into account the non linear mixed (kinematic and isotropic) hardening. Applications are made to hydro bulging tests using both circular and elliptical dies. The results obtained with different particular cases of the model such as the normal quadratic and the non normal non quadratic cases are compared and discussed with respect to the experimental results

Convexity Conditions and the Legendre-Fenchel Transform for the Product of Finitely Many Positive Definite Quadratic Forms

International Nuclear Information System (INIS)

Zhao Yunbin

2010-01-01

While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called 'scaled matrices' associated with quadratic forms involved. The main result claims that if the condition number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer's fixed point of a mapping) with a special structure. Thus, a broader question than the open 'Question 11' in Hiriart-Urruty (SIAM Rev. 49, 225-273, 2007) is addressed in this paper.

DQM: Decentralized Quadratically Approximated Alternating Direction Method of Multipliers

Science.gov (United States)

Mokhtari, Aryan; Shi, Wei; Ling, Qing; Ribeiro, Alejandro

2016-10-01

This paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function. Nodes cooperate to minimize the global objective by exchanging information with neighbors only. A decentralized version of the alternating directions method of multipliers (DADMM) is a common method for solving this category of problems. DADMM exhibits linear convergence rate to the optimal objective but its implementation requires solving a convex optimization problem at each iteration. This can be computationally costly and may result in large overall convergence times. The decentralized quadratically approximated ADMM algorithm (DQM), which minimizes a quadratic approximation of the objective function that DADMM minimizes at each iteration, is proposed here. The consequent reduction in computational time is shown to have minimal effect on convergence properties. Convergence still proceeds at a linear rate with a guaranteed constant that is asymptotically equivalent to the DADMM linear convergence rate constant. Numerical results demonstrate advantages of DQM relative to DADMM and other alternatives in a logistic regression problem.

Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

Science.gov (United States)

Laine, A. D.

2015-01-01

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

A perturbative solution for gravitational waves in quadratic gravity

International Nuclear Information System (INIS)

Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de

2003-01-01

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin

Attainable conditions and exact invariant for the time-dependent harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)

2006-09-22

The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.

Attainable conditions and exact invariant for the time-dependent harmonic oscillator

International Nuclear Information System (INIS)

Guasti, Manuel Fernandez

2006-01-01

The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system

An Extended Quadratic Frobenius Primality Test with Average Case Error Estimates

DEFF Research Database (Denmark)

Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg

2001-01-01

We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....

Adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems

International Nuclear Information System (INIS)

Baranger, M.; Veneroni, M.

1978-01-01

We show how to derive the parameters of a phenomenological collective model from a microscopic theory. The microscopic theory is Hartree-Fock, and we start from the time-dependent Hartree-Fock equation. To this we add the adiabatic approximation, which results in a collective kinetic energy quadratic in the velocities, with coefficients depending on the coordinates, as in the phenomenological models. The crucial step is the decomposition of the single-particle density matrix p in the form exp(i/sub chi/) rho/sub omicron/exp(-i/sub chi/), where rho/sub omicron/ represents a time-even Slater determinant and plays the role of coordinate. Then chi plays the role of momentum, and the adiabatic assumption is that chi is small. The energy is expanded in powers of chi, the zeroth-order being the collective potential energy. The analogy with classical mechanics is stressed and studied. The same adiabatic equations of motion are derived in three different ways (directly, from the Lagrangian, from the Hamiltonian), thus proving the consistency of the theory. The dynamical equation is not necessary for writing the energy or for the subsequent quantization which leads to a Schroedinger equation, but it must be used to check the validity of various approximation schemes, particularly to reduce the problem to a few degrees of freedom. The role of the adiabatic hypothesis, its definition, and range of validity, are analyzed in great detail. It assumes slow motion, but not small amplitude, and is therefore suitable for large-amplitude collective motion. The RPA is obtained as the limiting case where the amplitude is also small. The translational mass is correctly given, and the moment of inertia under rotation is that of Thouless and Valatin. For a quadrupole two-body force, the Baranger-Kumar formalism is recovered. The self-consistency brings additional terms to the Inglis cranking formula. Comparison is also made with generator coordinate methods

Bound constrained quadratic programming via piecewise

DEFF Research Database (Denmark)

Madsen, Kaj; Nielsen, Hans Bruun; Pinar, M. C.

1999-01-01

of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of lambda/sub 1/ , how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive......We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of lambda/sub 1/ , the smallest eigenvalue...

Repair-dependent cell radiation survival and transformation: an integrated theory

International Nuclear Information System (INIS)

Sutherland, John C

2014-01-01

The repair-dependent model of cell radiation survival is extended to include radiation-induced transformations. The probability of transformation is presumed to scale with the number of potentially lethal damages that are repaired in a surviving cell or the interactions of such damages. The theory predicts that at doses corresponding to high survival, the transformation frequency is the sum of simple polynomial functions of dose; linear, quadratic, etc, essentially as described in widely used linear-quadratic expressions. At high doses, corresponding to low survival, the ratio of transformed to surviving cells asymptotically approaches an upper limit. The low dose fundamental- and high dose plateau domains are separated by a downwardly concave transition region. Published transformation data for mammalian cells show the high-dose plateaus predicted by the repair-dependent model for both ultraviolet and ionizing radiation. For the neoplastic transformation experiments that were analyzed, the data can be fit with only the repair-dependent quadratic function. At low doses, the transformation frequency is strictly quadratic, but becomes sigmodial over a wider range of doses. Inclusion of data from the transition region in a traditional linear-quadratic analysis of neoplastic transformation frequency data can exaggerate the magnitude of, or create the appearance of, a linear component. Quantitative analysis of survival and transformation data shows good agreement for ultraviolet radiation; the shapes of the transformation components can be predicted from survival data. For ionizing radiations, both neutrons and x-rays, survival data overestimate the transforming ability for low to moderate doses. The presumed cause of this difference is that, unlike UV photons, a single x-ray or neutron may generate more than one lethal damage in a cell, so the distribution of such damages in the population is not accurately described by Poisson statistics. However, the complete

AUTOJOM, Quadratic Equation Coefficient for Conic Volume, Parallelepipeds, Wedges, Pyramids. JOMREAD, Check of 3-D Geometry Structure from Quadratic Surfaces

International Nuclear Information System (INIS)

2005-01-01

Nature of physical problem solved: AUTOJOM is a computer program that will generate the coefficients of any quadratic equation used to define conic volumes and also the coefficients of the planes needed to define parallelepipeds, wedges, and pyramids. JOMREAD is a computer code to check any 3D geometry composed of and constructed with quadratic surfaces

The stability of quadratic-reciprocal functional equation

Science.gov (United States)

Song, Aimin; Song, Minwei

2018-04-01

A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.

Orthogonal and Scaling Transformations of Quadratic Functions with ...

African Journals Online (AJOL)

In this paper we present a non-singular transformation that can reduce a given quadratic function defined on Rn to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that can reduce a ...

Quadratic Frequency Modulation Signals Parameter Estimation Based on Two-Dimensional Product Modified Parameterized Chirp Rate-Quadratic Chirp Rate Distribution.

Science.gov (United States)

Qu, Zhiyu; Qu, Fuxin; Hou, Changbo; Jing, Fulong

2018-05-19

In an inverse synthetic aperture radar (ISAR) imaging system for targets with complex motion, the azimuth echo signals of the target are always modeled as multicomponent quadratic frequency modulation (QFM) signals. The chirp rate (CR) and quadratic chirp rate (QCR) estimation of QFM signals is very important to solve the ISAR image defocus problem. For multicomponent QFM (multi-QFM) signals, the conventional QR and QCR estimation algorithms suffer from the cross-term and poor anti-noise ability. This paper proposes a novel estimation algorithm called a two-dimensional product modified parameterized chirp rate-quadratic chirp rate distribution (2D-PMPCRD) for QFM signals parameter estimation. The 2D-PMPCRD employs a multi-scale parametric symmetric self-correlation function and modified nonuniform fast Fourier transform-Fast Fourier transform to transform the signals into the chirp rate-quadratic chirp rate (CR-QCR) domains. It can greatly suppress the cross-terms while strengthening the auto-terms by multiplying different CR-QCR domains with different scale factors. Compared with high order ambiguity function-integrated cubic phase function and modified Lv's distribution, the simulation results verify that the 2D-PMPCRD acquires higher anti-noise performance and obtains better cross-terms suppression performance for multi-QFM signals with reasonable computation cost.

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

Science.gov (United States)

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 (0application of min-plus algebra. The approach can be applied in most of existing machine learning methods, including methods of data approximation and regularized and sparse regression, leading to the improvement in the computational cost/accuracy trade-off. We demonstrate that on synthetic and real-life datasets PQSQ-based machine learning methods achieve orders of magnitude faster computational performance than the corresponding state-of-the-art methods, having similar or better approximation accuracy. Copyright © 2016 Elsevier Ltd. All rights reserved.

A Quadratic Spring Equation

Science.gov (United States)

Fay, Temple H.

2010-01-01

Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier

DEFF Research Database (Denmark)

Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel

2016-01-01

We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system......, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic...... nonlinearities may generate additional amplitude–frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi...

Indirect quantum tomography of quadratic Hamiltonians

Energy Technology Data Exchange (ETDEWEB)

Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)

2011-01-15

A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.

On the initial conditions of time-dependent mean-field equations of evolution. Pt. 2

International Nuclear Information System (INIS)

Troudet, T.; Paris-11 Univ., 91 - Orsay

1986-01-01

We analyze the problem so far untouched of determining the initial mean-field wavefunction in the context of zero-temperature mean-field descriptions of time-dependent expectation values and quantum fluctuations of nuclear observables. The nucleus, at zero temperature, is taken to be in a low-lying excited many-body eigenstate and is approximated by the corresponding RPA wavefunction as a continuous superposition of coherent states (i.e. Slater determinants). A generating function Gsub(A)(lambda) for time-dependent expectation values and quantum fluctuations is constructed within the formalism of functional integration. By applying the saddle-point method to the functional action of Gsub(A)(lambda) and then taking its lambda-derivatives, we recover the well-known TDHF theory and propose a simple determination of the initial Slater determinant for an appropriate mean-field description of time-dependent expectation values. The analog mean-field description of quadratic-quantum fluctuations proceeds similarly and in addition includes the contribution of the uncorrelated TDHF-RPA phonons coupled to collective excitations of the initial (static) mean-field configuration. When the collective TDHF-RPA excitations are solely taken into account, we obtain an improved version of the Balian-Veneroni dispersion formula by showing how to determine the initial mean-field wavefunction. By first taking the lambda-derivatives of Gsub(A)(lambda) before applying the saddle-point method, the initial mean-field wavefunction is found to be non-linearly coupled to the mean-field dynamics themselves. In return, and in contrast to the first quantization scheme, these both depend non-trivially upon the observable A being measured so that approximations must be proposed to simplify the resulting mean-field equations. (orig.)

Quadratic Twists of Rigid Calabi–Yau Threefolds Over

DEFF Research Database (Denmark)

Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko

2013-01-01

of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...

Quadratic Hedging of Basis Risk

Directory of Open Access Journals (Sweden)

Hardy Hulley

2015-02-01

Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.

On Convex Quadratic Approximation

NARCIS (Netherlands)

den Hertog, D.; de Klerk, E.; Roos, J.

2000-01-01

In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of

Tip-tilt disturbance model identification based on non-linear least squares fitting for Linear Quadratic Gaussian control

Science.gov (United States)

Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing

2018-05-01

We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.

The Model and Quadratic Stability Problem of Buck Converter in DCM

Directory of Open Access Journals (Sweden)

Li Xiaojing

2016-01-01

Full Text Available Quadratic stability is an important performance for control systems. At first, the model of Buck Converter in DCM is built based on the theories of hybrid systems and switched linear systems primarily. Then quadratic stability of SLS and hybrid feedback switching rule are introduced. The problem of Buck Converter’s quadratic stability is researched afterwards. In the end, the simulation analysis and verification are provided. Both experimental verification and theoretical analysis results indicate that the output of Buck Converter in DCM has an excellent performance via quadratic stability control and switching rules.

Equivalence between deep energy-dependent and shallow angular momentum dependent potentials

International Nuclear Information System (INIS)

Fiedeldey, H.; Sofianos, S.A.; Papastylianos, A.; Amos, K.A.; Allen, L.J.

1989-01-01

Recently Baye showed that supersymmetry can be applied to determine a shallow l-dependent potential phase equivalent to a deep potential, assumed to be energy-independent and have Panli forbidden states (PFS), for α-α scattering. The PFS are eliminated by this procedure. Such deep potentials are generated as equivalent local potentials (ELP) to the Resonating Group Model (RGM) and are generally energy-dependent. To eliminate this E-dependence as required for the application of Baye's method, l-dependent, but E-independent, deep local potentials were generated by the exact inversion method of Marchenko. Subsequently, the supersymmetric method was used to eliminate the PFS, ensuring that the generalized Levinson theorem is satisfied. As an example, the method was applied to the simple model of two dineutrons scattering in the RGM, where the deep ELP of Horiuchi has a substantial energy-dependence and one PFS only for l=O. 16 refs., 5 figs

Nearly Quadratic n-Derivations on Non-Archimedean Banach Algebras

Directory of Open Access Journals (Sweden)

Madjid Eshaghi Gordji

2012-01-01

Full Text Available Let n>1 be an integer, let A be an algebra, and X be an A-module. A quadratic function D:A→X is called a quadratic n-derivation if D(∏i=1nai=D(a1a22⋯an2+a12D(a2a32⋯an2+⋯+a12a22⋯an−12D(an for all a1,...,an∈A. We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.

Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1981-01-01

Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices

Comment on 'Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential' [J. Math. Phys. 48, 073515 (2007)

International Nuclear Information System (INIS)

Castro, L. B.; Castro, A. S. de

2010-01-01

It is shown that the paper 'Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential' by Merad and Bensaid [J. Math. Phys. 48, 073515 (2007)] is not correct in using inadvertently a non-Hermitian Hamiltonian in a formalism that does require Hermitian Hamiltonians.

Determining the Optimal Solution for Quadratically Constrained Quadratic Programming (QCQP) on Energy-Saving Generation Dispatch Problem

Science.gov (United States)

Lesmana, E.; Chaerani, D.; Khansa, H. N.

2018-03-01

Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method

Dynamical control of matter-wave splitting using time-dependent optical lattices

DEFF Research Database (Denmark)

Park, Sung Jong; Andersen, Henrik Kjær; Mai, Sune

2012-01-01

We report on measurements of splitting Bose-Einstein condensates (BEC) by using a time-dependent optical lattice potential. First, we demonstrate the division of a BEC into a set of equally populated components by means of time-dependent control of Landau-Zener tunneling in a vertical lattice....... Finally, a combination of multiple Bragg reflections and Landau-Zener tunneling allows for the generation of macroscopic arrays of condensates with potential applications in atom optics and atom interferometry....

Guises and disguises of quadratic divergences

Energy Technology Data Exchange (ETDEWEB)

Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)

2014-12-15

In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

PSQP: Puzzle Solving by Quadratic Programming.

Science.gov (United States)

Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

2017-02-01

In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

Visualising the Roots of Quadratic Equations with Complex Coefficients

Science.gov (United States)

Bardell, Nicholas S.

2014-01-01

This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality

Science.gov (United States)

Acikmese, Ahmet Behcet; Martin, Corless

2004-01-01

We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.

Anisotropic, time-dependent solutions in maximally Gauss-Bonnet extended gravity

International Nuclear Information System (INIS)

Kitaura, Takayuki; Wheeler, J.T.

1991-01-01

In an arbitrary number of dimensions, we find the full exact anisotropic, time-dependent, diagonal-metric solutions to maximally Gauss-Bonnet extended gravity theory. This class of theories for which the lagrangian is an arbitrary linear combination of dimensionally extnded Euler forms, is the most general gravitational theory in which the field equations contain no more than second derivatives of the metric. We show that the space-time exponentially approaches an asymptotic state of constant, anisotropic curvature and prove three theorems concerning two generic types of singularities. The first theorem gives conditions for the existence of Kasner-like curvature singularities. For these the metric diverges as tsup(p i ) where Σp i = 2 k max -1 and k max is the highest power of the curvature in the lagrangian. Other critical point singularities can arise from the polynomial nature of the theory. The remaining theorems demonstrate that the generic solution is extendible at all of these other critical points and that the generic critical points occur at moments of extremal volume density of space-time. We give an explicit coordinate transformation which produces a smooth extension through the critical point. The space-time may therefore alternately expand and contract for many cycles before expanding forever or contracting to a singularity. Many particular cases are treated in detail including several power series solutions, the generalized Kasner solution to general relativity with or without cosmological constant, the perturbative solution for quadratic string gravity, and five-dimensional extended gravity. (orig.)

Scale-Invariant Rotating Black Holes in Quadratic Gravity

Directory of Open Access Journals (Sweden)

Guido Cognola

2015-07-01

Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.

A generalized linear-quadratic model incorporating reciprocal time pattern of radiation damage repair

International Nuclear Information System (INIS)

Huang, Zhibin; Mayr, Nina A.; Lo, Simon S.; Wang, Jian Z.; Jia Guang; Yuh, William T. C.; Johnke, Roberta

2012-01-01

Purpose: It has been conventionally assumed that the repair rate for sublethal damage (SLD) remains constant during the entire radiation course. However, increasing evidence from animal studies suggest that this may not the case. Rather, it appears that the repair rate for radiation-induced SLD slows down with increasing time. Such a slowdown in repair would suggest that the exponential repair pattern would not necessarily accurately predict repair process. As a result, the purpose of this study was to investigate a new generalized linear-quadratic (LQ) model incorporating a repair pattern with reciprocal time. The new formulas were tested with published experimental data. Methods: The LQ model has been widely used in radiation therapy, and the parameter G in the surviving fraction represents the repair process of sublethal damage with T r as the repair half-time. When a reciprocal pattern of repair process was adopted, a closed form of G was derived analytically for arbitrary radiation schemes. The published animal data adopted to test the reciprocal formulas. Results: A generalized LQ model to describe the repair process in a reciprocal pattern was obtained. Subsequently, formulas for special cases were derived from this general form. The reciprocal model showed a better fit to the animal data than the exponential model, particularly for the ED50 data (reduced χ 2 min of 2.0 vs 4.3, p = 0.11 vs 0.006), with the following gLQ parameters: α/β = 2.6-4.8 Gy, T r = 3.2-3.9 h for rat feet skin, and α/β = 0.9 Gy, T r = 1.1 h for rat spinal cord. Conclusions: These results of repair process following a reciprocal time suggest that the generalized LQ model incorporating the reciprocal time of sublethal damage repair shows a better fit than the exponential repair model. These formulas can be used to analyze the experimental and clinical data, where a slowing-down repair process appears during the course of radiation therapy.

Layer-dependent surface potential of phosphorene and anisotropic/layer-dependent charge transfer in phosphorene-gold hybrid systems.

Science.gov (United States)

Xu, Renjing; Yang, Jiong; Zhu, Yi; Yan, Han; Pei, Jiajie; Myint, Ye Win; Zhang, Shuang; Lu, Yuerui

2016-01-07

The surface potential and the efficiency of interfacial charge transfer are extremely important for designing future semiconductor devices based on the emerging two-dimensional (2D) phosphorene. Here, we directly measured the strong layer-dependent surface potential of mono- and few-layered phosphorene on gold, which is consistent with the reported theoretical prediction. At the same time, we used an optical way photoluminescence (PL) spectroscopy to probe charge transfer in the phosphorene-gold hybrid system. We firstly observed highly anisotropic and layer-dependent PL quenching in the phosphorene-gold hybrid system, which is attributed to the highly anisotropic/layer-dependent interfacial charge transfer.

Mapping the absolute magnetic field and evaluating the quadratic Zeeman-effect-induced systematic error in an atom interferometer gravimeter

Science.gov (United States)

Hu, Qing-Qing; Freier, Christian; Leykauf, Bastian; Schkolnik, Vladimir; Yang, Jun; Krutzik, Markus; Peters, Achim

2017-09-01

Precisely evaluating the systematic error induced by the quadratic Zeeman effect is important for developing atom interferometer gravimeters aiming at an accuracy in the μ Gal regime (1 μ Gal =10-8m /s2 ≈10-9g ). This paper reports on the experimental investigation of Raman spectroscopy-based magnetic field measurements and the evaluation of the systematic error in the gravimetric atom interferometer (GAIN) due to quadratic Zeeman effect. We discuss Raman duration and frequency step-size-dependent magnetic field measurement uncertainty, present vector light shift and tensor light shift induced magnetic field measurement offset, and map the absolute magnetic field inside the interferometer chamber of GAIN with an uncertainty of 0.72 nT and a spatial resolution of 12.8 mm. We evaluate the quadratic Zeeman-effect-induced gravity measurement error in GAIN as 2.04 μ Gal . The methods shown in this paper are important for precisely mapping the absolute magnetic field in vacuum and reducing the quadratic Zeeman-effect-induced systematic error in Raman transition-based precision measurements, such as atomic interferometer gravimeters.

