Hartree--Fock density matrix equation
International Nuclear Information System (INIS)
Cohen, L.; Frishberg, C.
1976-01-01
An equation for the Hartree--Fock density matrix is discussed and the possibility of solving this equation directly for the density matrix instead of solving the Hartree--Fock equation for orbitals is considered. Toward that end the density matrix is expanded in a finite basis to obtain the matrix representative equation. The closed shell case is considered. Two numerical schemes are developed and applied to a number of examples. One example is given where the standard orbital method does not converge while the method presented here does
Spatial charge motion on an uniform density matrix-general equations in opened and closed circuits
International Nuclear Information System (INIS)
Aguiar Monsanto, S. de.
1983-01-01
The motion of a space charge cloud embedded in a matrix of constant immobile charge density is studied in open as well as in closed circuit. In the first case, open circuit, the solution is almost trivial as compared as the other one in which, after some work, the problem is reduced to an ordinary differential equation. The method of solution is parallel to that employed in the study of monopolar free space charge motion. The voltage and the current produced by a system with no net charge but with unbalanced local charge density were calculated using the general equations derived in the first part of the work. (Author) [pt
Avanzini, Francesco; Moro, Giorgio J
2018-03-15
The quantum molecular trajectory is the deterministic trajectory, arising from the Bohm theory, that describes the instantaneous positions of the nuclei of molecules by assuring the agreement with the predictions of quantum mechanics. Therefore, it provides the suitable framework for representing the geometry and the motions of molecules without neglecting their quantum nature. However, the quantum molecular trajectory is extremely demanding from the computational point of view, and this strongly limits its applications. To overcome such a drawback, we derive a stochastic representation of the quantum molecular trajectory, through projection operator techniques, for the degrees of freedom of an open quantum system. The resulting Fokker-Planck operator is parametrically dependent upon the reduced density matrix of the open system. Because of the pilot role played by the reduced density matrix, this stochastic approach is able to represent accurately the main features of the open system motions both at equilibrium and out of equilibrium with the environment. To verify this procedure, the predictions of the stochastic and deterministic representation are compared for a model system of six interacting harmonic oscillators, where one oscillator is taken as the open quantum system of interest. The undeniable advantage of the stochastic approach is that of providing a simplified and self-contained representation of the dynamics of the open system coordinates. Furthermore, it can be employed to study the out of equilibrium dynamics and the relaxation of quantum molecular motions during photoinduced processes, like photoinduced conformational changes and proton transfers.
Kalthoff, Mona; Keim, Frederik; Krull, Holger; Uhrig, Götz S.
2017-05-01
The density matrix formalism and the equation of motion approach are two semi-analytical methods that can be used to compute the non-equilibrium dynamics of correlated systems. While for a bilinear Hamiltonian both formalisms yield the exact result, for any non-bilinear Hamiltonian a truncation is necessary. Due to the fact that the commonly used truncation schemes differ for these two methods, the accuracy of the obtained results depends significantly on the chosen approach. In this paper, both formalisms are applied to the quantum Rabi model. This allows us to compare the approximate results and the exact dynamics of the system and enables us to discuss the accuracy of the approximations as well as the advantages and the disadvantages of both methods. It is shown to which extent the results fulfill physical requirements for the observables and which properties of the methods lead to unphysical results.
On matrix fractional differential equations
Adem Kılıçman; Wasan Ajeel Ahmood
2017-01-01
The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objec...
On matrix fractional differential equations
Directory of Open Access Journals (Sweden)
Adem Kılıçman
2017-01-01
Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.
International Nuclear Information System (INIS)
March, N.H.
2009-08-01
In this Journal, March and Suhai have earlier set up a first-order Dirac idempotent density matrix theory for one- and two-level occupancy in which the only input required is the nonrelativistic ground-state electron density. Here, an analytic generalization is provided for the case of spherical electron densities for arbitrary level occupancy. Be-like atomic ions are referred to as an example, but 'almost spherical' molecules like SiH 4 and GeH 4 also become accessible. (author)
Minimal solution for inconsistent singular fuzzy matrix equations
Directory of Open Access Journals (Sweden)
M. Nikuie
2013-10-01
Full Text Available The fuzzy matrix equations $Ailde{X}=ilde{Y}$ is called a singular fuzzy matrix equations while the coefficients matrix of its equivalent crisp matrix equations be a singular matrix. The singular fuzzy matrix equations are divided into two parts: consistent singular matrix equations and inconsistent fuzzy matrix equations. In this paper, the inconsistent singular fuzzy matrix equations is studied and the effect of generalized inverses in finding minimal solution of an inconsistent singular fuzzy matrix equations are investigated.
About the solvability of matrix polynomial equations
Netzer, Tim; Thom, Andreas
2016-01-01
We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.
Some remarks on unilateral matrix equations
International Nuclear Information System (INIS)
Cerchiai, Bianca L.; Zumino, Bruno
2001-01-01
We briefly review the results of our paper LBNL-46775: We study certain solutions of left-unilateral matrix equations. These are algebraic equations where the coefficients and the unknown are square matrices of the same order, or, more abstractly, elements of an associative, but possibly noncommutative algebra, and all coefficients are on the left. Recently such equations have appeared in a discussion of generalized Born-Infeld theories. In particular, two equations, their perturbative solutions and the relation between them are studied, applying a unified approach based on the generalized Bezout theorem for matrix polynomials
Lax representations for matrix short pulse equations
Popowicz, Z.
2017-10-01
The Lax representation for different matrix generalizations of Short Pulse Equations (SPEs) is considered. The four-dimensional Lax representations of four-component Matsuno, Feng, and Dimakis-Müller-Hoissen-Matsuno equations are obtained. The four-component Feng system is defined by generalization of the two-dimensional Lax representation to the four-component case. This system reduces to the original Feng equation, to the two-component Matsuno equation, or to the Yao-Zang equation. The three-component version of the Feng equation is presented. The four-component version of the Matsuno equation with its Lax representation is given. This equation reduces the new two-component Feng system. The two-component Dimakis-Müller-Hoissen-Matsuno equations are generalized to the four-parameter family of the four-component SPE. The bi-Hamiltonian structure of this generalization, for special values of parameters, is defined. This four-component SPE in special cases reduces to the new two-component SPE.
Zhong, Zai-Zhe
2004-01-01
The partial separability of multipartite qubit density matrixes is strictly defined. We give a reduction way from N-partite qubit density matrixes to bipartite qubit density matrixes, and prove a necessary condition that a N-partite qubit density matrix to be partially separable is its reduced density matrix to satisfy PPT condition.
S-matrix approach to the equation of state of dilute nuclear matter
Indian Academy of Sciences (India)
2014-04-01
matrix framework, a method is presented to calculate the equation of state of dilute warm nuclear matter. The result is a model-independent virial series for the pressure and density that systematically includes contributions from ...
Minimal length, Friedmann equations and maximum density
Energy Technology Data Exchange (ETDEWEB)
Awad, Adel [Center for Theoretical Physics, British University of Egypt,Sherouk City 11837, P.O. Box 43 (Egypt); Department of Physics, Faculty of Science, Ain Shams University,Cairo, 11566 (Egypt); Ali, Ahmed Farag [Centre for Fundamental Physics, Zewail City of Science and Technology,Sheikh Zayed, 12588, Giza (Egypt); Department of Physics, Faculty of Science, Benha University,Benha, 13518 (Egypt)
2014-06-16
Inspired by Jacobson’s thermodynamic approach, Cai et al. have shown the emergence of Friedmann equations from the first law of thermodynamics. We extend Akbar-Cai derivation http://dx.doi.org/10.1103/PhysRevD.75.084003 of Friedmann equations to accommodate a general entropy-area law. Studying the resulted Friedmann equations using a specific entropy-area law, which is motivated by the generalized uncertainty principle (GUP), reveals the existence of a maximum energy density closed to Planck density. Allowing for a general continuous pressure p(ρ,a) leads to bounded curvature invariants and a general nonsingular evolution. In this case, the maximum energy density is reached in a finite time and there is no cosmological evolution beyond this point which leaves the big bang singularity inaccessible from a spacetime prospective. The existence of maximum energy density and a general nonsingular evolution is independent of the equation of state and the spacial curvature k. As an example we study the evolution of the equation of state p=ωρ through its phase-space diagram to show the existence of a maximum energy which is reachable in a finite time.
Correlated density matrix theory of spatially inhomogeneous Bose fluids
International Nuclear Information System (INIS)
Gernoth, K.A.; Clark, J.W.; Ristig, M.L.
1994-06-01
In this paper, the variational Hartree-Jastrow theory of the ground state of spatially inhomogeneous Bose systems is extended to finite temperatures. The theory presented here is a generalization also in the sense that it extends the correlated density matrix approach, formulated previously for uniform Bose fluids, to systems with nonuniform density profiles. The method provides a framework in which the effects of thermal excitations on the spatial structure of a Bose fluid, as represented by the density profile and the two-body distribution functions, may be discussed on the basis on an ab initio microscopic description of the system. Thermal excitations make their appearance through self-consistently determined one-body and two-body potentials which enter the nonlinear, coupled Euler-Lagrange equations for the one-body density and for the pair distribution function. Since back-flow correlations are neglected, the excitations are described by a Feynman eigenvalue equation, suitably generalized to nonzero temperatures. The only external quantities entering the correlated density matrix theory elaborated here are the bare two-body interaction potential and, in actual applications, the boundary conditions to be imposed on the one-body density. 30 refs
The matrix nonlinear Schrodinger equation in dimension 2
DEFF Research Database (Denmark)
Zuhan, L; Pedersen, Michael
2001-01-01
In this paper we study the existence of global solutions to the Cauchy problem for the matrix nonlinear Schrodinger equation (MNLS) in 2 space dimensions. A sharp condition for the global existence is obtained for this equation. This condition is in terms of an exact stationary solution...... of a semilinear elliptic equation. In the scalar case, the MNLS reduces to the well-known cubic nonlinear Schrodinger equation for which existence of solutions has been studied by many authors. (C) 2001 Academic Press....
Burnett, K.; Cooper, J.
1980-01-01
The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.
Functional equations in matrix normed spaces
Indian Academy of Sciences (India)
The abstract characterization given for linear spaces of bounded Hilbert space operators in terms of ... effect on operator algebra theory (see [12]). .... of functional equations for the proof of new fixed point theorems with applications. By.
Approximate Solution of LR Fuzzy Sylvester Matrix Equations
Directory of Open Access Journals (Sweden)
Xiaobin Guo
2013-01-01
Full Text Available The fuzzy Sylvester matrix equation AX~+X~B=C~ in which A,B are m×m and n×n crisp matrices, respectively, and C~ is an m×n LR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices, we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system. Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems. The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.
Linear matrix differential equations of higher-order and applications
Directory of Open Access Journals (Sweden)
Mustapha Rachidi
2008-07-01
Full Text Available In this article, we study linear differential equations of higher-order whose coefficients are square matrices. The combinatorial method for computing the matrix powers and exponential is adopted. New formulas representing auxiliary results are obtained. This allows us to prove properties of a large class of linear matrix differential equations of higher-order, in particular results of Apostol and Kolodner are recovered. Also illustrative examples and applications are presented.
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.
Three Interpretations of the Matrix Equation Ax = b
Larson, Christine; Zandieh, Michelle
2013-01-01
Many of the central ideas in an introductory undergraduate linear algebra course are closely tied to a set of interpretations of the matrix equation Ax = b (A is a matrix, x and b are vectors): linear combination interpretations, systems interpretations, and transformation interpretations. We consider graphic and symbolic representations for each,…
Exact solution of some linear matrix equations using algebraic methods
Djaferis, T. E.; Mitter, S. K.
1977-01-01
A study is done of solution methods for Linear Matrix Equations including Lyapunov's equation, using methods of modern algebra. The emphasis is on the use of finite algebraic procedures which are easily implemented on a digital computer and which lead to an explicit solution to the problem. The action f sub BA is introduced a Basic Lemma is proven. The equation PA + BP = -C as well as the Lyapunov equation are analyzed. Algorithms are given for the solution of the Lyapunov and comment is given on its arithmetic complexity. The equation P - A'PA = Q is studied and numerical examples are given.
String beta function equations from c=1 matrix model
Dhar, A; Wadia, S R; Dhar, Avinash; Mandal, Gautam; Wadia, Spenta R
1995-01-01
We derive the \\sigma-model tachyon \\beta-function equation of 2-dimensional string theory, in the background of flat space and linear dilaton, working entirely within the c=1 matrix model. The tachyon \\beta-function equation is satisfied by a \\underbar{nonlocal} and \\underbar{nonlinear} combination of the (massless) scalar field of the matrix model. We discuss the possibility of describing the `discrete states' as well as other possible gravitational and higher tensor backgrounds of 2-dimensional string theory within the c=1 matrix model. We also comment on the realization of the W-infinity symmetry of the matrix model in the string theory. The present work reinforces the viewpoint that a nonlocal (and nonlinear) transform is required to extract the space-time physics of 2-dimensional string theory from the c=1 matrix model.
Explicit treatment of N-body correlations within a density-matrix formalism
International Nuclear Information System (INIS)
Shun-Jin, W.; Cassing, W.
1985-01-01
The nuclear many-body problem is reformulated in the density-matrix approach such that n-body correlations are separated out from the reduced density matrix rho/sub n/. A set of equations for the time evolution of the n-body correlations c/sub n/ is derived which allows for physically transparent truncations with respect to the order of correlations. In the stationary limit (c/sub n/ = 0) a restriction to two-body correlations yields a generalized Bethe-Goldstone equation a restriction to body correlations yields generalized Faddeev equations in the density-matrix formulation. Furthermore it can be shown that any truncation of the set of equations (c/sub n/ = 0, n>m) is compatible with conservation laws, a quality which in general is not fulfilled if higher order correlations are treated perturbatively
Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.
2016-07-01
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
Exact many-body dynamics with stochastic one-body density matrix evolution
International Nuclear Information System (INIS)
Lacroix, D.
2004-05-01
In this article, we discuss some properties of the exact treatment of the many-body problem with stochastic Schroedinger equation (SSE). Starting from the SSE theory, an equivalent reformulation is proposed in terms of quantum jumps in the density matrix space. The technical details of the derivation a stochastic version of the Liouville von Neumann equation are given. It is shown that the exact Many-Body problem could be replaced by an ensemble of one-body density evolution, where each density matrix evolves according to its own mean-field augmented by a one-body noise. (author)
Density matrix in quantum electrodynamics, equivalence principle and Hawking effect
International Nuclear Information System (INIS)
Frolov, V.P.; Gitman, D.M.
1978-01-01
The expression for the density matrix describing particles of one sort (electrons or positrons) created by an external electromagnetic field from the vacuum is obtained. The explicit form of the density matrix is found for the case of constant and uniform electric field. Arguments are given for the presence of a connection between the thermal nature of the density matrix describing particles created by the gravitational field of a black hole and the equivalence principle. (author)
Conditional density matrix: systems and subsystems in quantum mechanics
International Nuclear Information System (INIS)
Belokurov, V.V.; Khrustalev, O.A.; Sadovnichij, V.A.; Timofeevskaya, O.D.
2003-01-01
A new quantum mechanical notion - Conditional Density Matrix - is discussed and is applied to describe some physical processes. This notion is a natural generalization of von Neumann density matrix for such processes as divisions of quantum systems into subsystems and reunifications of subsystems into new joint systems. Conditional Density Matrix assigns a quantum state to a subsystem of a composite system on condition that another part of the composite system is in some pure state
Watching excitons move: the time-dependent transition density matrix
Ullrich, Carsten
2012-02-01
Time-dependent density-functional theory allows one to calculate excitation energies and the associated transition densities in principle exactly. The transition density matrix (TDM) provides additional information on electron-hole localization and coherence of specific excitations of the many-body system. We have extended the TDM concept into the real-time domain in order to visualize the excited-state dynamics in conjugated molecules. The time-dependent TDM is defined as an implicit density functional, and can be approximately obtained from the time-dependent Kohn-Sham orbitals. The quality of this approximation is assessed in simple model systems. A computational scheme for real molecular systems is presented: the time-dependent Kohn-Sham equations are solved with the OCTOPUS code and the time-dependent Kohn-Sham TDM is calculated using a spatial partitioning scheme. The method is applied to show in real time how locally created electron-hole pairs spread out over neighboring conjugated molecular chains. The coupling mechanism, electron-hole coherence, and the possibility of charge separation are discussed.
Density matrix embedding in an antisymmetrized geminal power bath
International Nuclear Information System (INIS)
Tsuchimochi, Takashi; Welborn, Matthew; Van Voorhis, Troy
2015-01-01
Density matrix embedding theory (DMET) has emerged as a powerful tool for performing wave function-in-wave function embedding for strongly correlated systems. In traditional DMET, an accurate calculation is performed on a small impurity embedded in a mean field bath. Here, we extend the original DMET equations to account for correlation in the bath via an antisymmetrized geminal power (AGP) wave function. The resulting formalism has a number of advantages. First, it allows one to properly treat the weak correlation limit of independent pairs, which DMET is unable to do with a mean-field bath. Second, it associates a size extensive correlation energy with a given density matrix (for the models tested), which AGP by itself is incapable of providing. Third, it provides a reasonable description of charge redistribution in strongly correlated but non-periodic systems. Thus, AGP-DMET appears to be a good starting point for describing electron correlation in molecules, which are aperiodic and possess both strong and weak electron correlation
On the Solution of the Rational Matrix Equation
Directory of Open Access Journals (Sweden)
Faßbender Heike
2007-01-01
Full Text Available We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation , where is symmetric positive definite and is nonsingular. Such equations arise for instance in the analysis of stationary Gaussian reciprocal processes over a finite interval. Its unique largest positive definite solution coincides with the unique positive definite solution of a related discrete-time algebraic Riccati equation (DARE. We discuss how to use the butterfly algorithm to solve the DARE. This approach is compared to several fixed-point and doubling-type iterative methods suggested in the literature.
Minimal solution of linear formed fuzzy matrix equations
Directory of Open Access Journals (Sweden)
Maryam Mosleh
2012-10-01
Full Text Available In this paper according to the structured element method, the $mimes n$ inconsistent fuzzy matrix equation $Ailde{X}=ilde{B},$ which are linear formed by fuzzy structured element, is investigated. The necessary and sufficient condition for the existence of a fuzzy solution is also discussed. some examples are presented to illustrate the proposed method.
Minimal parameter solution of the orthogonal matrix differential equation
Bar-Itzhack, Itzhack Y.; Markley, F. Landis
1990-01-01
As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed emplying the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.
Single-particle density matrix of liquid 4He
International Nuclear Information System (INIS)
Vakarchuk, I.A.
2008-01-01
The density single-particle matrix in the coordinate notation was calculated based on the expression for the interacting Bose-particle N system density matrix. Under the low temperatures the mentioned matrix in the first approximation enables to reproduce the Bogoliubov theory results. In the classical terms the mentioned theory enables to reproduce the results of the theory of the classical fluids in the approximation of the chaotic phases. On the basis of the density single-particle matrix one managed to obtain the function of the pulse distribution of the particles, the Bose-liquid average kinetic energy, and to study the Bose-Einstein condensation phenomenon [ru
Loop equations for multi-cut matrix models
International Nuclear Information System (INIS)
Akemann, G.
1995-03-01
The loop equation for the complex one-matrix model with a multi-cut structure is derived and solved in the planar limit. An iterative scheme for higher genus contributions to the free energy and the multi-loop correlators is presented for the two-cut model, where explicit results are given up to and including genus two. The double-scaling limit is analyzed and the relation to the one-cut solution of the hermitian and complex one-matrix model is discussed. (orig.)
Density matrix of strongly coupled quantum dot - microcavity system
International Nuclear Information System (INIS)
Nguyen Van Hop
2009-01-01
Any two-level quantum system can be used as a quantum bit (qubit) - the basic element of all devices and systems for quantum information and quantum computation. Recently it was proposed to study the strongly coupled system consisting of a two-level quantum dot and a monoenergetic photon gas in a microcavity-the strongly coupled quantum dot-microcavity (QD-MC) system for short, with the Jaynes-Cumming total Hamiltonian, for the application in the quantum information processing. Different approximations were applied in the theoretical study of this system. In this work, on the basis of the exact solution of the Schrodinger equation for this system without dissipation we derive the exact formulae for its density matrix. The realization of a qubit in this system is discussed. The solution of the system of rate equation for the strongly coupled QD-MC system in the presence of the interaction with the environment was also established in the first order approximation with respect to this interaction.
Generalized Freud's equation and level densities with polynomial
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 81; Issue 2. Generalized Freud's equation and level densities with polynomial potential. Akshat Boobna Saugata Ghosh. Research Articles Volume 81 ... Keywords. Orthogonal polynomial; Freud's equation; Dyson–Mehta method; methods of resolvents; level density.