Approximate *-derivations and approximate quadratic *-derivations on C*-algebras

Directory of Open Access Journals (Sweden)

Park Choonkil

2011-01-01

Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.

Field equations for gravity quadratic in the curvature

International Nuclear Information System (INIS)

Rose, B.

1992-01-01

Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian-namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type-is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differs from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built. 6 refs

Results of radiotherapy in craniopharyngiomas analysed by the linear quadratic model

Energy Technology Data Exchange (ETDEWEB)

Guerkaynak, M. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Oezyar, E. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Zorlu, F. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Akyol, F.H. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey); Lale Atahan, I. [Dept. of Radiation Oncology, Hacettepe Univ., Ankara (Turkey)

1994-12-31

In 23 craniopharyngioma patients treated by limited surgery and external radiotherapy, the results concerning local control were analysed by linear quadratic formula. A biologically effective dose (BED) of 55 Gy, calculated with time factor and an {alpha}/{beta} value of 10 Gy, seemed to be adequate for local control. (orig.).

Vorticity vector-potential method based on time-dependent curvilinear coordinates for two-dimensional rotating flows in closed configurations

Science.gov (United States)

Fu, Yuan; Zhang, Da-peng; Xie, Xi-lin

2018-04-01

In this study, a vorticity vector-potential method for two-dimensional viscous incompressible rotating driven flows is developed in the time-dependent curvilinear coordinates. The method is applicable in both inertial and non-inertial frames of reference with the advantage of a fixed and regular calculation domain. The numerical method is applied to triangle and curved triangle configurations in constant and varying rotational angular velocity cases respectively. The evolutions of flow field are studied. The geostrophic effect, unsteady effect and curvature effect on the evolutions are discussed.

Analysis of Students' Error in Learning of Quadratic Equations

Science.gov (United States)

Zakaria, Effandi; Ibrahim; Maat, Siti Mistima

2010-01-01

The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…

Quadratic hamiltonians and relativistic quantum mechanics

International Nuclear Information System (INIS)

Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.

1981-01-01

For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru

Cyclic subgroups in class groups of real quadratic fields

International Nuclear Information System (INIS)

Washington, L.C.; Zhang Xianke.

1994-01-01

While examining the class numbers of the real quadratic field Q(√n 2 + 3n + 9), we observed that the class number is often a multiple of 3. There is a simple explanation for this, namely -27 = (2n + 3) 2 - 4(n 2 + 3n + 9), so the cubes of the prime ideals above 3 are principal. If the prime ideals themselves are non-principal then 3 must divide the class number. In the present paper, we study this idea from a couple different directions. In the first section we present a criterion that allows us to show that the ideal class group of a real quadratic field has a cyclic subgroup of a given order n. We then give several families of fields to which this criterion applies, hence in which the ideal class groups contain elements of order n. In the second section, we discuss the situation where there is only a potential element of order p (=an odd prime) in the class group, such as the situation described above. We present a modification of the Cohen-Lenstra heuristics for the probability that in this situation the class number is actually a multiple of p. We also extend this idea to predict how often the potential element of order p is actually non-trivial. Both of these predictions agree fairly well with the numerical data. (author). 14 refs, 2 tabs

Efficient exact-exchange time-dependent density-functional theory methods and their relation to time-dependent Hartree-Fock.

Science.gov (United States)

Hesselmann, Andreas; Görling, Andreas

2011-01-21

A recently introduced time-dependent exact-exchange (TDEXX) method, i.e., a response method based on time-dependent density-functional theory that treats the frequency-dependent exchange kernel exactly, is reformulated. In the reformulated version of the TDEXX method electronic excitation energies can be calculated by solving a linear generalized eigenvalue problem while in the original version of the TDEXX method a laborious frequency iteration is required in the calculation of each excitation energy. The lowest eigenvalues of the new TDEXX eigenvalue equation corresponding to the lowest excitation energies can be efficiently obtained by, e.g., a version of the Davidson algorithm appropriate for generalized eigenvalue problems. Alternatively, with the help of a series expansion of the new TDEXX eigenvalue equation, standard eigensolvers for large regular eigenvalue problems, e.g., the standard Davidson algorithm, can be used to efficiently calculate the lowest excitation energies. With the help of the series expansion as well, the relation between the TDEXX method and time-dependent Hartree-Fock is analyzed. Several ways to take into account correlation in addition to the exact treatment of exchange in the TDEXX method are discussed, e.g., a scaling of the Kohn-Sham eigenvalues, the inclusion of (semi)local approximate correlation potentials, or hybrids of the exact-exchange kernel with kernels within the adiabatic local density approximation. The lowest lying excitations of the molecules ethylene, acetaldehyde, and pyridine are considered as examples.

Existence for stationary mean-field games with congestion and quadratic Hamiltonians

KAUST Repository

Gomes, Diogo A.

2015-09-03

Here, we investigate the existence of solutions to a stationary mean-field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian and congestion effects. The fundamental difficulty of potential singular behavior is caused by congestion. Thanks to a new class of a priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions. © 2015 Springer Basel

Adaptive dynamic programming for discrete-time linear quadratic regulation based on multirate generalised policy iteration

Science.gov (United States)

Chun, Tae Yoon; Lee, Jae Young; Park, Jin Bae; Choi, Yoon Ho

2018-06-01

In this paper, we propose two multirate generalised policy iteration (GPI) algorithms applied to discrete-time linear quadratic regulation problems. The proposed algorithms are extensions of the existing GPI algorithm that consists of the approximate policy evaluation and policy improvement steps. The two proposed schemes, named heuristic dynamic programming (HDP) and dual HDP (DHP), based on multirate GPI, use multi-step estimation (M-step Bellman equation) at the approximate policy evaluation step for estimating the value function and its gradient called costate, respectively. Then, we show that these two methods with the same update horizon can be considered equivalent in the iteration domain. Furthermore, monotonically increasing and decreasing convergences, so called value iteration (VI)-mode and policy iteration (PI)-mode convergences, are proved to hold for the proposed multirate GPIs. Further, general convergence properties in terms of eigenvalues are also studied. The data-driven online implementation methods for the proposed HDP and DHP are demonstrated and finally, we present the results of numerical simulations performed to verify the effectiveness of the proposed methods.

Fast Detection of Compressively Sensed IR Targets Using Stochastically Trained Least Squares and Compressed Quadratic Correlation Filters

KAUST Repository

Millikan, Brian; Dutta, Aritra; Sun, Qiyu; Foroosh, Hassan

2017-01-01

Target detection of potential threats at night can be deployed on a costly infrared focal plane array with high resolution. Due to the compressibility of infrared image patches, the high resolution requirement could be reduced with target detection capability preserved. For this reason, a compressive midwave infrared imager (MWIR) with a low-resolution focal plane array has been developed. As the most probable coefficient indices of the support set of the infrared image patches could be learned from the training data, we develop stochastically trained least squares (STLS) for MWIR image reconstruction. Quadratic correlation filters (QCF) have been shown to be effective for target detection and there are several methods for designing a filter. Using the same measurement matrix as in STLS, we construct a compressed quadratic correlation filter (CQCF) employing filter designs for compressed infrared target detection. We apply CQCF to the U.S. Army Night Vision and Electronic Sensors Directorate dataset. Numerical simulations show that the recognition performance of our algorithm matches that of the standard full reconstruction methods, but at a fraction of the execution time.

Fast Detection of Compressively Sensed IR Targets Using Stochastically Trained Least Squares and Compressed Quadratic Correlation Filters

KAUST Repository

Millikan, Brian

2017-05-02

Target detection of potential threats at night can be deployed on a costly infrared focal plane array with high resolution. Due to the compressibility of infrared image patches, the high resolution requirement could be reduced with target detection capability preserved. For this reason, a compressive midwave infrared imager (MWIR) with a low-resolution focal plane array has been developed. As the most probable coefficient indices of the support set of the infrared image patches could be learned from the training data, we develop stochastically trained least squares (STLS) for MWIR image reconstruction. Quadratic correlation filters (QCF) have been shown to be effective for target detection and there are several methods for designing a filter. Using the same measurement matrix as in STLS, we construct a compressed quadratic correlation filter (CQCF) employing filter designs for compressed infrared target detection. We apply CQCF to the U.S. Army Night Vision and Electronic Sensors Directorate dataset. Numerical simulations show that the recognition performance of our algorithm matches that of the standard full reconstruction methods, but at a fraction of the execution time.

Quadratic Finite Element Method for 1D Deterministic Transport

International Nuclear Information System (INIS)

Tolar, D R Jr.; Ferguson, J M

2004-01-01

In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ((und r)) and angular ((und (Omega))) dependences on the angular flux ψ(und r),(und (Omega))are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of ψ(und r),(und (Omega)). Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable (μ) in developing the one-dimensional (1D) spherical geometry S N equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S N algorithms

Sketching the General Quadratic Equation Using Dynamic Geometry Software

Science.gov (United States)

Stols, G. H.

2005-01-01

This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

Tangent Lines without Derivatives for Quadratic and Cubic Equations

Science.gov (United States)

Carroll, William J.

2009-01-01

In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

An Extended Quadratic Frobenius Primality Test with Average and Worst Case Error Estimates

DEFF Research Database (Denmark)

Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg

2003-01-01

We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....

An Extended Quadratic Frobenius Primality Test with Average- and Worst-Case Error Estimate

DEFF Research Database (Denmark)

Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg

2006-01-01

We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to an extends the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability, namely 256/331776t for t...... for the error probability of this algorithm as well as a general closed expression bounding the error. For instance, it is at most 2-143 for k = 500, t = 2. Compared to earlier similar results for the Miller-Rabin test, the results indicates that our test in the average case has the effect of 9 Miller......-Rabin tests, while only taking time equivalent to about 2 such tests. We also give bounds for the error in case a prime is sought by incremental search from a random starting point....

Time-dependent Wigner distribution function employed in coherent Schroedinger cat states: |Ψ(t))=N-1/2(|α)+eiφ|-α))

International Nuclear Information System (INIS)

Choi, Jeong Ryeol; Yeon, Kyu Hwang

2008-01-01

The Wigner distribution function for the time-dependent quadratic Hamiltonian system in the coherent Schroedinger cat state is investigated. The type of state we consider is a superposition of two coherent states, which are by an angle of π out of phase with each other. The exact Wigner distribution function of the system is evaluated under a particular choice of phase, δ c,q . Our development is employed for two special cases, namely, the Caldirola-Kanai oscillator and the frequency stable damped harmonic oscillator. On the basis of the diverse values of the Wigner distribution function that were plotted, we analyze the nonclassical behavior of the systems.

Time-dependent Autler-Townes spectroscopy

International Nuclear Information System (INIS)

Qamar, Sajid; Zhu, S.-Y.; Zubairy, M Suhail

2003-01-01

Autler-Townes spontaneous emission spectroscopy is revisited for a time-dependent case. We report the results of spontaneous emission spectra for nonstationary scattered light signals using the definition of the time-dependent physical spectrum. This is a rare example of problems where time-dependent spectra can be calculated exactly

Time-dependent Autler-Townes spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Qamar, Sajid [Institute for Quantum Studies, Department of Physics, Texas A and M University, College Station, TX 77843-4242 (United States); Zhu, S.-Y. [Institute for Quantum Studies, Department of Physics, Texas A and M University, College Station, TX 77843-4242 (United States); Zubairy, M Suhail [Institute for Quantum Studies, Department of Physics, Texas A and M University, College Station, TX 77843-4242 (United States)

2003-04-01

Autler-Townes spontaneous emission spectroscopy is revisited for a time-dependent case. We report the results of spontaneous emission spectra for nonstationary scattered light signals using the definition of the time-dependent physical spectrum. This is a rare example of problems where time-dependent spectra can be calculated exactly.

Time-dependent behavior of concrete

International Nuclear Information System (INIS)

Pfeiffer, P.A.; Tanabe, Tada-aki

1992-01-01

This paper is a condensed version of the material presented at the International Workshop on Finite Element Analysis of Reinforced Concrete, Session 4 -- Time Dependent Behavior, held at Columbia University, New York on June 3--6, 1991. Dr. P.A. Pfeiffer presented recent developments in time-dependent behavior of concrete and Professor T. Tanabe presented a review of research in Japan on time-dependent behavior of concrete. The paper discusses the recent research of time-dependent behavior of concrete in the past few years. 6 refs

Impurity solitons with quadratic nonlinearities

DEFF Research Database (Denmark)

Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis

1998-01-01

We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...

Cascaded Quadratic Soliton Compression in Waveguide Structures

DEFF Research Database (Denmark)

Guo, Hairun

between the Kerr nonlinear effects and the dispersive effects in the medium. A Kerr-like nonlinearity is produced through the cascaded phase mismatched quadratic process, e.g. the second harmonic generation process, which can be flexibly tuned in both the sign and the amplitude, making possible a strong......-phase-matching technology is not necessarily needed. In large-RI-changed waveguides, CQSC is extended to the mid-infrared range to generate single-cycle pulses with purely nonlinear interactions, since an all-normal dispersion profile could be achieved within the guidance band. We believe that CQSC in quadratic waveguides...

A Trust-region-based Sequential Quadratic Programming Algorithm

DEFF Research Database (Denmark)

Henriksen, Lars Christian; Poulsen, Niels Kjølstad

This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints.......This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....

Support for the existence of invertible maps between electronic densities and non-analytic 1-body external potentials in non-relativistic time-dependent quantum mechanics

Science.gov (United States)

Mosquera, Martín A.

2017-10-01

Provided the initial state, the Runge-Gross theorem establishes that the time-dependent (TD) external potential of a system of non-relativistic electrons determines uniquely their TD electronic density, and vice versa (up to a constant in the potential). This theorem requires the TD external potential and density to be Taylor-expandable around the initial time of the propagation. This paper presents an extension without this restriction. Given the initial state of the system and evolution of the density due to some TD scalar potential, we show that a perturbative (not necessarily weak) TD potential that induces a non-zero divergence of the external force-density, inside a small spatial subset and immediately after the initial propagation time, will cause a change in the density within that subset, implying that the TD potential uniquely determines the TD density. In this proof, we assume unitary evolution of wavefunctions and first-order differentiability (which does not imply analyticity) in time of the internal and external force-densities, electronic density, current density, and their spatial derivatives over the small spatial subset and short time interval.

Electroweak vacuum stability and finite quadratic radiative corrections

Energy Technology Data Exchange (ETDEWEB)

Masina, Isabella [Ferrara Univ. (Italy). Dipt. di Fisica e Scienze della Terra; INFN, Sezione di Ferrara (Italy); Southern Denmark Univ., Odense (Denmark). CP3-Origins; Southern Denmark Univ., Odense (Denmark). DIAS; Nardini, Germano [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Quiros, Mariano [Institucio Catalana de Recerca i Estudis Avancats (ICREA), Barcelona (Spain); IFAE-IAB, Barcelona (Spain)

2015-07-15

If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale Λ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative Ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales the cutoff is not unique and each SM sector has its own UV cutoff Λ{sub i}. We have performed this calculation assuming the Minimal Supersymmetric Standard Model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs Λ{sub i}, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the Focus Point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.

The quadratic reciprocity law a collection of classical proofs

CERN Document Server

Baumgart, Oswald

2015-01-01

This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.

Decay of autoionizing states in time-dependent density functional and reduced density matrix functional theory

Energy Technology Data Exchange (ETDEWEB)

Kapoor, Varun; Brics, Martins; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)

2013-07-01

Autoionizing states are inaccessible to time-dependent density functional theory (TDDFT) using known, adiabatic Kohn-Sham (KS) potentials. We determine the exact KS potential for a numerically exactly solvable model Helium atom interacting with a laser field that is populating an autoionizing state. The exact single-particle density of the population in the autoionizing state corresponds to that of the energetically lowest quasi-stationary state in the exact KS potential. We describe how this exact potential controls the decay by a barrier whose height and width allows for the density to tunnel out and decay with the same rate as in the ab initio time-dependent Schroedinger calculation. However, devising a useful exchange-correlation potential that is capable of governing such a scenario in general and in more complex systems is hopeless. As an improvement over TDDFT, time-dependent reduced density matrix functional theory has been proposed. We are able to obtain for the above described autoionization process the exact time-dependent natural orbitals (i.e., the eigenfunctions of the exact, time-dependent one-body reduced density matrix) and study the potentials that appear in the equations of motion for the natural orbitals and the structure of the two-body density matrix expanded in them.

A nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term

International Nuclear Information System (INIS)

Wang, Xiao-Lu; Fan, Xiang-Yu; Nie, Ren-Shi; Huang, Quan-Hua; He, Yong-Ming

2013-01-01

Based on material balance and Darcy's law, the governing equation with the quadratic pressure gradient term was deduced. Then the nonlinear model for fluid flow in a multiple-zone composite reservoir including the quadratic gradient term was established and solved using a Laplace transform. A series of standard log–log type curves of 1-zone (homogeneous), 2-zone and 3-zone reservoirs were plotted and nonlinear flow characteristics were analysed. The type curves governed by the coefficient of the quadratic gradient term (β) gradually deviate from those of a linear model with time elapsing. Qualitative and quantitative analyses were implemented to compare the solutions of the linear and nonlinear models. The results showed that differences of pressure transients between the linear and nonlinear models increase with elapsed time and β. At the end, a successful application of the theoretical model data against the field data shows that the nonlinear model will be a good tool to evaluate formation parameters more accurately. (paper)

Real time process algebra with time-dependent conditions

NARCIS (Netherlands)

Baeten, J.C.M.; Middelburg, C.A.

We extend the main real time version of ACP presented in [6] with conditionals in which the condition depends on time. This extension facilitates flexible dependence of proccess behaviour on initialization time. We show that the conditions concerned generalize the conditions introduced earlier

Dependable Real-Time Systems

Science.gov (United States)

1991-09-30

0196 or 413 545-0720 PI E-mail Address: krithi@nirvan.cs.umass.edu, stankovic(ocs.umass.edu Grant or Contract Title: Dependable Real - Time Systems Grant...Dependable Real - Time Systems " Grant or Contract Number: N00014-85-k-0398 L " Reporting Period: 1 Oct 87 - 30 Sep 91 , 2. Summary of Accomplishments ’ 2.1 Our...in developing a sound approach to scheduling tasks in complex real - time systems , (2) developed a real-time operating system kernel, a preliminary

Holographic complexity for time-dependent backgrounds

Energy Technology Data Exchange (ETDEWEB)

Momeni, Davood, E-mail: davoodmomeni78@gmail.com [Eurasian International Center for Theoretical Physics and Department of General Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Faizal, Mir, E-mail: mirfaizalmir@googlemail.com [Irving K. Barber School of Arts and Sciences, University of British Columbia, Okanagan, 3333 University Way, Kelowna, British Columbia V1V 1V7 (Canada); Department of Physics and Astronomy, University of Lethbridge, Lethbridge, Alberta, T1K 3M4 (Canada); Bahamonde, Sebastian, E-mail: sebastian.beltran.14@ucl.ac.uk [Department of Mathematics, University College London, Gower Street, London, WC1E 6BT (United Kingdom); Myrzakulov, Ratbay [Eurasian International Center for Theoretical Physics and Department of General Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan)

2016-11-10

In this paper, we will analyze the holographic complexity for time-dependent asymptotically AdS geometries. We will first use a covariant zero mean curvature slicing of the time-dependent bulk geometries, and then use this co-dimension one spacelike slice of the bulk spacetime to define a co-dimension two minimal surface. The time-dependent holographic complexity will be defined using the volume enclosed by this minimal surface. This time-dependent holographic complexity will reduce to the usual holographic complexity for static geometries. We will analyze the time-dependence as a perturbation of the asymptotically AdS geometries. Thus, we will obtain time-dependent asymptotically AdS geometries, and we will calculate the holographic complexity for such time-dependent geometries.

Non-Gaussian lineshapes and dynamics of time-resolved linear and nonlinear (correlation) spectra.

Science.gov (United States)

Dinpajooh, Mohammadhasan; Matyushov, Dmitry V

2014-07-17

Signatures of nonlinear and non-Gaussian dynamics in time-resolved linear and nonlinear (correlation) 2D spectra are analyzed in a model considering a linear plus quadratic dependence of the spectroscopic transition frequency on a Gaussian nuclear coordinate of the thermal bath (quadratic coupling). This new model is contrasted to the commonly assumed linear dependence of the transition frequency on the medium nuclear coordinates (linear coupling). The linear coupling model predicts equality between the Stokes shift and equilibrium correlation functions of the transition frequency and time-independent spectral width. Both predictions are often violated, and we are asking here the question of whether a nonlinear solvent response and/or non-Gaussian dynamics are required to explain these observations. We find that correlation functions of spectroscopic observables calculated in the quadratic coupling model depend on the chromophore's electronic state and the spectral width gains time dependence, all in violation of the predictions of the linear coupling models. Lineshape functions of 2D spectra are derived assuming Ornstein-Uhlenbeck dynamics of the bath nuclear modes. The model predicts asymmetry of 2D correlation plots and bending of the center line. The latter is often used to extract two-point correlation functions from 2D spectra. The dynamics of the transition frequency are non-Gaussian. However, the effect of non-Gaussian dynamics is limited to the third-order (skewness) time correlation function, without affecting the time correlation functions of higher order. The theory is tested against molecular dynamics simulations of a model polar-polarizable chromophore dissolved in a force field water.

Timing intervals using population synchrony and spike timing dependent plasticity

Directory of Open Access Journals (Sweden)

Wei Xu

2016-12-01

Full Text Available We present a computational model by which ensembles of regularly spiking neurons can encode different time intervals through synchronous firing. We show that a neuron responding to a large population of convergent inputs has the potential to learn to produce an appropriately-timed output via spike-time dependent plasticity. We explain why temporal variability of this population synchrony increases with increasing time intervals. We also show that the scalar property of timing and its violation at short intervals can be explained by the spike-wise accumulation of jitter in the inter-spike intervals of timing neurons. We explore how the challenge of encoding longer time intervals can be overcome and conclude that this may involve a switch to a different population of neurons with lower firing rate, with the added effect of producing an earlier bias in response. Experimental data on human timing performance show features in agreement with the model’s output.

Exact solutions of time-dependent Dirac equations and the quantum-classical correspondence

International Nuclear Information System (INIS)

Zhang Zhiguo

2006-01-01

Exact solutions to the Dirac equations with a time-dependent mass and a static magnetic field or a time-dependent linear potential are given. Matrix elements of the coordinate, momentum and velocity operator are calculated. In the large quantum number limit, these matrix elements give the classical solution

How Parallel Are Excited State Potential Energy Surfaces from Time-Independent and Time-Dependent DFT? A BODIPY Dye Case Study.

Science.gov (United States)

Komoto, Keenan T; Kowalczyk, Tim

2016-10-06

To support the development and characterization of chromophores with targeted photophysical properties, excited-state electronic structure calculations should rapidly and accurately predict how derivatization of a chromophore will affect its excitation and emission energies. This paper examines whether a time-independent excited-state density functional theory (DFT) approach meets this need through a case study of BODIPY chromophore photophysics. A restricted open-shell Kohn-Sham (ROKS) treatment of the S 1 excited state of BODIPY dyes is contrasted with linear-response time-dependent density functional theory (TDDFT). Vertical excitation energies predicted by the two approaches are remarkably different due to overestimation by TDDFT and underestimation by ROKS relative to experiment. Overall, ROKS with a standard hybrid functional provides the more accurate description of the S 1 excited state of BODIPY dyes, but excitation energies computed by the two methods are strongly correlated. The two approaches also make similar predictions of shifts in the excitation energy upon functionalization of the chromophore. TDDFT and ROKS models of the S 1 potential energy surface are then examined in detail for a representative BODIPY dye through molecular dynamics sampling on both model surfaces. We identify the most significant differences in the sampled surfaces and analyze these differences along selected normal modes. Differences between ROKS and TDDFT descriptions of the S 1 potential energy surface for this BODIPY derivative highlight the continuing need for validation of widely used approximations in excited state DFT through experimental benchmarking and comparison to ab initio reference data.

On quadratic variation of martingales

Indian Academy of Sciences (India)

On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...

Quadratic prediction of factor scores

NARCIS (Netherlands)

Wansbeek, T

1999-01-01

Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic

Absence of both auditory evoked potentials and auditory percepts dependent on timing cues.

Science.gov (United States)

Starr, A; McPherson, D; Patterson, J; Don, M; Luxford, W; Shannon, R; Sininger, Y; Tonakawa, L; Waring, M

1991-06-01

An 11-yr-old girl had an absence of sensory components of auditory evoked potentials (brainstem, middle and long-latency) to click and tone burst stimuli that she could clearly hear. Psychoacoustic tests revealed a marked impairment of those auditory perceptions dependent on temporal cues, that is, lateralization of binaural clicks, change of binaural masked threshold with changes in signal phase, binaural beats, detection of paired monaural clicks, monaural detection of a silent gap in a sound, and monaural threshold elevation for short duration tones. In contrast, auditory functions reflecting intensity or frequency discriminations (difference limens) were only minimally impaired. Pure tone audiometry showed a moderate (50 dB) bilateral hearing loss with a disproportionate severe loss of word intelligibility. Those auditory evoked potentials that were preserved included (1) cochlear microphonics reflecting hair cell activity; (2) cortical sustained potentials reflecting processing of slowly changing signals; and (3) long-latency cognitive components (P300, processing negativity) reflecting endogenous auditory cognitive processes. Both the evoked potential and perceptual deficits are attributed to changes in temporal encoding of acoustic signals perhaps occurring at the synapse between hair cell and eighth nerve dendrites. The results from this patient are discussed in relation to previously published cases with absent auditory evoked potentials and preserved hearing.

The regular indefinite linear-quadratic problem with linear endpoint constraints

NARCIS (Netherlands)

Soethoudt, J.M.; Trentelman, H.L.

1989-01-01

This paper deals with the infinite horizon linear-quadratic problem with indefinite cost. Given a linear system, a quadratic cost functional and a subspace of the state space, we consider the problem of minimizing the cost functional over all inputs for which the state trajectory converges to that

Eigenfunctions of quadratic hamiltonians in Wigner representation

International Nuclear Information System (INIS)

Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.

1984-01-01

Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail

Remarks on second-order quadratic systems in algebras

Directory of Open Access Journals (Sweden)

Art Sagle

2017-10-01

Full Text Available This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.

A Linear Programming Reformulation of the Standard Quadratic Optimization Problem

NARCIS (Netherlands)

de Klerk, E.; Pasechnik, D.V.

2005-01-01

The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an (exponentially

Estimating sample size for a small-quadrat method of botanical ...

African Journals Online (AJOL)

Reports the results of a study conducted to determine an appropriate sample size for a small-quadrat method of botanical survey for application in the Mixed Bushveld of South Africa. Species density and grass density were measured using a small-quadrat method in eight plant communities in the Nylsvley Nature Reserve.

Topic 5: Time-Dependent Behavior

International Nuclear Information System (INIS)

Pfeiffer, P.A.; Tanabe, Tada-aki

1991-01-01

This chapter is a report of the material presented at the International Workshop on Finite Element Analysis of Reinforced Concrete, Session 4 -- Time Dependent Behavior, held at Columbia University, New York on June 3--6, 1991. Dr. P.A. Pfeiffer presented recent developments in time-dependent behavior of concrete and Professor T. Tanabe presented a review of research in Japan on time-dependent behavior of concrete. The chapter discusses the recent research of time-dependent behavior of concrete in the past few years in both the USA-European and Japanese communities. The author appreciates the valuable information provided by Zdenek P. Bazant in preparing the USA-European Research section

Approximations of time-dependent phenomena in quantum mechanics: adiabatic versus sudden processes

International Nuclear Information System (INIS)

Melnichuk, S V; Dijk, W van; Nogami, Y

2005-01-01

By means of a one-dimensional model of a particle in an infinite square-well potential with one wall moving at a constant speed, we examine aspects of time-dependent phenomena in quantum mechanics such as adiabatic and sudden processes. The particle is assumed to be initially in the ground state of the potential with its initial width. The time dependence of the wavefunction of the particle in the well is generally more complicated when the potential well is compressed than when it is expanded. We are particularly interested in the case in which the potential well is suddenly compressed. The so-called sudden approximation is not applicable in this case. We also study the energy of the particle in the changing well as a function of time for expansion and contraction as well as for expansion followed by contraction and vice versa

Quadratic divergences and dimensional regularisation

International Nuclear Information System (INIS)

Jack, I.; Jones, D.R.T.

1990-01-01

We present a detailed analysis of quadratic and quartic divergences in dimensionally regulated renormalisable theories. We perform explicit three-loop calculations for a general theory of scalars and fermions. We find that the higher-order quartic divergences are related to the lower-order ones by the renormalisation group β-functions. (orig.)

Facets for the Cardinality Constrained Quadratic Knapsack Problem and the Quadratic Selective Travelling Salesman Problem

DEFF Research Database (Denmark)

Mak, Vicky; Thomadsen, Tommy

2004-01-01

A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...

Integrated vehicle dynamics control using State Dependent Riccati Equations

NARCIS (Netherlands)

Bonsen, B.; Mansvelders, R.; Vermeer, E.

2010-01-01

In this paper we discuss a State Dependent Riccati Equations (SDRE) solution for Integrated Vehicle Dynamics Control (IVDC). The SDRE approach is a nonlinear variant of the well known Linear Quadratic Regulator (LQR) and implements a quadratic cost function optimization. A modified version of this

Time Dependent Quantum Mechanics

OpenAIRE

Morrison, Peter G.

2012-01-01

We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained finite systems from this formalism. Once this has been achieved we go on to calculate the wavevector as a function of time, in order to demonstrate the use of matrix methods with respect to several concrete examples. Interesting results are derived for elliptic ...

Noisy time-dependent spectra

International Nuclear Information System (INIS)

Shore, B.W.; Eberly, J.H.

1983-01-01

The definition of a time-dependent spectrum registered by an idealized spectrometer responding to a time-varying electromagnetic field as proposed by Eberly and Wodkiewicz and subsequently applied to the spectrum of laser-induced fluorescence by Eberly, Kunasz, and Wodkiewicz is here extended to allow a stochastically fluctuating (interruption model) environment: we provide an algorithm for numerical determination of the time-dependent fluorescence spectrum of an atom subject to excitation by an intense noisy laser and interruptive relaxation

Isotropy of quadratic forms

Indian Academy of Sciences (India)

V. Suresh University Of Hyderabad Hyderabad

2008-10-31

Oct 31, 2008 ... We say that (a1,··· ,an) is a zero of the polynomial f if f (a1,··· ,an) = 0. One of the main problems in Mathematics is to determine whether the given polynomial has a (non-trivial) zero or not. For example, let us recall the Fermat's last theorem: V. Suresh University Of Hyderabad Hyderabad. Isotropy of quadratic ...

The Feynman integral for time-dependent anharmonic oscillators

International Nuclear Information System (INIS)

Grothaus, M.; Khandekar, D.C.; da Silva, J.L.; Streit, L.

1997-01-01

We review some basic notions and results of white noise analysis that are used in the construction of the Feynman integrand as a generalized white noise functional. We show that the Feynman integrand for the time-dependent harmonic oscillator in an external potential is a Hida distribution. copyright 1997 American Institute of Physics

Determination of viscosity through terminal velocity: use of the drag force with a quadratic term in velocity

DEFF Research Database (Denmark)

Vertchenko, Lev; Vertchenko, Larissa

2017-01-01

A correction to the term with quadratic dependency of the velocity in the Oseen´s drag force by a dimensionless factor is proposed in order to determine the viscosity of glycerin through the measurement of the terminal velocity of spheres falling inside the fluid. This factor incorporates the eff...

Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras

Science.gov (United States)

Escobar-Ruiz, Mauricio A.; Kalnins, Ernest G.; Miller, Willar, Jr.; Subag, Eyal

2017-03-01

Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra {so}(4,C) to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of {e}(2,C) and {so}(3,C) and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.

Treatment-time-dependence models of early and delayed radiation injury in rat small intestine

International Nuclear Information System (INIS)

Denham, James W.; Hauer-Jensen, Martin; Kron, Tomas; Langberg, Carl W.

2000-01-01

Background: The present study modeled data from a large series of experiments originally designed to investigate the influence of time, dose, and fractionation on early and late pathologic endpoints in rat small intestine after localized irradiation. The objective was to obtain satisfactory descriptions of the regenerative response to injury together with the possible relationships between early and late endpoints. Methods: Two- and 26-week pathologic radiation injury data in groups of Sprague-Dawley rats irradiated with 27 different fractionation schedules were modeled using the incomplete repair (IR) version of the linear-quadratic model with or without various time correction models. The following time correction models were tested: (1) No time correction; (2) A simple exponential (SE) regenerative response beginning at an arbitrary time after starting treatment; and (3) A bi-exponential response with its commencement linked to accumulated cellular depletion and fraction size (the 'intelligent response model' [INTR]). Goodness of fit of the various models was assessed by correlating the predicted biological effective dose for each dose group with the observed radiation injury score. Results: (1) The incomplete repair model without time correction did not provide a satisfactory description of either the 2- or 26-week data. (2) The models using SE time correction performed better, providing modest descriptions of the data. (3) The INTR model provided reasonable descriptions of both the 2- and 26-week data, confirming a treatment time dependence of both early and late pathological endpoints. (4) The most satisfactory descriptions of the data by the INTR model were obtained when the regenerative response was assumed to cease 2 weeks after irradiation rather than at the end of irradiation. A fraction-size-dependent delay of the regenerative response was also suggested in the best fitting models. (5) Late endpoints were associated with low-fractionation sensitivity

Sinusoidal Parameter Estimation Using Quadratic Interpolation around Power-Scaled Magnitude Spectrum Peaks

Directory of Open Access Journals (Sweden)

Kurt James Werner

2016-10-01

Full Text Available The magnitude of the Discrete Fourier Transform (DFT of a discrete-time signal has a limited frequency definition. Quadratic interpolation over the three DFT samples surrounding magnitude peaks improves the estimation of parameters (frequency and amplitude of resolved sinusoids beyond that limit. Interpolating on a rescaled magnitude spectrum using a logarithmic scale has been shown to improve those estimates. In this article, we show how to heuristically tune a power scaling parameter to outperform linear and logarithmic scaling at an equivalent computational cost. Although this power scaling factor is computed heuristically rather than analytically, it is shown to depend in a structured way on window parameters. Invariance properties of this family of estimators are studied and the existence of a bias due to noise is shown. Comparing to two state-of-the-art estimators, we show that an optimized power scaling has a lower systematic bias and lower mean-squared-error in noisy conditions for ten out of twelve common windowing functions.

New robust chaotic system with exponential quadratic term

International Nuclear Information System (INIS)

Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping

2008-01-01

This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)

Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

Science.gov (United States)

Vaiyavutjamai, Pongchawee; Clements, M. A.

2006-01-01

Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

Quadratic Functionals with General Boundary Conditions

International Nuclear Information System (INIS)

Dosla, Z.; Dosly, O.

1997-01-01

The purpose of this paper is to give the Reid 'Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in terms of Riccati equation solutions

Scheduling with time-dependent execution times

NARCIS (Netherlands)

Woeginger, G.J.

1995-01-01

We consider systems of tasks where the task execution times are time-dependent and where all tasks have some common deadline. We describe how to compute in polynomial time a schedule that minimizes the number of late tasks. This answers a question raised in a recent paper by Ho, Leung and Wei.

Exact results on diffusion in a piecewise linear potential with a time-dependent sink

Energy Technology Data Exchange (ETDEWEB)

Diwaker, E-mail: diwakerphysics@gmail.com [Central University of Himachal Pradesh, School of Physical and Astronomical Sciences (India); Chakraborty, Aniruddha [Indian Institute of Technology Mandi (India)

2016-02-15

The Smoluchowski equation with a time-dependent sink term is solved exactly. In this method, knowing the probability distribution P(0, s) at the origin, allows deriving the probability distribution P(x, s) at all positions. Exact solutions of the Smoluchowski equation are also provided in different cases where the sink term has linear, constant, inverse, and exponential variation in time.

The Time-Dependent Structure of the Electron Reconnection Layer

Science.gov (United States)

Hesse, Michael; Zenitani, Seiji; Kuznetsova, Masha; Klimas, Alex

2009-01-01

Collisionless magnetic reconnection is often associated with time-dependent behavior. Specifically, current layers in the diffusion region can become unstable to tearing-type instabilities on one hand, or to instabilities with current-aligned wave vectors on the other. In the former case, the growth of tearing instabilities typically leads to the production of magnetic islands, which potentially provide feedback on the reconnection process itself, as well as on the rate of reconnection. The second class of instabilities tend to modulate the current layer along the direction of the current flow, for instance generating kink-type perturbations, or smaller-scale turbulence with the potential to broaden the current layer. All of these processes contribute to rendering magnetic reconnection time-dependent. In this presentation, we will provide a summary of these effects, and a discussion of how much they contribute to the overall magnetic reconnection rate.

Geometrical Solutions of Some Quadratic Equations with Non-Real Roots

Science.gov (United States)

Pathak, H. K.; Grewal, A. S.

2002-01-01

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

Concentration- and time-dependent genotoxicity profiles of isoprene monoepoxides and diepoxide, and the cross-linking potential of isoprene diepoxide in cells

Directory of Open Access Journals (Sweden)

Yan Li

2014-01-01

Full Text Available Isoprene, a possible carcinogen, is a petrochemical and a natural product being primarily produced by plants. It is biotransformed to 2-ethenyl-2-methyloxirane (IP-1,2-O and 2-(1-methylethenyloxirane (IP-3,4-O, both of which can be further metabolized to 2-methyl-2,2′-bioxirane (MBO. MBO is mutagenic, but IP-1,2-O and IP-3,4-O are not. While IP-1,2-O has been reported being genotoxic, the genotoxicity of IP-3,4-O and MBO, and the cross-linking potential of MBO have not been examined. In the present study, we used the comet assay to investigate the concentration- and time-dependent genotoxicity profiles of the three metabolites and the cross-linking potential of MBO in human hepatocyte L02 cells. For the incubation time of 1 h, all metabolites showed positive concentration-dependent profiles with a potency rank order of IP-3,4-O > MBO > IP-1,2-O. In human hepatocellular carcinoma (HepG2 and human leukemia (HL60 cells, IP-3,4-O was still more potent in inducing DNA breaks than MBO at high concentrations (>200 μM, although at low concentrations (≤200 μM IP-3,4-O exhibited slightly lower or similar potency to MBO. Interestingly, their time-dependent genotoxicity profiles (0.5–4 h in L02 cells were different from each other: IP-1,2-O and MBO (200 μM exhibited negative and positive profiles, respectively, with IP-3,4-O lying in between, namely, IP-3,4-O-caused DNA breaks did not change over the exposure time. Further experiments demonstrated that hydrolysis of IP-1,2-O contributed to the negative profile and MBO induced cross-links at high concentrations and long incubation times. Collectively, the results suggested that IP-3,4-O might play a significant role in the toxicity of isoprene.

Geometrical and Graphical Solutions of Quadratic Equations.

Science.gov (United States)

Hornsby, E. John, Jr.

1990-01-01

Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)

Solar Potential Analysis and Integration of the Time-Dependent Simulation Results for Semantic 3d City Models Using Dynamizers

Science.gov (United States)

Chaturvedi, K.; Willenborg, B.; Sindram, M.; Kolbe, T. H.

2017-10-01

Semantic 3D city models play an important role in solving complex real-world problems and are being adopted by many cities around the world. A wide range of application and simulation scenarios directly benefit from the adoption of international standards such as CityGML. However, most of the simulations involve properties, whose values vary with respect to time, and the current generation semantic 3D city models do not support time-dependent properties explicitly. In this paper, the details of solar potential simulations are provided operating on the CityGML standard, assessing and estimating solar energy production for the roofs and facades of the 3D building objects in different ways. Furthermore, the paper demonstrates how the time-dependent simulation results are better-represented inline within 3D city models utilizing the so-called Dynamizer concept. This concept not only allows representing the simulation results in standardized ways, but also delivers a method to enhance static city models by such dynamic property values making the city models truly dynamic. The dynamizer concept has been implemented as an Application Domain Extension of the CityGML standard within the OGC Future City Pilot Phase 1. The results are given in this paper.

Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

Science.gov (United States)

Acikmese, Ahmet Behcet; Corless, Martin

2004-01-01

We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

Commuting quantum traces for quadratic algebras

International Nuclear Information System (INIS)

Nagy, Zoltan; Avan, Jean; Doikou, Anastasia; Rollet, Genevieve

2005-01-01

Consistent tensor products on auxiliary spaces, hereafter denoted 'fusion procedures', and commuting transfer matrices are defined for general quadratic algebras, nondynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures then yield integer-indexed families of commuting Hamiltonians

Bound-state Dirac eigenvalues for scalar potentials

International Nuclear Information System (INIS)

Ram, B.; Arafah, M.

1981-01-01

The Dirac equation is solved with a linear and a quadratic scalar potential using an approach in which the Dirac equation is first transformed to a one-dimensional Schroedinger equation with an effective potential. The WKB method is used to obtain the energy eigenvalues. The eigenvalues for the quadratic scalar potential are real just as they are for the linear potential. The results with the linear potential agree well with those obtained by Critchfield. (author)

Resolving Actuator Redundancy - Control Allocation vs. Linear Quadratic Control

OpenAIRE

Härkegård, Ola

2004-01-01

When designing control laws for systems with more inputs than controlled variables, one issue to consider is how to deal with actuator redundancy. Two tools for distributing the control effort among a redundant set of actuators are control allocation and linear quadratic control design. In this paper, we investigate the relationship between these two design tools when a quadratic performance index is used for control allocation. We show that for a particular class of linear systems, they give...