Monodromy of the matrix Schroedinger equations and Darboux transformations
Goncharenko, V M
1998-01-01
A Schroedinger operator L=-d sup 2 /dz sup 2 +U(z) with a matrix-valued rational potential U(z) is said to have trivial monodromy if all the solutions of the corresponding Schroedinger equations L psi=lambda psi are single-valued in the complex plane z is an element of C for any lambda. A local criterion of this property in terms of the Laurent coefficients of the potential U near its singularities, which are assumed to be regular, is found. It is proved that any such operator with a potential vanishing at infinity can be obtained by a matrix analogue of the Darboux transformation from the Schroedinger operator L sub o =-d sup 2 /dz sup 2. This generalizes the well known Duistermaat-Gruenbaum result to the matrix case and gives the explicit description of the Schroedinger operators with trivial monodromy in this case. (author)
Reduced density matrix functional theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Baldsiefen, Tim
2012-10-15
Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to
Reduced density matrix functional theory at finite temperature
International Nuclear Information System (INIS)
Baldsiefen, Tim
2012-10-01
Density functional theory (DFT) is highly successful in many fields of research. There are, however, areas in which its performance is rather limited. An important example is the description of thermodynamical variables of a quantum system in thermodynamical equilibrium. Although the finite-temperature version of DFT (FT-DFT) rests on a firm theoretical basis and is only one year younger than its brother, groundstate DFT, it has been successfully applied to only a few problems. Because FT-DFT, like DFT, is in principle exact, these shortcomings can be attributed to the difficulties of deriving valuable functionals for FT-DFT. In this thesis, we are going to present an alternative theoretical description of quantum systems in thermal equilibrium. It is based on the 1-reduced density matrix (1RDM) of the system, rather than on its density and will rather cumbersomly be called finite-temperature reduced density matrix functional theory (FT-RDMFT). Its zero-temperature counterpart (RDMFT) proved to be successful in several fields, formerly difficult to address via DFT. These fields include, for example, the calculation of dissociation energies or the calculation of the fundamental gap, also for Mott insulators. This success is mainly due to the fact that the 1RDM carries more directly accessible ''manybody'' information than the density alone, leading for example to an exact description of the kinetic energy functional. This sparks the hope that a description of thermodynamical systems employing the 1RDM via FT-RDMFT can yield an improvement over FT-DFT. Giving a short review of RDMFT and pointing out difficulties when describing spin-polarized systems initiates our work. We then lay the theoretical framework for FT-RDMFT by proving the required Hohenberg-Kohn-like theorems, investigating and determining the domain of FT-RDMFT functionals and by deriving several properties of the exact functional. Subsequently, we present a perturbative method to iteratively construct
On the statistical interpretation of quantum mechanics: evolution of the density matrix
International Nuclear Information System (INIS)
Benzecri, J.-P.
1986-01-01
Using two classical examples (the Young slit experiment and coherent and incoherent crystal diffraction of neutrons) we show in a general framework, that for a system viewed as consisting of two components, depolarisation of the density matrix by one of these can result from the application of the Schroedinger equation to the global system [fr
A J matrix engine for density functional theory calculations
International Nuclear Information System (INIS)
White, C.A.; Head-Gordon, M.
1996-01-01
We introduce a new method for the formation of the J matrix (Coulomb interaction matrix) within a basis of Cartesian Gaussian functions, as needed in density functional theory and Hartree endash Fock calculations. By summing the density matrix into the underlying Gaussian integral formulas, we have developed a J matrix open-quote open-quote engine close-quote close-quote which forms the exact J matrix without explicitly forming the full set of two electron integral intermediates. Several precomputable quantities have been identified, substantially reducing the number of floating point operations and memory accesses needed in a J matrix calculation. Initial timings indicate a speedup of greater than four times for the (pp parallel pp) class of integrals with speedups increasing to over ten times for (ff parallel ff) integrals. copyright 1996 American Institute of Physics
Gradient-based stochastic estimation of the density matrix
Wang, Zhentao; Chern, Gia-Wei; Batista, Cristian D.; Barros, Kipton
2018-03-01
Fast estimation of the single-particle density matrix is key to many applications in quantum chemistry and condensed matter physics. The best numerical methods leverage the fact that the density matrix elements f(H)ij decay rapidly with distance rij between orbitals. This decay is usually exponential. However, for the special case of metals at zero temperature, algebraic decay of the density matrix appears and poses a significant numerical challenge. We introduce a gradient-based probing method to estimate all local density matrix elements at a computational cost that scales linearly with system size. For zero-temperature metals, the stochastic error scales like S-(d+2)/2d, where d is the dimension and S is a prefactor to the computational cost. The convergence becomes exponential if the system is at finite temperature or is insulating.
Dresselhaus, Thomas; Neugebauer, Johannes; Knecht, Stefan; Keller, Sebastian; Ma, Yingjin; Reiher, Markus
2015-01-28
We present the first implementation of a density matrix renormalization group algorithm embedded in an environment described by density functional theory. The frozen density embedding scheme is used with a freeze-and-thaw strategy for a self-consistent polarization of the orbital-optimized wavefunction and the environmental densities with respect to each other.
Reduced-density-matrix theory and algebraic structures
International Nuclear Information System (INIS)
Kryachko, E.S.
1978-01-01
A survey of recent work on algebraic structures and reduced-density-matrix theory is presented. The approach leads to a method of classifying reduced density matrices and generalizes the notion of open and closed shells in many-body theory. 6 references
Soirat, Arnaud J. A.
Density Matrix Theory is a Quantum Mechanical formalism in which the wavefunction is eliminated and its role taken over by reduced density matrices. The interest of this is that, it allows one, in principle, to calculate any electronic property of a physical system, without having to solve the Schrodinger equation, using only two entities much simpler than an N-body wavefunction: first and second -order reduced density matrices. In practice, though, this very promising possibility faces the tremendous theoretical problem of N-representability, which has been solved for the former, but, until now, voids any hope of theoretically determining the latter. However, it has been shown that single determinant reduced density matrices of any order may be recovered from coherent X-ray diffraction data, if one provides a proper Quantum Mechanical description of the Crystallography experiment. A deeper investigation of this method is the purpose of this work, where we, first, further study the calculation of X-ray reduced density matrices N-representable by a single Slater determinant. In this context, we independently derive necessary and sufficient conditions for the uniqueness of the method. We then show how to account for electron correlation in this model. For the first time, indeed, we derive highly accurate, yet practical, density matrices approximately N-representable by correlated-determinant wavefunctions. The interest of such a result lies in the Quantum Mechanical validity of these density matrices, their property of being entirely obtainable from X-ray coherent diffraction data, their very high accuracy conferred by this known property of the N-representing wavefunction, as well as their definition as explicit functionals of the density. All of these properties are finally used in both a theoretical and a numerical application: in the former, we show that these density matrices may be used in the context of Density Functional Theory to highly accurately determine
International Nuclear Information System (INIS)
Park, Yujin; Kazantzis, Nikolaos; Parlos, Alexander G.; Chong, Kil To
2013-01-01
Highlights: • Numerical solution for stiff differential equations using matrix exponential method. • The approximation is based on First Order Hold assumption. • Various input examples applied to the point kinetics equations. • The method shows superior useful and effective activity. - Abstract: A system of nonlinear differential equations is derived to model the dynamics of neutron density and the delayed neutron precursors within a point kinetics equation modeling framework for a nuclear reactor. The point kinetic equations are mathematically characterized as stiff, occasionally nonlinear, ordinary differential equations, posing significant challenges when numerical solutions are sought and traditionally resulting in the need for smaller time step intervals within various computational schemes. In light of the above realization, the present paper proposes a new discretization method inspired by system-theoretic notions and technically based on a combination of the matrix exponential method (MEM) and the First-Order Hold (FOH) assumption. Under the proposed time discretization structure, the sampled-data representation of the nonlinear point kinetic system of equations is derived. The performance of the proposed time discretization procedure is evaluated using several case studies with sinusoidal reactivity profiles and multiple input examples (reactivity and neutron source function). It is shown, that by applying the proposed method under a First-Order Hold for the neutron density and the precursor concentrations at each time step interval, the stiffness problem associated with the point kinetic equations can be adequately addressed and resolved. Finally, as evidenced by the aforementioned detailed simulation studies, the proposed method retains its validity and accuracy for a wide range of reactor operating conditions, including large sampling periods dictated by physical and/or technical limitations associated with the current state of sensor and
The ab-initio density matrix renormalization group in practice.
Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic
2015-01-21
The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
The ab-initio density matrix renormalization group in practice
Energy Technology Data Exchange (ETDEWEB)
Olivares-Amaya, Roberto; Hu, Weifeng; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Nakatani, Naoki [Department of Chemistry, Princeton University, Princeton, New Jersey 08544 (United States); Catalysis Research Center, Hokkaido University, Kita 21 Nishi 10, Sapporo, Hokkaido 001-0021 (Japan)
2015-01-21
The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
Transition matrices and orbitals from reduced density matrix theory
Energy Technology Data Exchange (ETDEWEB)
Etienne, Thibaud [Université de Lorraine – Nancy, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy (France); CNRS, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy (France); Unité de Chimie Physique Théorique et Structurale, Université de Namur, Rue de Bruxelles 61, 5000 Namur (Belgium)
2015-06-28
In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.
External field as the functional of inhomogeneous density and the density matrix functional approach
Bobrov, V.B.; Trigger, S.A.; Vlasov, Y.P.
2012-01-01
Based on the Hohenberg-Kohn lemma and the hypotheses of the density functional existence for the external-field potential, it is shown that the strict result of the density functional theory is the equation of the external-field potential as the density functional. This result leads to the
Possibility of Quantum Teleportation and the Reduced Density Matrix
Institute of Scientific and Technical Information of China (English)
朱红波; 曾谨言
2001-01-01
It is shown that only the maximally entangled two-particle (spin 1/2) states whose one-particle reduced density matrix is p (i) = (1/2)I2 can realize the teleportation of an arbitrary one-particle spin state. Based on this,to teleport an arbitrary k-particle spin state, one must prepare an N-particle entangled state whose k-particle (k ＜ N) reduced density matrix has the structure 2-kI2k (I2k being the 2k × 2k identity matrix). The N-particle Greenberger-Horne-Zeilinger states cannot realize the teleportation of an arbitrary k-particle (N＞k≥2) state,except for special states with only two components.
Generalized Freud's equation and level densities with polynomial potential
Boobna, Akshat; Ghosh, Saugata
2013-08-01
We study orthogonal polynomials with weight $\\exp[-NV(x)]$, where $V(x)=\\sum_{k=1}^{d}a_{2k}x^{2k}/2k$ is a polynomial of order 2d. We derive the generalised Freud's equations for $d=3$, 4 and 5 and using this obtain $R_{\\mu}=h_{\\mu}/h_{\\mu -1}$, where $h_{\\mu}$ is the normalization constant for the corresponding orthogonal polynomials. Moments of the density functions, expressed in terms of $R_{\\mu}$, are obtained using Freud's equation and using this, explicit results of level densities as $N\\rightarrow\\infty$ are derived.
Power-spectral-density relationship for retarded differential equations
Barker, L. K.
1974-01-01
The power spectral density (PSD) relationship between input and output of a set of linear differential-difference equations of the retarded type with real constant coefficients and delays is discussed. The form of the PSD relationship is identical with that applicable to unretarded equations. Since the PSD relationship is useful if and only if the system described by the equations is stable, the stability must be determined before applying the PSD relationship. Since it is sometimes difficult to determine the stability of retarded equations, such equations are often approximated by simpler forms. It is pointed out that some common approximations can lead to erroneous conclusions regarding the stability of a system and, therefore, to the possibility of obtaining PSD results which are not valid.
Orbital functionals in density-matrix- and current-density-functional theory
Energy Technology Data Exchange (ETDEWEB)
Helbig, N
2006-05-15
Density-Functional Theory (DFT), although widely used and very successful in the calculation of several observables, fails to correctly describe strongly correlated materials. In the first part of this work we, therefore, introduce reduced-densitymatrix- functional theory (RDMFT) which is one possible way to treat electron correlation beyond DFT. Within this theory the one-body reduced density matrix (1- RDM) is used as the basic variable. Our main interest is the calculation of the fundamental gap which proves very problematic within DFT. In order to calculate the fundamental gap we generalize RDMFT to fractional particle numbers M by describing the system as an ensemble of an N and an N+1 particle system (with N{<=}M{<=}N+1). For each fixed particle number, M, the total energy is minimized with respect to the natural orbitals and their occupation numbers. This leads to the total energy as a function of M. The derivative of this function with respect to the particle number has a discontinuity at integer particle number which is identical to the gap. In addition, we investigate the necessary and sufficient conditions for the 1- RDM of a system with fractional particle number to be N-representable. Numerical results are presented for alkali atoms, small molecules, and periodic systems. Another problem within DFT is the description of non-relativistic many-electron systems in the presence of magnetic fields. It requires the paramagnetic current density and the spin magnetization to be used as basic variables besides the electron density. However, electron-gas-based functionals of current-spin-density-functional Theory (CSDFT) exhibit derivative discontinuities as a function of the magnetic field whenever a new Landau level is occupied, which makes them difficult to use in practice. Since the appearance of Landau levels is, intrinsically, an orbital effect it is appealing to use orbital-dependent functionals. We have developed a CSDFT version of the optimized
Local density approximation for a perturbative equation of state
International Nuclear Information System (INIS)
Astrakharchik, G. E.
2005-01-01
Knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic 'perturbative' equation of state of a homogeneous ultracold gas we make predictions for the properties of the gas in the presence of harmonic confinement. The local density approximation is used to obtain the chemical potential, total and release energies, Thomas-Fermi size, and density profile of a trapped system in three-, two-, and one-dimensional geometries. The frequencies of the lowest breathing modes are calculated using scaling and sum-rule approaches and could be used in an experiment as a high-precision tool for obtaining the expansion terms of the equation of state. The derived formalism is applied to dilute Bose and Fermi gases in different dimensions and to integrable one-dimensional models. The physical meaning of the expansion terms in a number of systems is discussed
An algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equations
Daud, Wan Suhana Wan; Ahmad, Nazihah; Malkawi, Ghassan
2017-11-01
Sylvester matrix equations played a prominent role in various areas including control theory. Considering to any un-certainty problems that can be occurred at any time, the Sylvester matrix equation has to be adapted to the fuzzy environment. Therefore, in this study, an algorithm for solving an arbitrary triangular fully fuzzy Sylvester matrix equation is constructed. The construction of the algorithm is based on the max-min arithmetic multiplication operation. Besides that, an associated arbitrary matrix equation is modified in obtaining the final solution. Finally, some numerical examples are presented to illustrate the proposed algorithm.
PERTURBATION ESTIMATES FOR THE MAXIMAL SOLUTION OF A NONLINEAR MATRIX EQUATION
Directory of Open Access Journals (Sweden)
Vejdi I. Hasanov
2017-06-01
Full Text Available In this paper a nonlinear matrix equation is considered. Perturba- tion estimations for the maximal solution of the considered equation are obtained. The results are illustrated by the use of numerical ex- amples.
The time-dependent density matrix renormalisation group method
Ma, Haibo; Luo, Zhen; Yao, Yao
2018-04-01
Substantial progress of the time-dependent density matrix renormalisation group (t-DMRG) method in the recent 15 years is reviewed in this paper. By integrating the time evolution with the sweep procedures in density matrix renormalisation group (DMRG), t-DMRG provides an efficient tool for real-time simulations of the quantum dynamics for one-dimensional (1D) or quasi-1D strongly correlated systems with a large number of degrees of freedom. In the illustrative applications, the t-DMRG approach is applied to investigate the nonadiabatic processes in realistic chemical systems, including exciton dissociation and triplet fission in polymers and molecular aggregates as well as internal conversion in pyrazine molecule.
The density-matrix renormalization group: a short introduction.
Schollwöck, Ulrich
2011-07-13
The density-matrix renormalization group (DMRG) method has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. The DMRG is a method that shares features of a renormalization group procedure (which here generates a flow in the space of reduced density operators) and of a variational method that operates on a highly interesting class of quantum states, so-called matrix product states (MPSs). The DMRG method is presented here entirely in the MPS language. While the DMRG generally fails in larger two-dimensional systems, the MPS picture suggests a straightforward generalization to higher dimensions in the framework of tensor network states. The resulting algorithms, however, suffer from difficulties absent in one dimension, apart from a much more unfavourable efficiency, such that their ultimate success remains far from clear at the moment.
A real-space stochastic density matrix approach for density functional electronic structure.
Beck, Thomas L
2015-12-21
The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.
Computing the Density Matrix in Electronic Structure Theory on Graphics Processing Units.
Cawkwell, M J; Sanville, E J; Mniszewski, S M; Niklasson, Anders M N
2012-11-13
The self-consistent solution of a Schrödinger-like equation for the density matrix is a critical and computationally demanding step in quantum-based models of interatomic bonding. This step was tackled historically via the diagonalization of the Hamiltonian. We have investigated the performance and accuracy of the second-order spectral projection (SP2) algorithm for the computation of the density matrix via a recursive expansion of the Fermi operator in a series of generalized matrix-matrix multiplications. We demonstrate that owing to its simplicity, the SP2 algorithm [Niklasson, A. M. N. Phys. Rev. B2002, 66, 155115] is exceptionally well suited to implementation on graphics processing units (GPUs). The performance in double and single precision arithmetic of a hybrid GPU/central processing unit (CPU) and full GPU implementation of the SP2 algorithm exceed those of a CPU-only implementation of the SP2 algorithm and traditional matrix diagonalization when the dimensions of the matrices exceed about 2000 × 2000. Padding schemes for arrays allocated in the GPU memory that optimize the performance of the CUBLAS implementations of the level 3 BLAS DGEMM and SGEMM subroutines for generalized matrix-matrix multiplications are described in detail. The analysis of the relative performance of the hybrid CPU/GPU and full GPU implementations indicate that the transfer of arrays between the GPU and CPU constitutes only a small fraction of the total computation time. The errors measured in the self-consistent density matrices computed using the SP2 algorithm are generally smaller than those measured in matrices computed via diagonalization. Furthermore, the errors in the density matrices computed using the SP2 algorithm do not exhibit any dependence of system size, whereas the errors increase linearly with the number of orbitals when diagonalization is employed.
Spectral function from Reduced Density Matrix Functional Theory
Romaniello, Pina; di Sabatino, Stefano; Berger, Jan A.; Reining, Lucia
2015-03-01
In this work we focus on the calculation of the spectral function, which determines, for example, photoemission spectra, from reduced density matrix functional theory. Starting from its definition in terms of the one-body Green's function we derive an expression for the spectral function that depends on the natural occupation numbers and on an effective energy which accounts for all the charged excitations. This effective energy depends on the two-body as well as higher-order density matrices. Various approximations to this expression are explored by using the exactly solvable Hubbard chains.
Matrix form of Legendre polynomials for solving linear integro-differential equations of high order
Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.
2017-04-01
This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.
Stationary solution of a time dependent density matrix formalism
International Nuclear Information System (INIS)
Tohyama, Mitsuru
1994-01-01
A stationary solution of a time-dependent density-matrix formalism, which is an extension of the time-dependent Hartree-Fock theory to include the effects of two-body correlations, is obtained for the Lipkin model hamiltonian, using an adiabatic treatment of the two-body interaction. It is found that the obtained result is a reasonable approximation for the exact solution of the model. (author)
One-body density matrix and the momentum density in 4He and 3He
International Nuclear Information System (INIS)
Whitlock, P.A.; Panoff, R.M.
1984-01-01
The one-body density matrix and the momentum density for liquid and solid 4 He, determined from Green's Function Monte Carlo calculations using the HFDHE2 pair potential, are described. Values for the condensate fraction and the kinetic energy derived from these calculations are given and compared to recent experimental results. Preliminary results from variational Monte Carlo calculations on n(r) and n(k) for liquid 3 He are also reported
International Nuclear Information System (INIS)
Requist, Ryan; Pankratov, Oleg
2011-01-01
We prove that if the two-body terms in the equation of motion for the one-body reduced density matrix are approximated by ground-state functionals, the eigenvalues of the one-body reduced density matrix (occupation numbers) remain constant in time. This deficiency is related to the inability of such an approximation to account for relative phases in the two-body reduced density matrix. We derive an exact differential equation giving the functional dependence of these phases in an interacting Landau-Zener model and study their behavior in short- and long-time regimes. The phases undergo resonances whenever the occupation numbers approach the boundaries of the interval [0,1]. In the long-time regime, the occupation numbers display correlation-induced oscillations and the memory dependence of the functionals assumes a simple form.
The structure of solutions of the matrix linear unilateral polynomial equation with two variables
Directory of Open Access Journals (Sweden)
N. S. Dzhaliuk
2017-07-01
Full Text Available We investigate the structure of solutions of the matrix linear polynomial equation $A(\\lambdaX(\\lambda+B(\\lambdaY(\\lambda=C(\\lambda,$ in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices $A (\\lambda, B(\\lambda$ \\ and \\ $C(\\lambda$ are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomial equation solutions. Necessary and sufficient conditions for the uniqueness of a solution with a minimal degree are established. An effective method for constructing minimal degree solutions of the equations is suggested. In this article, unlike well-known results about the estimations of the degrees of the solutions of the matrix polynomial equations in which both matrix coefficients are regular or at least one of them is regular, we have considered the case when the matrix polynomial equation has arbitrary matrix coefficients $A(\\lambda$ and $B(\\lambda.$
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi
2002-01-01
We show that the Wigner function W = Tr(△ρ) (an ensemble average of the density operator ρ, △ is theWigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting fromquantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangledstates are defined in the enlarged Fock space with a fictitious freedom.
Time dependent density matrix theory and effective interaction
Energy Technology Data Exchange (ETDEWEB)
Tohyama, Mitsuru [Kyorin Univ., Mitaka, Tokyo (Japan). School of Medicine
1998-07-01
A correlated ground state of {sup 16}O and an E2 giant resonance built on it are calculated using an extended version of the time-dependent Hartree-Fock theory called the time-dependent density-matrix theory (TDDM). The Skyrme force is used in the calculation of both a mean field and two-body correlations. It is found that TDDM gives reasonable ground-state correlations and a large spreading width of the E2 giant resonance when single-particle states in the continuum are treated appropriately. (author)
Many-body localization from one particle density matrix
Energy Technology Data Exchange (ETDEWEB)
Bera, Soumya; Bardarson, Jens [Max Planck Institute for the Physics of Complex Systems, Dresden (Germany); Schomerus, Henning [Lancaster University, Lancaster (United Kingdom); Heidrich-Meisner, Fabian [Ludwig-Maximilians-Universitaet Muenchen (Germany)
2016-07-01
We show that the one-particle density matrix ρ can be used to characterize the interaction-driven many-body localization transition in isolated fermionic systems. The natural orbitals (the eigenstates) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues) reveals the distinctive Fock- space structure of the many-body eigenstates, exhibiting a step-like discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition.