Quadratic Interpolation and Linear Lifting Design

Directory of Open Access Journals (Sweden)

Joel Solé

2007-03-01

Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.

Time-dependent approach to collisional ionization using exterior complex scaling

International Nuclear Information System (INIS)

McCurdy, C. William; Horner, Daniel A.; Rescigno, Thomas N.

2002-01-01

We present a time-dependent formulation of the exterior complex scaling method that has previously been used to treat electron-impact ionization of the hydrogen atom accurately at low energies. The time-dependent approach solves a driven Schroedinger equation, and scales more favorably with the number of electrons than the original formulation. The method is demonstrated in calculations for breakup processes in two dimensions (2D) and three dimensions for systems involving short-range potentials and in 2D for electron-impact ionization in the Temkin-Poet model for electron-hydrogen atom collisions

The cyclicity of period annulus of a quadratic reversible Lotka–Volterra system

International Nuclear Information System (INIS)

Li, Chengzhi; Llibre, Jaume

2009-01-01

We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka–Volterra differential system, inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles

Energy dependence of nonlocal optical potentials

Science.gov (United States)

Lovell, A. E.; Bacq, P.-L.; Capel, P.; Nunes, F. M.; Titus, L. J.

2017-11-01

Recently, a variety of studies have shown the importance of including nonlocality in the description of reactions. The goal of this work is to revisit the phenomenological approach to determining nonlocal optical potentials from elastic scattering. We perform a χ2 analysis of neutron elastic scattering data off 40Ca, 90Zr, and 208Pb at energies E ≈5 -40 MeV, assuming a Perey and Buck [Nucl. Phys. 32, 353 (1962), 10.1016/0029-5582(62)90345-0] or Tian et al. [Int. J. Mod. Phys. E 24, 1550006 (2015), 10.1142/S0218301315500068] nonlocal form for the optical potential. We introduce energy and asymmetry dependencies in the imaginary part of the potential and refit the data to obtain a global parametrization. Independently of the starting point in the minimization procedure, an energy dependence in the imaginary depth is required for a good description of the data across the included energy range. We present two parametrizations, both of which represent an improvement over the original potentials for the fitted nuclei as well as for other nuclei not included in our fit. Our results show that, even when including the standard Gaussian nonlocality in optical potentials, a significant energy dependence is required to describe elastic-scattering data.

Quadratic contributions of softly broken supersymmetry in the light of loop regularization

Energy Technology Data Exchange (ETDEWEB)

Bai, Dong [Chinese Academy of Sciences, Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences, School of Physical Sciences, Beijing (China); Wu, Yue-Liang [Chinese Academy of Sciences, Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Beijing (China); International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); University of Chinese Academy of Sciences, School of Physical Sciences, Beijing (China)

2017-09-15

Loop regularization (LORE) is a novel regularization scheme in modern quantum field theories. It makes no change to the spacetime structure and respects both gauge symmetries and supersymmetry. As a result, LORE should be useful in calculating loop corrections in supersymmetry phenomenology. To further demonstrate its power, in this article we revisit in the light of LORE the old issue of the absence of quadratic contributions (quadratic divergences) in softly broken supersymmetric field theories. It is shown explicitly by Feynman diagrammatic calculations that up to two loops the Wess-Zumino model with soft supersymmetry breaking terms (WZ' model), one of the simplest models with the explicit supersymmetry breaking, is free of quadratic contributions. All the quadratic contributions cancel with each other perfectly, which is consistent with results dictated by the supergraph techniques. (orig.)

On quadratic residue codes and hyperelliptic curves

Directory of Open Access Journals (Sweden)

David Joyner

2008-01-01

Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''

Designing Camera Networks by Convex Quadratic Programming

KAUST Repository

Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao

2015-01-01

be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution

Solving symmetric-definite quadratic lambda-matrix problems without factorization

International Nuclear Information System (INIS)

Scott, D.S.; Ward, R.C.

1982-01-01

Algorithms are presented for computing some of the eigenvalues and their associated eigenvectors of the quadratic lambda-matrix M lambda 2 C lambda + K. M, C, and K are assumed to have special symmetry-type properties which insure that theory analogous to the standard symmetric eigenproblem exists. The algorithms are based on a generalization of the Rayleigh quotient and the Lanczos method for computing eigenpairs of standard symmetric eigenproblems. Monotone quadratic convergence of the basic method is proved. Test examples are presented

Comparing of the Reaction Time in Substance-Dependent and Non-Dependent Individuals

Directory of Open Access Journals (Sweden)

Mohammad Narimani

2012-11-01

Full Text Available Aim: The aim of this study was to compare the simple, selective, and discrimination reaction time in substance-dependent and non-dependent individuals. Method: In this causal-comparative study, the population included of 425 males (opium and crystal dependents who were referred to addiction rehabilitation centers in Tabriz. By random sampling, 16 opium dependents, 16 crystal dependents, and 16 non-dependent individuals with no history of dependency as the compare group were selected. All groups peered in age, and marital status. For gathering data, “Addicts Admit Questionnaire” and laboratory device known as the "Reaction Time Assay" have been used. Results: The results of this study showed that there are significant differences among all groups in simple reaction time, choice reaction time and reaction time to auditory stimuli, but no significant difference in discrimination reaction time and reaction time to visual stimulus observed. Conclusion: The reaction time of substance-dependent groups is slower than non-dependent groups.

Nuclear three-body problem and energy-dependent potentials

International Nuclear Information System (INIS)

Abdurakhmanov, A.; Akhmadkhodzhaev, B.; Zubarev, A.L.; Irgaziev, B.F.

1985-01-01

Energy-dependent potentials in the three-body problem are being considered. Three-particle equations for the case of pairing energy-dependent potentials are generalized and the problems related to this ambiguous generalization are investigated. In terms of the equations obtained the tritium binding energy and vertex coupling constants (Tdn) and (Tdν) are evaluated. The binding energy and, especially, coupling constants are shown to be sensitive to a shape of the energy-dependent potential

Riccati and Ermakov Equations in Time-Dependent and Time-Independent Quantum Systems

Directory of Open Access Journals (Sweden)

Dieter Schuch

2008-05-01

Full Text Available The time-evolution of the maximum and the width of exact analytic wave packet (WP solutions of the time-dependent Schrödinger equation (SE represents the particle and wave aspects, respectively, of the quantum system. The dynamics of the maximum, located at the mean value of position, is governed by the Newtonian equation of the corresponding classical problem. The width, which is directly proportional to the position uncertainty, obeys a complex nonlinear Riccati equation which can be transformed into a real nonlinear Ermakov equation. The coupled pair of these equations yields a dynamical invariant which plays a key role in our investigation. It can be expressed in terms of a complex variable that linearizes the Riccati equation. This variable also provides the time-dependent parameters that characterize the Green's function, or Feynman kernel, of the corresponding problem. From there, also the relation between the classical and quantum dynamics of the systems can be obtained. Furthermore, the close connection between the Ermakov invariant and the Wigner function will be shown. Factorization of the dynamical invariant allows for comparison with creation/annihilation operators and supersymmetry where the partner potentials fulfil (real Riccati equations. This provides the link to a nonlinear formulation of time-independent quantum mechanics in terms of an Ermakov equation for the amplitude of the stationary state wave functions combined with a conservation law. Comparison with SUSY and the time-dependent problems concludes our analysis.

Schur Stability Regions for Complex Quadratic Polynomials

Science.gov (United States)

Cheng, Sui Sun; Huang, Shao Yuan

2010-01-01

Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

A Novel Single Switch Transformerless Quadratic DC/DC Buck-Boost Converter

DEFF Research Database (Denmark)

Mostaan, Ali; A. Gorji, Saman; N. Soltani, Mohsen

2017-01-01

A novel quadratic buck-boost DC/DC converter is presented in this study. The proposed converter utilizes only one active switch and can step-up/down the input voltage, while the existing single switch quadratic buck/boost converters can only work in step-up or step-down mode. First, the proposed ...

Dynamics of a bright soliton in Bose-Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential

International Nuclear Information System (INIS)

Liang, Z.X.; Zhang, Z.D.; Liu, W.M.

2005-01-01

We present a family of exact solutions of the one-dimensional nonlinear Schroedinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background

On a quadratic inverse eigenvalue problem

International Nuclear Information System (INIS)

Cai, Yunfeng; Xu, Shufang

2009-01-01

This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable

Large N saddle formulation of quadratic building block theories

International Nuclear Information System (INIS)

Halpern, M.B.

1980-01-01

I develop a large N saddle point formulation for the broad class of 'theories of quadratic building blocks'. Such theories are those on which the sums over internal indices are contained in quadratic building blocks, e.g. PHI 2 = Σsup(N)sub(a-1)PHi sup(a)sup(a). The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N. (orig.)

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

International Nuclear Information System (INIS)

Lo, C.F.

2009-01-01

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schroedinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for some parametric moving boundaries as well. (general)

Universality of quadratic to linear magnetoresistance crossover in disordered conductors

Science.gov (United States)

Lara, Silvia; Ramakrishnan, Navneeth; Lai, Ying Tong; Adam, Shaffique

Many experiments measuring Magnetoresistance (MR) showed unsaturating linear behavior at high magnetic fields and quadratic behavior at low fields. In the literature, two very different theoretical models have been used to explain this classical MR as a consequence of sample disorder. The phenomenological Random Resistor Network (RRN) model constructs a grid of four-terminal resistors each with a varying random resistance. The Effective Medium Theory (EMT) model imagines a smoothly varying disorder potential that causes a continuous variation of the local conductivity. In this theoretical work, we demonstrate numerically that both the RRN and EMT models belong to the same universality class, and that a single parameter (the ratio of the fluctuations in the carrier density to the average carrier density) completely determines both the magnitude of the MR and the B-field scale for the crossover from quadratic to linear MR. By considering several experimental data sets in the literature, ranging from thin films of InSb to graphene to Weyl semimetals like Na3Bi, we show that this disorder-induced mechanism for MR is in good agreement with the experiments, and that this comparison of MR with theory reveals information about the spatial carrier density inhomogeneity. This work was supported by the National Research Foundation of Singapore (NRF-NRFF2012-01).

The Quadratic Selective Travelling Salesman Problem

DEFF Research Database (Denmark)

Thomadsen, Tommy; Stidsen, Thomas K.

2003-01-01

A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025

On Quadratic Variation of Martingales

Indian Academy of Sciences (India)

where D ( [ 0 , ∞ ) , R ) denotes the class of real valued r.c.l.l. functions on [ 0 , ∞ ) such that for a locally square integrable martingale ( M t ) with r.c.l.l. paths,. Ψ ( M . ( ) ) = A . ( ). gives the quadratic variation process (written usually as [ M , M ] t ) of ( M t ) . We also show that this process ( A t ) is the unique increasing ...

Exact solutions to quadratic gravity

Czech Academy of Sciences Publication Activity Database

Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.

2017-01-01

Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025

Hydrodynamic perspective on memory in time-dependent density-functional theory

International Nuclear Information System (INIS)

Thiele, M.; Kuemmel, S.

2009-01-01

The adiabatic approximation of time-dependent density-functional theory is studied in the context of nonlinear excitations of two-electron singlet systems. We compare the exact time evolution of these systems to the adiabatically exact one obtained from time-dependent Kohn-Sham calculations relying on the exact ground-state exchange-correlation potential. Thus, we can show under which conditions the adiabatic approximation breaks down and memory effects become important. The hydrodynamic formulation of quantum mechanics allows us to interpret these results and relate them to dissipative effects in the Kohn-Sham system. We show how the breakdown of the adiabatic approximation can be inferred from the rate of change of the ground-state noninteracting kinetic energy.

Constraints on cosmological birefringence energy dependence from CMB polarization data

International Nuclear Information System (INIS)

Gubitosi, G.; Paci, F.

2013-01-01

We study the possibility of constraining the energy dependence of cosmological birefringence by using CMB polarization data. We consider four possible behaviors, characteristic of different theoretical scenarios: energy-independent birefringence motivated by Chern-Simons interactions of the electromagnetic field, linear energy dependence motivated by a 'Weyl' interaction of the electromagnetic field, quadratic energy dependence, motivated by quantum gravity modifications of low-energy electrodynamics, and inverse quadratic dependence, motivated by Faraday rotation generated by primordial magnetic fields. We constrain the parameters associated to each kind of dependence and use our results to give constraints on the models mentioned. We forecast the sensitivity that Planck data will be able to achieve in this respect

Visualizing Influential Observations in Dependent Data

KAUST Repository

Genton, Marc G.

2010-01-01

We introduce the hair-plot to visualize influential observations in dependent data. It consists of all trajectories of the value of an estimator when each observation is modified in turn by an additive perturbation. We define two measures of influence: the local influence which describes the rate of departure from the original estimate due to a small perturbation of each observation; and the asymptotic influence which indicates the influence on the original estimate of the most extreme contamination for each observation. The cases of estimators defined as quadratic forms or ratios of quadratic forms are investigated in detail. Sample autocovariances, covariograms, and variograms belong to the first case. Sample autocorrelations, correlograms, and indices of spatial autocorrelation such as Moran\\'s I belong to the second case.We illustrate our approach on various datasets from time series analysis and spatial statistics. This article has supplementary material online. © 2010 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

Numerical Methods for Solution of the Extended Linear Quadratic Control Problem

DEFF Research Database (Denmark)

Jørgensen, John Bagterp; Frison, Gianluca; Gade-Nielsen, Nicolai Fog

2012-01-01

In this paper we present the extended linear quadratic control problem, its efficient solution, and a discussion of how it arises in the numerical solution of nonlinear model predictive control problems. The extended linear quadratic control problem is the optimal control problem corresponding...... to the Karush-Kuhn-Tucker system that constitute the majority of computational work in constrained nonlinear and linear model predictive control problems solved by efficient MPC-tailored interior-point and active-set algorithms. We state various methods of solving the extended linear quadratic control problem...... and discuss instances in which it arises. The methods discussed in the paper have been implemented in efficient C code for both CPUs and GPUs for a number of test examples....

Estimating nonlinear selection gradients using quadratic regression coefficients: double or nothing?

Science.gov (United States)

Stinchcombe, John R; Agrawal, Aneil F; Hohenlohe, Paul A; Arnold, Stevan J; Blows, Mark W

2008-09-01

The use of regression analysis has been instrumental in allowing evolutionary biologists to estimate the strength and mode of natural selection. Although directional and correlational selection gradients are equal to their corresponding regression coefficients, quadratic regression coefficients must be doubled to estimate stabilizing/disruptive selection gradients. Based on a sample of 33 papers published in Evolution between 2002 and 2007, at least 78% of papers have not doubled quadratic regression coefficients, leading to an appreciable underestimate of the strength of stabilizing and disruptive selection. Proper treatment of quadratic regression coefficients is necessary for estimation of fitness surfaces and contour plots, canonical analysis of the gamma matrix, and modeling the evolution of populations on an adaptive landscape.

Time-Dependent Behaviors of Granite: Loading-Rate Dependence, Creep, and Relaxation

Science.gov (United States)

Hashiba, K.; Fukui, K.

2016-07-01

To assess the long-term stability of underground structures, it is important to understand the time-dependent behaviors of rocks, such as their loading-rate dependence, creep, and relaxation. However, there have been fewer studies on crystalline rocks than on tuff, mudstone, and rock salt, because the high strength of crystalline rocks makes the detection of their time-dependent behaviors much more difficult. Moreover, studies on the relaxation, temporal change of stress and strain (TCSS) conditions, and relations between various time-dependent behaviors are scarce for not only granites, but also other rocks. In this study, previous reports on the time-dependent behaviors of granites were reviewed and various laboratory tests were conducted using Toki granite. These tests included an alternating-loading-rate test, creep test, relaxation test, and TCSS test. The results showed that the degree of time dependence of Toki granite is similar to other granites, and that the TCSS resembles the stress-relaxation curve and creep-strain curve. A viscoelastic constitutive model, proposed in a previous study, was modified to investigate the relations between the time-dependent behaviors in the pre- and post-peak regions. The modified model reproduced the stress-strain curve, creep, relaxation, and the results of the TCSS test. Based on a comparison of the results of the laboratory tests and numerical simulations, close relations between the time-dependent behaviors were revealed quantitatively.

A comparison of three time-dependent wave packet methods for calculating electron--atom elastic scattering cross sections

International Nuclear Information System (INIS)

Judson, R.S.; McGarrah, D.B.; Sharafeddin, O.A.; Kouri, D.J.; Hoffman, D.K.

1991-01-01

We compare three time-dependent wave packet methods for performing elastic scattering calculations from screened Coulomb potentials. The three methods are the time-dependent amplitude density method (TDADM), what we term a Cayley-transform method (CTM), and the Chebyshev propagation method of Tal-Ezer and Kosloff. Both the TDADM and the CTM are based on a time-dependent integral equation for the wave function. In the first, we propagate the time-dependent amplitude density, |ζ(t)right-angle=U|ψ(t)right-angle, where U is the interaction potential and |ψ(t)right-angle is the usual time-dependent wave function. In the other two, the wave function is propagated. As a numerical example, we calculate phase shifts and cross sections using a screened Coulomb, Yukawa type potential over the range 200--1000 eV. One of the major advantages of time-dependent methods such as these is that we get scattering information over this entire range of energies from one propagation. We find that in most cases, all three methods yield comparable accuracy and are about equally efficient computationally. However for l=0, where the Coulomb well is not screened by the centrifugal potential, the TDADM requires smaller grid spacings to maintain accuracy

Quantum tomography and classical propagator for quadratic quantum systems

International Nuclear Information System (INIS)

Man'ko, O.V.

1999-03-01

The classical propagator for tomographic probability (which describes the quantum state instead of wave function or density matrix) is presented for quadratic quantum systems and its relation to the quantum propagator is considered. The new formalism of quantum mechanics, based on the probability representation of the state, is applied to particular quadratic systems - the harmonic oscillator, particle's free motion, problems of an ion in a Paul trap and in asymmetric Penning trap, and to the process of stimulated Raman scattering. The classical propagator for these systems is written in an explicit form. (author)

Competing risks and time-dependent covariates

DEFF Research Database (Denmark)

Cortese, Giuliana; Andersen, Per K

2010-01-01

Time-dependent covariates are frequently encountered in regression analysis for event history data and competing risks. They are often essential predictors, which cannot be substituted by time-fixed covariates. This study briefly recalls the different types of time-dependent covariates......, as classified by Kalbfleisch and Prentice [The Statistical Analysis of Failure Time Data, Wiley, New York, 2002] with the intent of clarifying their role and emphasizing the limitations in standard survival models and in the competing risks setting. If random (internal) time-dependent covariates...

Using Localised Quadratic Functions on an Irregular Grid for Pricing High-Dimensional American Options

NARCIS (Netherlands)

Berridge, S.J.; Schumacher, J.M.

2004-01-01

We propose a method for pricing high-dimensional American options on an irregular grid; the method involves using quadratic functions to approximate the local effect of the Black-Scholes operator.Once such an approximation is known, one can solve the pricing problem by time stepping in an explicit

Time-dependent gravitating solitons in five dimensional warped space-times

CERN Document Server

Giovannini, Massimo

2007-01-01

Time-dependent soliton solutions are explicitly derived in a five-dimensional theory endowed with one (warped) extra-dimension. Some of the obtained geometries, everywhere well defined and technically regular, smoothly interpolate between two five-dimensional anti-de Sitter space-times for fixed value of the conformal time coordinate. Time dependent solutions containing both topological and non-topological sectors are also obtained. Supplementary degrees of freedom can be also included and, in this case, the resulting multi-soliton solutions may describe time-dependent kink-antikink systems.

A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

Directory of Open Access Journals (Sweden)

Yong Li

2014-01-01

Full Text Available The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features.

Time-dependent crack growth in Alloy 718: An interim assessment

International Nuclear Information System (INIS)

James, L.A.

1982-08-01

Previous results on the time-dependent nature of fatigue-crack propagation (FCP) in Alloy 718 at elevated temperatures were reviewed. Additional experiments were conducted to further define certain aspects of the time-dependent crack growth behavior. it was found that loading waveform influenced FCP behavior, with tensile hold-times producing higher growth rates than continuous cycling at the same frequency. Crack growth rates under hold-time conditions tended to increase with decreasing grain size. Finally, experiments were conducted which tended to cast some doubt upon the ability of linear-elastic fracture mechanics (LEFM) techniques to characterize cracking behavior in this alloy under hold-time conditions. However, since a superior correlating parameter has not yet been proven, it is suggested that LEFM methods be used in the interim with appropriate safety factors to account for the potential errors. 34 refs., 10 figs., 4 tabs

Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views

Science.gov (United States)

Aziz, T. A.; Pramudiani, P.; Purnomo, Y. W.

2018-01-01

Difference between quadratic equation and quadratic function as perceived by Indonesian pre-service secondary mathematics teachers (N = 55) who enrolled at one private university in Jakarta City was investigated. Analysis of participants’ written responses and interviews were conducted consecutively. Participants’ written responses highlighted differences between quadratic equation and function by referring to their general terms, main characteristics, processes, and geometrical aspects. However, they showed several obstacles in describing the differences such as inappropriate constraints and improper interpretations. Implications of the study are discussed.

Exploiting Group Symmetry in Semidefinite Programming Relaxations of the Quadratic Assignment Problem

NARCIS (Netherlands)

de Klerk, E.; Sotirov, R.

2007-01-01

We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E. Burkard,

Staff turnover in hotels : exploring the quadratic and linear relationships.

OpenAIRE

Mohsin, A.; Lengler, J.F.B.; Aguzzoli, R.L.

2015-01-01

The aim of this study is to assess whether the relationship between intention to leave the job and its antecedents is quadratic or linear. To explore those relationships a theoretical model (see Fig. 1) and eight hypotheses are proposed. Each linear hypothesis is followed by an alternative quadratic hypothesis. The alternative hypotheses propose that the relationship between the four antecedent constructs and intention to leave the job might not be linear, as the existing literature suggests....

A method for untriggered time-dependent searches for multiple flares from neutrino point sources

International Nuclear Information System (INIS)

Gora, D.; Bernardini, E.; Cruz Silva, A.H.

2011-04-01

A method for a time-dependent search for flaring astrophysical sources which can be potentially detected by large neutrino experiments is presented. The method uses a time-clustering algorithm combined with an unbinned likelihood procedure. By including in the likelihood function a signal term which describes the contribution of many small clusters of signal-like events, this method provides an effective way for looking for weak neutrino flares over different time-scales. The method is sensitive to an overall excess of events distributed over several flares which are not individually detectable. For standard cases (one flare) the discovery potential of the method is worse than a standard time-dependent point source analysis with unknown duration of the flare by a factor depending on the signal-to-background level. However, for flares sufficiently shorter than the total observation period, the method is more sensitive than a time-integrated analysis. (orig.)

A method for untriggered time-dependent searches for multiple flares from neutrino point sources

Energy Technology Data Exchange (ETDEWEB)

Gora, D. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Institute of Nuclear Physics PAN, Cracow (Poland); Bernardini, E.; Cruz Silva, A.H. [Institute of Nuclear Physics PAN, Cracow (Poland)

2011-04-15

A method for a time-dependent search for flaring astrophysical sources which can be potentially detected by large neutrino experiments is presented. The method uses a time-clustering algorithm combined with an unbinned likelihood procedure. By including in the likelihood function a signal term which describes the contribution of many small clusters of signal-like events, this method provides an effective way for looking for weak neutrino flares over different time-scales. The method is sensitive to an overall excess of events distributed over several flares which are not individually detectable. For standard cases (one flare) the discovery potential of the method is worse than a standard time-dependent point source analysis with unknown duration of the flare by a factor depending on the signal-to-background level. However, for flares sufficiently shorter than the total observation period, the method is more sensitive than a time-integrated analysis. (orig.)

Time-dependent field equations for paraxial relativistic electron beams: Beam Research Program

International Nuclear Information System (INIS)

Sharp, W.M.; Yu, S.S.; Lee, E.P.

1987-01-01

A simplified set of field equations for a paraxial relativistic electron beam is presented. These equations for the beam electrostatic potential phi and pinch potential Phi identical to A/sub z/ - phi retain previously neglected time-dependent terms and for axisymmetric beams reduce exactly to Maxwell's equations

orthogonal and scaling transformations of quadratic functions

African Journals Online (AJOL)

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functions of sub-problems of various nonlinear programming problems that employ methods such as sequential quadratic programming and trust-region methods (Sorensen, 1982; Eldersveld,. 1991; Nocedal and Wright, 1999). Various problems in Algebra, Functional Analysis,. Analytic Geometry and Computational Mathe-.

Smoothing optimization of supporting quadratic surfaces with Zernike polynomials

Science.gov (United States)

Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu

2018-03-01

A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.

Are ghost surfaces quadratic-flux-minimizing?

International Nuclear Information System (INIS)

Hudson, S.R.; Dewar, R.L.

2009-01-01

Two candidates for 'almost-invariant' toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest descent of magnetic action, ∫A.dl. A generalized Hamiltonian definition of ghost surfaces is given and specialized to the usual Lagrangian definition. A modified Hamilton's Principle is introduced that allows the use of Lagrangian integration for calculation of the QFMin pseudo-orbits. Numerical calculations show QFMin and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field perturbed from an integrable case, and this is explained using a perturbative construction of an auxiliary poloidal angle for which QFMin and Lagrangian ghost surfaces are the same up to second order. While presented in the context of 3-dimensional magnetic field line systems, the concepts are applicable to defining almost-invariant tori in other 11/2 degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.

Time and frequency-dependent modulation of local field potential synchronization by deep brain stimulation.

Directory of Open Access Journals (Sweden)

Clinton B McCracken

Full Text Available High-frequency electrical stimulation of specific brain structures, known as deep brain stimulation (DBS, is an effective treatment for movement disorders, but mechanisms of action remain unclear. We examined the time-dependent effects of DBS applied to the entopeduncular nucleus (EP, the rat homolog of the internal globus pallidus, a target used for treatment of both dystonia and Parkinson's disease (PD. We performed simultaneous multi-site local field potential (LFP recordings in urethane-anesthetized rats to assess the effects of high-frequency (HF, 130 Hz; clinically effective, low-frequency (LF, 15 Hz; ineffective and sham DBS delivered to EP. LFP activity was recorded from dorsal striatum (STR, ventroanterior thalamus (VA, primary motor cortex (M1, and the stimulation site in EP. Spontaneous and acute stimulation-induced LFP oscillation power and functional connectivity were assessed at baseline, and after 30, 60, and 90 minutes of stimulation. HF EP DBS produced widespread alterations in spontaneous and stimulus-induced LFP oscillations, with some effects similar across regions and others occurring in a region- and frequency band-specific manner. Many of these changes evolved over time. HF EP DBS produced an initial transient reduction in power in the low beta band in M1 and STR; however, phase synchronization between these regions in the low beta band was markedly suppressed at all time points. DBS also enhanced low gamma synchronization throughout the circuit. With sustained stimulation, there were significant reductions in low beta synchronization between M1-VA and STR-VA, and increases in power within regions in the faster frequency bands. HF DBS also suppressed the ability of acute EP stimulation to induce beta oscillations in all regions along the circuit. This dynamic pattern of synchronizing and desynchronizing effects of EP DBS suggests a complex modulation of activity along cortico-BG-thalamic circuits underlying the therapeutic

Permanent vegetation quadrats on Olkiluoto island. Establishment and results from the first inventory

Energy Technology Data Exchange (ETDEWEB)

Huhta, A.P.; Korpela, L. [Finnish Forest Research Institute, Helsinki (Finland)

2006-05-15

This report describes in detail the vegetation quadrats established inside the permanent, follow-up sample plots (Forest Extensive High-level monitoring plots, FEH) on Olkiluoto Island. During summer 2005 a total of 94 sample plots (a 30 m{sup 2}), each containing eight quadrats (a 1m{sup 2}), were investigated. The total number of sampled quadrats was 752. Seventy of the 94 plots represent coniferous stands: 57 Norway spruce-dominated and 13 Scots pine-dominated stands. Ten of the plots represent deciduous, birch-dominated (Betula spp.) stands, 7 plots common alder-dominated (Alnus glutinosa) stands, and seven plots are mires. The majority of the coniferous tree stands were growing on sites representing various succession stages of the Myrtillus, Vaccinium-Myrtillus and Deschampsia-Myrtillus forest site types. The pine-dominated stands growing on exposed bedrock clearly differed from the other coniferous stands: the vegetation was characterised by the Cladina, Calluna-Cladina and Empetrum-Vaccinium vitis-idaea/Vaccinium Myrtillus forest site types. The deciduous stands were characterized by tall grasses, especially Calamagrostis epigejos, C. purpurea and Deschampsia flexuosa. The vegetation of the deciduous stands dominated by common alder represented grove-like sites and seashore groves. Typical species for mires included Calamagrostis purpurea, Calla palustris, Equisetum sylvaticum, and especially white mosses (Sphagnum spp.). A total of 184 vascular plant species were found growing within the quadrats. Due to the high number of quadrats in these forests, the spruce stands had the highest total number of species, but the birch and alder-dominated forests had the highest average number of species per quadrat. This basic inventory of the permanent vegetation quadrats on Olkiluoto Island provides a sound starting point for future vegetation surveys. Guidelines for future inventories and supplementary sampling are given in the discussion part of this report. (orig.)

Permanent vegetation quadrats on Olkiluoto island. Establishment and results from the first inventory

International Nuclear Information System (INIS)

Huhta, A.P.; Korpela, L.

2006-05-01

This report describes in detail the vegetation quadrats established inside the permanent, follow-up sample plots (Forest Extensive High-level monitoring plots, FEH) on Olkiluoto Island. During summer 2005 a total of 94 sample plots (a 30 m 2 ), each containing eight quadrats (a 1m 2 ), were investigated. The total number of sampled quadrats was 752. Seventy of the 94 plots represent coniferous stands: 57 Norway spruce-dominated and 13 Scots pine-dominated stands. Ten of the plots represent deciduous, birch-dominated (Betula spp.) stands, 7 plots common alder-dominated (Alnus glutinosa) stands, and seven plots are mires. The majority of the coniferous tree stands were growing on sites representing various succession stages of the Myrtillus, Vaccinium-Myrtillus and Deschampsia-Myrtillus forest site types. The pine-dominated stands growing on exposed bedrock clearly differed from the other coniferous stands: the vegetation was characterised by the Cladina, Calluna-Cladina and Empetrum-Vaccinium vitis-idaea/Vaccinium Myrtillus forest site types. The deciduous stands were characterized by tall grasses, especially Calamagrostis epigejos, C. purpurea and Deschampsia flexuosa. The vegetation of the deciduous stands dominated by common alder represented grove-like sites and seashore groves. Typical species for mires included Calamagrostis purpurea, Calla palustris, Equisetum sylvaticum, and especially white mosses (Sphagnum spp.). A total of 184 vascular plant species were found growing within the quadrats. Due to the high number of quadrats in these forests, the spruce stands had the highest total number of species, but the birch and alder-dominated forests had the highest average number of species per quadrat. This basic inventory of the permanent vegetation quadrats on Olkiluoto Island provides a sound starting point for future vegetation surveys. Guidelines for future inventories and supplementary sampling are given in the discussion part of this report. (orig.)

Photon–phonon parametric oscillation induced by quadratic coupling in an optomechanical resonator

International Nuclear Information System (INIS)

Zhang, Lin; Ji, Fengzhou; Zhang, Xu; Zhang, Weiping

2017-01-01

A direct photon–phonon parametric effect of quadratic coupling on the mean-field dynamics of an optomechanical resonator in the large-scale-movement regime is found and investigated. Under a weak pumping power, the mechanical resonator damps to a steady state with a nonlinear static response sensitively modified by the quadratic coupling. When the driving power increases beyond the static energy balance, the steady states lose their stabilities via Hopf bifurcations, and the resonator produces stable self-sustained oscillation (limit-circle behavior) of discrete energies with step-like amplitudes due to the parametric effect of quadratic coupling, which can be understood roughly by the power balance between gain and loss on the resonator. A further increase in the pumping power can induce a chaotic dynamic of the resonator via a typical routine of period-doubling bifurcation, but which can be stabilized by the parametric effect through an inversion-bifurcation process back to the limit-circle states. The bifurcation-to-inverse-bifurcation transitions are numerically verified by the maximal Lyapunov exponents of the dynamics, which indicate an efficient way of suppressing the chaotic behavior of the optomechanical resonator by quadratic coupling. Furthermore, the parametric effect of quadratic coupling on the dynamic transitions of an optomechanical resonator can be conveniently detected or traced by the output power spectrum of the cavity field. (paper)

STABILIZED SEQUENTIAL QUADRATIC PROGRAMMING: A SURVEY

Directory of Open Access Journals (Sweden)

Damián Fernández

2014-12-01

Full Text Available We review the motivation for, the current state-of-the-art in convergence results, and some open questions concerning the stabilized version of the sequential quadratic programming algorithm for constrained optimization. We also discuss the tools required for its local convergence analysis, globalization challenges, and extentions of the method to the more general variational problems.

TUNING PARAMETER LINEAR QUADRATIC TRACKING MENGGUNAKAN ALGORITMA GENETIKA UNTUK PENGENDALIAN GERAK LATERAL QUADCOPTER

Directory of Open Access Journals (Sweden)

Farid Choirul Akbar

2016-04-01

Full Text Available Gerakan lateral quadcopter dapat dilakukan apabila quadcopter dapat menjaga kestabilan pada saat hover, sehingga quadcopter dapat melakukan gerak rotasi. Perubahan sudut roll akan mengakibatkan gerak translasi pada sumbu Y, sedangkan perubahan sudut pitch akan mengakibatkan gerak translasi pada sumbu X. Disisi lain, quadcopter merupakan suatu sistem non-linear dan memiliki kestabilan yang rendah sehingga rentan terhadap gangguan. Pada penelitian Tugas Akhir ini dirancang pengendalian gerak rotasi quadcopter menggunakan Linear Quadratic Regulator (LQR dan Linear Quadratic Tracking (LQT untuk pengendalian gerak translasi. Untuk mendapatkan parameter dari LQT digunakan Algoritma Genetika (GA. Hasil tuning GA yang digunakan pada LQT memiliki nilai Qx 700,1884, nilai Qy 700,6315, nilai Rx 0,1568, dan  nilai Ry 0,1579. Respon LQT tersebut memiliki RMSE pada sumbu X dan sumbu Y sebesar 1,99 % serta memiliki time lagging 0,35 detik. Dengan hasil tersebut quadcopter mampu men-tracking trajectory berbentuk segitigaTekni

Quaternion orders, quadratic forms, and Shimura curves

CERN Document Server

Alsina, Montserrat

2004-01-01

Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...

Some notes on time dependent Thomas Fermi approximation

International Nuclear Information System (INIS)

Holzwarth, G.

1979-01-01

The successful use of effective density-dependent potentials in static Hartree-Fock calculations for nuclear ground-state properties has led to the question whether it is possible to obtain significant further simplification by approximating also the kinetic energy part of the ground state energy by a functional of the local density alone. The great advantage of such an approach is that its complexity is independent of particle number; the size of the system enters only through parameters, Z and N. The simple 'extended Thomas Fermi' functionals are based on the assumption of a spherically symmetric local Fermi surface throughout the nucleus and they represent the 'liquid drop' part of the static total energy. Given this static formalism which is solved directly for the local density without considering individual particles one might ask for a possible dynamical extension in the same sense as TDHF is a dynamical extension of the static HF approach. The aim of such a Time Dependent Thomas Fermi (TDTF) approximation would be to determine directly the time-dependent local single-particle density from given initial conditions and the single-particle current density without following each particle on its individual orbit

Unit-time scheduling problems with time dependent resources

NARCIS (Netherlands)

Tautenhahn, T.; Woeginger, G.

1997-01-01

We investigate the computational complexity of scheduling problems, where the operations consume certain amounts of renewable resources which are available in time-dependent quantities. In particular, we consider unit-time open shop problems and unit-time scheduling problems with identical parallel

Permeability dependence of streaming potential coefficient in porous media

NARCIS (Netherlands)

Thanh, L.D.; Sprik, R.

2015-01-01

In theory, the streaming potential coefficient depends not only on the zeta potential but also on the permeability of the rocks that partially determines the surface conductivity of the rocks. However, in practice, it is hard to show the permeability dependence of streaming potential coefficients

Models for dependent time series

CERN Document Server

Tunnicliffe Wilson, Granville; Haywood, John

2015-01-01

Models for Dependent Time Series addresses the issues that arise and the methodology that can be applied when the dependence between time series is described and modeled. Whether you work in the economic, physical, or life sciences, the book shows you how to draw meaningful, applicable, and statistically valid conclusions from multivariate (or vector) time series data.The first four chapters discuss the two main pillars of the subject that have been developed over the last 60 years: vector autoregressive modeling and multivariate spectral analysis. These chapters provide the foundational mater

Numerical solution of large nonlinear boundary value problems by quadratic minimization techniques

International Nuclear Information System (INIS)

Glowinski, R.; Le Tallec, P.

1984-01-01

The objective of this paper is to describe the numerical treatment of large highly nonlinear two or three dimensional boundary value problems by quadratic minimization techniques. In all the different situations where these techniques were applied, the methodology remains the same and is organized as follows: 1) derive a variational formulation of the original boundary value problem, and approximate it by Galerkin methods; 2) transform this variational formulation into a quadratic minimization problem (least squares methods) or into a sequence of quadratic minimization problems (augmented lagrangian decomposition); 3) solve each quadratic minimization problem by a conjugate gradient method with preconditioning, the preconditioning matrix being sparse, positive definite, and fixed once for all in the iterative process. This paper will illustrate the methodology above on two different examples: the description of least squares solution methods and their application to the solution of the unsteady Navier-Stokes equations for incompressible viscous fluids; the description of augmented lagrangian decomposition techniques and their application to the solution of equilibrium problems in finite elasticity

Improved effective potential by nonlinear canonical transformations

International Nuclear Information System (INIS)

Ritschel, U.

1990-01-01

We generalize the familiar gaussian-effective-potential formalism to a class of non-gaussian trial states. With the help of exact nonlinear canonical transformations, expectation values can be calculated analytically and in closed form. A detailed description of our method, particularly for quadratic and cubic transformations, and of the related renormalization procedure is given. Applications to φ 4 -models in various dimensionalities are treated. We find the expected critical behaviour in two space-time dimensions. In three and four dimensions we observe instabilities which go back the incompleteness of the gaussian-based renormalization. In the appendices it is shown that the quadratic transformation leads to a coherent state in a certain limiting case, and the generalization to systems at finite temperature is performed. (orig.)

Dhage Iteration Method for Generalized Quadratic Functional Integral Equations

Directory of Open Access Journals (Sweden)

Bapurao C. Dhage

2015-01-01

Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.

Subgroups of class groups of algebraic quadratic function fields

International Nuclear Information System (INIS)

Wang Kunpeng; Zhang Xianke

2001-09-01

Ideal class groups H(K) of algebraic quadratic function fields K are studied, by using mainly the theory of continued fractions of algebraic functions. Properties of such continued fractions are discussed first. Then a necessary and sufficient condition is given for the class group H(K) to contain a cyclic subgroup of any order n, this criterion condition holds true for both real and imaginary fields K. Furthermore, several series of function fields K, including real, inertia imaginary, as well as ramified imaginary quadratic function fields, are given, and their class groups H(K) are proved to contain cyclic subgroups of order n. (author)

Genetic algorithm–based varying parameter linear quadratic regulator control for four-wheel independent steering vehicle

Directory of Open Access Journals (Sweden)

Linlin Gao

2015-11-01

Full Text Available From the perspective of vehicle dynamics, the four-wheel independent steering vehicle dynamics stability control method is studied, and a four-wheel independent steering varying parameter linear quadratic regulator control system is proposed with the help of expert control method. In the article, a four-wheel independent steering linear quadratic regulator controller for model following purpose is designed first. Then, by analyzing the four-wheel independent steering vehicle dynamic characteristics and the influence of linear quadratic regulator control parameters on control performance, a linear quadratic regulator control parameter adjustment strategy based on vehicle steering state is proposed to achieve the adaptive adjustment of linear quadratic regulator control parameters. In addition, to further improve the control performance, the proposed varying parameter linear quadratic regulator control system is optimized by genetic algorithm. Finally, simulation studies have been conducted by applying the proposed control system to the 8-degree-of-freedom four-wheel independent steering vehicle dynamics model. The simulation results indicate that the proposed control system has better performance and robustness and can effectively improve the stability and steering safety of the four-wheel independent steering vehicle.

Form-preserving Transformations for the Time-dependent Schroedinger Equation in (n + 1) Dimensions

International Nuclear Information System (INIS)

Schulze-Halberg, Axel

2006-01-01

We define a form-preserving transformation (also called point canonical transformation) for the time-dependent Schroedinger equation (TDSE) in (n+1) dimensions. The form-preserving transformation is shown to be invertible and to preserve L 2 -normalizability. We give a class of time-dependent TDSEs that can be mapped onto stationary Schroedinger equations by our form-preserving transformation. As an example, we generate a solvable, time-dependent potential of Coulombic ring-shaped type together with the corresponding exact solution of the TDSE in (3+1) dimensions. We further consider TDSEs with position-dependent (effective) masses and show that there is no form-preserving transformation between them and the conventional TDSEs, if the spatial dimension of the system is higher than one

Time-dependent Bragg diffraction and short-pulse reflection by one-dimensional photonic crystals

International Nuclear Information System (INIS)

André, Jean-Michel; Jonnard, Philippe

2015-01-01

The time-dependence of the Bragg diffraction by one-dimensional photonic crystals and its influence on the short pulse reflection are studied in the framework of the coupled-wave theory. The indicial response of the photonic crystal is calculated and it appears that it presents a time-delay effect with a transient time conditioned by the extinction length. A numerical simulation is presented for a Bragg mirror in the x-ray domain and a pulse envelope modelled by a sine-squared shape. The potential consequences of the time-delay effect in time-dependent optics of short-pulses are emphasized. (paper)

Electron laser acceleration in vacuum by a quadratically chirped laser pulse

International Nuclear Information System (INIS)

Salamin, Yousef I; Jisrawi, Najeh M

2014-01-01

Single MeV electrons in vacuum subjected to single high-intensity quadratically chirped laser pulses are shown to gain multi-GeV energies. The laser pulses are modelled by finite-duration trapezoidal and cos  2 pulse-shapes and the equations of motion are solved numerically. It is found that, typically, the maximum energy gain from interaction with a quadratic chirp is about half of what would be gained from a linear chirp. (paper)

Estimating negative binomial parameters from occurrence data with detection times.