A New Pseudoinverse Matrix Method For Balancing Chemical Equations And Their Stability
International Nuclear Information System (INIS)
Risteski, Ice B.
2008-01-01
In this work is given a new pseudoniverse matrix method for balancing chemical equations. Here offered method is founded on virtue of the solution of a Diophantine matrix equation by using of a Moore-Penrose pseudoinverse matrix. The method has been tested on several typical chemical equations and found to be very successful for the all equations in our extensive balancing research. This method, which works successfully without any limitations, also has the capability to determine the feasibility of a new chemical reaction, and if it is feasible, then it will balance the equation. Chemical equations treated here possess atoms with fractional oxidation numbers. Also, in the present work are introduced necessary and sufficient criteria for stability of chemical equations over stability of their extended matrices
Darboux transformations for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix
International Nuclear Information System (INIS)
Schulze-Halberg, Axel
2012-01-01
We construct a Darboux transformation for (1+2)-dimensional Fokker-Planck equations with constant diffusion matrix. Our transformation is based on the two-dimensional supersymmetry formalism for the Schrödinger equation. The transformed Fokker-Planck equation and its solutions are obtained in explicit form.
Bessel equation as an operator identity's matrix element in quantum mechanics
International Nuclear Information System (INIS)
Fan Hongyi; Li Chao
2004-01-01
We study the well-known Bessel equation itself in the framework of quantum mechanics. We show that the Bessel equation is a spontaneous result of an operator identity's matrix element in some definite entangled state representations, which is a fresh look. Application of this operator formalism in the Hankel transform of Laplace equation is presented
From Real Materials to Model Hamiltonians With Density Matrix Downfolding
Directory of Open Access Journals (Sweden)
Huihuo Zheng
2018-05-01
Full Text Available Due to advances in computer hardware and new algorithms, it is now possible to perform highly accurate many-body simulations of realistic materials with all their intrinsic complications. The success of these simulations leaves us with a conundrum: how do we extract useful physical models and insight from these simulations? In this article, we present a formal theory of downfolding–extracting an effective Hamiltonian from first-principles calculations. The theory maps the downfolding problem into fitting information derived from wave functions sampled from a low-energy subspace of the full Hilbert space. Since this fitting process most commonly uses reduced density matrices, we term it density matrix downfolding (DMD.
Soliton solutions for ABS lattice equations: I. Cauchy matrix approach
Nijhoff, Frank; Atkinson, James; Hietarinta, Jarmo
2009-10-01
In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations 'of KdV type' that were known since the late 1970s and early 1980s. In this paper, we review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.
The problem of the universal density functional and the density matrix functional theory
International Nuclear Information System (INIS)
Bobrov, V. B.; Trigger, S. A.
2013-01-01
The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.
International Nuclear Information System (INIS)
March, N.H.
2006-08-01
A differential equation for the Dirac density matrix γ(r, r'), given ground-state electron- and kinetic energy-densities, has been derived by March and Suhai for one- and two-level occupancy. For ten-electron spin-compensated spherical systems, it is shown here that γ ≡ γ[ρ, t g ] where ρ and t g are electron- and kinetic energy-densities. The philosophy of March and Suhai is confirmed beyond two-level filling. An important byproduct of the present approach is an explicit expression for the one-body potential of DFT in terms of the p-shell electron density. (author)
The density matrix - The story of a failed transfer
Energy Technology Data Exchange (ETDEWEB)
Blum, Alexander [MPI fuer Wissenschaftsgeschichte, Berlin (Germany)
2013-07-01
With the discovery of the positron in 1933, Paul Dirac (along with most other physicists) was forced to really take seriously his earlier suggestion that in the world as we know it all negative energy states are occupied and we are thus surrounded by an infinite sea of electrons. What was needed was a way to treat this large number of electrons in a manageable fashion. Dirac resorted to the use of the density matrix, a technique he had earlier used to describe the large number of electrons in complex atoms. Initially, this transfer from atomic physics to what we would nowadays call particle physics was quite successful, and for a few years the density matrix was the state of the art in describing the Dirac electron sea, but then rapidly fell out of favor. I investigate the causes of this ultimately failed transfer and how it relates to changes in the physical notion of the vacuum, changes which eventually eliminated the analogy on which the transfer had been based in the first place.
Development and application of a density dependent matrix ...
Ranging along the Atlantic coast from US Florida to the Maritime Provinces of Canada, the Atlantic killifish (Fundulus heteroclitus) is an important and well-studied model organism for understanding the effects of pollutants and other stressors in estuarine and marine ecosystems. Matrix population models are useful tools for ecological risk assessment because they integrate effects across the life cycle, provide a linkage between endpoints observed in the individual and ecological risk to the population as a whole, and project outcomes for many generations in the future. We developed a density dependent matrix population model for Atlantic killifish by modifying a model developed for fathead minnow (Pimephales promelas) that has proved to be extremely useful, e.g. to incorporate data from laboratory studies and project effects of endocrine disrupting chemicals. We developed a size-structured model (as opposed to one that is based upon developmental stages or age class structure) so that we could readily incorporate output from a Dynamic Energy Budget (DEB) model, currently under development. Due to a lack of sufficient data to accurately define killifish responses to density dependence, we tested a number of scenarios realistic for other fish species in order to demonstrate the outcome of including this ecologically important factor. We applied the model using published data for killifish exposed to dioxin-like compounds, and compared our results to those using
Global quantum discord and matrix product density operators
Huang, Hai-Lin; Cheng, Hong-Guang; Guo, Xiao; Zhang, Duo; Wu, Yuyin; Xu, Jian; Sun, Zhao-Yu
2018-06-01
In a previous study, we have proposed a procedure to study global quantum discord in 1D chains whose ground states are described by matrix product states [Z.-Y. Sun et al., Ann. Phys. 359, 115 (2015)]. In this paper, we show that with a very simple generalization, the procedure can be used to investigate quantum mixed states described by matrix product density operators, such as quantum chains at finite temperatures and 1D subchains in high-dimensional lattices. As an example, we study the global discord in the ground state of a 2D transverse-field Ising lattice, and pay our attention to the scaling behavior of global discord in 1D sub-chains of the lattice. We find that, for any strength of the magnetic field, global discord always shows a linear scaling behavior as the increase of the length of the sub-chains. In addition, global discord and the so-called "discord density" can be used to indicate the quantum phase transition in the model. Furthermore, based upon our numerical results, we make some reliable predictions about the scaling of global discord defined on the n × n sub-squares in the lattice.
Transfer equations for spectral densities of inhomogeneous MHD turbulence
International Nuclear Information System (INIS)
Tu, C.-Y.; Marsch, E.
1990-01-01
On the basis of the dynamic equations governing the evolution of magnetohydrodynamic fluctuations expressed in terms of Elsaesser variables and of their correlation functions derived by Marsch and Tu, a new set of equations is presented describing the evolutions of the energy spectrum e ± and of the residual energy spectra e R and e S of MHD turbulence in an inhomogeneous magnetofluid. The nonlinearities associated with triple correlations in these equations are analysed in detail and evaluated approximately. The resulting energy-transfer functions across wavenumber space are discussed. For e ± they are shown to be approximately energy-conserving if the gradients of the flow speed and density are weak. New cascading functions are heuristically determined by an appropriate dimensional analysis and plausible physical arguments, following the standard phenomenology of fluid turbulence. However, for e R the triple correlations do not correspond to an 'energy' conserving process, but also represent a nonlinear source term for e R . If this source term can be neglected, the spectrum equations are found to be closed. The problem of dealing with the nonlinear source terms remains to be solved in future investigations. (author)
Hierarchical matrix techniques for the solution of elliptic equations
Chá vez, Gustavo; Turkiyyah, George; Yokota, Rio; Keyes, David E.
2014-01-01
Hierarchical matrix approximations are a promising tool for approximating low-rank matrices given the compactness of their representation and the economy of the operations between them. Integral and differential operators have been the major
Dehghan, Mehdi; Hajarian, Masoud
2012-08-01
A matrix P is called a symmetric orthogonal if P = P T = P -1. A matrix X is said to be a generalised bisymmetric with respect to P if X = X T = PXP. It is obvious that any symmetric matrix is also a generalised bisymmetric matrix with respect to I (identity matrix). By extending the idea of the Jacobi and the Gauss-Seidel iterations, this article proposes two new iterative methods, respectively, for computing the generalised bisymmetric (containing symmetric solution as a special case) and skew-symmetric solutions of the generalised Sylvester matrix equation ? (including Sylvester and Lyapunov matrix equations as special cases) which is encountered in many systems and control applications. When the generalised Sylvester matrix equation has a unique generalised bisymmetric (skew-symmetric) solution, the first (second) iterative method converges to the generalised bisymmetric (skew-symmetric) solution of this matrix equation for any initial generalised bisymmetric (skew-symmetric) matrix. Finally, some numerical results are given to illustrate the effect of the theoretical results.
International Nuclear Information System (INIS)
Muender, W; Weichselbaum, A; Holzner, A; Delft, Jan von; Henley, C L
2010-01-01
A useful concept for finding numerically the dominant correlations of a given ground state in an interacting quantum lattice system in an unbiased way is the correlation density matrix (CDM). For two disjoint, separated clusters, it is defined to be the density matrix of their union minus the direct product of their individual density matrices and contains all the correlations between the two clusters. We show how to extract from the CDM a survey of the relative strengths of the system's correlations in different symmetry sectors and the nature of their decay with distance (power law or exponential), as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. To achieve this goal, we introduce a new method of analysing the CDM, termed the dominant operator basis (DOB) method, which identifies in an unbiased fashion a small set of operators for each cluster that serve as a basis for the dominant correlations of the system. We illustrate this method by analysing the CDM for a spinless extended Hubbard model that features a competition between charge density correlations and pairing correlations, and show that the DOB method successfully identifies their relative strengths and dominant correlators. To calculate the ground state of this model, we use the density matrix renormalization group, formulated in terms of a variational matrix product state (MPS) approach within which subsequent determination of the CDM is very straightforward. In an extended appendix, we give a detailed tutorial introduction to our variational MPS approach for ground state calculations for one-dimensional quantum chain models. We present in detail how MPSs overcome the problem of large Hilbert space dimensions in these models and describe all the techniques needed for handling them in practice.
Density-matrix formalism for the photoion-electron entanglement in atomic photoionization
International Nuclear Information System (INIS)
Radtke, T.; Fritzsche, S.; Surzhykov, A.
2006-01-01
The density-matrix theory, based on Dirac's relativistic equation, is applied for studying the entanglement between the photoelectron and residual ion in the course of the photoionization of atoms and ions. In particular, emphasis is placed on deriving the final-state density matrix of the overall system 'photoion+electron', including interelectronic effects and the higher multipoles of the radiation field. This final-state density matrix enables one immediately to analyze the change of entanglement as a function of the energy, angle and the polarization of the incoming light. Detailed computations have been carried out for the 5s photoionization of neutral strontium, leading to a photoion in a 5s 2 S J f =1/2 level. It is found that the photoion-electron entanglement decreases significantly near the ionization threshold and that, in general, it depends on both the photon energy and angle. The possibility to extract photoion-electron pairs with a well-defined degree of entanglement may have far-reaching consequences for quantum information and elsewhere
P A M Dirac meets M G Krein: matrix orthogonal polynomials and Dirac's equation
International Nuclear Information System (INIS)
Duran, Antonio J; Gruenbaum, F Alberto
2006-01-01
The solution of several instances of the Schroedinger equation (1926) is made possible by using the well-known orthogonal polynomials associated with the names of Hermite, Legendre and Laguerre. A relativistic alternative to this equation was proposed by Dirac (1928) involving differential operators with matrix coefficients. In 1949 Krein developed a theory of matrix-valued orthogonal polynomials without any reference to differential equations. In Duran A J (1997 Matrix inner product having a matrix symmetric second order differential operator Rocky Mt. J. Math. 27 585-600), one of us raised the question of determining instances of these matrix-valued polynomials going along with second order differential operators with matrix coefficients. In Duran A J and Gruenbaum F A (2004 Orthogonal matrix polynomials satisfying second order differential equations Int. Math. Res. Not. 10 461-84), we developed a method to produce such examples and observed that in certain cases there is a connection with the instance of Dirac's equation with a central potential. We observe that the case of the central Coulomb potential discussed in the physics literature in Darwin C G (1928 Proc. R. Soc. A 118 654), Nikiforov A F and Uvarov V B (1988 Special Functions of Mathematical Physics (Basle: Birkhauser) and Rose M E 1961 Relativistic Electron Theory (New York: Wiley)), and its solution, gives rise to a matrix weight function whose orthogonal polynomials solve a second order differential equation. To the best of our knowledge this is the first instance of a connection between the solution of the first order matrix equation of Dirac and the theory of matrix-valued orthogonal polynomials initiated by M G Krein
Directory of Open Access Journals (Sweden)
Thomas Gomez
2018-04-01
Full Text Available Atomic structure of N-electron atoms is often determined by solving the Hartree-Fock equations, which are a set of integro-differential equations. The integral part of the Hartree-Fock equations treats electron exchange, but the Hartree-Fock equations are not often treated as an integro-differential equation. The exchange term is often approximated as an inhomogeneous or an effective potential so that the Hartree-Fock equations become a set of ordinary differential equations (which can be solved using the usual shooting methods. Because the Hartree-Fock equations are an iterative-refinement method, the inhomogeneous term relies on the previous guess of the wavefunction. In addition, there are numerical complications associated with solving inhomogeneous differential equations. This work uses matrix methods to solve the Hartree-Fock equations as an integro-differential equation. It is well known that a derivative operator can be expressed as a matrix made of finite-difference coefficients; energy eigenvalues and eigenvectors can be obtained by using linear-algebra packages. The integral (exchange part of the Hartree-Fock equation can be approximated as a sum and written as a matrix. The Hartree-Fock equations can be solved as a matrix that is the sum of the differential and integral matrices. We compare calculations using this method against experiment and standard atomic structure calculations. This matrix method can also be used to solve for free-electron wavefunctions, thus improving how the atoms and free electrons interact. This technique is important for spectral line broadening in two ways: it improves the atomic structure calculations, and it improves the motion of the plasma electrons that collide with the atom.
Matrix product density operators: Renormalization fixed points and boundary theories
Energy Technology Data Exchange (ETDEWEB)
Cirac, J.I. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Pérez-García, D., E-mail: dperezga@ucm.es [Departamento de Análisis Matemático, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid (Spain); ICMAT, Nicolas Cabrera, Campus de Cantoblanco, 28049 Madrid (Spain); Schuch, N. [Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching (Germany); Verstraete, F. [Department of Physics and Astronomy, Ghent University (Belgium); Vienna Center for Quantum Technology, University of Vienna (Austria)
2017-03-15
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).
Hierarchical matrix techniques for the solution of elliptic equations
Chávez, Gustavo
2014-05-04
Hierarchical matrix approximations are a promising tool for approximating low-rank matrices given the compactness of their representation and the economy of the operations between them. Integral and differential operators have been the major applications of this technology, but they can be applied into other areas where low-rank properties exist. Such is the case of the Block Cyclic Reduction algorithm, which is used as a direct solver for the constant-coefficient Poisson quation. We explore the variable-coefficient case, also using Block Cyclic reduction, with the addition of Hierarchical Matrices to represent matrix blocks, hence improving the otherwise O(N2) algorithm, into an efficient O(N) algorithm.
On the solution of Stein's equation and Fisher information matrix of an ARMAX process
Klein, A.; Spreij, P.
2004-01-01
The main goal of this paper consists in expressing the solution of a Stein equation in terms of the Fisher information matrix (FIM) of a scalar ARMAX process. A condition for expressing the FIM in terms of a solution to a Stein equation is also set forth. Such interconnections can be derived when a
Population density equations for stochastic processes with memory kernels
Lai, Yi Ming; de Kamps, Marc
2017-06-01
We present a method for solving population density equations (PDEs)-a mean-field technique describing homogeneous populations of uncoupled neurons—where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the master equation implicit in many formulations of the PDE formalism by a generalization called the generalized Montroll-Weiss equation—a recent result from random network theory—describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- and quadratic-integrate and fire neurons subject to spike trains with Poisson and gamma-distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.
Efficient perturbation theory to improve the density matrix renormalization group
Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej
2017-02-01
The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j= ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.
Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation
Directory of Open Access Journals (Sweden)
S. Balaji
2014-01-01
Full Text Available A Legendre wavelet operational matrix method (LWM is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.
Covariant field equations, gauge fields and conservation laws from Yang-Mills matrix models
International Nuclear Information System (INIS)
Steinacker, Harold
2009-01-01
The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.
Energy Technology Data Exchange (ETDEWEB)
Buecking, N
2007-11-05
In this work a new theoretical formalism is introduced in order to simulate the phononinduced relaxation of a non-equilibrium distribution to equilibrium at a semiconductor surface numerically. The non-equilibrium distribution is effected by an optical excitation. The approach in this thesis is to link two conventional, but approved methods to a new, more global description: while semiconductor surfaces can be investigated accurately by density-functional theory, the dynamical processes in semiconductor heterostructures are successfully described by density matrix theory. In this work, the parameters for density-matrix theory are determined from the results of density-functional calculations. This work is organized in two parts. In Part I, the general fundamentals of the theory are elaborated, covering the fundamentals of canonical quantizations as well as the theory of density-functional and density-matrix theory in 2{sup nd} order Born approximation. While the formalism of density functional theory for structure investigation has been established for a long time and many different codes exist, the requirements for density matrix formalism concerning the geometry and the number of implemented bands exceed the usual possibilities of the existing code in this field. A special attention is therefore attributed to the development of extensions to existing formulations of this theory, where geometrical and fundamental symmetries of the structure and the equations are used. In Part II, the newly developed formalism is applied to a silicon (001)surface in a 2 x 1 reconstruction. As first step, density-functional calculations using the LDA functional are completed, from which the Kohn-Sham-wave functions and eigenvalues are used to calculate interaction matrix elements for the electron-phonon-coupling an the optical excitation. These matrix elements are determined for the optical transitions from valence to conduction bands and for electron-phonon processes inside the
Energy Technology Data Exchange (ETDEWEB)
Brics, Martins; Kapoor, Varun; Bauer, Dieter [Institut fuer Physik, Universitaet Rostock, 18051 Rostock (Germany)
2013-07-01
Time-dependent density functional theory (TDDFT) with known and practicable exchange-correlation potentials does not capture highly correlated electron dynamics such as single-photon double ionization, autoionization, or nonsequential ionization. Time-dependent reduced density matrix functional theory (TDRDMFT) may remedy these problems. The key ingredients in TDRDMFT are the natural orbitals (NOs), i.e., the eigenfunctions of the one-body reduced density matrix (1-RDM), and the occupation numbers (OCs), i.e., the respective eigenvalues. The two-body reduced density matrix (2-RDM) is then expanded in NOs, and equations of motion for the NOs can be derived. If the expansion coefficients of the 2-RDM were known exactly, the problem at hand would be solved. In practice, approximations have to be made. We study the prospects of TDRDMFT following a top-down approach. We solve the exact two-electron time-dependent Schroedinger equation for a model Helium atom in intense laser fields in order to study highly correlated phenomena such as the population of autoionizing states or single-photon double ionization. From the exact wave function we calculate the exact NOs, OCs, the exact expansion coefficients of the 2-RDM, and the exact potentials in the equations of motion. In that way we can identify how many NOs and which level of approximations are necessary to capture such phenomena.
Thorne, Lawrence R.
2011-01-01
I propose a novel approach to balancing equations that is applicable to all chemical-reaction equations; it is readily accessible to students via scientific calculators and basic computer spreadsheets that have a matrix-inversion application. The new approach utilizes the familiar matrix-inversion operation in an unfamiliar and innovative way; its purpose is not to identify undetermined coefficients as usual, but, instead, to compute a matrix null space (or matrix kernel). The null space then...
Matrix-valued Boltzmann equation for the nonintegrable Hubbard chain.
Fürst, Martin L R; Mendl, Christian B; Spohn, Herbert
2013-07-01
The standard Fermi-Hubbard chain becomes nonintegrable by adding to the nearest neighbor hopping additional longer range hopping amplitudes. We assume that the quartic interaction is weak and investigate numerically the dynamics of the chain on the level of the Boltzmann type kinetic equation. Only the spatially homogeneous case is considered. We observe that the huge degeneracy of stationary states in the case of nearest neighbor hopping is lost and the convergence to the thermal Fermi-Dirac distribution is restored. The convergence to equilibrium is exponentially fast. However for small next-nearest neighbor hopping amplitudes one has a rapid relaxation towards the manifold of quasistationary states and slow relaxation to the final equilibrium state.
The solution space of the unitary matrix model string equation and the Sato Grassmannian
International Nuclear Information System (INIS)
Anagnostopoulos, K.N.; Bowick, M.J.; Schwarz, A.
1992-01-01
The space of all solutions to the string equation of the symmetric unitary one-matrix model is determined. It is shown that the string equations is equivalent to simple conditions on points V 1 and V 2 in the big cell Gr (0) of the Sato Grassmannian Gr. This is a consequence of a well-defined continuum limit in which the string equation has the simple form [P, 2 - ]=1, with P and 2 - 2x2 matrices of differential operators. These conditions on V 1 and V 2 yield a simple system of first order differential equations whose analysis determines the space of all solutions to the string equation. This geometric formulation leads directly to the Virasoro constraints L n (n≥0), where L n annihilate the two modified-KdV τ-functions whose product gives the partition function of the Unitary Matrix Model. (orig.)
Force-balance and differential equation for the ground-state electron density in atoms and molecules
International Nuclear Information System (INIS)
Amovilli, C.; March, N.H.; Gal, T.; Nagy, A.