Science.gov (United States)

Hwang, Wen-Han; Huggins, Richard; Stoklosa, Jakub

2016-11-01

The negative binomial distribution is a common model for the analysis of count data in biology and ecology. In many applications, we may not observe the complete frequency count in a quadrat but only that a species occurred in the quadrat. If only occurrence data are available then the two parameters of the negative binomial distribution, the aggregation index and the mean, are not identifiable. This can be overcome by data augmentation or through modeling the dependence between quadrat occupancies. Here, we propose to record the (first) detection time while collecting occurrence data in a quadrat. We show that under what we call proportionate sampling, where the time to survey a region is proportional to the area of the region, that both negative binomial parameters are estimable. When the mean parameter is larger than two, our proposed approach is more efficient than the data augmentation method developed by Solow and Smith (, Am. Nat. 176, 96-98), and in general is cheaper to conduct. We also investigate the effect of misidentification when collecting negative binomially distributed data, and conclude that, in general, the effect can be simply adjusted for provided that the mean and variance of misidentification probabilities are known. The results are demonstrated in a simulation study and illustrated in several real examples. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The time-dependent Hartree-Fock equations with Coulomb two-body interaction

International Nuclear Information System (INIS)

Chadam, J.M.; Glassey, R.T.

1975-06-01

The existence and uniqueness of global solutions to the Cauchy problem is proved in the space of ''smooth'' density matrices for the time-dependent Hartree-Fock equations describing the motion of finite Fermi systems interacting via a Coulomb two-body potential [fr

Time-dependent translocation and potential impairment on central nervous system by intranasally instilled TiO2 nanoparticles

International Nuclear Information System (INIS)

Wang Jiangxue; Liu Ying; Jiao Fang; Lao Fang; Li Wei; Gu Yiqun; Li Yufeng; Ge Cuicui; Zhou Guoqiang; Li Bai; Zhao Yuliang; Chai Zhifang; Chen Chunying

2008-01-01

Nanoparticles can be administered via nasal, oral, intraocular, intratracheal (pulmonary toxicity), tail vein and other routes. Here, we focus on the time-dependent translocation and potential damage of TiO 2 nanoparticles on central nervous system (CNS) through intranasal instillation. Size and structural properties are important to assess biological effects of TiO 2 nanoparticles. In present study, female mice were intranasally instilled with two types of well-characterized TiO 2 nanoparticles (i.e. 80 nm, rutile and 155 nm, anatase; purity > 99%) every other day. Pure water instilled mice were served as controls. The brain tissues were collected and evaluated for accumulation and distribution of TiO 2 , histopathology, oxidative stress, and inflammatory markers at post-instillation time points of 2, 10, 20 and 30 days. The titanium contents in the sub-brain regions including olfactory bulb, cerebral cortex, hippocampus, and cerebellum were determined by inductively coupled plasma mass spectrometry (ICP-MS). Results indicated that the instilled TiO 2 directly entered the brain through olfactory bulb in the whole exposure period, especially deposited in the hippocampus region. After exposure for 30 days, the pathological changes were observed in the hippocampus and olfactory bulb using Nissl staining and transmission electron microscope. The oxidative damage expressed as lipid peroxidation increased significantly, in particular in the exposed group of anatase TiO 2 particles at 30 days postexposure. Exposure to anatase TiO 2 particles also produced higher inflammation responses, in association with the significantly increased tumor necrosis factor alpha (TNF-α) and interleukin (IL-1β) levels. We conclude that subtle differences in responses to anatase TiO 2 particles versus the rutile ones could be related to crystal structure. Thus, based on these results, rutile ultrafine-TiO 2 particles are expected to have a little lower risk potential for producing adverse

Obstacle Avoidance for Redundant Manipulators Utilizing a Backward Quadratic Search Algorithm

Directory of Open Access Journals (Sweden)

Tianjian Hu

2016-06-01

Full Text Available Obstacle avoidance can be achieved as a secondary task by appropriate inverse kinematics (IK resolution of redundant manipulators. Most prior literature requires the time-consuming determination of the closest point to the obstacle for every calculation step. Aiming at the relief of computational burden, this paper develops what is termed a backward quadratic search algorithm (BQSA as another option for solving IK problems in obstacle avoidance. The BQSA detects possible collisions based on the root property of a category of quadratic functions, which are derived from ellipse-enveloped obstacles and the positions of each link's end-points. The algorithm executes a backward search for possible obstacle collisions, from the end-effector to the base, and avoids obstacles by utilizing a hybrid IK scheme, incorporating the damped least-squares method, the weighted least-norm method and the gradient projection method. Some details of the hybrid IK scheme, such as values of the damped factor, weights and the clamping velocity, are discussed, along with a comparison of computational load between previous methods and BQSA. Simulations of a planar seven-link manipulator and a PUMA 560 robot verify the effectiveness of BQSA.

Simple exercises to flatten your potential

Energy Technology Data Exchange (ETDEWEB)

Dong, Xi; Horn, Bart; Silverstein, Eva [Stanford Univ., Stanford, CA (United States). SLAC and Dept. of Physics; California Univ., Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Stanford Univ., Stanford, CA (United States). SLAC and Dept. of Physics

2010-11-15

We show how backreaction of the inflation potential energy on heavy scalar fields can flatten the inflationary potential, as the heavy fields adjust to their most energetically favorable configuration. This mechanism operates in previous UV-complete examples of axion monodromy inflation - flattening a would-be quadratic potential to one linear in the inflaton field - but occurs more generally, and we illustrate the effect with several examples. Special choices of compactification minimizing backreaction may realize chaotic inflation with a quadratic potential, but we argue that a flatter potential such as power-law inflation V({phi}){proportional_to} {phi}{sup p} with p<2 is a more generic option at sufficiently large values of {phi}. (orig.)

Simple exercises to flatten your potential

International Nuclear Information System (INIS)

Dong, Xi; Horn, Bart; Silverstein, Eva; California Univ., Santa Barbara, CA; Westphal, Alexander; Stanford Univ., Stanford, CA

2010-11-01

We show how backreaction of the inflation potential energy on heavy scalar fields can flatten the inflationary potential, as the heavy fields adjust to their most energetically favorable configuration. This mechanism operates in previous UV-complete examples of axion monodromy inflation - flattening a would-be quadratic potential to one linear in the inflaton field - but occurs more generally, and we illustrate the effect with several examples. Special choices of compactification minimizing backreaction may realize chaotic inflation with a quadratic potential, but we argue that a flatter potential such as power-law inflation V(φ)∝ φ p with p<2 is a more generic option at sufficiently large values of φ. (orig.)

Low-power implementation of polyphase filters in Quadratic Residue Number System

DEFF Research Database (Denmark)

Cardarilli, Gian Carlo; Re, Andrea Del; Nannarelli, Alberto

2004-01-01

The aim of this work is the reduction of the power dissipated in digital filters, while maintaining the timing unchanged. A polyphase filter bank in the Quadratic Residue Number System (QRNS) has been implemented and then compared, in terms of performance, area, and power dissipation...... to the implementation of a polyphase filter bank in the traditional two's complement system (TCS). The resulting implementations, designed to have the same clock rates, show that the QRNS filter is smaller and consumes less power than the TCS one....

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

Science.gov (United States)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

Absorption dynamics and delay time in complex potentials

Science.gov (United States)

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

2018-05-01

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

Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory

International Nuclear Information System (INIS)

Zhang, Xing; Herbert, John M.

2014-01-01

We revisit the calculation of analytic derivative couplings for configuration interaction singles (CIS), and derive and implement these couplings for its spin-flip variant for the first time. Our algorithm is closely related to the CIS analytic energy gradient algorithm and should be straightforward to implement in any quantum chemistry code that has CIS analytic energy gradients. The additional cost of evaluating the derivative couplings is small in comparison to the cost of evaluating the gradients for the two electronic states in question. Incorporation of an exchange-correlation term provides an ad hoc extension of this formalism to time-dependent density functional theory within the Tamm-Dancoff approximation, without the need to invoke quadratic response theory or evaluate third derivatives of the exchange-correlation functional. Application to several different conical intersections in ethylene demonstrates that minimum-energy crossing points along conical seams can be located at substantially reduced cost when analytic derivative couplings are employed, as compared to use of a branching-plane updating algorithm that does not require these couplings. Application to H 3 near its D 3h geometry demonstrates that correct topology is obtained in the vicinity of a conical intersection involving a degenerate ground state

Quadratic grating apodized photon sieves for simultaneous multiplane microscopy

Science.gov (United States)

Cheng, Yiguang; Zhu, Jiangping; He, Yu; Tang, Yan; Hu, Song; Zhao, Lixin

2017-10-01

We present a new type of imaging device, named quadratic grating apodized photon sieve (QGPS), used as the objective for simultaneous multiplane imaging in X-rays. The proposed QGPS is structured based on the combination of two concepts: photon sieves and quadratic gratings. Its design principles are also expounded in detail. Analysis of imaging properties of QGPS in terms of point-spread function shows that QGPS can image multiple layers within an object field onto a single image plane. Simulated and experimental results in visible light both demonstrate the feasibility of QGPS for simultaneous multiplane imaging, which is extremely promising to detect dynamic specimens by X-ray microscopy in the physical and life sciences.

Nonadiabatic Dynamics in Single-Electron Tunneling Devices with Time-Dependent Density-Functional Theory

Science.gov (United States)

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

2018-04-01

We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead in time-dependent density-functional theory. Based on this system, we develop a time-nonlocal exchange-correlation potential by exploiting analogies with quantum-transport theory. The time nonlocality manifests itself in a dynamical potential step. We explicitly link the time evolution of the dynamical step to physical relaxation timescales of the electron dynamics. Finally, we discuss prospects for simulations of larger mesoscopic systems.

Effect of the δ-potential on spin-dependent electron tunneling in double barrier semiconductor heterostructure

Science.gov (United States)

Chandrasekar, L. Bruno; Gnanasekar, K.; Karunakaran, M.

2018-06-01

The effect of δ-potential was studied in GaAs/Ga0.6Al0·4As double barrier heterostructure with Dresselhaus spin-orbit interaction. The role of barrier height and position of the δ- potential in the well region was analysed on spin-dependent electron tunneling using transfer matrix method. The spin-separation between spin-resonances on energy scale depends on both height and position of the δ- potential, whereas the tunneling life time of electrons highly influenced by the position of the δ- potential and not on the height. These results might be helpful for the fabrication of spin-filters.

Fundamental quadratic variational principle underlying general relativity

International Nuclear Information System (INIS)

Atkins, W.K.

1983-01-01

The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed

Investigating Students' Mathematical Difficulties with Quadratic Equations

Science.gov (United States)

O'Connor, Bronwyn Reid; Norton, Stephen

2016-01-01

This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…

Time scale dependent negative emission potential of forests and biomass plantations via wood burial, torrefied biomass, biochar and pyrogas condensate sequestration in soil

Science.gov (United States)

Schmidt, Hans-Peter; Kammann, Claudia; Lucht, Wolfgang; Gerten, Dieter; Foidl, Nikolaus

2017-04-01

The efficiency of Negative Emission Technologies (NET) is dependent on (1) the transformation of the biomass carbon into a form that can be sequestered, (2) the mean residence time of the sequestered carbon, (3) the regrowth and thus carbon re-accumulation of the harvested biomass, and (4) the positive or negative priming of soil carbon. These four parameters define the time scale dependent C-balance of various NET-Systems and permit a global economic and environmental evaluation. As far as geologic CO2 storage is considered to be feasible with close to zero losses and if the energy for transport, transformation and disposal is taken from the process bioenergy, conventional BE-CCS has a C sequestration potential of 50 - 70 % depending on the type of biomass and the technology used. Beside unknown risks of deep stored CO2 and high costs, regrowth of C-accumulating biomass is hampered in the long-term as not only carbon but also essential soil nutrients are mined. Under this scenario, biomass regrowth is expected to slow down and soil carbon content to decrease. These factors enlarge the time horizon until a BE-CCS system becomes carbon neutral and eventual carbon negative (when biomass regrowth exceeds the difference between the harvested biomass carbon and BE-CCS stored carbon). Thermal treatment of biomass under a low oxygen regime (torrefaction, pyrolysis, gasification) can transform up to 85% of biomass carbon into various solid and liquid forms of recalcitrant carbon that can be sequestered. Depending on the process parameters and temperature, the mean residence time of the torrefied or pyrolysed biomass can last from several decennials to centennials when applied to the soil of the biomass production site. The carbon can thus be stored at comparatively low costs within the ecosystem itself. As the thermal treatment preserves most of the biomass-accumulated nutrients (except N), natural nutrient cycles are maintained within the biomass system. Depending on the

One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

Science.gov (United States)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.

Analytic Expression of Arbitrary Matrix Elements for Boson Exponential Quadratic Polynomial Operators

Institute of Scientific and Technical Information of China (English)

XU Xiu-Wei; REN Ting-Qi; LIU Shu-Yan; MA Qiu-Ming; LIU Sheng-Dian

2007-01-01

Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators (BEQPO's), we present the analytic expression of arbitrary matrix elements for BEQPO's. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO's.

Factorization method of quadratic template

Science.gov (United States)

Kotyrba, Martin

2017-07-01

Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.

Time-dependent reliability analysis of flood defences

International Nuclear Information System (INIS)

Buijs, F.A.; Hall, J.W.; Sayers, P.B.; Gelder, P.H.A.J.M. van

2009-01-01

This paper describes the underlying theory and a practical process for establishing time-dependent reliability models for components in a realistic and complex flood defence system. Though time-dependent reliability models have been applied frequently in, for example, the offshore, structural safety and nuclear industry, application in the safety-critical field of flood defence has to date been limited. The modelling methodology involves identifying relevant variables and processes, characterisation of those processes in appropriate mathematical terms, numerical implementation, parameter estimation and prediction. A combination of stochastic, hierarchical and parametric processes is employed. The approach is demonstrated for selected deterioration mechanisms in the context of a flood defence system. The paper demonstrates that this structured methodology enables the definition of credible statistical models for time-dependence of flood defences in data scarce situations. In the application of those models one of the main findings is that the time variability in the deterioration process tends to be governed the time-dependence of one or a small number of critical attributes. It is demonstrated how the need for further data collection depends upon the relevance of the time-dependence in the performance of the flood defence system.

Design of variable-weight quadratic congruence code for optical CDMA

Science.gov (United States)

Feng, Gang; Cheng, Wen-Qing; Chen, Fu-Jun

2015-09-01

A variable-weight code family referred to as variable-weight quadratic congruence code (VWQCC) is constructed by algebraic transformation for incoherent synchronous optical code division multiple access (OCDMA) systems. Compared with quadratic congruence code (QCC), VWQCC doubles the code cardinality and provides the multiple code-sets with variable code-weight. Moreover, the bit-error rate (BER) performance of VWQCC is superior to those of conventional variable-weight codes by removing or padding pulses under the same chip power assumption. The experiment results show that VWQCC can be well applied to the OCDMA with quality of service (QoS) requirements.

Time-dependent Kohn-Sham approach to quantum electrodynamics

International Nuclear Information System (INIS)

Ruggenthaler, M.; Mackenroth, F.; Bauer, D.

2011-01-01

We prove a generalization of the van Leeuwen theorem toward quantum electrodynamics, providing the formal foundations of a time-dependent Kohn-Sham construction for coupled quantized matter and electromagnetic fields. We circumvent the symmetry-causality problems associated with the action-functional approach to Kohn-Sham systems. We show that the effective external four-potential and four-current of the Kohn-Sham system are uniquely defined and that the effective four-current takes a very simple form. Further we rederive the Runge-Gross theorem for quantum electrodynamics.

Time dependent photon and neutrino emission from Mkr 421 in the context of the one-zone leptohadronic model

Directory of Open Access Journals (Sweden)

Mastichiadis Apostolos

2013-12-01

Full Text Available We apply a recently developed time-dependent one-zone leptohadronic model to study the emission of the blazar Mrk 421. Both processes involving proton-photon interactions, i.e. photopair (Bethe-Heitler and photopion, have been modeled in great detail using the results of Monte Carlo simulations, like the SOPHIA event generator, in a self-consistent scheme that couples energy losses and secondary injection. We find that TeV gamma-rays can be attributed to synchrotron radiation either from relativistic protons or, alternatively, from secondary leptons produced via photohadronic processes. We also study the variability patterns that each scenario predicts and we find that while the former is more energetically favored, it is the latter that produces, in a more natural way, the usual quadratic behavior between X-rays and TeV gamma-rays. We also use the obtained SEDs to calculate in detail the expected neutron and neutrino fluxes that each model predicts.

Mixmaster cosmological model in theories of gravity with a quadratic Lagrangian

International Nuclear Information System (INIS)

Barrow, J.D.; Sirousse-Zia, H.

1989-01-01

We use the method of matched asymptotic expansions to examine the behavior of the vacuum Bianchi type-IX mixmaster universe in a gravity theory derived from a purely quadratic gravitational Lagrangian. The chaotic behavior characteristic of the general-relativistic mixmaster model disappears and the asymptotic behavior is of the monotonic, nonchaotic form found in the exactly soluble Bianchi type-I models of the quadratic theory. The asymptotic behavior far from the singularity is also found to be of monotonic nonchaotic type

Integrable Time-Dependent Quantum Hamiltonians

Science.gov (United States)

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

2018-05-01

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

Taylor O(h³) Discretization of ZNN Models for Dynamic Equality-Constrained Quadratic Programming With Application to Manipulators.

Science.gov (United States)

Liao, Bolin; Zhang, Yunong; Jin, Long

2016-02-01

In this paper, a new Taylor-type numerical differentiation formula is first presented to discretize the continuous-time Zhang neural network (ZNN), and obtain higher computational accuracy. Based on the Taylor-type formula, two Taylor-type discrete-time ZNN models (termed Taylor-type discrete-time ZNNK and Taylor-type discrete-time ZNNU models) are then proposed and discussed to perform online dynamic equality-constrained quadratic programming. For comparison, Euler-type discrete-time ZNN models (called Euler-type discrete-time ZNNK and Euler-type discrete-time ZNNU models) and Newton iteration, with interesting links being found, are also presented. It is proved herein that the steady-state residual errors of the proposed Taylor-type discrete-time ZNN models, Euler-type discrete-time ZNN models, and Newton iteration have the patterns of O(h(3)), O(h(2)), and O(h), respectively, with h denoting the sampling gap. Numerical experiments, including the application examples, are carried out, of which the results further substantiate the theoretical findings and the efficacy of Taylor-type discrete-time ZNN models. Finally, the comparisons with Taylor-type discrete-time derivative model and other Lagrange-type discrete-time ZNN models for dynamic equality-constrained quadratic programming substantiate the superiority of the proposed Taylor-type discrete-time ZNN models once again.

Time-dependent resilience assessment and improvement of urban infrastructure systems

Science.gov (United States)

Ouyang, Min; Dueñas-Osorio, Leonardo

2012-09-01

This paper introduces an approach to assess and improve the time-dependent resilience of urban infrastructure systems, where resilience is defined as the systems' ability to resist various possible hazards, absorb the initial damage from hazards, and recover to normal operation one or multiple times during a time period T. For different values of T and its position relative to current time, there are three forms of resilience: previous resilience, current potential resilience, and future potential resilience. This paper mainly discusses the third form that takes into account the systems' future evolving processes. Taking the power transmission grid in Harris County, Texas, USA as an example, the time-dependent features of resilience and the effectiveness of some resilience-inspired strategies, including enhancement of situational awareness, management of consumer demand, and integration of distributed generators, are all simulated and discussed. Results show a nonlinear nature of resilience as a function of T, which may exhibit a transition from an increasing function to a decreasing function at either a threshold of post-blackout improvement rate, a threshold of load profile with consumer demand management, or a threshold number of integrated distributed generators. These results are further confirmed by studying a typical benchmark system such as the IEEE RTS-96. Such common trends indicate that some resilience strategies may enhance infrastructure system resilience in the short term, but if not managed well, they may compromise practical utility system resilience in the long run.

Caffeine and length dependence of staircase potentiation in skeletal muscle.

Science.gov (United States)

Rassier, D E; Tubman, L A; MacIntosh, B R

1998-01-01

Skeletal muscle sensitivity to Ca2+ is greater at long lengths, and this results in an optimal length for twitch contractions that is longer than optimal length for tetanic contractions. Caffeine abolishes this length dependence of Ca2+ sensitivity. Muscle length (ML) also affects the degree of staircase potentiation. Since staircase potentiation is apparently caused by an increased Ca2+ sensitivity of the myofilaments, we tested the hypothesis that caffeine depresses the length dependence of staircase potentiation. In situ isometric twitch contractions of rat gastrocnemius muscle before and after 10 s of 10-Hz stimulation were analyzed at seven different lengths to evaluate the length dependence of staircase potentiation. In the absence of caffeine, length dependence of Ca2+ sensitivity was observed, and the degree of potentiation after 10-Hz stimulation showed a linear decrease with increased length (DT = 1.47 - 0.05 ML, r2 = 0.95, where DT is developed tension). Length dependence of Ca2+ sensitivity was decreased by caffeine when caffeine was administered in amounts estimated to result in 0.5 and 0.75 mM concentrations. Furthermore, the negative slope of the relationship between staircase potentiation and muscle length was diminished at the lower caffeine dose, and the slope was not different from zero after the higher dose (DT = 1.53 - 0.009 ML, r2 = 0.43). Our study shows that length dependence of Ca2+ sensitivity in intact skeletal muscle is diminished by caffeine. Caffeine also suppressed the length dependence of staircase potentiation, suggesting that the mechanism of this length dependence may be closely related to the mechanism for length dependence of Ca2+ sensitivity.

Exponential time-dependent perturbation theory in rotationally inelastic scattering

International Nuclear Information System (INIS)

Cross, R.J.

1983-01-01

An exponential form of time-dependent perturbation theory (the Magnus approximation) is developed for rotationally inelastic scattering. A phase-shift matrix is calculated as an integral in time over the anisotropic part of the potential. The trajectory used for this integral is specified by the diagonal part of the potential matrix and the arithmetic average of the initial and final velocities and the average orbital angular momentum. The exponential of the phase-shift matrix gives the scattering matrix and the various cross sections. A special representation is used where the orbital angular momentum is either treated classically or may be frozen out to yield the orbital sudden approximation. Calculations on Ar+N 2 and Ar+TIF show that the theory generally gives very good agreement with accurate calculations, even where the orbital sudden approximation (coupled-states) results are seriously in error

Geometric Methods in the Algebraic Theory of Quadratic Forms : Summer School

CERN Document Server

2004-01-01

The geometric approach to the algebraic theory of quadratic forms is the study of projective quadrics over arbitrary fields. Function fields of quadrics have been central to the proofs of fundamental results since the renewal of the theory by Pfister in the 1960's. Recently, more refined geometric tools have been brought to bear on this topic, such as Chow groups and motives, and have produced remarkable advances on a number of outstanding problems. Several aspects of these new methods are addressed in this volume, which includes - an introduction to motives of quadrics by Alexander Vishik, with various applications, notably to the splitting patterns of quadratic forms under base field extensions; - papers by Oleg Izhboldin and Nikita Karpenko on Chow groups of quadrics and their stable birational equivalence, with application to the construction of fields which carry anisotropic quadratic forms of dimension 9, but none of higher dimension; - a contribution in French by Bruno Kahn which lays out a general fra...

A high-performance Riccati based solver for tree-structured quadratic programs

DEFF Research Database (Denmark)

Frison, Gianluca; Kouzoupis, Dimitris; Diehl, Moritz

2017-01-01

the online solution of such problems challenging and the development of tailored solvers crucial. In this paper, an interior point method is presented that can solve Quadratic Programs (QPs) arising in multi-stage MPC efficiently by means of a tree-structured Riccati recursion and a high-performance linear...... algebra library. A performance comparison with code-generated and general purpose sparse QP solvers shows that the computation times can be significantly reduced for all problem sizes that are practically relevant in embedded MPC applications. The presented implementation is freely available as part...

Time dependent policy-based access control

DEFF Research Database (Denmark)

Vasilikos, Panagiotis; Nielson, Flemming; Nielson, Hanne Riis

2017-01-01

also on other attributes of the environment such as the time. In this paper, we use systems of Timed Automata to model distributed systems and we present a logic in which one can express time-dependent policies for access control. We show how a fragment of our logic can be reduced to a logic......Access control policies are essential to determine who is allowed to access data in a system without compromising the data's security. However, applications inside a distributed environment may require those policies to be dependent on the actual content of the data, the flow of information, while...... that current model checkers for Timed Automata such as UPPAAL can handle and we present a translator that performs this reduction. We then use our translator and UPPAAL to enforce time-dependent policy-based access control on an example application from the aerospace industry....

Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions

Science.gov (United States)

Valchev, T. I.

2016-02-01

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m + n)/S(U(m) × U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schrödinger equation which serves as a motivational example for our general considerations. We extensively discuss how one can apply Zakharov-Shabat's dressing procedure to derive reflectionless potentials obeying zero boundary conditions. Those could be used for one to construct fast decaying solutions to any nonlinear equation belonging to the same hierarchy. One can distinguish between generic soliton type solutions and rational solutions.

Classification of the quantum two dimensional superintegrable systems with quadratic integrals and the Stackel transforms

International Nuclear Information System (INIS)

Dakaloyannis, C.

2006-01-01

Full text: (author)The two dimensional quantum superintegrable systems with quadratic integrals of motion on a manifold are classified by using the quadratic associative algebra of the integrals of motion. There are six general fundamental classes of quantum superintegrable systems corresponding to the classical ones. Analytic formulas for the involved integrals are calculated in all the cases. All the known quantum superintegrable systems with quadratic integrals are classified as special cases of these six general classes. The coefficients of the quadratic associative algebra of integrals are calculated and they are compared to the coefficients of the corresponding coefficients of the Poisson quadratic algebra of the classical systems. The quantum coefficients are similar as the classical ones multiplied by a quantum coefficient -n 2 plus a quantum deformation of order n 4 and n 6 . The systems inside the classes are transformed using Stackel transforms in the quantum case as in the classical case and general form is discussed. The idea of the Jacobi Hamiltonian corresponding to the Jacobi metric in the classical case is discussed

Time dependent resonating Hartree-Bogoliubov theory

International Nuclear Information System (INIS)

Nishiyama, Seiya; Fukutome, Hideo.

1989-01-01

Very recently, we have developed a theory of excitations in superconducting Fermion systems with large quantum fluctuations that can be described by resonance of time dependent non-orthogonal Hartree-Bogoliubov (HB) wave functions with different correlation structures. We have derived a new kind of variation equation called the time dependent Resonating HB equation, in order to determine both the time dependent Resonating HB wave functions and coefficients of a superposition of the HB wave functions. Further we have got a new approximation for excitations from time dependent small fluctuations of the Resonating HB ground state, i.e., the Resonating HB RPA. The Res HB RPA equation is represented in a given single particle basis. It, however, has drawbacks that the constraints for the Res HB RPA amplitudes are not taken into account and the equation contains equations which are not independent. We shall derive another form of the Res HB RPA equation eliminating these drawbacks. The Res HB RPA gives a unified description of the vibrons and resonons and their interactions. (author)

Quadratic Variation by Markov Chains

DEFF Research Database (Denmark)

Hansen, Peter Reinhard; Horel, Guillaume

We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...

Coherent states for quadratic Hamiltonians

International Nuclear Information System (INIS)

Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes

2011-01-01

The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.

Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations

DEFF Research Database (Denmark)

Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip

2016-01-01

We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...

X-ray absorption in insulators with non-Hermitian real-time time-dependent density functional theory.

Science.gov (United States)

Fernando, Ranelka G; Balhoff, Mary C; Lopata, Kenneth

2015-02-10

Non-Hermitian real-time time-dependent density functional theory was used to compute the Si L-edge X-ray absorption spectrum of α-quartz using an embedded finite cluster model and atom-centered basis sets. Using tuned range-separated functionals and molecular orbital-based imaginary absorbing potentials, the excited states spanning the pre-edge to ∼20 eV above the ionization edge were obtained in good agreement with experimental data. This approach is generalizable to TDDFT studies of core-level spectroscopy and dynamics in a wide range of materials.

Evaluation of Time-Dependent Behavior of Soils

DEFF Research Database (Denmark)

Augustesen, Anders; Liingaard, Morten; Lade, Poul V.

2004-01-01

The time-dependent behavior of soils has been investigated extensively through one-dimensional and triaxial test conditions. Most of the observations in literature have focused on the determination of the time-dependent behavior of clayey soils, whereas the reported experimental studies of granular...... situation for soils. That is whether the time-dependent behavior can be characterized as isotach or nonisotach. It seems that the isotach behavior is adequate for describing the time effects in clays in most situations. But for sand, the isotach description is inadequate. Further, the phenomenon...

Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers

Directory of Open Access Journals (Sweden)

E. George Walters III

2015-11-01

Full Text Available This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev-series approximation and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24 bits (IEEE single precision. Designs for linear and quadratic interpolators that implement the 1/x, 1/ √ x, log2(1+2x, log2(x and 2x functions are presented and analyzed as examples. Results show that a proposed 24-bit interpolator computing 1/x with a design specification of ±1 unit in the last place of the product (ulp error uses 16.4% less area and 15.3% less power than a comparable standard interpolator with the same error specification. Sixteen-bit linear interpolators for other functions are shown to use up to 17.3% less area and 12.1% less power, and 16-bit quadratic interpolators are shown to use up to 25.8% less area and 24.7% less power.

Quadratic mass relations in topological bootstrap theory

International Nuclear Information System (INIS)

Jones, C.E.; Uschersohn, J.

1980-01-01

From the requirement of reality of discontinuities of scattering amplitudes at the spherical level of the topological bootstrap theory, a large number of mass relations for hadrons is derived. Quadratic mass formulas for the symmetry-breaking pattern of both mesons and baryon is obtained and their relation to conventional models of symmetry breaking is briefly discussed

Spike-timing dependent plasticity in the striatum

Directory of Open Access Journals (Sweden)

Elodie Fino

2010-06-01

Full Text Available The striatum is the major input nucleus of basal ganglia, an ensemble of interconnected sub-cortical nuclei associated with fundamental processes of action-selection and procedural learning and memory. The striatum receives afferents from the cerebral cortex and the thalamus. In turn, it relays the integrated information towards the basal ganglia output nuclei through which it operates a selected activation of behavioral effectors. The striatal output neurons, the GABAergic medium-sized spiny neurons (MSNs, are in charge of the detection and integration of behaviorally relevant information. This property confers to the striatum the ability to extract relevant information from the background noise and select cognitive-motor sequences adapted to environmental stimuli. As long-term synaptic efficacy changes are believed to underlie learning and memory, the corticostriatal long-term plasticity provides a fundamental mechanism for the function of the basal ganglia in procedural learning. Here, we reviewed the different forms of spike-timing dependent plasticity (STDP occurring at corticostriatal synapses. Most of the studies have focused on MSNs and their ability to develop long-term plasticity. Nevertheless, the striatal interneurons (the fast-spiking GABAergic, the NO synthase and cholinergic interneurons also receive monosynaptic afferents from the cortex and tightly regulated corticostriatal information processing. Therefore, it is important to take into account the variety of striatal neurons to fully understand the ability of striatum to develop long-term plasticity. Corticostriatal STDP with various spike-timing dependence have been observed depending on the neuronal sub-populations and experimental conditions. This complexity highlights the extraordinary potentiality in term of plasticity of the corticostriatal pathway.

Asymptotic performance of regularized quadratic discriminant analysis based classifiers

KAUST Repository

Elkhalil, Khalil

2017-12-13

This paper carries out a large dimensional analysis of the standard regularized quadratic discriminant analysis (QDA) classifier designed on the assumption that data arise from a Gaussian mixture model. The analysis relies on fundamental results from random matrix theory (RMT) when both the number of features and the cardinality of the training data within each class grow large at the same pace. Under some mild assumptions, we show that the asymptotic classification error converges to a deterministic quantity that depends only on the covariances and means associated with each class as well as the problem dimensions. Such a result permits a better understanding of the performance of regularized QDA and can be used to determine the optimal regularization parameter that minimizes the misclassification error probability. Despite being valid only for Gaussian data, our theoretical findings are shown to yield a high accuracy in predicting the performances achieved with real data sets drawn from popular real data bases, thereby making an interesting connection between theory and practice.

Vacuum solutions of Bianchi cosmologies in quadratic gravity

International Nuclear Information System (INIS)

Deus, Juliano Alves de; Muller, Daniel

2011-01-01

Full text: In this work we solve numerically the vacuum solutions of field equations of Bianchi homogeneous universes in the context of Semiclassical theory. Our interest is to study the quadratic theory of gravity with regard in the cosmological description of our universe in periods of intense fields. Bianchi cosmologies are anisotropic homogeneous cosmological models, but can include the isotropic models as particular cases (Bianchi I, VII and IX include homogeneous and isotropic Friedmann models plane, hyperbolic and spherical, respectively). Homogeneous models are good cosmological representations of our universe. With focus in solutions for intense fields, like the early universe, where isotropy is not necessarily required, the adopted scenario is the vacuum solutions, where the geometry is dominant in determining the gravitation. Still following in this way, the Semiclassical theory, which considers quantum matter fields propagating in classical geometrical background, is addressed to give the field equations. This formalism leads to fourth-order ordinary differential equations, in contrast to second-order equations from General Relativity. The Lagrangian of the theory is quadratic in the Ricci scalar and in the Ricci tensor. The equations system is highly non-linear and can be only numerically solved, except perhaps for few particular cases. We obtained numerical solutions for Bianchi V II A evolving to Minkowski and to de Sitter solutions, and also to singularities. The both first and second solutions were obtained choosing initial conditions near from respective exact vacuum solutions from Einstein theory, which are also exact solutions of the quadratic theory. Other Bianchi types are still under study. (author)

Reconstructing time-dependent dynamics

OpenAIRE

Clemson, Philip; Lancaster, Gemma; Stefanovska, Aneta

2016-01-01

The usefulness of the information extracted from biomedical data relies heavily on the underlying theory of the methods used in its extraction. The assumptions of stationarity and autonomicity traditionally applied to dynamical systems break down when considering living systems, due to their inherent time-variability. Living systems are thermodynamically open, and thus constantly interacting with their environment. This results in highly nonlinear, time-dependent dynamics. The aim of signal a...

Walking solitons in quadratic nonlinear media

OpenAIRE

Torner Sabata, Lluís; Mazilu, D; Mihalache, Dumitru

1996-01-01

We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications. Peer Reviewed

Stochastic Linear Quadratic Optimal Control Problems

International Nuclear Information System (INIS)

Chen, S.; Yong, J.

2001-01-01

This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well

Prospects for time-dependent asymmetries at LHCb

CERN Document Server

INSPIRE-00260500

2012-01-01

LHCb is already providing leading measurements of time-dependent CP asymmetries with 1 fb$^{-1}$ of data. With the LHCb detector, and further one with the LHCb upgrade, very high-precision time-dependent CP measurements are expected to stringently test the CKM paradigm and to the search for possible small NP effects. A review of the current precision and the prospects for these time-dependent quantities with the LHCb and LHCb upgraded detectors are summarised in this paper.

Time-dependent switched discrete-time linear systems control and filtering

CERN Document Server

Zhang, Lixian; Shi, Peng; Lu, Qiugang

2016-01-01

This book focuses on the basic control and filtering synthesis problems for discrete-time switched linear systems under time-dependent switching signals. Chapter 1, as an introduction of the book, gives the backgrounds and motivations of switched systems, the definitions of the typical time-dependent switching signals, the differences and links to other types of systems with hybrid characteristics and a literature review mainly on the control and filtering for the underlying systems. By summarizing the multiple Lyapunov-like functions (MLFs) approach in which different requirements on comparisons of Lyapunov function values at switching instants, a series of methodologies are developed for the issues on stability and stabilization, and l2-gain performance or tube-based robustness for l∞ disturbance, respectively, in Chapters 2 and 3. Chapters 4 and 5 are devoted to the control and filtering problems for the time-dependent switched linear systems with either polytopic uncertainties or measurable time-varying...

On misclassication probabilities of linear and quadratic classiers ...

African Journals Online (AJOL)

We study the theoretical misclassication probability of linear and quadratic classiers and examine the performance of these classiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift. Keywords: ...

Time dependent accessibility

OpenAIRE

Kaza, Nikhil

2015-01-01

Many place based accessibility studies ignore the time component. Relying on theoretical frameworks that treat distance between two fixed points as constant, these methods ignore the diurnal and seasonal changes in accessibility. Network distances between two nodes are dependent on the network structure and weight distribution on the edges. These weights can change quite frequently and the network structure itself is subject to modification because of availability and unavailability of links ...

Mechanistic formulation of a lineal-quadratic-linear (LQL) model: Split-dose experiments and exponentially decaying sources

International Nuclear Information System (INIS)

Guerrero, Mariana; Carlone, Marco

2010-01-01

Purpose: In recent years, several models were proposed that modify the standard linear-quadratic (LQ) model to make the predicted survival curve linear at high doses. Most of these models are purely phenomenological and can only be applied in the particular case of acute doses per fraction. The authors consider a mechanistic formulation of a linear-quadratic-linear (LQL) model in the case of split-dose experiments and exponentially decaying sources. This model provides a comprehensive description of radiation response for arbitrary dose rate and fractionation with only one additional parameter. Methods: The authors use a compartmental formulation of the LQL model from the literature. They analytically solve the model's differential equations for the case of a split-dose experiment and for an exponentially decaying source. They compare the solutions of the survival fraction with the standard LQ equations and with the lethal-potentially lethal (LPL) model. Results: In the case of the split-dose experiment, the LQL model predicts a recovery ratio as a function of dose per fraction that deviates from the square law of the standard LQ. The survival fraction as a function of time between fractions follows a similar exponential law as the LQ but adds a multiplicative factor to the LQ parameter β. The LQL solution for the split-dose experiment is very close to the LPL prediction. For the decaying source, the differences between the LQL and the LQ solutions are negligible when the half-life of the source is much larger than the characteristic repair time, which is the clinically relevant case. Conclusions: The compartmental formulation of the LQL model can be used for arbitrary dose rates and provides a comprehensive description of dose response. When the survival fraction for acute doses is linear for high dose, a deviation of the square law formula of the recovery ratio for split doses is also predicted.

The Interaction of Magnetizations with an External Electromagnetic Field and a Time-Dependent Magnetic Aharonov-Bohm Effect

International Nuclear Information System (INIS)

Afanas'ev, G.N.; Stepanovskij, Yu.P.

1994-01-01

We investigate how the choice of the magnetization distribution inside the sample affects its interaction with the external electromagnetic field. The strong selectivity to the time dependence of the external electromagnetic field arises for the particular magnetizations. This can be used for the storage and ciphering of information. We propose a time-dependent Aharonov-Bohm-like experiment in which the phase of the wave function is changed by the time-dependent vector magnetic potential. The arising time-dependent interference picture may be viewed as a new channel for the information transfer. 15 refs., 4 figs

Environmentally dependent bond-order potentials: New ...

Indian Academy of Sciences (India)

Environmentally dependent bond-order potentials: New developments and applications ... for modelling amorphous structure we found that the and bond integrals are not only transferable between graphite and diamond structures but they are also strongly anisotropic due to inter-plan bonding between graphite sheets.

Global dependence of optical potential parameters for alpha particles with energies up to 80 MeV

International Nuclear Information System (INIS)

Kuterbekov, K.A.; Zholdybaev, T.K.; Sadykov, B.M.; Mukhambetzhan, A.; Kukhtina, I.N.; Penionzhkevich, Yu.Eh.

2002-01-01

Global (energy and mass) dependences of optical potential for α-particles with energies up to 80 MeV have been received. A Woods-Saxon form factor for macroscopic potential has been used. Energy and mass dependences of the semi-microscopic α-particle potential parameters have been investigated for the first time. In general, a good description of elastic and inelastic differential and total reactions cross sections for different nuclei using the revealed global parameters has been received within the framework of macroscopic and semi-microscopic approaches

ANALYSIS AND PERFORMANCE MEASUREMENT OF EXISTING SOLUTION METHODS OF QUADRATIC ASSIGNMENT PROBLEM

Directory of Open Access Journals (Sweden)

Morteza KARAMI

2014-01-01

Full Text Available Quadratic Assignment Problem (QAP is known as one of the most difficult combinatorial optimization problems that is classified in the category of NP-hard problems. Quadratic Assignment Problem Library (QAPLIB is a full database of QAPs which contains several problems from different authors and different sizes. Many exact and meta-heuristic solution methods have been introduced to solve QAP. In this study we focus on previously introduced solution methods of QAP e.g. Branch and Bound (B&B, Simulated Annealing (SA Algorithm, Greedy Randomized Adaptive Search Procedure (GRASP for dense and sparse QAPs. The codes of FORTRAN for these methods were downloaded from QAPLIB. All problems of QAPLIB were solved by the abovementioned methods. Several results were obtained from the computational experiments part. The Results show that the Branch and Bound method is able to introduce a feasible solution for all problems while Simulated Annealing Algorithm and GRASP methods are not able to find any solution for some problems. On the other hand, Simulated Annealing and GRASP methods have shorter run time comparing to the Branch and Bound method. In addition, the performance of the methods on the objective function value is discussed.