2000-01-01
Holas and March (1995) established a force-balance equation from the many-electron Schroedinger equation. Here, the authors propose this as a basis for the construction of a (usually approximate) differential equation for the ground-state electron density. By way of example they present the simple case of two-electron systems with different external potentials but with weak electron-electron Coulomb repulsion λe 2 /r 12 . In this case first-order Rayleigh-Schroedinger (RS) perturbation theory of the ground-state wave function is known to lead to a compact expression for the first-order density matrix γ(r,rprime) in terms of its diagonal density ρ(r) and the density corresponding to λ = 0. This result allows the force-balance equation to be written as a third-order linear, differential homogeneous equation for the ground-state electron density ρ(r). The example of the two-electron Hookean atom is treated: For this case one can also transcend the first-order RS perturbation theory and get exact results for discrete choices of force constants (external potential)
Solving eigenvalue response matrix equations with nonlinear techniques
International Nuclear Information System (INIS)
Roberts, Jeremy A.; Forget, Benoit
2014-01-01
Highlights: • High performance solvers were applied within ERMM for the first time. • Accelerated fixed-point methods were developed that reduce computational times by 2–3. • A nonlinear, Newton-based ERMM led to similar improvement and more robustness. • A 3-D, SN-based ERMM shows how ERMM can apply fine-mesh methods to full-core analysis. - Abstract: This paper presents new algorithms for use in the eigenvalue response matrix method (ERMM) for reactor eigenvalue problems. ERMM spatially decomposes a domain into independent nodes linked via boundary conditions approximated as truncated orthogonal expansions, the coefficients of which are response functions. In its simplest form, ERMM consists of a two-level eigenproblem: an outer Picard iteration updates the k-eigenvalue via balance, while the inner λ-eigenproblem imposes neutron balance between nodes. Efficient methods are developed for solving the inner λ-eigenvalue problem within the outer Picard iteration. Based on results from several diffusion and transport benchmark models, it was found that the Krylov–Schur method applied to the λ-eigenvalue problem reduces Picard solver times (excluding response generation) by a factor of 2–5. Furthermore, alternative methods, including Picard acceleration schemes, Steffensen’s method, and Newton’s method, are developed in this paper. These approaches often yield faster k-convergence and a need for fewer k-dependent response function evaluations, which is important because response generation is often the primary cost for problems using responses computed online (i.e., not from a precomputed database). Accelerated Picard iteration was found to reduce total computational times by 2–3 compared to the unaccelerated case for problems dominated by response generation. In addition, Newton’s method was found to provide nearly the same performance with improved robustness
International Nuclear Information System (INIS)
Dzhamay, Anton
2009-01-01
We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this space is given by a mix of residue eigenvectors of the matrix and its inverse. Our approach is motivated by the theory of discrete isomonodromic transformations and their relationship with difference Painleve equations. In particular, in these coordinates, basic isomonodromic transformations take the form of the discrete Euler-Lagrange equations. Secondly we show that dPV equations, previously obtained in this context by D Arinkin and A Borodin, can be understood as simple relationships between the residues of such matrices and their inverses.
Reduced density-matrix functional theory: Correlation and spectroscopy.
Di Sabatino, S; Berger, J A; Reining, L; Romaniello, P
2015-07-14
In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.
TOEPLITZ, Solution of Linear Equation System with Toeplitz or Circulant Matrix
International Nuclear Information System (INIS)
Garbow, B.
1984-01-01
Description of program or function: TOEPLITZ is a collection of FORTRAN subroutines for solving linear systems Ax=b, where A is a Toeplitz matrix, a Circulant matrix, or has one or several block structures based on Toeplitz or Circulant matrices. Such systems arise in problems of electrodynamics, acoustics, mathematical statistics, algebra, in the numerical solution of integral equations with a difference kernel, and in the theory of stationary time series and signals
O(N)-matrix difference equations and a nested Bethe ansatz
International Nuclear Information System (INIS)
Babujian, Hrachya M; Foerster, Angela; Karowski, Michael
2012-01-01
A system of O(N)-matrix difference equations is solved by means of the off-shell version of the nested algebraic Bethe ansatz. In the nesting process, a new object, the Π-matrix, is introduced to overcome the complexities of the O(N)-group structure. The highest weight property of the solutions is proved and some explicit examples are discussed. (paper)
Solution of the Lyapunov matrix equation for a system with a time-dependent stiffness matrix
DEFF Research Database (Denmark)
Pommer, Christian; Kliem, Wolfhard
2004-01-01
The stability of the linearized model of a rotor system with non-symmetric strain and axial loads is investigated. Since we are using a fixed reference system, the differential equations have the advantage to be free of Coriolis and centrifugal forces. A disadvantage is nevertheless the occurrence...
Quasi-particle energy spectra in local reduced density matrix functional theory.
Lathiotakis, Nektarios N; Helbig, Nicole; Rubio, Angel; Gidopoulos, Nikitas I
2014-10-28
Recently, we introduced [N. N. Lathiotakis, N. Helbig, A. Rubio, and N. I. Gidopoulos, Phys. Rev. A 90, 032511 (2014)] local reduced density matrix functional theory (local RDMFT), a theoretical scheme capable of incorporating static correlation effects in Kohn-Sham equations. Here, we apply local RDMFT to molecular systems of relatively large size, as a demonstration of its computational efficiency and its accuracy in predicting single-electron properties from the eigenvalue spectrum of the single-particle Hamiltonian with a local effective potential. We present encouraging results on the photoelectron spectrum of molecular systems and the relative stability of C20 isotopes. In addition, we propose a modelling of the fractional occupancies as functions of the orbital energies that further improves the efficiency of the method useful in applications to large systems and solids.
International Nuclear Information System (INIS)
Krishnaswami, Govind S.
2006-01-01
Large-N multi-matrix loop equations are formulated as quadratic difference equations in concatenation of gluon correlations. Though non-linear, they involve highest rank correlations linearly. They are underdetermined in many cases. Additional linear equations for gluon correlations, associated to symmetries of action and measure are found. Loop equations aren't differential equations as they involve left annihilation, which doesn't satisfy the Leibnitz rule with concatenation. But left annihilation is a derivation of the commutative shuffle product. Moreover shuffle and concatenation combine to define a bialgebra. Motivated by deformation quantization, we expand concatenation around shuffle in powers of q, whose physical value is 1. At zeroth order the loop equations become quadratic PDEs in the shuffle algebra. If the variation of the action is linear in iterated commutators of left annihilations, these quadratic PDEs linearize by passage to shuffle reciprocal of correlations. Remarkably, this is true for regularized versions of the Yang-Mills, Chern-Simons and Gaussian actions. But the linear equations are underdetermined just as the loop equations were. For any particular solution, the shuffle reciprocal is explicitly inverted to get the zeroth order gluon correlations. To go beyond zeroth order, we find a Poisson bracket on the shuffle algebra and associative q-products interpolating between shuffle and concatenation. This method, and a complementary one of deforming annihilation rather than product are shown to give over and underestimates for correlations of a gaussian matrix model
The finite temperature density matrix and two-point correlations in the antiferromagnetic XXZ chain
Göhmann, Frank; Hasenclever, Nils P.; Seel, Alexander
2005-10-01
We derive finite temperature versions of integral formulae for the two-point correlation functions in the antiferromagnetic XXZ chain. The derivation is based on the summation of density matrix elements characterizing a finite chain segment of length m. On this occasion we also supply a proof of the basic integral formula for the density matrix presented in an earlier publication.
On the Solution of the Rational Matrix Equation X=Q+LX−1LT
Directory of Open Access Journals (Sweden)
Heike Faßbender
2007-01-01
Full Text Available We study numerical methods for finding the maximal symmetric positive definite solution of the nonlinear matrix equation X=Q+LX−1LT, where Q is symmetric positive definite and L is nonsingular. Such equations arise for instance in the analysis of stationary Gaussian reciprocal processes over a finite interval. Its unique largest positive definite solution coincides with the unique positive definite solution of a related discrete-time algebraic Riccati equation (DARE. We discuss how to use the butterfly SZ algorithm to solve the DARE. This approach is compared to several fixed-point and doubling-type iterative methods suggested in the literature.
Explicit solutions of the cubic matrix nonlinear Schrödinger equation
International Nuclear Information System (INIS)
Demontis, Francesco; Mee, Cornelis van der
2008-01-01
In this paper, we derive a class of explicit solutions, global in (x, t) is an element of R 2 , of the focusing matrix nonlinear Schrödinger equation using straightforward linear algebra. We obtain both the usual and multiple pole multisoliton solutions as well as a new class of solutions exponentially decaying as x → ±∞
On the solution of a rational matrix equation arising in G-networks
B. Meini (Beatrice); T. Nesti (Tommaso)
2017-01-01
textabstractWe consider the problem of solving a rational matrix equation arising in the solution of G-networks. We propose and analyze two numerical methods: a fixed point iteration and the Newton–Raphson method. The fixed point iteration is shown to be globally convergent with linear convergence
Solution of the scattering T matrix equation in discrete complex momentum space
International Nuclear Information System (INIS)
Rawitscher, G.H.; Delic, G.
1984-01-01
The scattering solution to the Lippmann-Schwinger equation is expanded into a set of spherical Bessel functions of complex wave numbers, K/sub j/, with j = 1,2 , . . . , M. The value of each K/sub j/ is determined from the condition that the spherical Bessel function smoothly matches onto an asymptotically outgoing spherical Hankel (or Coulomb) function of the correct physical wave number at a matching point R. The spherical Bessel functions thus determined are Sturmian functions, and they form a complete set in the interval 0 to R. The coefficients of the expansion of the scattering function are determined by matrix inversion of a linear set of algebraic equations, which are equivalent to the solution of the T-matrix equation in complex momentum space. In view of the presence of a matching radius, no singularities are encountered for the Green's functions, and the inclusion of Coulomb potentials offers no computational difficulties. Three numerical examples are performed in order to illustrate the convergence of the elastic scattering matrix S with M. One of these consists of a set of coupled equations which describe the breakup of a deuteron as it scatters from the nucleus on 58 Ni. A value of M of 15 or less is found sufficient to reproduce the exact S matrix element to an accuracy of four figures after the decimal point
Matrix Solution of Coupled Differential Equations and Looped Car Following Models
McCartney, Mark
2008-01-01
A simple mathematical model for the behaviour of how vehicles follow each other along a looped stretch of road is described. The resulting coupled first order differential equations are solved using appropriate matrix techniques and the physical significance of the model is discussed. A number possible classroom exercises are suggested to help…
Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel
El-Gebeily, M.; Yushau, B.
2008-01-01
In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…
Modifying a numerical algorithm for solving the matrix equation X + AX T B = C
Vorontsov, Yu. O.
2013-06-01
Certain modifications are proposed for a numerical algorithm solving the matrix equation X + AX T B = C. By keeping the intermediate results in storage and repeatedly using them, it is possible to reduce the total complexity of the algorithm from O( n 4) to O( n 3) arithmetic operations.
Directory of Open Access Journals (Sweden)
Marina Popolizio
2018-01-01
Full Text Available Multiterm fractional differential equations (MTFDEs nowadays represent a widely used tool to model many important processes, particularly for multirate systems. Their numerical solution is then a compelling subject that deserves great attention, not least because of the difficulties to apply general purpose methods for fractional differential equations (FDEs to this case. In this paper, we first transform the MTFDEs into equivalent systems of FDEs, as done by Diethelm and Ford; in this way, the solution can be expressed in terms of Mittag–Leffler (ML functions evaluated at matrix arguments. We then propose to compute it by resorting to the matrix approach proposed by Garrappa and Popolizio. Several numerical tests are presented that clearly show that this matrix approach is very accurate and fast, also in comparison with other numerical methods.
Numerical solution of quadratic matrix equations for free vibration analysis of structures
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.
Two-body density matrix for closed s-d shell nuclei
International Nuclear Information System (INIS)
Dimitrova, S.S.; Kadrev, D.N.; Antonov, A.N.; Stoitsov, M.V.
2000-01-01
The two-body density matrix for 4 He, 16 O and 40 Ca within the Low-order approximation of the Jastrow correlation method is considered. Closed analytical expressions for the two-body density matrix, the center of mass and relative local densities and momentum distributions are presented. The effects of the short-range correlations on the two-body nuclear characteristics are investigated. (orig.)
Lyapunov Functions and Solutions of the Lyapunov Matrix Equation for Marginally Stable Systems
DEFF Research Database (Denmark)
Kliem, Wolfhard; Pommer, Christian
2000-01-01
We consider linear systems of differential equations $I \\ddot{x}+B \\dot{x}+C{x}={0}$ where $I$ is the identity matrix and $B$ and $C$ are general complex $n$ x $n$ matrices. Our main interest is to determine conditions for complete marginalstability of these systems. To this end we find solutions...... of the Lyapunov matrix equation and characterize the set of matrices $(B, C)$ which guarantees marginal stability. The theory is applied to gyroscopic systems, to indefinite damped systems, and to circulatory systems, showing how to choose certain parameter matrices to get sufficient conditions for marginal...... stability.Comparison is made with some known results for equations with real system matrices.Moreover more general cases are investigated and several examples are given....
A Globally Convergent Matrix-Free Method for Constrained Equations and Its Linear Convergence Rate
Directory of Open Access Journals (Sweden)
Min Sun
2014-01-01
Full Text Available A matrix-free method for constrained equations is proposed, which is a combination of the well-known PRP (Polak-Ribière-Polyak conjugate gradient method and the famous hyperplane projection method. The new method is not only derivative-free, but also completely matrix-free, and consequently, it can be applied to solve large-scale constrained equations. We obtain global convergence of the new method without any differentiability requirement on the constrained equations. Compared with the existing gradient methods for solving such problem, the new method possesses linear convergence rate under standard conditions, and a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that it is promising in practice.
An improved V-Lambda solution of the matrix Riccati equation
Bar-Itzhack, Itzhack Y.; Markley, F. Landis
1988-01-01
The authors present an improved algorithm for computing the V-Lambda solution of the matrix Riccati equation. The improvement is in the reduction of the computational load, results from the orthogonality of the eigenvector matrix that has to be solved for. The orthogonality constraint reduces the number of independent parameters which define the matrix from n-squared to n (n - 1)/2. The authors show how to specify the parameters, how to solve for them and how to form from them the needed eigenvector matrix. In the search for suitable parameters, the analogy between the present problem and the problem of attitude determination is exploited, resulting in the choice of Rodrigues parameters.
On conserved densities and asymptotic behaviour for the potential Kadomtsev-Petviashvili equation
International Nuclear Information System (INIS)
Rosenhaus, V
2006-01-01
We study local conservation laws with non-vanishing conserved densities and corresponding boundary conditions for the potential Kadomtsev-Petviashvili equation. We analyse an infinite symmetry group of the equation, and generate a finite number of conserved densities corresponding to infinite symmetries through appropriate boundary conditions
Reduced density matrix functional theory via a wave function based approach
Energy Technology Data Exchange (ETDEWEB)
Schade, Robert; Bloechl, Peter [Institute for Theoretical Physics, Clausthal University of Technology, Clausthal (Germany); Pruschke, Thomas [Institute for Theoretical Physics, University of Goettingen, Goettingen (Germany)
2016-07-01
We propose a new method for the calculation of the electronic and atomic structure of correlated electron systems based on reduced density matrix functional theory (rDMFT). The density-matrix functional is evaluated on the fly using Levy's constrained search formalism. The present implementation rests on a local approximation of the interaction reminiscent to that of dynamical mean field theory (DMFT). We focus here on additional approximations to the exact density-matrix functional in the local approximation and evaluate their performance.
Directory of Open Access Journals (Sweden)
Ning Li
2013-01-01
Full Text Available The matrix equation ∑l=1uAlXBl+∑s=1vCsXTDs=F, which includes some frequently investigated matrix equations as its special cases, plays important roles in the system theory. In this paper, we propose an iterative algorithm for solving the quaternion matrix equation ∑l=1uAlXBl+∑s=1vCsXTDs=F over generalized (P,Q-reflexive matrices. The proposed iterative algorithm automatically determines the solvability of the quaternion matrix equation over generalized (P,Q-reflexive matrices. When the matrix equation is consistent over generalized (P,Q-reflexive matrices, the sequence {X(k} generated by the introduced algorithm converges to a generalized (P,Q-reflexive solution of the quaternion matrix equation. And the sequence {X(k} converges to the least Frobenius norm generalized (P,Q-reflexive solution of the quaternion matrix equation when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate generalized (P,Q-reflexive solution for a given generalized (P,Q-reflexive matrix X0 can be derived. The numerical results indicate that the iterative algorithm is quite efficient.
Preconditioned Krylov and Gauss-Seidel solutions of response matrix equations
International Nuclear Information System (INIS)
Lewis, E.E.; Smith, M.A.; Yang, W.S.; Wollaber, A.
2011-01-01
The use of preconditioned Krylov methods is examined as an alternative to the partitioned matrix acceleration applied to red-black Gauss Seidel (RBGS) iteration that is presently used in the variational nodal code, VARIANT. We employ the GMRES algorithm to treat non-symmetric response matrix equations. A pre conditioner is formulated for the within-group diffusion equation which is equivalent to partitioned matrix acceleration of RBGS iterations. We employ the pre conditioner, which closely parallels two-level p multigrid, to improve RBGS and GMRES algorithms. Of the accelerated algorithms, GMRES converges with less computational effort than RBGS and therefore is chosen for further development. The p multigrid pre conditioner requires response matrices with two or more degrees of freedom (DOF) per interface that are polynomials, which are both orthogonal and hierarchical. It is therefore not directly applicable to very fine mesh calculations that are both slow to converge and that are often modeled with response matrices with only one DOF per interface. Orthogonal matrix aggregation (OMA) is introduced to circumvent this difficulty by combining N×N fine mesh response matrices with one DOF per interface into a coarse mesh response matrix with N orthogonal DOF per interface. Numerical results show that OMA used alone or in combination with p multigrid preconditioning substantially accelerates GMRES solutions. (author)
Preconditioned Krylov and Gauss-Seidel solutions of response matrix equations
Energy Technology Data Exchange (ETDEWEB)
Lewis, E.E., E-mail: e-lewis@northwestern.edu [Department of Mechanical Engineering, Northwestern University, Evanston, IL (United States); Smith, M.A.; Yang, W.S.; Wollaber, A., E-mail: masmith@anl.gov, E-mail: wsyang@anl.gov, E-mail: wollaber@lanl.gov [Nuclear Engineering Division, Argonne National Laboratory, Argonne, IL (United States)
2011-07-01
The use of preconditioned Krylov methods is examined as an alternative to the partitioned matrix acceleration applied to red-black Gauss Seidel (RBGS) iteration that is presently used in the variational nodal code, VARIANT. We employ the GMRES algorithm to treat non-symmetric response matrix equations. A pre conditioner is formulated for the within-group diffusion equation which is equivalent to partitioned matrix acceleration of RBGS iterations. We employ the pre conditioner, which closely parallels two-level p multigrid, to improve RBGS and GMRES algorithms. Of the accelerated algorithms, GMRES converges with less computational effort than RBGS and therefore is chosen for further development. The p multigrid pre conditioner requires response matrices with two or more degrees of freedom (DOF) per interface that are polynomials, which are both orthogonal and hierarchical. It is therefore not directly applicable to very fine mesh calculations that are both slow to converge and that are often modeled with response matrices with only one DOF per interface. Orthogonal matrix aggregation (OMA) is introduced to circumvent this difficulty by combining N×N fine mesh response matrices with one DOF per interface into a coarse mesh response matrix with N orthogonal DOF per interface. Numerical results show that OMA used alone or in combination with p multigrid preconditioning substantially accelerates GMRES solutions. (author)
Splitting of the rate matrix as a definition of time reversal in master equation systems
International Nuclear Information System (INIS)
Liu Fei; Le, Hong
2012-01-01
Motivated by recent progress in nonequilibrium fluctuation relations, we present a generalized time reversal for stochastic master equation systems with discrete states, which is defined as a splitting of the rate matrix into irreversible and reversible parts. An immediate advantage of this definition is that a variety of fluctuation relations can be attributed to different matrix splittings. Additionally, we find that the accustomed total entropy production formula and conditions of the detailed balance must be modified appropriately to account for the reversible rate part, which was previously ignored. (paper)
International Nuclear Information System (INIS)
Howard, I.A.; March, N.H.; Nieto, L.M.
2002-01-01
In 1959, March and Young (Nucl. Phys. 12 237) rewrote the equation of motion for the Dirac density matrix γ(x, x 0 ) in terms of sum and difference variables. Here, γ(r-bar, r-bar 0 ) for the d-dimensional isotropic harmonic oscillator for an arbitrary number of closed shells is shown to satisfy, using the variables vertical bar r-bar + r-bar 0 vertical bar/2 and vertical bar r-bar - r-bar 0 vertical bar/2, a generalized partial differential equation embracing the March-Young equation for d=1. As applications, we take in turn the cases d=1, 2, 3 and 4, and obtain both the density matrix γ (r-bar, r-bar 0 ) and the diagonal density ρ(r)=γ(r-bar, r-bar 0 ) vertical bar r-bar 0 =r-bar, this diagonal element already being known to satisfy a third-order linear homogeneous differential equation for d=1 through 3. Some comments are finally made on the d-dimensional kinetic energy density, which is important for first-principles density functional theory in allowing one to bypass one-particle Schroedinger equations (the so-called Slater-Kohn-Sham equations). (author)
Loop equations and topological recursion for the arbitrary-$\\beta$ two-matrix model
Bergère, Michel; Marchal, Olivier; Prats-Ferrer, Aleix
2012-01-01
We write the loop equations for the $\\beta$ two-matrix model, and we propose a topological recursion algorithm to solve them, order by order in a small parameter. We find that to leading order, the spectral curve is a "quantum" spectral curve, i.e. it is given by a differential operator (instead of an algebraic equation for the hermitian case). Here, we study the case where that quantum spectral curve is completely degenerate, it satisfies a Bethe ansatz, and the spectral curve is the Baxter TQ relation.