Length dependence of staircase potentiation: interactions with caffeine and dantrolene sodium.

Science.gov (United States)

Rassier, D E; MacIntosh, B R

2000-04-01

In skeletal muscle, there is a length dependence of staircase potentiation for which the mechanism is unclear. In this study we tested the hypothesis that abolition of this length dependence by caffeine is effected by a mechanism independent of enhanced Ca2+ release. To test this hypothesis we have used caffeine, which abolishes length dependence of potentiation, and dantrolene sodium, which inhibits Ca2+ release. In situ isometric twitch contractions of rat gastrocnemius muscle before and after 20 s of repetitive stimulation at 5 Hz were analyzed at optimal length (Lo), Lo - 10%, and Lo + 10%. Potentiation was observed to be length dependent, with an increase in developed tension (DT) of 78 +/- 12, 51 +/- 5, and 34 +/- 9% (mean +/- SEM), at Lo - 10%, Lo, and Lo + 10%, respectively. Caffeine diminished the length dependence of activation and suppressed the length dependence of staircase potentiation, giving increases in DT of 65+/-13, 53 +/- 11, and 45 +/- 12% for Lo - 10%, Lo, and Lo + 10%, respectively. Dantrolene administered after caffeine did not reverse this effect. Dantrolene alone depressed the potentiation response, but did not affect the length dependence of staircase potentiation, with increases in DT of 58 +/- 17, 26 +/- 8, and 18 +/- 7%, respectively. This study confirms that there is a length dependence of staircase potentiation in mammalian skeletal muscle which is suppressed by caffeine. Since dantrolene did not alter this suppression of the length dependence of potentiation by caffeine, it is apparently not directly modulated by Ca2+ availability in the myoplasm.

Slab albedo for linearly and quadratically anisotropic scattering kernel with modified F{sub N} method

Energy Technology Data Exchange (ETDEWEB)

Tuereci, R. Goekhan [Kirikkale Univ. (Turkey). Kirikkale Vocational School; Tuereci, D. [Ministry of Education, Ankara (Turkey). 75th year Anatolia High School

2017-11-15

One speed, time independent and homogeneous medium neutron transport equation is solved with the anisotropic scattering which includes both the linearly and the quadratically anisotropic scattering kernel. Having written Case's eigenfunctions and the orthogonality relations among of these eigenfunctions, slab albedo problem is investigated as numerically by using Modified F{sub N} method. Selected numerical results are presented in tables.

Newton's method for solving a quadratic matrix equation with special coefficient matrices

International Nuclear Information System (INIS)

Seo, Sang-Hyup; Seo, Jong Hyun; Kim, Hyun-Min

2014-01-01

We consider the iterative method for solving a quadratic matrix equation with special coefficient matrices which arises in the quasi-birth-death problem. In this paper, we show that the elementwise minimal positive solvents to quadratic matrix equations can be obtained using Newton's method. We also prove that the convergence rate of the Newton iteration is quadratic if the Fréchet derivative at the elementwise minimal positive solvent is nonsingular. However, if the Fréchet derivative is singular, the convergence rate is at least linear. Numerical experiments of the convergence rate are given.(This is summarized a paper which is to appear in Honam Mathematical Journal.)

K shortest paths in stochastic time-dependent networks

DEFF Research Database (Denmark)

Nielsen, Lars Relund; Pretolani, Daniele; Andersen, Kim Allan

2004-01-01

A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks, the ...... present a computational comparison of time-adaptive and a priori route choices, pointing out the effect of travel time and cost distributions. The reported results show that, under realistic distributions, our solution methods are effective.......A substantial amount of research has been devoted to the shortest path problem in networks where travel times are stochastic or (deterministic and) time-dependent. More recently, a growing interest has been attracted by networks that are both stochastic and time-dependent. In these networks...

Decentralized linear quadratic power system stabilizers for multi ...

Indian Academy of Sciences (India)

Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not ...

On Fredholm-Stieltjes quadratic integral equation with supremum

International Nuclear Information System (INIS)

Darwish, M.A.

2007-08-01

We prove an existence theorem of monotonic solutions for a quadratic integral equation of Fredholm-Stieltjes type in C[0,1]. The concept of measure of non-compactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof. (author)

Quadratic Hierarchy Flavor Rule as the Origin of Dirac CP-Violating Phases

OpenAIRE

Lipmanov, E. M.

2007-01-01

The premise of an organizing quadratic hierarchy rule in lepton-quark flavor physics was used earlier for explanation of the hierarchy patterns of four generic pairs of flavor quantities 1) charged-lepton and 2) neutrino deviations from mass-degeneracy, 3) deviations of lepton mixing from maximal magnitude and 4) deviations of quark mixing from minimal one. Here it is shown that the quadratic hierarchy equation that is uniquely related to three flavor particle generations may have yet another...

On the Equivalence of Quadratic Optimization Problems Commonly Used in Portfolio Theory

OpenAIRE

Taras Bodnar; Nestor Parolya; Wolfgang Schmid

2012-01-01

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-variance utility function and the quadratic utility.Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean-variance optimal portfolios. It is shown that the solutions of the Markowitz optimization prob...

On bent and semi-bent quadratic Boolean functions

DEFF Research Database (Denmark)

Charpin, P.; Pasalic, Enes; Tavernier, C.

2005-01-01

correlation and high nonlinearity. We say that such a sequence is generated by a semi-bent function. Some new families of such function, represented by f(x) = Sigma(i=1)(n-1/2) c(i)Tr(x(2t+1)), n odd and c(i) is an element of F-2, have recently (2002) been introduced by Khoo et al. We first generalize......The maximum-length sequences, also called m-sequences, have received a lot of attention since the late 1960s. In terms of linear-feedback shift register (LFSR) synthesis they are usually generated by certain power polynomials over a finite field and in addition are characterized by a low cross...... their results to even n. We further investigate the conditions on the choice of ci for explicit definitions of new infinite families having three and four trace terms. Also, a class of nonpermutation polynomials whose composition with a quadratic function yields again a quadratic semi-bent function is specified...

Single Machine Scheduling and Due Date Assignment with Past-Sequence-Dependent Setup Time and Position-Dependent Processing Time

Directory of Open Access Journals (Sweden)

Chuan-Li Zhao

2014-01-01

Full Text Available This paper considers single machine scheduling and due date assignment with setup time. The setup time is proportional to the length of the already processed jobs; that is, the setup time is past-sequence-dependent (p-s-d. It is assumed that a job's processing time depends on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs, and the cost of due date assignment. We analyze these problems with two different due date assignment methods. We first consider the model with job-dependent position effects. For each case, by converting the problem to a series of assignment problems, we proved that the problems can be solved in On4 time. For the model with job-independent position effects, we proved that the problems can be solved in On3 time by providing a dynamic programming algorithm.

Emotion suppression moderates the quadratic association between RSA and executive function.

Science.gov (United States)

Spangler, Derek P; Bell, Martha Ann; Deater-Deckard, Kirby

2015-09-01

There is uncertainty about whether respiratory sinus arrhythmia (RSA), a cardiac marker of adaptive emotion regulation, is involved in relatively low or high executive function performance. In the present study, we investigated (a) whether RSA during rest and tasks predict both relatively low and high executive function within a larger quadratic association among the two variables, and (b) the extent to which this quadratic trend was moderated by individual differences in emotion regulation. To achieve these aims, a sample of ethnically and socioeconomically diverse women self-reported reappraisal and emotion suppression. They next experienced a 2-min resting period during which electrocardiogram (ECG) was continually assessed. In the next phase, the women completed an array of executive function and nonexecutive cognitive tasks while ECG was measured throughout. As anticipated, resting RSA showed a quadratic association with executive function that was strongest for high suppression. These results suggest that relatively high resting RSA may predict poor executive function ability when emotion regulation consumes executive control resources needed for ongoing cognitive performance. © 2015 Society for Psychophysiological Research.

Time-dependent reliability sensitivity analysis of motion mechanisms

International Nuclear Information System (INIS)

Wei, Pengfei; Song, Jingwen; Lu, Zhenzhou; Yue, Zhufeng

2016-01-01

Reliability sensitivity analysis aims at identifying the source of structure/mechanism failure, and quantifying the effects of each random source or their distribution parameters on failure probability or reliability. In this paper, the time-dependent parametric reliability sensitivity (PRS) analysis as well as the global reliability sensitivity (GRS) analysis is introduced for the motion mechanisms. The PRS indices are defined as the partial derivatives of the time-dependent reliability w.r.t. the distribution parameters of each random input variable, and they quantify the effect of the small change of each distribution parameter on the time-dependent reliability. The GRS indices are defined for quantifying the individual, interaction and total contributions of the uncertainty in each random input variable to the time-dependent reliability. The envelope function method combined with the first order approximation of the motion error function is introduced for efficiently estimating the time-dependent PRS and GRS indices. Both the time-dependent PRS and GRS analysis techniques can be especially useful for reliability-based design. This significance of the proposed methods as well as the effectiveness of the envelope function method for estimating the time-dependent PRS and GRS indices are demonstrated with a four-bar mechanism and a car rack-and-pinion steering linkage. - Highlights: • Time-dependent parametric reliability sensitivity analysis is presented. • Time-dependent global reliability sensitivity analysis is presented for mechanisms. • The proposed method is especially useful for enhancing the kinematic reliability. • An envelope method is introduced for efficiently implementing the proposed methods. • The proposed method is demonstrated by two real planar mechanisms.

Influence of time dependent effects on the disposal environments of low and intermediate level radioactive wastes

International Nuclear Information System (INIS)

1984-12-01

Reviews are presented firstly of potential events and processes which may affect the evolution of the disposal environments of low and intermediate level radioactive wastes in Britain and secondly of previous studies carried out worldwide in the field of time dependent effects. From the latter review available methodologies for incorporating time dependence into radiological assessments are identified. Finally, proposals are presented for the design and development of a time dependent effects model, based on the existing far field state model (FFSM) developed for ONWI in USA. (author)

Time-dependent density-functional theory in massively parallel computer architectures: the OCTOPUS project.

Science.gov (United States)

Andrade, Xavier; Alberdi-Rodriguez, Joseba; Strubbe, David A; Oliveira, Micael J T; Nogueira, Fernando; Castro, Alberto; Muguerza, Javier; Arruabarrena, Agustin; Louie, Steven G; Aspuru-Guzik, Alán; Rubio, Angel; Marques, Miguel A L

2012-06-13

Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this paper we present the ongoing efforts to achieve the parallelization of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time. This approach has great potential for execution in massively parallel systems such as modern supercomputers with thousands of processors and graphics processing units (GPUs). For harvesting the potential of conventional supercomputers, the main strategy is a multi-level parallelization scheme that combines the inherent scalability of real-time TDDFT with a real-space grid domain-partitioning approach. A scalable Poisson solver is critical for the efficiency of this scheme. For GPUs, we show how using blocks of Kohn-Sham states provides the required level of data parallelism and that this strategy is also applicable for code optimization on standard processors. Our results show that real-time TDDFT, as implemented in octopus, can be the method of choice for studying the excited states of large molecular systems in modern parallel architectures.

Time-dependent density-functional theory in massively parallel computer architectures: the octopus project

Science.gov (United States)

Andrade, Xavier; Alberdi-Rodriguez, Joseba; Strubbe, David A.; Oliveira, Micael J. T.; Nogueira, Fernando; Castro, Alberto; Muguerza, Javier; Arruabarrena, Agustin; Louie, Steven G.; Aspuru-Guzik, Alán; Rubio, Angel; Marques, Miguel A. L.

2012-06-01

Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this paper we present the ongoing efforts to achieve the parallelization of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time. This approach has great potential for execution in massively parallel systems such as modern supercomputers with thousands of processors and graphics processing units (GPUs). For harvesting the potential of conventional supercomputers, the main strategy is a multi-level parallelization scheme that combines the inherent scalability of real-time TDDFT with a real-space grid domain-partitioning approach. A scalable Poisson solver is critical for the efficiency of this scheme. For GPUs, we show how using blocks of Kohn-Sham states provides the required level of data parallelism and that this strategy is also applicable for code optimization on standard processors. Our results show that real-time TDDFT, as implemented in octopus, can be the method of choice for studying the excited states of large molecular systems in modern parallel architectures.

Time-dependent density-functional theory in massively parallel computer architectures: the octopus project

International Nuclear Information System (INIS)

Andrade, Xavier; Aspuru-Guzik, Alán; Alberdi-Rodriguez, Joseba; Rubio, Angel; Strubbe, David A; Louie, Steven G; Oliveira, Micael J T; Nogueira, Fernando; Castro, Alberto; Muguerza, Javier; Arruabarrena, Agustin; Marques, Miguel A L

2012-01-01

Octopus is a general-purpose density-functional theory (DFT) code, with a particular emphasis on the time-dependent version of DFT (TDDFT). In this paper we present the ongoing efforts to achieve the parallelization of octopus. We focus on the real-time variant of TDDFT, where the time-dependent Kohn-Sham equations are directly propagated in time. This approach has great potential for execution in massively parallel systems such as modern supercomputers with thousands of processors and graphics processing units (GPUs). For harvesting the potential of conventional supercomputers, the main strategy is a multi-level parallelization scheme that combines the inherent scalability of real-time TDDFT with a real-space grid domain-partitioning approach. A scalable Poisson solver is critical for the efficiency of this scheme. For GPUs, we show how using blocks of Kohn-Sham states provides the required level of data parallelism and that this strategy is also applicable for code optimization on standard processors. Our results show that real-time TDDFT, as implemented in octopus, can be the method of choice for studying the excited states of large molecular systems in modern parallel architectures. (topical review)

Spike-timing dependent plasticity in a transistor-selected resistive switching memory

International Nuclear Information System (INIS)

Ambrogio, S; Balatti, S; Nardi, F; Facchinetti, S; Ielmini, D

2013-01-01

In a neural network, neuron computation is achieved through the summation of input signals fed by synaptic connections. The synaptic activity (weight) is dictated by the synchronous firing of neurons, inducing potentiation/depression of the synaptic connection. This learning function can be supported by the resistive switching memory (RRAM), which changes its resistance depending on the amplitude, the pulse width and the bias polarity of the applied signal. This work shows a new synapse circuit comprising a MOS transistor as a selector and a RRAM as a variable resistance, displaying spike-timing dependent plasticity (STDP) similar to the one originally experienced in biological neural networks. We demonstrate long-term potentiation and long-term depression by simulations with an analytical model of resistive switching. Finally, the experimental demonstration of the new STDP scheme is presented. (paper)

Extending the accuracy of the SNAP interatomic potential form

Science.gov (United States)

Wood, Mitchell A.; Thompson, Aidan P.

2018-06-01

The Spectral Neighbor Analysis Potential (SNAP) is a classical interatomic potential that expresses the energy of each atom as a linear function of selected bispectrum components of the neighbor atoms. An extension of the SNAP form is proposed that includes quadratic terms in the bispectrum components. The extension is shown to provide a large increase in accuracy relative to the linear form, while incurring only a modest increase in computational cost. The mathematical structure of the quadratic SNAP form is similar to the embedded atom method (EAM), with the SNAP bispectrum components serving as counterparts to the two-body density functions in EAM. The effectiveness of the new form is demonstrated using an extensive set of training data for tantalum structures. Similar to artificial neural network potentials, the quadratic SNAP form requires substantially more training data in order to prevent overfitting. The quality of this new potential form is measured through a robust cross-validation analysis.

Linear-quadratic dose kinetics or dose-dependent repair/misrepair

International Nuclear Information System (INIS)

Braby, L.A.; Nelson, J.M.

1992-01-01

Models for the response of cells exposed to low (LET) linear energy transfer radiation can be grouped into three general types on the basis of assumptions about the nature of the interaction which results in the shoulder of the survival curve. The three forms of interaction are 1) sublethal damage becoming lethal, 2) potentially lethal damage becoming irreparable, and 3) potentially lethal damage ''saturating'' a repair system. The effects that these three forms of interaction would have on the results of specific types of experiments are investigated. Comparisons with experimental results indicate that only the second type is significant in determining the response of typical cultured mammalian cells. (author)

Time-dependent Dyson orbital theory

NARCIS (Netherlands)

Gritsenko, O.V.; Baerends, E.J.

2016-01-01

Although time-dependent density functional theory (TDDFT) has become the tool of choice for real-time propagation of the electron density ρN(t) of N-electron systems, it also encounters problems in this application. The first problem is the neglect of memory effects stemming from the, in TDDFT

General quadratic gauge theory: constraint structure, symmetries and physical functions

Energy Technology Data Exchange (ETDEWEB)

Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V [Lebedev Physics Institute, Moscow (Russian Federation)

2005-06-17

How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation to specific features of the theory in the Lagrangian formulation, especially relate the constraint structure to the gauge transformation structure of the Lagrangian action? How can we construct the general expression for the gauge charge if the constraint structure in the Hamiltonian formulation is known? Whether we can identify the physical functions defined as commuting with first-class constraints in the Hamiltonian formulation and the physical functions defined as gauge invariant functions in the Lagrangian formulation? The aim of the present paper is to consider the general quadratic gauge theory and to answer the above questions for such a theory in terms of strict assertions. To fulfil such a programme, we demonstrate the existence of the so-called superspecial phase-space variables in terms of which the quadratic Hamiltonian action takes a simple canonical form. On the basis of such a representation, we analyse a functional arbitrariness in the solutions of the equations of motion of the quadratic gauge theory and derive the general structure of symmetries by analysing a symmetry equation. We then use these results to identify the two definitions of physical functions and thus prove the Dirac conjecture.

On the Impact of a Quadratic Acceleration Term in the Analysis of Position Time Series

Science.gov (United States)

Bogusz, Janusz; Klos, Anna; Bos, Machiel Simon; Hunegnaw, Addisu; Teferle, Felix Norman

2016-04-01

The analysis of Global Navigation Satellite System (GNSS) position time series generally assumes that each of the coordinate component series is described by the sum of a linear rate (velocity) and various periodic terms. The residuals, the deviations between the fitted model and the observations, are then a measure of the epoch-to-epoch scatter and have been used for the analysis of the stochastic character (noise) of the time series. Often the parameters of interest in GNSS position time series are the velocities and their associated uncertainties, which have to be determined with the highest reliability. It is clear that not all GNSS position time series follow this simple linear behaviour. Therefore, we have added an acceleration term in the form of a quadratic polynomial function to the model in order to better describe the non-linear motion in the position time series. This non-linear motion could be a response to purely geophysical processes, for example, elastic rebound of the Earth's crust due to ice mass loss in Greenland, artefacts due to deficiencies in bias mitigation models, for example, of the GNSS satellite and receiver antenna phase centres, or any combination thereof. In this study we have simulated 20 time series with different stochastic characteristics such as white, flicker or random walk noise of length of 23 years. The noise amplitude was assumed at 1 mm/y-/4. Then, we added the deterministic part consisting of a linear trend of 20 mm/y (that represents the averaged horizontal velocity) and accelerations ranging from minus 0.6 to plus 0.6 mm/y2. For all these data we estimated the noise parameters with Maximum Likelihood Estimation (MLE) using the Hector software package without taken into account the non-linear term. In this way we set the benchmark to then investigate how the noise properties and velocity uncertainty may be affected by any un-modelled, non-linear term. The velocities and their uncertainties versus the accelerations for

Time-dependent scattering in resonance lines

International Nuclear Information System (INIS)

Kunasz, P.B.

1983-01-01

A numerical finite-difference method is presented for the problem of time-dependent line transfer in a finite slab in which material density is sufficiently low that the time of flight between scatterings greatly exceeds the relaxation time of the upper state of the scattering transition. The medium is assumed to scatter photons isotropically, with complete frequency redistribution. Numerical solutions are presented for a homogeneous, time-independent slab illuminated by an externally imposed radiation field which enters the slab at t = 0. Graphical results illustrate relaxation to steady state of trapped internal radiation, emergent energy, and emergent profiles. A review of the literature is also given in which the time-dependent line transfer problem is discussed in the context of recent analytical work

Exact solutions for oscillators with quadratic damping and mixed-parity nonlinearity

International Nuclear Information System (INIS)

Lai, S K; Chow, K W

2012-01-01

Exact vibration modes of a nonlinear oscillator, which contains both quadratic friction and a mixed-parity restoring force, are derived analytically. Two families of exact solutions are obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behaviour of the system in response to changes in physical parameters that concern nonlinearity. The physical significance of the signs (i.e. attractive or repulsive nature) of the linear, quadratic and cubic restoring forces is discussed. A qualitative analysis is also conducted to provide valuable physical insight into the nature of the system. (paper)