Solving Eigenvalue response matrix equations with Jacobian-Free Newton-Krylov methods
International Nuclear Information System (INIS)
Roberts, Jeremy A.; Forget, Benoit
2011-01-01
The response matrix method for reactor eigenvalue problems is motivated as a technique for solving coarse mesh transport equations, and the classical approach of power iteration (PI) for solution is described. The method is then reformulated as a nonlinear system of equations, and the associated Jacobian is derived. A Jacobian-Free Newton-Krylov (JFNK) method is employed to solve the system, using an approximate Jacobian coupled with incomplete factorization as a preconditioner. The unpreconditioned JFNK slightly outperforms PI, and preconditioned JFNK outperforms both PI and Steffensen-accelerated PI significantly. (author)
A self-consistent nodal method in response matrix formalism for the multigroup diffusion equations
International Nuclear Information System (INIS)
Malambu, E.M.; Mund, E.H.
1996-01-01
We develop a nodal method for the multigroup diffusion equations, based on the transverse integration procedure (TIP). The efficiency of the method rests upon the convergence properties of a high-order multidimensional nodal expansion and upon numerical implementation aspects. The discrete 1D equations are cast in response matrix formalism. The derivation of the transverse leakage moments is self-consistent i.e. does not require additional assumptions. An outstanding feature of the method lies in the linear spatial shape of the local transverse leakage for the first-order scheme. The method is described in the two-dimensional case. The method is validated on some classical benchmark problems. (author)
Solving Matrix Equations on Multi-Core and Many-Core Architectures
Directory of Open Access Journals (Sweden)
Peter Benner
2013-11-01
Full Text Available We address the numerical solution of Lyapunov, algebraic and differential Riccati equations, via the matrix sign function, on platforms equipped with general-purpose multicore processors and, optionally, one or more graphics processing units (GPUs. In particular, we review the solvers for these equations, as well as the underlying methods, analyze their concurrency and scalability and provide details on their parallel implementation. Our experimental results show that this class of hardware provides sufficient computational power to tackle large-scale problems, which only a few years ago would have required a cluster of computers.
Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations
Directory of Open Access Journals (Sweden)
Farahnaz Soleimani
2015-11-01
Full Text Available An application of iterative methods for computing the Moore–Penrose inverse in balancing chemical equations is considered. With the aim to illustrate proposed algorithms, an improved high order hyper-power matrix iterative method for computing generalized inverses is introduced and applied. The improvements of the hyper-power iterative scheme are based on its proper factorization, as well as on the possibility to accelerate the iterations in the initial phase of the convergence. Although the effectiveness of our approach is confirmed on the basis of the theoretical point of view, some numerical comparisons in balancing chemical equations, as well as on randomly-generated matrices are furnished.
Jarlebring, E.; Hochstenbach, M.E.
2009-01-01
Several recent methods used to analyze asymptotic stability of delay-differential equations (DDEs) involve determining the eigenvalues of a matrix, a matrix pencil or a matrix polynomial constructed by Kronecker products. Despite some similarities between the different types of these so-called
Tetrahedron equations and the relativistic S-matrix of straight-strings in 2+1-dimensions
International Nuclear Information System (INIS)
Zamolodchikov, A.B.
1981-01-01
The quantum S-matrix theory of straight-strings (infinite one-dimensioanl objects like straight domain walls) in 2 + 1-dimensions is considered. The S-matrix is supposed to be purely elastic and factorized. The tetrahedron equations (which are the factorization conditions) are investigated for the special two-colour model. The relativistic three-string S-matrix, which apparently satisfies this tetrahedron equation, is proposed. (orig.)
Solution of the Multigroup-Diffusion equation by the response matrix method
International Nuclear Information System (INIS)
Oliveira, C.R.E.
1980-10-01
A preliminary analysis of the response matrix method is made, considering its application to the solution of the multigroup diffusion equations. The one-dimensional formulation is presented and used to test some flux expansions, seeking the application of the method to the two-dimensional problem. This formulation also solves the equations that arise from the integro-differential synthesis algorithm. The slow convergence of the power method, used to solve the eigenvalue problem, and its acceleration by means of the Chebyshev polynomial method, are also studied. An algorithm for the estimation of the dominance ratio is presented, based on the residues of two successive iteration vectors. This ratio, which is not known a priori, is fundamental for the efficiency of the method. Some numerical problems are solved, testing the 1D formulation of the response matrix method, its application to the synthesis algorithm and also, at the same time, the algorithm to accelerate the source problem. (Author) [pt
The ESS and replicator equation in matrix games under time constraints.
Garay, József; Cressman, Ross; Móri, Tamás F; Varga, Tamás
2018-06-01
Recently, we introduced the class of matrix games under time constraints and characterized the concept of (monomorphic) evolutionarily stable strategy (ESS) in them. We are now interested in how the ESS is related to the existence and stability of equilibria for polymorphic populations. We point out that, although the ESS may no longer be a polymorphic equilibrium, there is a connection between them. Specifically, the polymorphic state at which the average strategy of the active individuals in the population is equal to the ESS is an equilibrium of the polymorphic model. Moreover, in the case when there are only two pure strategies, a polymorphic equilibrium is locally asymptotically stable under the replicator equation for the pure-strategy polymorphic model if and only if it corresponds to an ESS. Finally, we prove that a strict Nash equilibrium is a pure-strategy ESS that is a locally asymptotically stable equilibrium of the replicator equation in n-strategy time-constrained matrix games.
Massively parallel red-black algorithms for x-y-z response matrix equations
International Nuclear Information System (INIS)
Hanebutte, U.R.; Laurin-Kovitz, K.; Lewis, E.E.
1992-01-01
Recently, both discrete ordinates and spherical harmonic (S n and P n ) methods have been cast in the form of response matrices. In x-y geometry, massively parallel algorithms have been developed to solve the resulting response matrix equations on the Connection Machine family of parallel computers, the CM-2, CM-200, and CM-5. These algorithms utilize two-cycle iteration on a red-black checkerboard. In this work we examine the use of massively parallel red-black algorithms to solve response matric equations in three dimensions. This longer term objective is to utilize massively parallel algorithms to solve S n and/or P n response matrix problems. In this exploratory examination, however, we consider the simple 6 x 6 response matrices that are derivable from fine-mesh diffusion approximations in three dimensions
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.)
Ecological edge effects are sensitive to landscape context. In particular, edge effects can be altered by matrix type and by the presence of other nearby edges. We experimentally altered patch configurations in an African savanna to determine how edge density and matrix type influence edge effect de...
A novel matrix approach for controlling the invariant densities of chaotic maps
International Nuclear Information System (INIS)
Rogers, Alan; Shorten, Robert; Heffernan, Daniel M.
2008-01-01
Recent work on positive matrices has resulted in a new matrix method for generating chaotic maps with arbitrary piecewise constant invariant densities, sometimes known as the inverse Frobenius-Perron problem (IFPP). In this paper, we give an extensive introduction to the IFPP, describing existing methods for solving it, and we describe our new matrix approach for solving the IFPP
Directory of Open Access Journals (Sweden)
Ayşe Betül Koç
2014-01-01
Full Text Available A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. By using this method, approximate solutions of the problems are easily obtained in form of the truncated Fibonacci series. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method. Then, the numerical results are compared with other methods.
GHOLAMI, SAEID; BABOLIAN, ESMAIL; JAVIDI, MOHAMMAD
2016-01-01
This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and fig...
Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations
Soleimani, Farahnaz; Stanimirovi´c, Predrag; Soleymani, Fazlollah
2015-01-01
An application of iterative methods for computing the Moore–Penrose inverse in balancing chemical equations is considered. With the aim to illustrate proposed algorithms, an improved high order hyper-power matrix iterative method for computing generalized inverses is introduced and applied. The improvements of the hyper-power iterative scheme are based on its proper factorization, as well as on the possibility to accelerate the iterations in the initial phase of the convergence. Although the ...
Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.
1988-11-01
Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.
Equation satisfied by electron-electron mutual Coulomb repulsion energy density functional
Joubert, Daniel P.
2011-01-01
The electron-electron mutual Coulomb repulsion energy density functional satisfies an equation that links functionals and functional derivatives at N-electron and (N-1)-electron densities for densities determined from the same adiabatic scaled external potential for the N-electron system.
Alpha particle spectroscopy for CR-39 detector utilizing matrix of energy equations
Energy Technology Data Exchange (ETDEWEB)
Awad, E.M. [Department of General Sciences, Yanbu Industrial College, PO Box 30436, Madinat Yanbu Al-Sinaiya (Saudi Arabia); Physics Department, Faculty of Science, Menofia University, Shebin El-Koom (Egypt)], E-mail: ayawad@yahoo.com; Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish), Suez Canal University, AL-Arish 45111 (Egypt); Department of Mathematics, Teacher' s College (Bisha), King Khalid University, Bisha, PO Box 551 (Saudi Arabia)], E-mail: asoliman_99@yahoo.com; Rammah, Y.S. [Physics Department, Faculty of Science, Menofia University, Shebin El-Koom (Egypt)
2007-10-01
A method for determining alpha-particle energy using CR-39 detector by utilizing matrix of energy equation was described. The matrix was composed from two axes; the track minor axis (m) and diameter of etched out track end (d) axis of some selected elliptical tracks. The energy E in (m,d) coordinate was approximated by matrix of energy equations given by: E{sub k}={sigma}{sub i,j=0}{sup 2}a{sub ij}d{sub k}{sup i}m{sub k}{sup j}, which was identified using two different approaches. First, i and j were treated as power exponents for d and m. The adjusting parameters values a{sub ij} were obtained and the energy of a given track was deduced directly from it. Second, i and j were treated as indices of some chosen tracks that were fitted to obtain iso-energy curves that were superimposed on m-d scatter plot as calibration curves. The energy between any two successive iso-energy curves in this case was assumed varied linearly with d for a given m. The energy matrix in both cases was solved numerically. Results of the two approaches were compared.
DEFF Research Database (Denmark)
Hedegård, Erik D.; Knecht, Stefan; Kielberg, Jesper Skau
2015-01-01
We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electroncorrelation...... effects in multiconfigurational electronic structure problems....
Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan
2018-01-01
In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.
International Nuclear Information System (INIS)
Pavlov, R.L.; Pavlov, L.I.; Raychev, P.P.; Garistov, V.P.; Dimitrova-Ivanovich, M.
2002-01-01
The matrix elements and expectation values of the hyperfine interaction operators are presented in a form suitable for numerical implementation in density matrix methods. The electron-nuclear spin-spin (dipolar and contact) interactions are considered, as well as the interaction between nuclear spin and electron-orbital motions. These interactions from the effective Breit-Pauli Hamiltonian determine the hyperfine structure in ESR spectra and contribute to chemical shifts in NMR. Applying the Wigner-Eckart theorem in the irreducible tensor-operator technique and the spin-space separation scheme, the matrix elements and expectation values of these relativistic corrections are expressed in analytical form. The final results are presented as products, or sums of products, of factors determined by the spin and (or) angular momentum symmetry and a spatial part determined by the action of the symmetrized tensor-operators on the normalized matrix or function of the spin or charge distribution.
Bond index: relation to second-order density matrix and charge fluctuations
International Nuclear Information System (INIS)
Giambiagi, M.S. de; Giambiagi, M.; Jorge, F.E.
1985-01-01
It is shown that, in the same way as the atomic charge is an invariant built from the first-order density matrix, the closed-shell generalized bond index is an invariant associated with the second-order reduced density matrix. The active charge of an atom (sum of bond indices) is shown to be the sum of all density correlation functions between it and the other atoms in the molecule; similarly, the self-charge is the fluctuation of its total charge. (Author) [pt
Bhatt, Ramakrishna T.; Kiser, Lames D.
1990-01-01
The room temperature mechanical properties were measured for SiC fiber reinforced reaction-bonded silicon nitride composites (SiC/RBSN) of different densities. The composites consisted of approx. 30 vol percent uniaxially aligned 142 micron diameter SiC fibers (Textron SCS-6) in a reaction-bonded Si3N4 matrix. The composite density was varied by changing the consolidation pressure during RBSN processing and by hot isostatically pressing the SiC/RBSN composites. Results indicate that as the consolidation pressure was increased from 27 to 138 MPa, the average pore size of the nitrided composites decreased from 0.04 to 0.02 microns and the composite density increased from 2.07 to 2.45 gm/cc. Nonetheless, these improvements resulted in only small increases in the first matrix cracking stress, primary elastic modulus, and ultimate tensile strength values of the composites. In contrast, HIP consolidation of SiC/RBSN resulted in a fully dense material whose first matrix cracking stress and elastic modulus were approx. 15 and 50 percent higher, respectively, and ultimate tensile strength values were approx. 40 percent lower than those for unHIPed SiC/RBSN composites. The modulus behavior for all specimens can be explained by simple rule-of-mixture theory. Also, the loss in ultimate strength for the HIPed composites appears to be related to a degradation in fiber strength at the HIP temperature. However, the density effect on matrix fracture strength was much less than would be expected based on typical monolithic Si3N4 behavior, suggesting that composite theory is indeed operating. Possible practical implications of these observations are discussed.
Truncation scheme of time-dependent density-matrix approach II
Energy Technology Data Exchange (ETDEWEB)
Tohyama, Mitsuru [Kyorin University School of Medicine, Mitaka, Tokyo (Japan); Schuck, Peter [Institut de Physique Nucleaire, IN2P3-CNRS, Universite Paris-Sud, Orsay (France); Laboratoire de Physique et de Modelisation des Milieux Condenses, CNRS et Universite Joseph Fourier, Grenoble (France)
2017-09-15
A truncation scheme of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for reduced density matrices, where a three-body density matrix is approximated by two-body density matrices, is improved to take into account a normalization effect. The truncation scheme is tested for the Lipkin model. It is shown that the obtained results are in good agreement with the exact solutions. (orig.)
P A M Dirac meets M G Krein: matrix orthogonal polynomials and Dirac's equation
Energy Technology Data Exchange (ETDEWEB)
Duran, Antonio J [Departamento de Analisis Matematico, Universidad de Sevilla, Apdo (PO BOX) 1160, 41080 Sevilla (Spain); Gruenbaum, F Alberto [Department of Mathematics, University of California, Berkeley, CA 94720 (United States)
2006-04-07
The solution of several instances of the Schroedinger equation (1926) is made possible by using the well-known orthogonal polynomials associated with the names of Hermite, Legendre and Laguerre. A relativistic alternative to this equation was proposed by Dirac (1928) involving differential operators with matrix coefficients. In 1949 Krein developed a theory of matrix-valued orthogonal polynomials without any reference to differential equations. In Duran A J (1997 Matrix inner product having a matrix symmetric second order differential operator Rocky Mt. J. Math. 27 585-600), one of us raised the question of determining instances of these matrix-valued polynomials going along with second order differential operators with matrix coefficients. In Duran A J and Gruenbaum F A (2004 Orthogonal matrix polynomials satisfying second order differential equations Int. Math. Res. Not. 10 461-84), we developed a method to produce such examples and observed that in certain cases there is a connection with the instance of Dirac's equation with a central potential. We observe that the case of the central Coulomb potential discussed in the physics literature in Darwin C G (1928 Proc. R. Soc. A 118 654), Nikiforov A F and Uvarov V B (1988 Special Functions of Mathematical Physics (Basle: Birkhauser) and Rose M E 1961 Relativistic Electron Theory (New York: Wiley)), and its solution, gives rise to a matrix weight function whose orthogonal polynomials solve a second order differential equation. To the best of our knowledge this is the first instance of a connection between the solution of the first order matrix equation of Dirac and the theory of matrix-valued orthogonal polynomials initiated by M G Krein.
Nanofiber density determines endothelial cell behavior on hydrogel matrix
Energy Technology Data Exchange (ETDEWEB)
Berti, Fernanda V., E-mail: fernanda@intelab.ufsc.br [Department of Chemical and Food Engineering, Federal University of Santa Catarina, 88040-900 Florianópolis, SC (Brazil); Rambo, Carlos R. [Department of Electrical Engineering, Federal University of Santa Catarina, 88040-900 Florianópolis, SC (Brazil); Dias, Paulo F. [Department of Cell Biology, Embryology and Genetics, Federal University of Santa Catarina, 88040-900 Florianópolis, SC (Brazil); Porto, Luismar M. [Department of Chemical and Food Engineering, Federal University of Santa Catarina, 88040-900 Florianópolis, SC (Brazil)
2013-12-01
When cultured under static conditions, bacterial cellulose pellicles, by the nature of the polymer synthesis that involves molecular oxygen, are characterized by two distinct surface sides. The upper surface is denser in fibers (entangled) than the lower surface that shows greater surface porosity. Human umbilical vein endothelial cells (HUVECs) were used to exploit how the microarchitecture (i.e., surface porosity, fiber network structure, surface topology, and fiber density) of bacterial cellulose pellicle surfaces influence cell–biomaterial interaction and therefore cell behavior. Adhesion, cell ingrowth, proliferation, viability and cell death mechanisms were evaluated on the two pellicle surface sides. Cell behavior, including secondary necrosis, is influenced only by the microarchitecture of the surface, since the biomaterial is extremely pure (constituted of cellulose and water only). Cell–cellulose fiber interaction is the determinant signal in the cell–biomaterial responses, isolated from other frequently present interferences such as protein and other chemical traces usually present in cell culture matrices. Our results suggest that microarchitecture of hydrogel materials might determine the performance of biomedical products, such as bacterial cellulose tissue engineering constructs (BCTECs). - Highlights: • Topography of BC pellicle is relevant to determine endothelial cells' fate. • Cell–biomaterial response is affected by the topography of BC-pellicle surface. • Endothelial cells exhibit different behavior depending on the BC topography. • Apoptosis and necrosis of endothelial cells were affected by the BC topography.
Nanofiber density determines endothelial cell behavior on hydrogel matrix
International Nuclear Information System (INIS)
Berti, Fernanda V.; Rambo, Carlos R.; Dias, Paulo F.; Porto, Luismar M.
2013-01-01
When cultured under static conditions, bacterial cellulose pellicles, by the nature of the polymer synthesis that involves molecular oxygen, are characterized by two distinct surface sides. The upper surface is denser in fibers (entangled) than the lower surface that shows greater surface porosity. Human umbilical vein endothelial cells (HUVECs) were used to exploit how the microarchitecture (i.e., surface porosity, fiber network structure, surface topology, and fiber density) of bacterial cellulose pellicle surfaces influence cell–biomaterial interaction and therefore cell behavior. Adhesion, cell ingrowth, proliferation, viability and cell death mechanisms were evaluated on the two pellicle surface sides. Cell behavior, including secondary necrosis, is influenced only by the microarchitecture of the surface, since the biomaterial is extremely pure (constituted of cellulose and water only). Cell–cellulose fiber interaction is the determinant signal in the cell–biomaterial responses, isolated from other frequently present interferences such as protein and other chemical traces usually present in cell culture matrices. Our results suggest that microarchitecture of hydrogel materials might determine the performance of biomedical products, such as bacterial cellulose tissue engineering constructs (BCTECs). - Highlights: • Topography of BC pellicle is relevant to determine endothelial cells' fate. • Cell–biomaterial response is affected by the topography of BC-pellicle surface. • Endothelial cells exhibit different behavior depending on the BC topography. • Apoptosis and necrosis of endothelial cells were affected by the BC topography
Parallel Computation of the Jacobian Matrix for Nonlinear Equation Solvers Using MATLAB
Rose, Geoffrey K.; Nguyen, Duc T.; Newman, Brett A.
2017-01-01
Demonstrating speedup for parallel code on a multicore shared memory PC can be challenging in MATLAB due to underlying parallel operations that are often opaque to the user. This can limit potential for improvement of serial code even for the so-called embarrassingly parallel applications. One such application is the computation of the Jacobian matrix inherent to most nonlinear equation solvers. Computation of this matrix represents the primary bottleneck in nonlinear solver speed such that commercial finite element (FE) and multi-body-dynamic (MBD) codes attempt to minimize computations. A timing study using MATLAB's Parallel Computing Toolbox was performed for numerical computation of the Jacobian. Several approaches for implementing parallel code were investigated while only the single program multiple data (spmd) method using composite objects provided positive results. Parallel code speedup is demonstrated but the goal of linear speedup through the addition of processors was not achieved due to PC architecture.
International Nuclear Information System (INIS)
Iagolnitzer, D.
1983-11-01
Recent axiomatic results on the (non holonomic) analytic structure of the multiparticle S matrix and Green functions are reviewed and related general conjectures are described: (i) formal expansions of Green functions in terms of (holonomic) Feynman-type integrals in which each vertex represents an irreducible kernel, and (ii) ''graph by graph unitarity'' and other discontinuity formulae of the latter. These conjectures are closely linked with unitarity or asymptotic completeness equations, which they yield in a formal sense. In constructive field theory, a direct proof of the first conjecture (together with an independent proof of the second) would thus imply, as a first step, asymptotic completeness in that sense
Efficient propagation of the hierarchical equations of motion using the matrix product state method
Shi, Qiang; Xu, Yang; Yan, Yaming; Xu, Meng
2018-05-01
We apply the matrix product state (MPS) method to propagate the hierarchical equations of motion (HEOM). It is shown that the MPS approximation works well in different type of problems, including boson and fermion baths. The MPS method based on the time-dependent variational principle is also found to be applicable to HEOM with over one thousand effective modes. Combining the flexibility of the HEOM in defining the effective modes and the efficiency of the MPS method thus may provide a promising tool in simulating quantum dynamics in condensed phases.
The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations
Chakravarthy, S. R.; Anderson, D. A.; Salas, M. D.
1980-01-01
The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.
Solution of quadratic matrix equations for free vibration analysis of structures.
Gupta, K. K.
1973-01-01
An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.
Liu, C; Liu, J; Yao, Y X; Wu, P; Wang, C Z; Ho, K M
2016-10-11
We recently proposed the correlation matrix renormalization (CMR) theory to treat the electronic correlation effects [Phys. Rev. B 2014, 89, 045131 and Sci. Rep. 2015, 5, 13478] in ground state total energy calculations of molecular systems using the Gutzwiller variational wave function (GWF). By adopting a number of approximations, the computational effort of the CMR can be reduced to a level similar to Hartree-Fock calculations. This paper reports our recent progress in minimizing the error originating from some of these approximations. We introduce a novel sum-rule correction to obtain a more accurate description of the intersite electron correlation effects in total energy calculations. Benchmark calculations are performed on a set of molecules to show the reasonable accuracy of the method.
Xiang-Guo, Meng; Ji-Suo, Wang; Hong-Yi, Fan; Cheng-Wei, Xia
2016-04-01
We solve the fermionic master equation for a thermal bath to obtain its explicit Kraus operator solutions via the fermionic state approach. The normalization condition of the Kraus operators is proved. The matrix representation for these solutions is obtained, which is incongruous with the result in the book completed by Nielsen and Chuang [Quantum Computation and Quantum Information, Cambridge University Press, 2000]. As especial cases, we also present the Kraus operator solutions to master equations for describing the amplitude-decay model and the diffusion process at finite temperature. Project supported by the National Natural Science Foundation of China (Grant No. 11347026), the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2013AM012 and ZR2012AM004), and the Research Fund for the Doctoral Program and Scientific Research Project of Liaocheng University, Shandong Province, China.
International Nuclear Information System (INIS)
Bonn, M; Ueba, H; Wolf, M
2005-01-01
A generalized theory of frequency- and time-resolved vibrational sum-frequency generation (SFG) spectroscopy of adsorbates at surfaces is presented using the density matrix formalism. Our theoretical treatment is specifically aimed at addressing issues that accompany the relatively novel SFG approach using broadband infrared pulses. The ultrashort duration of these pulses makes them ideally suited for time-resolved investigations, for which we present a complete theoretical treatment. A second key characteristic of these pulses is their large bandwidth and high intensity, which allow for highly non-linear effects, including vibrational ladder climbing of surface vibrations. We derive general expressions relating the density matrix to SFG spectra, and apply these expressions to specific experimental results by solving the coupled optical Bloch equations of the density matrix elements. Thus, we can theoretically reproduce recent experimentally demonstrated hot band SFG spectra using femtosecond broadband infrared excitation of carbon monoxide (CO) on a Ru(001) surface
Equation of state at finite net-baryon density using Taylor coefficients up to sixth order
International Nuclear Information System (INIS)
Huovinen, Pasi; Petreczky, Péter; Schmidt, Christian
2014-01-01
We employ the lattice QCD data on Taylor expansion coefficients up to sixth order to construct an equation of state at finite net-baryon density. When we take into account how hadron masses depend on lattice spacing and quark mass, the coefficients evaluated using the p4 action are equal to those of hadron resonance gas at low temperature. Thus the parametrised equation of state can be smoothly connected to the hadron resonance gas equation of state. We see that the equation of state using Taylor coefficients up to second order is realistic only at low densities, and that at densities corresponding to s/n B ≳40, the expansion converges by the sixth order term
Effects of matrix elasticity and cell density on human mesenchymal stem cells differentiation.
Xue, Ruyue; Li, Julie Yi-Shuan; Yeh, Yiting; Yang, Li; Chien, Shu
2013-09-01
Human mesenchymal stem cells (hMSCs) can differentiate into various cell types, including osteogenic and chondrogenic cells. The matrix elasticity and cell seeding density are important factors in hMSCs differentiation. We cultured hMSCs at different seeding densities on polyacrylamide hydrogels with different stiffness corresponding to Young's moduli of 1.6 ± 0.3 and 40 ± 3.6 kPa. The promotion of osteogenic marker expression by hard gel is overridden by a high seeding density. Cell seeding density, however, did not influence the chondrogenic marker expressions induced by soft gel. These findings suggest that interplays between cell-matrix and cell-cell interactions contribute to hMSCs differentiation. The promotion of osteogenic differentiation on hard matrix was shown to be mediated through the Ras pathway. Inhibition of Ras (RasN17) significantly decreased ERK, Smad1/5/8 and AKT activation, and osteogenic markers expression. However, constitutively active Ras (RasV12) had little effect on osteogenic marker expression, suggesting that the Ras pathways are necessary but not sufficient for osteogenesis. Taken together, our results indicate that matrix elasticity and cell density are important microenvironmental cues driving hMSCs proliferation and differentiation. Copyright © 2013 Orthopaedic Research Society.
The response matrix discrete ordinates solution to the 1D radiative transfer equation
International Nuclear Information System (INIS)
Ganapol, Barry D.
2015-01-01
The discrete ordinates method (DOM) of solution to the 1D radiative transfer equation has been an effective method of solution for nearly 70 years. During that time, the method has experienced numerous improvements as numerical and computational techniques have become more powerful and efficient. Here, we again consider the analytical solution to the discrete radiative transfer equation in a homogeneous medium by proposing a new, and consistent, form of solution that improves upon previous forms. Aided by a Wynn-epsilon convergence acceleration, its numerical evaluation can achieve extreme precision as demonstrated by comparison with published benchmarks. Finally, we readily extend the solution to a heterogeneous medium through the star product formulation producing a novel benchmark for closed form Henyey–Greenstein scattering as an example. - Highlights: • Presents a new solution to the RTE called the response matrix DOM (RM/DOM). • Solution representations avoid the instability common in exponential solutions. • Explicit form in terms of matrix hyperbolic functions. • Extreme accuracy through Wynn-epsilon acceleration checked by published benchmarks. • Provides a more transparent numerical evaluation than found previously
Energy Technology Data Exchange (ETDEWEB)
Faisal, F H.M. [Bielefeld Univ. (Germany, F.R.). Fakultaet fuer Physik
1976-06-11
In this work the perturbation theory for multiphoton processes at high intensities is investigated and it is described an analytical method of summing the perturbation series to extract the contribution from all terms that give rise to the absorption of N photons by an atomic system. The method is first applied to the solution of a simple model problem and the result is confirmed by direct integration of the model Schroedinger equation. The usual lowest (nonvanishing)-order perturbation-theoretical calculation is also carried out for this model to demonstrate explicitly that the full result correctly reproduces that of the lowest-order theory in the limit of low intensity. The method is then extended to the case of an atomic system with well-developed spectrum (e.g. H atom) and the N-photon T-matrix is derived in terms of a ''photon matrix'' asub(N), for which a three-term recurrence relation is established. Next, from the vantage point of the general result obtained here, A probe is made into the nature of several approximate nonperturbative solutions that have appeared in the literature in the past. It is shown here that their applicability is severely restricted by the requirement of the essential spectral degeneracy of the atomic system. Finally, appendix A outlines a prescription of computing the photon matrix asub(N), which (as in the usual lowest-order perturbation-theoretical calculation)requires a knowledge of the eigenfunctions and eigenvalues of the atomic Hamiltonian only.
Reduced one-body density matrix of Tonks–Girardeau gas at finite temperature
International Nuclear Information System (INIS)
Fu Xiao-Chen; Hao Ya-Jiang
2015-01-01
With thermal Bose–Fermi mapping method, we investigate the Tonks–Girardeau gas at finite temperature. It is shown that at low temperature, the Tonks gas displays the Fermi-like density profiles, and with the increase in temperature, the Tonks gas distributes in wider region. The reduced one-body density matrix is diagonal dominant in the whole temperature region, and the off-diagonal elements shall vanish rapidly with the deviation from the diagonal part at high temperature. (paper)
Exact differential equation for the density and ionization energy of a many-particle system
Levy, M.; Perdew, J. P.; Sahni, V.
1984-01-01
The present investigation is concerned with relations studied by Hohenberg and Kohn (1964) and Kohn and Sham (1965). The properties of a ground-state many-electron system are determined by the electron density. The correct differential equation for the density, as dictated by density-functional theory, is presented. It is found that the ground-state density n of a many-electron system obeys a Schroedinger-like differential equation which may be solved by standard Kohn-Sham programs. Results are connected to the traditional exact Kohn-Sham theory. It is pointed out that the results of the current investigations are readily extended to spin-density functional theory.
Directory of Open Access Journals (Sweden)
Abdel-Shakoor M Sarhan
2016-05-01
Full Text Available Abstract We consider two nonlinear matrix equations X r ± ∑ i = 1 m A i ∗ X δ i A i = I $X^{r} \\pm \\sum_{i = 1}^{m} A_{i}^{*}X^{\\delta_{i}}A_{i} = I$ , where − 1 < δ i < 0 $- 1 < \\delta_{i} < 0$ , and r, m are positive integers. For the first equation (plus case, we prove the existence of positive definite solutions and extremal solutions. Two algorithms and proofs of their convergence to the extremal positive definite solutions are constructed. For the second equation (negative case, we prove the existence and the uniqueness of a positive definite solution. Moreover, the algorithm given in (Duan et al. in Linear Algebra Appl. 429:110-121, 2008 (actually, in (Shi et al. in Linear Multilinear Algebra 52:1-15, 2004 for r = 1 $r = 1$ is proved to be valid for any r. Numerical examples are given to illustrate the performance and effectiveness of all the constructed algorithms. In Appendix, we analyze the ordering on the positive cone P ( n ‾ $\\overline{P(n}$ .
International Nuclear Information System (INIS)
Itagaki, Masafumi; Sahashi, Naoki.
1997-01-01
The multiple reciprocity boundary element method has been applied to three-dimensional two-group neutron diffusion problems. A matrix-type boundary integral equation has been derived to solve the first and the second group neutron diffusion equations simultaneously. The matrix-type fundamental solutions used here satisfy the equation which has a point source term and is adjoint to the neutron diffusion equations. A multiple reciprocity method has been employed to transform the matrix-type domain integral related to the fission source into an equivalent boundary one. The higher order fundamental solutions required for this formulation are composed of a series of two types of analytic functions. The eigenvalue itself is also calculated using only boundary integrals. Three-dimensional test calculations indicate that the present method provides stable and accurate solutions for criticality problems. (author)
A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics
Kretchmer, Joshua S.; Chan, Garnet Kin-Lic
2018-02-01
We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a simplified single-impurity time-dependent formulation as a first step toward a multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem are derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the mean-field TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as expected from analogous behavior in static DMET, the constrained structure of the real-time DMET wavefunction leads to a slower convergence with respect to active space size, in the single-impurity formulation, relative to TD-CASSCF. Our initial results suggest that real-time DMET provides a promising framework to simulate non-equilibrium electron dynamics in which strong electron correlation plays an important role, and lays the groundwork for future multi-impurity formulations.
Collagen Matrix Density Drives the Metabolic Shift in Breast Cancer Cells
Directory of Open Access Journals (Sweden)
Brett A. Morris
2016-11-01
Full Text Available Increased breast density attributed to collagen I deposition is associated with a 4–6 fold increased risk of developing breast cancer. Here, we assessed cellular metabolic reprogramming of mammary carcinoma cells in response to increased collagen matrix density using an in vitro 3D model. Our initial observations demonstrated changes in functional metabolism in both normal mammary epithelial cells and mammary carcinoma cells in response to changes in matrix density. Further, mammary carcinoma cells grown in high density collagen matrices displayed decreased oxygen consumption and glucose metabolism via the tricarboxylic acid (TCA cycle compared to cells cultured in low density matrices. Despite decreased glucose entry into the TCA cycle, levels of glucose uptake, cell viability, and ROS were not different between high and low density matrices. Interestingly, under high density conditions the contribution of glutamine as a fuel source to drive the TCA cycle was significantly enhanced. These alterations in functional metabolism mirrored significant changes in the expression of metabolic genes involved in glycolysis, oxidative phosphorylation, and the serine synthesis pathway. This study highlights the broad importance of the collagen microenvironment to cellular expression profiles, and shows that changes in density of the collagen microenvironment can modulate metabolic shifts of cancer cells.
A density matrix renormalization group study of low-lying excitations ...
Indian Academy of Sciences (India)
Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited 2 symmetry and spin parity of the system to obtain excited states of ...
On the statistical interpretation of quantum mechanics: evolution of the density matrix
International Nuclear Information System (INIS)
Benzecri, J.P.
1986-01-01
Without attempting to identify ontological interpretation with a mathematical structure, we reduce philosophical speculation to five theses. In the discussion of these, a central role is devoted to the mathematical problem of the evolution of the density matrix. This article relates to the first 3 of these 5 theses [fr
Relativistic density matrix in the diagonal momentum representation. Bose-gas
International Nuclear Information System (INIS)
Makhlin, A.N.; Sinyukov, Yu.M.
1984-01-01
The relativistic-invariance treatment of the ideal Bose-system arising from the diagonal momentum representation for the density matrix is developed. The average occupation members and their correlators for statistical systems in arbitrary inertial frames are found on the equal-time hypersurfaces. The relativistic partition function method for the calculation of thermodynamic properties of gases moving as a whole is constructed
Spin observables in antiproton-proton to AntiLambda-Lambda and density-matrix constraints
Elchikh, Mokhtar; Richard, Jean-Marc
2005-01-01
The positivity conditions of the spin density matrix constrain the spin observables of the reaction antiproton-proton to AntiLambda-Lambda, leading to model-independent, non-trivial inequalities. The formalism is briefly presented and examples of inequalities are provided.
Spin observables in p-barp → ΛΛ and density-matrix constraints
International Nuclear Information System (INIS)
Elchikh, Mokhtar; Richard, Jean-Marc
2005-01-01
The positivity conditions of the spin density matrix constrain the spin observables of the reaction p-barp → Λ-barΛ, leading to model-independent, non-trivial inequalities. The formalism is briefly presented and examples of inequalities are provided
TREATMENT OF NONADIABATIC TRANSITIONS BY DENSITY-MATRIX EVOLUTION AND MOLECULAR-DYNAMICS SIMULATIONS
MAVRI, J; BERENDSEN, HJC
1994-01-01
A density matrix evolution (DME) method (H.J.C. Berendsen and J. Mavri, J. Phys. Chem., 97 (1993) 13469) to simulate the dynamics of quantum systems embedded in a classical environment is presented. The DME method allows treatment of nonadiabatic transitions. As numerical examples the collinear
The problem of the universal density functional and the density matrix functional theory
Bobrov, V.B.; Trigger, S.A.
2013-01-01
The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the
A new equation of state for porous materials with ultra-low densities
Geng Hua Yun; Wu Qiang
2002-01-01
A thermodynamic equation of state is derived which is appropriate for investigating the thermodynamic variations along isobaric paths to predict compression behaviours of porous materials. This equation-of-state model is tested on porous iron, copper, lead and tungsten with different initial densities. The calculated Hugoniots are in good agreement with the corresponding experimental data published previously. This shows that this model can satisfactorily predict the Hugoniots of porous materials with wide porosity and pressure ranges.
Wills, John M.; Mattsson, Ann E.
2012-02-01
Density functional theory (DFT) provides a formally predictive base for equation of state properties. Available approximations to the exchange/correlation functional provide accurate predictions for many materials in the periodic table. For heavy materials however, DFT calculations, using available functionals, fail to provide quantitative predictions, and often fail to be even qualitative. This deficiency is due both to the lack of the appropriate confinement physics in the exchange/correlation functional and to approximations used to evaluate the underlying equations. In order to assess and develop accurate functionals, it is essential to eliminate all other sources of error. In this talk we describe an efficient first-principles electronic structure method based on the Dirac equation and compare the results obtained with this method with other methods generally used. Implications for high-pressure equation of state of relativistic materials are demonstrated in application to Ce and the light actinides. Sandia National Laboratories is a multi-program laboratory managed andoperated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Saitow, Masaaki; Kurashige, Yuki; Yanai, Takeshi
2013-07-28
We report development of the multireference configuration interaction (MRCI) method that can use active space scalable to much larger size references than has previously been possible. The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry offers the ability to describe static correlation in a large active space. The present MRCI method provides a critical correction to the DMRG reference by including high-level dynamic correlation through the CI treatment. When the DMRG and MRCI theories are combined (DMRG-MRCI), the full internal contraction of the reference in the MRCI ansatz, including contraction of semi-internal states, plays a central role. However, it is thought to involve formidable complexity because of the presence of the five-particle rank reduced-density matrix (RDM) in the Hamiltonian matrix elements. To address this complexity, we express the Hamiltonian matrix using commutators, which allows the five-particle rank RDM to be canceled out without any approximation. Then we introduce an approximation to the four-particle rank RDM by using a cumulant reconstruction from lower-particle rank RDMs. A computer-aided approach is employed to derive the exceedingly complex equations of the MRCI in tensor-contracted form and to implement them into an efficient parallel computer code. This approach extends to the size-consistency-corrected variants of MRCI, such as the MRCI+Q, MR-ACPF, and MR-AQCC methods. We demonstrate the capability of the DMRG-MRCI method in several benchmark applications, including the evaluation of single-triplet gap of free-base porphyrin using 24 active orbitals.
QCD equation of state of hot deconfined matter at finite baryon density. A quasiparticle perspective
International Nuclear Information System (INIS)
Bluhm, Marcus
2008-01-01
The quasiparticle model, based on quark and gluon degrees of freedom, has been developed for the description of the thermodynamics of a hot plasma of strongly interacting matter which is of enormous relevance in astrophysics, cosmology and for relativistic heavy-ion collisions as well. In the present work, this phenomenological model is extended into the realm of imaginary chemical potential and towards including, in general, different and independent quark flavour chemical potentials. In this way, nonzero net baryon-density effects in the equation of state are selfconsistently attainable. Furthermore, a chain of approximations based on formal mathematical manipulations is presented which outlines the connection of the quasiparticle model with the underlying gauge field theory of strong interactions, QCD, putting the model on firmer ground. The applicability of the model to extrapolate the equation of state known from lattice QCD at zero baryon density to nonzero baryon densities is shown. In addition, the ability of the model to extrapolate results to the chiral limit and to asymptotically large temperatures is illustrated by confrontation with available first-principle lattice QCD results. Basing on these successful comparisons supporting the idea that the hot deconfined phase can be described in a consistent picture by dressed quark and gluon degrees of freedom, a reliable QCD equation of state is constructed and baryon-density effects are examined, also along isentropic evolutionary paths. Scaling properties of the equation of state with fundamental QCD parameters such as the number of active quark flavour degrees of freedom, the entering quark mass parameters or the numerical value of the deconfinement transition temperature are discussed, and the robustness of the equation of state in the regions of small and large energy densities is shown. Uncertainties arising in the transition region are taken into account by constructing a family of equations of state
International Nuclear Information System (INIS)
Na, Y. W.; Park, C. E.; Lee, S. Y.
2009-01-01
main object of this work is not to investigate the whole transient behavior of the models at hand but to focus on the behavior of numerical solutions part of the sparse asymmetric matrix equations in the transient of hydraulic system. It is outside of the scope of this work to improve the diagonal dominance or to pre-condition the matrix in the process of differencing and linearizing the governing equation, even though it is better to do it that way before applying the solver if there is any efficient way available
Single-particle density matrix and superfluidity in the two-dimensional Bose Coulomb fluid
International Nuclear Information System (INIS)
Minguzzi, A.; Tosi, M.P.; Davoudi, B.
2002-01-01
A study by Magro and Ceperley [Phys. Rev. Lett. 73, 826 (1994)] has shown that the ground state of the two-dimensional fluid of charged bosons with logarithmic interactions is not Bose condensed, but exhibits algebraic off-diagonal order in the single-particle density matrix ρ(r). We use a hydrodynamic Hamiltonian expressed in terms of density and phase operators, in combination with an f-sum rule on the superfluid fraction, to reproduce these results and to extend the evaluation of the density matrix to finite temperature T. This approach allows us to treat the liquid as a superfluid in the absence of a condensate. The algebraic decay of the one-body density matrix is due to correlations between phase fluctuations, and we find that the exponent in the power law is determined by the superfluid density n s (T). We also find that the plasmon gap in the single-particle energy spectrum at long wavelengths decreases with increasing T and closes at the critical temperature for the onset of superfluidity
Directory of Open Access Journals (Sweden)
WANG Xiang
2016-02-01
Full Text Available A new bandwidth optimization method of normal equation matrix in bundle block adjustment in multi-baseline rotational close range photography by image index re-sorting is proposed. The equivalent exposure station of each image is calculated by its object space coverage and the relationship with other adjacent images. Then, according to the coordinate relations between equivalent exposure stations, new logical indices of all images are computed, based on which, the optimized bandwidth value can be obtained. Experimental results show that the bandwidth determined by our proposed method is significantly better than its original value, thus the operational efficiency, as well as the memory consumption of multi-baseline rotational close range photography in real-data applications, is optimized to a certain extent.
New matrix bounds and iterative algorithms for the discrete coupled algebraic Riccati equation
Liu, Jianzhou; Wang, Li; Zhang, Juan
2017-11-01
The discrete coupled algebraic Riccati equation (DCARE) has wide applications in control theory and linear system. In general, for the DCARE, one discusses every term of the coupled term, respectively. In this paper, we consider the coupled term as a whole, which is different from the recent results. When applying eigenvalue inequalities to discuss the coupled term, our method has less error. In terms of the properties of special matrices and eigenvalue inequalities, we propose several upper and lower matrix bounds for the solution of DCARE. Further, we discuss the iterative algorithms for the solution of the DCARE. In the fixed point iterative algorithms, the scope of Lipschitz factor is wider than the recent results. Finally, we offer corresponding numerical examples to illustrate the effectiveness of the derived results.
Directory of Open Access Journals (Sweden)
Yan Chen
2017-03-01
Full Text Available Based on the vectorised and cache optimised kernel, a parallel lower upper decomposition with a novel communication avoiding pivoting scheme is developed to solve dense complex matrix equations generated by the method of moments. The fine-grain data rearrangement and assembler instructions are adopted to reduce memory accessing times and improve CPU cache utilisation, which also facilitate vectorisation of the code. Through grouping processes in a binary tree, a parallel pivoting scheme is designed to optimise the communication pattern and thus reduces the solving time of the proposed solver. Two large electromagnetic radiation problems are solved on two supercomputers, respectively, and the numerical results demonstrate that the proposed method outperforms those in open source and commercial libraries.
Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.
1988-11-01
Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.
Postsynaptic density protein 95 in the striosome and matrix compartments of the human neostriatum.
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Ryoma eMorigaki
2015-11-01
Full Text Available The human neostriatum consists of two functional subdivisions referred to as the striosome (patch and matrix compartments. The striosome-matrix dopamine systems play a central role in cortico-thalamo-basal ganglia circuits, and their involvement is thought to underlie the genesis of multiple movement and behavioral disorders, and of drug addiction. Human neuropathology also has shown that striosomes and matrix have differential vulnerability patterns in several striatal neurodegenerative diseases. Postsynaptic density protein 95 (PSD-95, also known as DLG4, is a major scaffolding protein in the postsynaptic densities of dendritic spines. PSD-95 is now known to negatively regulate not only N-methyl-D-aspartate glutamate signaling, but also dopamine D1 signals at sites of postsynaptic transmission. Accordingly, a neuroprotective role for PSD-95 against dopamine D1 receptor (D1R-mediated neurotoxicity in striatal neurodegeneration also has been suggested. Here, we used a highly sensitive immunohistochemistry technique to show that in the human neostriatum, PSD-95 is differentially concentrated in the striosome and matrix compartments, with a higher density of PSD-95 labeling in the matrix compartment than in the striosomes. This compartment-specific distribution of PSD-95 was strikingly complementary to that of D1R. In addition to the possible involvement of PSD-95-mediated synaptic function in compartment-specific dopamine signals, we suggest that the striosomes might be more susceptible to D1R-mediated neurotoxicity than the matrix compartment. This notion may provide new insight into the compartment-specific vulnerability of MSNs in striatal neurodegeneration.
Links between matrix bulk density, macropore characteristics and hydraulic behavior of soils
DEFF Research Database (Denmark)
Katuwal, Sheela; Møldrup, Per; Lamandé, Mathieu
2013-01-01
characteristics on soil hydraulic functions has rarely been studied. With the objective of studying the links between these parameters we quantified macropore characteristics of intact soil columns (19 cm diameter x 20 cm high) from two agricultural field sites (Silstrup and Faardrup) in Denmark using coarse...... resolution X-ray CT and linked them with laboratory measurements of air permeability and leaching experiment. In addition to macropore characteristics, we also quantified the CT-number of the matrix as a measure of the bulk density of the matrix, i.e., excluding macropores in the soil. Soils from the two...
The energy density distribution of an ideal gas and Bernoulli’s equations
Santos, Leonardo S. F.
2018-05-01
This work discusses the energy density distribution in an ideal gas and the consequences of Bernoulli’s equation and the corresponding relation for compressible fluids. The aim of this work is to study how Bernoulli’s equation determines the energy flow in a fluid, although Bernoulli’s equation does not describe the energy density itself. The model from molecular dynamic considerations that describes an ideal gas at rest with uniform density is modified to explore the gas in motion with non-uniform density and gravitational effects. The difference between the component of the speed of a particle that is parallel to the gas speed and the gas speed itself is called ‘parallel random speed’. The pressure from the ‘parallel random speed’ is denominated as parallel pressure. The modified model predicts that the energy density is the sum of kinetic and potential gravitational energy densities plus two terms with static and parallel pressures. The application of Bernoulli’s equation and the corresponding relation for compressible fluids in the energy density expression has resulted in two new formulations. For incompressible and compressible gas, the energy density expressions are written as a function of stagnation, static and parallel pressures, without any dependence on kinetic or gravitational potential energy densities. These expressions of the energy density are the main contributions of this work. When the parallel pressure was uniform, the energy density distribution for incompressible approximation and compressible gas did not converge to zero for the limit of null static pressure. This result is rather unusual because the temperature tends to zero for null pressure. When the gas was considered incompressible and the parallel pressure was equal to static pressure, the energy density maintained this unusual behaviour with small pressures. If the parallel pressure was equal to static pressure, the energy density converged to zero for the limit of the
Navarro Pérez, R.; Schunck, N.; Dyhdalo, A.; Furnstahl, R. J.; Bogner, S. K.
2018-05-01
Background: Energy density functional methods provide a generic framework to compute properties of atomic nuclei starting from models of nuclear potentials and the rules of quantum mechanics. Until now, the overwhelming majority of functionals have been constructed either from empirical nuclear potentials such as the Skyrme or Gogny forces, or from systematic gradient-like expansions in the spirit of the density functional theory for atoms. Purpose: We seek to obtain a usable form of the nuclear energy density functional that is rooted in the modern theory of nuclear forces. We thus consider a functional obtained from the density matrix expansion of local nuclear potentials from chiral effective field theory. We propose a parametrization of this functional carefully calibrated and validated on selected ground-state properties that is suitable for large-scale calculations of nuclear properties. Methods: Our energy functional comprises two main components. The first component is a non-local functional of the density and corresponds to the direct part (Hartree term) of the expectation value of local chiral potentials on a Slater determinant. Contributions to the mean field and the energy of this term are computed by expanding the spatial, finite-range components of the chiral potential onto Gaussian functions. The second component is a local functional of the density and is obtained by applying the density matrix expansion to the exchange part (Fock term) of the expectation value of the local chiral potential. We apply the UNEDF2 optimization protocol to determine the coupling constants of this energy functional. Results: We obtain a set of microscopically constrained functionals for local chiral potentials from leading order up to next-to-next-to-leading order with and without three-body forces and contributions from Δ excitations. These functionals are validated on the calculation of nuclear and neutron matter, nuclear mass tables, single-particle shell structure
A matrix formalism to solve interface condition equations in a reactor system
Energy Technology Data Exchange (ETDEWEB)
Matausek, M V [Boris Kidric Institute of Nuclear Sciences Vinca, Beograd (Yugoslavia)
1970-05-15
When a nuclear reactor or a reactor lattice cell is treated by an approximate procedure to solve the neutron transport equation, as the last computational step often appears a problem of solving systems of algebraic equations stating the interface and boundary conditions for the neutron flux moments. These systems have usually the coefficient matrices of the block-bi diagonal type, containing thus a large number of zero elements. In the present report it is shown how such a system can be solved efficiently accounting for all the zero elements both in the coefficient matrix and in the free term vector. The procedure is presented here for the case of multigroup P{sub 3} calculation of neutron flux distribution in a cylindrical reactor lattice cell. Compared with the standard gaussian elimination method, this procedure is more advantageous both in respect to the number of operations needed to solve a given problem and in respect to the computer memory storage requirements. A similar formalism can also be applied for other approximate methods, for instance for multigroup diffusion treatment of a multi zone reactor. (author)
International Nuclear Information System (INIS)
Fano, G.; Ortolani, F.; Ziosi, L.
1997-10-01
The density matrix renormalization group (DMRG) method introduced by White for the study of strongly interacting electron systems is reviewed; the method is variational and considers a system of localized electrons as the union of two adjacent fragments A,B. A density matrix ρ is introduced, whose eigenvectors corresponding to the largest eigenvalues are the most significant, the most probable states of A in the presence of B; these states are retained, while states corresponding to small eigenvalues of ρ are neglected. It is conjectured that the decreasing behaviour of the eigenvalues is gaussian. The DMRG method is tested on the Pariser-Parr-Pople Hamiltonian of a cyclic polyene (CH) N up to N = 34. A Hilbert space of dimension 5. x 10 18 is explored. The ground state energy is 10 -3 eV within the full Cl value in the case N = 18. The DMRG method compares favourably also with coupled cluster approximations. The unrestricted Hartree-Fock solution (which presents spin density waves) is briefly reviewed, and a comparison is made with the DMRG energy values. Finally, the spin-spin and density-density correlation functions are computed; the results suggest that the antiferromagnetic order of the exact solution does not extend up to large distances but exists locally. No charge density waves are present. (author)
High-density equation of state for helium and its application to bubbles in solids
International Nuclear Information System (INIS)
Wolfer, W.G.
1980-06-01
Helium, produced by transmutations or injected, causes bubble formation in solids at elevated temperatures. For small bubbles, the gas pressure required to balance the surface tension reaches values which far exceed those obtainable in experiments to measure the equation of state for helium gas. Therefore, empirical gas laws cannot be considered applicable to the fluid-like densities existing in small bubbles. In order to remedy this situation, an equation of state for helium was developed from the theory of the liquid state. At very low densities, this theoretically derived equation of state agrees with experimental results. For high densities, however, gas pressures are predicted which are significantly higher than those derived from the ideal gas law, but also significantly lower than pressures obtained with the van der Waals law. When applied to equilibrium bubbles in solids, it is found that the high-density equation of state leads to less bubble swelling than the van der Waals law, but more than the ideal gas law. Furthermore, the number of helium atoms in equilibrium bubbles is nearly independent of temperature
International Nuclear Information System (INIS)
Sato, M.
1991-01-01
The Saha equation for a plasma in thermodynamic equilibrium (TE) is approximately solved to give the temperature as an explicit function of population densities. It is shown that the derived expressions for the Saha temperature are valid approximations to the exact solution. An application of the approximate temperature to the calculation of TE plasma parameters is also described. (orig.)
Neutron star models with realistic high-density equations of state
International Nuclear Information System (INIS)
Malone, R.C.; Johnson, M.B.; Bethe, H.A.
1975-01-01
We calculate neutron star models using four realistic high-density models of the equation of state. We conclude that the maximum mass of a neutron star is unlikely to exceed 2 M/sub sun/. All of the realistic models are consistent with current estimates of the moment of inertia of the Crab pulsar
Directory of Open Access Journals (Sweden)
Jinliang Xu
2013-06-01
Full Text Available This paper investigates the filtering problem for multivariate continuous nonlinear non-Gaussian systems based on an improved minimum error entropy (MEE criterion. The system is described by a set of nonlinear continuous equations with non-Gaussian system noises and measurement noises. The recently developed generalized density evolution equation is utilized to formulate the joint probability density function (PDF of the estimation errors. Combining the entropy of the estimation error with the mean squared error, a novel performance index is constructed to ensure the estimation error not only has small uncertainty but also approaches to zero. According to the conjugate gradient method, the optimal filter gain matrix is then obtained by minimizing the improved minimum error entropy criterion. In addition, the condition is proposed to guarantee that the estimation error dynamics is exponentially bounded in the mean square sense. Finally, the comparative simulation results are presented to show that the proposed MEE filter is superior to nonlinear unscented Kalman filter (UKF.
Energy Technology Data Exchange (ETDEWEB)
Belavin, Vladimir [I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute,Leninsky Avenue 53, 119991 Moscow (Russian Federation); Department of Quantum Physics, Institute for Information Transmission Problems,Bolshoy Karetny per. 19, 127994 Moscow (Russian Federation); Moscow Institute of Physics and Technology,Dolgoprudnyi, 141700 Moscow region (Russian Federation); Cao, Xiangyu [LPTMS, CNRS (UMR 8626), Université Paris-Saclay,15 rue Georges Clémenceau, 91405 Orsay (France); Estienne, Benoit [LPTHE, CNRS and Université Pierre et Marie Curie, Sorbonne Universités,4 Place Jussieu, 75252 Paris Cedex 05 (France); Santachiara, Raoul [LPTMS, CNRS (UMR 8626), Université Paris-Saclay,15 rue Georges Clémenceau, 91405 Orsay (France)
2017-03-02
In a recent study we considered W{sub 3} Toda 4-point functions that involve matrix elements of a primary field with the highest-weight in the adjoint representation of sl{sub 3}. We generalize this result by considering a semi-degenerate primary field, which has one null vector at level two. We obtain a sixth-order Fuchsian differential equation for the conformal blocks. We discuss the presence of multiplicities, the matrix elements and the fusion rules.
Yi, Sun; Nelson, Patrick W; Ulsoy, A Galip
2007-04-01
In a turning process modeled using delay differential equations (DDEs), we investigate the stability of the regenerative machine tool chatter problem. An approach using the matrix Lambert W function for the analytical solution to systems of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis. The Lambert W function, known to be useful for solving scalar first-order DDEs, has recently been extended to a matrix Lambert W function approach to solve systems of DDEs. The essential advantages of the matrix Lambert W approach are not only the similarity to the concept of the state transition matrix in lin ear ordinary differential equations, enabling its use for general classes of linear delay differential equations, but also the observation that we need only the principal branch among an infinite number of roots to determine the stability of a system of DDEs. The bifurcation method combined with Sturm sequences provides an algorithm for determining the stability of DDEs without restrictive geometric analysis. With this approach, one can obtain the critical values of delay, which determine the stability of a system and hence the preferred operating spindle speed without chatter. We apply both the matrix Lambert W function and the bifurcation analysis approach to the problem of chatter stability in turning, and compare the results obtained to existing methods. The two new approaches show excellent accuracy and certain other advantages, when compared to traditional graphical, computational and approximate methods.
New Jacobian Matrix and Equations of Motion for a 6 d.o.f Cable-Driven Robot
Directory of Open Access Journals (Sweden)
Ali Afshari
2007-03-01
Full Text Available In this paper, we introduce a new method and new motion variables to study kinematics and dynamics of a 6 d.o.f cable-driven robot. Using these new variables and Lagrange equations, we achieve new equations of motion which are different in appearance and several aspects from conventional equations usually used to study 6 d.o.f cable robots. Then, we introduce a new Jacobian matrix which expresses kinematical relations of the robot via a new approach and is basically different from the conventional Jacobian matrix. One of the important characteristics of the new method is computational efficiency in comparison with the conventional method. It is demonstrated that using the new method instead of the conventional one, significantly reduces the computation time required to determine workspace of the robot as well as the time required to solve the equations of motion.
Liang, Wenkel; Isborn, Christine M.; Li, Xiaosong
2009-11-01
The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the α and β electrons to achieve the two-electron excited states of minimal basis H2 and HeH+ [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H2, HeH+, lithium hydride, ethylene, and butadiene.
Low- and high-density nuclear equation of state and the hyperon puzzle
Energy Technology Data Exchange (ETDEWEB)
Colucci, Giuseppe; Sedrakian, Armen [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik
2013-07-01
The measurements of the unusually high mass of the millisecond pulsar PSR J1614-2230 (1.97 ± 0.04 M {sub CircleDot}) imposes a strong constraint on the nuclear Equation of State (EoS), in particular for what concerns the finite density behaviour of nuclear and neutron matter. In my talk I first discuss a model for the low-density part of the EoS, based on chiral one-pion exchange. I consider a self-consistent approach at finite temperature and density and show that even in a fully-relativistic theory the one-pion exchange contribution is dominated by a contact interaction. Then, a relativistic mean-field approach is used to discuss the high-density part of the EoS, including the presence of hyperons. In the latter, a density dependent parametrization is used and a parameter study on the hyperon-scalar meson coupling is performed.
Correlated random-phase approximation from densities and in-medium matrix elements
Energy Technology Data Exchange (ETDEWEB)
Trippel, Richard; Roth, Robert [Institut fuer Kernphysik, Technische Universitaet Darmstadt (Germany)
2016-07-01
The random-phase approximation (RPA) as well as the second RPA (SRPA) are established tools for the study of collective excitations in nuclei. Addressing the well known lack of correlations, we derived a universal framework for a fully correlated RPA based on the use of one- and two-body densities. We apply densities from coupled cluster theory and investigate the impact of correlations. As an alternative approach to correlations we use matrix elements transformed via in-medium similarity renormalization group (IM-SRG) in combination with RPA and SRPA. We find that within SRPA the use of IM-SRG matrix elements leads to the disappearance of instabilities of low-lying states. For the calculations we use normal-ordered two- plus three-body interactions derived from chiral effective field theory. We apply different Hamiltonians to a number of doubly-magic nuclei and calculate electric transition strengths.
Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic
2010-01-14
We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu(2)O(2)](2+) core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu(2)O(2)](2+).
Metal-insulator transition in disordered systems from the one-body density matrix
DEFF Research Database (Denmark)
Olsen, Thomas; Resta, Raffaele; Souza, Ivo
2017-01-01
The insulating state of matter can be probed by means of a ground state geometrical marker, which is closely related to the modern theory of polarization (based on a Berry phase). In the present work we show that this marker can be applied to determine the metal-insulator transition in disordered...... the one-body density matrix. The approach has a general ab initio formulation and could in principle be applied to realistic disordered materials by standard electronic structure methods....... systems. In particular, for noninteracting systems the geometrical marker can be obtained from the configurational average of the norm-squared one-body density matrix, which can be calculated within open as well as periodic boundary conditions. This is in sharp contrast to a classification based...
Homocomposites of chopped fluorinated polyethylene fiber with low-density polyethylene matrix
International Nuclear Information System (INIS)
Maity, J.; Jacob, C.; Das, C.K.; Alam, S.; Singh, R.P.
2008-01-01
Conventional composites are generally prepared by adding reinforcing agent to a matrix and the matrix wherein the reinforcing agents are different in chemical composition with the later having superior mechanical properties. This work presents the preparation and properties of homocomposites consisting of a low-density polyethylene (LDPE) matrix and an ultra high molecular weight polyethylene (UHMWPE) fiber reinforcing phase. Direct fluorination is an important surface modification process by which only a thin upper layer is modified, the bulk properties of the polymer remaining unchanged. In this work, surface fluorination of UHMWPE fiber was done and then fiber characterization was performed. It was observed that after fluorination the fiber surface became rough. Composites were then prepared using both fluorinated and non-fluorinated polyethylene fiber with a low-density polyethylene (LDPE) matrix to prepare single polymer composites. It was found that the thermal stability and mechanical properties were improved for fluorinated fiber composites. X-ray diffraction (XRD) analysis showed that the crystallinity of the composites increased and it is maximum for fluorinated fiber composites. Tensile strength (TS) and modulus also increased while elongation at break (EB) decreased for fiber composites and was a maximum for fluorinated fiber composites. Scanning electron microscopic analysis indicates that that the distribution of fiber into the matrix is homogeneous. It also indicates the better adhesion between the matrix and the reinforcing agent for modified fiber composites. We also did surface fluorination of the prepared composites and base polymer for knowing its application to different fields such as printability wettability, etc. To determine the various properties such as printability, wettability and adhesion properties, contact angle measurement was done. It was observed that the surface energies of surface modified composites and base polymer increases
A simplified density matrix minimization for linear scaling self-consistent field theory
International Nuclear Information System (INIS)
Challacombe, M.
1999-01-01
A simplified version of the Li, Nunes and Vanderbilt [Phys. Rev. B 47, 10891 (1993)] and Daw [Phys. Rev. B 47, 10895 (1993)] density matrix minimization is introduced that requires four fewer matrix multiplies per minimization step relative to previous formulations. The simplified method also exhibits superior convergence properties, such that the bulk of the work may be shifted to the quadratically convergent McWeeny purification, which brings the density matrix to idempotency. Both orthogonal and nonorthogonal versions are derived. The AINV algorithm of Benzi, Meyer, and Tuma [SIAM J. Sci. Comp. 17, 1135 (1996)] is introduced to linear scaling electronic structure theory, and found to be essential in transformations between orthogonal and nonorthogonal representations. These methods have been developed with an atom-blocked sparse matrix algebra that achieves sustained megafloating point operations per second rates as high as 50% of theoretical, and implemented in the MondoSCF suite of linear scaling SCF programs. For the first time, linear scaling Hartree - Fock theory is demonstrated with three-dimensional systems, including water clusters and estane polymers. The nonorthogonal minimization is shown to be uncompetitive with minimization in an orthonormal representation. An early onset of linear scaling is found for both minimal and double zeta basis sets, and crossovers with a highly optimized eigensolver are achieved. Calculations with up to 6000 basis functions are reported. The scaling of errors with system size is investigated for various levels of approximation. copyright 1999 American Institute of Physics
Reduced density matrix embedding. General formalism and inter-domain correlation functional.
Pernal, Katarzyna
2016-08-03
An embedding method for a one-electron reduced density matrix (1-RDM) is proposed. It is based on partitioning of 1-RDM into domains and describing each domain in the effective potential of the other ones. To assure N-representability of the total 1-RDM N-representability and strong-orthogonality conditions are imposed on the domains. The total energy is given as a sum of single-domain energies and domain-domain electron interaction contributions. Higher than two-body inter-domain interaction terms are neglected. The two-body correlation terms are approximated by deriving inter-domain correlation from couplings of density fluctuations of two domains at a time. Unlike in most density embedding methods kinetic energy is treated exactly and it is not required that densities pertaining to the domains are only weakly overlapping. We propose to treat each domain by a corrected perfect-pairing functional. On a few examples it is shown that the embedding reduced density matrix functional method (ERDMF) yields excellent results for molecules that are well described by a single Lewis structure even if strong static intra-domain or dynamic inter-domain correlation effects must be accounted for.
Off-diagonal helicity density matrix elements for vector mesons produced at LEP
International Nuclear Information System (INIS)
Anselmino, M.; Bertini, M.; Quintairos, P.
1997-05-01
Final state q q-bar interactions may give origin to non zero values of the off-diagonal element ρ 1 of the helicity density matrix of vector mesons produced in e + e - annihilations, as confirmed by recent OPAL data on φ and D * 's. Predictions are given for ρ1,-1 of several mesons produced at large z and small PT, collinear with the parent jet; the values obtained for θ and D * are in agreement with data. (author)
Directory of Open Access Journals (Sweden)
Jianping Liu
2016-01-01
Full Text Available An operational matrix technique is proposed to solve variable order fractional differential-integral equation based on the second kind of Chebyshev polynomials in this paper. The differential operational matrix and integral operational matrix are derived based on the second kind of Chebyshev polynomials. Using two types of operational matrixes, the original equation is transformed into the arithmetic product of several dependent matrixes, which can be viewed as an algebraic system after adopting the collocation points. Further, numerical solution of original equation is obtained by solving the algebraic system. Finally, several examples show that the numerical algorithm is computationally efficient.
International Nuclear Information System (INIS)
Dumonteil, E.; Diop, C. M.
2009-01-01
This paper derives an unbiased minimum variance estimator (UMVE) of a matrix exponential function of a normal wean. The result is then used to propose a reference scheme to solve Boltzmann/Bateman coupled equations, thanks to Monte Carlo transport codes. The last section will present numerical results on a simple example. (authors)
Analytic solution of the BCS gap equation with a logarithmic singularity in the density of states
International Nuclear Information System (INIS)
Bhardwaj, A.; Muthu, S.K.
1999-01-01
The Bardeen-Cooper-Schrieffer (BCS) gap equation is solved analytically for a density of states function with a logarithmic singularity. It is an extension of our earlier work where we had assumed a constant density of states. We continue to work in the weak-coupling limit and consider both phononic and non-phononic pairings. Expressions are obtained for T c , Δ 0 (the gap at T=0), and the jump in the electronic specific heat at T=T c . We also calculate the isotope exponent and show that it is possible to reproduce the broad features of the experimental results in this framework. (orig.)
Sun, Hongbing; Feistel, Rainer; Koch, Manfred; Markoe, Andrew
2008-10-01
A set of fitted polynomial equations for calculating the physical variables density, entropy, heat capacity and potential temperature of a thermal saline fluid for a temperature range of 0-374 °C, pressure range of 0.1-100 MPa and absolute salinity range of 0-40 g/kg is established. The freshwater components of the equations are extracted from the recently released tabulated data of freshwater properties of Wagner and Pruß [2002. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. Journal of Physical and Chemical Reference Data 31, 387-535]. The salt water component of the equation is based on the near-linear relationship between density, salinity and specific heat capacity and is extracted from the data sets of Feistel [2003. A new extended Gibbs thermodynamic potential of seawater. Progress in Oceanography 58, 43-114], Bromley et al. [1970. Heat capacities and enthalpies of sea salt solutions to 200 °C. Journal of Chemical and Engineering Data 15, 246-253] and Grunberg [1970. Properties of sea water concentrates. In: Third International Symposium on Fresh Water from the Sea, vol. 1, pp. 31-39] in a temperature range 0-200 °C, practical salinity range 0-40, and varying pressure and is also calibrated by the data set of Millero et al. [1981. Summary of data treatment for the international high pressure equation of state for seawater. UNESCO Technical Papers in Marine Science 38, 99-192]. The freshwater and salt water components are combined to establish a workable multi-polynomial equation, whose coefficients were computed through standard linear regression analysis. The results obtained in this way for density, entropy and potential temperature are comparable with those of existing models, except that our new equations cover a wider temperature—(0-374 °C) than the traditional (0-40 °C) temperature range. One can apply these newly established equations to the calculation of in-situ or
The Dirac–Frenkel Principle for Reduced Density Matrices, and the Bogoliubov–de Gennes Equations
DEFF Research Database (Denmark)
Benedikter, Niels; Sok, Jérémy; Solovej, Jan Philip
2018-01-01
The derivation of effective evolution equations is central to the study of non-stationary quantum many-body systems, and widely used in contexts such as superconductivity, nuclear physics, Bose–Einstein condensation and quantum chemistry. We reformulate the Dirac–Frenkel approximation principle...... in terms of reduced density matrices and apply it to fermionic and bosonic many-body systems. We obtain the Bogoliubov–de Gennes and Hartree–Fock–Bogoliubov equations, respectively. While we do not prove quantitative error estimates, our formulation does show that the approximation is optimal within...... the class of quasifree states. Furthermore, we prove well-posedness of the Bogoliubov–de Gennes equations in energy space and discuss conserved quantities....
Extending the range of real time density matrix renormalization group simulations
Kennes, D. M.; Karrasch, C.
2016-03-01
We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement these modifications within any standard matrix product state (MPS) based formulation of the method. Most importantly, we show how to 'combine' the Schrödinger and Heisenberg time evolutions of arbitrary pure states | ψ 〉 and operators A in the evaluation of 〈A〉ψ(t) = 〈 ψ | A(t) | ψ 〉 . This includes quantum quenches. The generalization to (non-)thermal mixed state dynamics 〈A〉ρ(t) =Tr [ ρA(t) ] induced by an initial density matrix ρ is straightforward. In the context of linear response (ground state or finite temperature T > 0) correlation functions, one can extend the simulation time by a factor of two by 'exploiting time translation invariance', which is efficiently implementable within MPS DMRG. We present a simple analytic argument for why a recently-introduced disentangler succeeds in reducing the effort of time-dependent simulations at T > 0. Finally, we advocate the python programming language as an elegant option for beginners to set up a DMRG code.
Melting-pressure and density equations of 3He at temperatures from 0.001 to 30 K
International Nuclear Information System (INIS)
Huang Yonghua; Chen Guobang
2005-01-01
Nonsegmented equations for melting pressure and density at temperatures from 0.001 K to 30 K have been developed to fit the reference data. The maximum and average deviations between the melting pressure equation and the totaling 298 reference data are 2.17% and 0.218%, respectively. For the density equations, the average deviations are 0.236% for the liquid side and 0.218% for the solid side. Both the melting pressure curve and melting density curves predicted by the submitted equations approach their minimums at about 0.315 K
Consolidation of titanium matrix composites to maximum density by different hot pressing techniques
International Nuclear Information System (INIS)
Montealegre Melendez, I.; Neubauer, E.; Danninger, H.
2010-01-01
In this present work, TiMMCs were manufactured through conventional and inductive hot pressing techniques. The starting materials were two titanium based powders as metal matrices, and two types of reinforcements, carbon nanofibres and nano-micro-boron particles. After several manufacturing runs with varying parameters, especially, optimized hot pressing parameters, the titanium compacts were characterized. Density and hardness measurements, chemical analyses and microstructural studies were conducted. The two objectives of this work were achieved. On one hand the influence, in the properties of TiMMCs, of the starting materials as matrix powder and reinforcements was determined. Higher content of impurities from the starting materials affected the hardness and the microstructure of the composites, independently of the manufacturing process. On another hand, the study of variations of the manufacturing process as temperature of consolidation and soaking time was reported. Higher densification was obtained at higher consolidation temperature; however, reaction between the matrix and the carbonaceous reinforcement was detected.
The {P,Q,k+1}-Reflexive Solution to System of Matrix Equations AX=C, XB=D
Directory of Open Access Journals (Sweden)
Chang-Zhou Dong
2015-01-01
Full Text Available Let P∈Cm×m and Q∈Cn×n be Hermitian and {k+1}-potent matrices; that is, Pk+1=P=P⁎ and Qk+1=Q=Q⁎, where ·⁎ stands for the conjugate transpose of a matrix. A matrix X∈Cm×n is called {P,Q,k+1}-reflexive (antireflexive if PXQ=X (PXQ=-X. In this paper, the system of matrix equations AX=C and XB=D subject to {P,Q,k+1}-reflexive and antireflexive constraints is studied by converting into two simpler cases: k=1 and k=2. We give the solvability conditions and the general solution to this system; in addition, the least squares solution is derived; finally, the associated optimal approximation problem for a given matrix is considered.
Comment on "Nonuniqueness of algebraic first-order density-matrix functionals"
Gritsenko, O. V.
2018-02-01
Wang and Knowles (WK) [Phys. Rev. A 92, 012520 (2015), 10.1103/PhysRevA.92.012520] have given a counterexample to the conventional in reduced density-matrix functional theory representation of the second-order reduced density matrix (2RDM) Γi j ,k l in the basis of the natural orbitals as a function Γi j ,k l(n ) of the orbital occupation numbers (ONs) ni. The observed nonuniqueness of Γi j ,k l for prototype systems of different symmetry has been interpreted as the inherent inability of ON functions to reproduce the 2RDM, due to the insufficient information contained in the 1RDM spectrum. In this Comment, it is argued that, rather than totally invalidating Γi j ,k l(n ) , the WK example exposes its symmetry dependence which, as well as the previously established analogous dependence in density functional theory, is demonstrated with a general formulation based on the Levy constrained search.
LINPACK, Subroutine Library for Linear Equation System Solution and Matrix Calculation
International Nuclear Information System (INIS)
Dongarra, J.J.
1979-01-01
1 - Description of problem or function: LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE: General, GB: General band, PO: Positive definite, PP: Positive definite packed, PB: Positive definite band, SI: Symmetric indefinite, SP: Symmetric indefinite packed, HI: Hermitian indefinite, HP: Hermitian indefinite packed, TR: Triangular, GT: General tridiagonal, PT: Positive definite tridiagonal, CH: Cholesky decomposition, QR: Orthogonal-triangular decomposition, SV: Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA: Factor, CO: Factor and estimate condition, SL: Solve, DI: Determinant and/or inverse and/or inertia, DC: Decompose, UD: Update, DD: Down-date, EX Exchange. The following chart shows all the LINPACK subroutines. The initial 'S' in the names may be replaced by D, C or Z and the initial 'C' in the complex-only names may be replaced by a Z. SGE: FA, CO, SL, DI; SGB: FA, CO, SL, DI; SPO: FA, CO, SL, DI; SPP: FA, CO, SL, DI; SPB: FA, CO, SL, DI; SSI: FA, CO, SL, DI; SSP: FA, CO, SL, DI; CHI: FA, CO, SL, DI; CHP: FA, CO, SL, DI; STR
A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide
Allen, Rebecca
2013-01-01
The storage of CO2 in fluid-filled geological formations has been carried out for more than a decade in locations around the world. After CO2 has been injected into the aquifer and has moved laterally under the aquifer\\'s cap-rock, density-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE) to formulate a model for a similar scenario when a solute diffuses into a fluid and density differences lead to convective mixing. The LBE is a promising alternative to the traditional methods of computational fluid dynamics. Rather than discretizing the system of partial differential equations of classical continuum mechanics directly, the LBE is derived from a velocity-space truncation of the Boltzmann equation of classical kinetic theory. We propose an extension to the LBE, which can accurately predict the transport of dissolved CO2 in water, as a step towards fluid-filled porous media simulations. This is achieved by coupling two LBEs, one for the fluid flow and one for the convection and diffusion of CO2. Unlike existing lattice Boltzmann equations for porous media flow, our model is derived from a system of moment equations and a Crank-Nicolson discretization of the velocity-truncated Boltzmann equation. The forcing terms are updated locally without the need for additional central difference approximation. Therefore our model preserves all the computational advantages of the single-phase lattice Boltzmann equation and is formally second-order accurate in both space and time. Our new model also features a novel implementation of boundary conditions, which is simple to implement and does not suffer from the grid-dependent error that is present in the standard "bounce-back" condition. The significance of using the LBE in this work lies in the ability to efficiently
A new equation of state for better liquid density prediction of natural gas systems
Nwankwo, Princess C.
Equations of state formulations, modifications and applications have remained active research areas since the success of van der Waal's equation in 1873. The need for better reservoir fluid modeling and characterization is of great importance to petroleum engineers who deal with thermodynamic related properties of petroleum fluids at every stage of the petroleum "life span" from its drilling, to production through the wellbore, to transportation, metering and storage. Equations of state methods are far less expensive (in terms of material cost and time) than laboratory or experimental forages and the results are interestingly not too far removed from the limits of acceptable accuracy. In most cases, the degree of accuracy obtained, by using various EOS's, though not appreciable, have been acceptable when considering the gain in time. The possibility of obtaining an equation of state which though simple in form and in use, could have the potential of further narrowing the present existing bias between experimentally determined and popular EOS estimated results spurred the interest that resulted in this study. This research study had as its chief objective, to develop a new equation of state that would more efficiently capture the thermodynamic properties of gas condensate fluids, especially the liquid phase density, which is the major weakness of other established and popular cubic equations of state. The set objective was satisfied by a new semi analytical cubic three parameter equation of state, derived by the modification of the attraction term contribution to pressure of the van der Waal EOS without compromising either structural simplicity or accuracy of estimating other vapor liquid equilibria properties. The application of new EOS to single and multi-component light hydrocarbon fluids recorded far lower error values than does the popular two parameter, Peng-Robinson's (PR) and three parameter Patel-Teja's (PT) equations of state. Furthermore, this research
Simulating variable-density flows with time-consistent integration of Navier-Stokes equations
Lu, Xiaoyi; Pantano, Carlos
2017-11-01
In this talk, we present several features of a high-order semi-implicit variable-density low-Mach Navier-Stokes solver. A new formulation to solve pressure Poisson-like equation of variable-density flows is highlighted. With this formulation of the numerical method, we are able to solve all variables with a uniform order of accuracy in time (consistent with the time integrator being used). The solver is primarily designed to perform direct numerical simulations for turbulent premixed flames. Therefore, we also address other important elements, such as energy-stable boundary conditions, synthetic turbulence generation, and flame anchoring method. Numerical examples include classical non-reacting constant/variable-density flows, as well as turbulent premixed flames.
A parton shower based on factorization of the quantum density matrix
Nagy, Zoltan; Soper, Davison E.
2014-01-01
We present first results from a new parton shower event generator, D eductor . Anticipating a need for an improved treatment of parton color and spin, the structure of the generator is based on the quantum density matrix in color and spin space. So far, D eductor implements only a standard spin-averaged treatment of spin in parton splittings. Although D eductor implements an improved treatment of color, in this paper we present results in the standard leading color approximation so that we ca...
Charge-constrained auxiliary-density-matrix methods for the Hartree–Fock exchange contribution
DEFF Research Database (Denmark)
Merlot, Patrick; Izsak, Robert; Borgoo, Alex
2014-01-01
Three new variants of the auxiliary-density-matrix method (ADMM) of Guidon, Hutter, and VandeVondele [J. Chem. Theory Comput. 6, 2348 (2010)] are presented with the common feature thatthey have a simplified constraint compared with the full orthonormality requirement of the earlier ADMM1 method. ....... All ADMM variants are tested for accuracy and performance in all-electron B3LYP calculations with several commonly used basis sets. The effect of the choice of the exchange functional for the ADMM exchange–correction term is also investigated....
Schmitteckert, Peter
2018-04-01
We present an infinite lattice density matrix renormalization group sweeping procedure which can be used as a replacement for the standard infinite lattice blocking schemes. Although the scheme is generally applicable to any system, its main advantages are the correct representation of commensurability issues and the treatment of degenerate systems. As an example we apply the method to a spin chain featuring a highly degenerate ground-state space where the new sweeping scheme provides an increase in performance as well as accuracy by many orders of magnitude compared to a recently published work.
Differential cross sections and spin density matrix elements for the reaction gamma p -> p omega
Energy Technology Data Exchange (ETDEWEB)
M. Williams, D. Applegate, M. Bellis, C.A. Meyer
2009-12-01
High-statistics differential cross sections and spin density matrix elements for the reaction gamma p -> p omega have been measured using the CLAS at Jefferson Lab for center-of-mass (CM) energies from threshold up to 2.84 GeV. Results are reported in 112 10-MeV wide CM energy bins, each subdivided into cos(theta_CM) bins of width 0.1. These are the most precise and extensive omega photoproduction measurements to date. A number of prominent structures are clearly present in the data. Many of these have not previously been observed due to limited statistics in earlier measurements.
Spin Density Matrix Elements in exclusive production of ω mesons at Hermes
Directory of Open Access Journals (Sweden)
Marianski B.
2014-03-01
Full Text Available Spin density matrix elements have been determined for exclusive ω meson production on hydrogen and deuterium targets, in the kinematic region of 1.0 < Q2 < 10.0 GeV2, 3.0 < W < 6.3 GeV and –t' < 0.2 GeV2. The data, from which SDMEs are determined, were accumulated with the HERMES forward spectrometer during the running period of 1996 to 2007 using the 27.6 GeV electron or positron beam of HERA. A sizable contribution of unnatural parity exchange amplitudes is found for exclusive ω meson production.
A parton shower based on factorization of the quantum density matrix
International Nuclear Information System (INIS)
Nagy, Zoltan; Soper, Davison E.
2014-01-01
We present rst results from a new parton shower event generator, DEDUCTOR. Anticipating a need for an improved treatment of parton color and spin, the structure of the generator is based on the quantum density matrix in color and spin space. So far, DEDUCTOR implements only a standard spin-averaged treatment of spin in parton splittings. Although DEDUCTOR implements an improved treatment of color, in this paper we present results in the standard leading color approximation so that we can compare to the generator PYTHIA. The algorithms used incorporate a virtuality based shower ordering parameter and massive initial state bottom and charm quarks.
Frozen and broken color: a matrix Schroedinger equation in the semiclassical limit
International Nuclear Information System (INIS)
Orbach, H.S.
1981-01-01
We consider the case of frozen color, i.e, where global color symmetry remains exact, but where colored states have a mass large compared to color-singlet mesons. Using semiclassical WKB formalism, we construct the spectrum of bound states. In order to determine the charge of the constituents, we then consider deep-inelastic scattering of an external probe (e.g., lepton) from our one-dimensional meson. We calculate explicitly the structure function, W, in the WKB limit and show how Lipkin's mechanism is manifested, as well as how scaling behavior comes. We derive the WKB formalism as a special case of a method of obtaining WKB type solutions for generalized Schroedinger equations for which the Hamiltonian is an arbitrary matrix function of any number of pairs of canonical operators. We generalize these considerations to the case of broken color symmetry - but where the breaking is not so strong as to allow low-lying states to have a large amount of mixing with the colored states. In this case, the degeneracy of excited colored states can be broken. We find that local excitation of color guarantees global excitation of color; i.e., if at a given energy colored semiclassical states can be constructed with size comparable to that of the ground state wave function, colored states of that energy will also exist in the spectrum of the full theory and will be observed. However, global existence of color does not guarantee the excitation of colored states via deep-inelastic processes
International Nuclear Information System (INIS)
Sandhas, W.
1978-01-01
In the N-body problem mappings between channel states and scattering states are studied. It is shown in particular that the (2sup(N-1)-1) two-fragment MOELLER operators introduced on the whole Hilbert space are sufficient to provide all multi-fragment scattering states. Hence, each of these states is uniquely determined by (2sup(N-1)-1) Lippmann-Schwinger (LS) equations. Rewriting every set of LS equations as one matrix equation, current few-body approaches are incorporated in a rather natural way. The typical uniqueness questions of such coupled systems are discussed, and it is shown that Faddeev-type couplings lead to unique equations for arbitrary N. (author)
International Nuclear Information System (INIS)
Sandhas, W.
1978-04-01
In the N-body problem mappings between channel states and scattering states are studied. It is shown in particular that the (2sup(N-1)-1) two-fragment Moeller operators introduced on the whole Hilbert space are sufficient to provide all multifragment scattering states. Hence, each of these states is uniquly determined by (2sup(N-1)-1) Lippmann-Schwinger (LS) equations. Rewriting every set of LS equations as one matrix equation, current few-body approaches are incorporated in a rather natural way. The typical uniqueness questions of such coupled systems are discussed, and it si shown that Faddeev-type couplings lead to unique equations for arbitrary N. (orig.) [de
First principles calculations using density matrix divide-and-conquer within the SIESTA methodology
International Nuclear Information System (INIS)
Cankurtaran, B O; Gale, J D; Ford, M J
2008-01-01
The density matrix divide-and-conquer technique for the solution of Kohn-Sham density functional theory has been implemented within the framework of the SIESTA methodology. Implementation details are provided where the focus is on the scaling of the computation time and memory use, in both serial and parallel versions. We demonstrate the linear-scaling capabilities of the technique by providing ground state calculations of moderately large insulating, semiconducting and (near-) metallic systems. This linear-scaling technique has made it feasible to calculate the ground state properties of quantum systems consisting of tens of thousands of atoms with relatively modest computing resources. A comparison with the existing order-N functional minimization (Kim-Mauri-Galli) method is made between the insulating and semiconducting systems
Sorokin, Sergey V
2011-03-01
Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 2011 Acoustical Society of America
Bartels, Robert E.
2002-01-01
A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.
A Fast Newton-Shamanskii Iteration for a Matrix Equation Arising from M/G/1-Type Markov Chains
Directory of Open Access Journals (Sweden)
Pei-Chang Guo
2017-01-01
Full Text Available For the nonlinear matrix equations arising in the analysis of M/G/1-type and GI/M/1-type Markov chains, the minimal nonnegative solution G or R can be found by Newton-like methods. We prove monotone convergence results for the Newton-Shamanskii iteration for this class of equations. Starting with zero initial guess or some other suitable initial guess, the Newton-Shamanskii iteration provides a monotonically increasing sequence of nonnegative matrices converging to the minimal nonnegative solution. A Schur decomposition method is used to accelerate the Newton-Shamanskii iteration. Numerical examples illustrate the effectiveness of the Newton-Shamanskii iteration.
Directory of Open Access Journals (Sweden)
Waleed M. Abd-Elhameed
2016-09-01
Full Text Available Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fibonacci expansion were carefully investigated. Some numerical examples with comparisons are presented to ensure the efficiency, applicability and high accuracy of the proposed algorithms. Two accurate semi-analytic polynomial solutions for linear and nonlinear fractional differential equations are the result.
Perturbation theory corrections to the two-particle reduced density matrix variational method.
Juhasz, Tamas; Mazziotti, David A
2004-07-15
In the variational 2-particle-reduced-density-matrix (2-RDM) method, the ground-state energy is minimized with respect to the 2-particle reduced density matrix, constrained by N-representability conditions. Consider the N-electron Hamiltonian H(lambda) as a function of the parameter lambda where we recover the Fock Hamiltonian at lambda=0 and we recover the fully correlated Hamiltonian at lambda=1. We explore using the accuracy of perturbation theory at small lambda to correct the 2-RDM variational energies at lambda=1 where the Hamiltonian represents correlated atoms and molecules. A key assumption in the correction is that the 2-RDM method will capture a fairly constant percentage of the correlation energy for lambda in (0,1] because the nonperturbative 2-RDM approach depends more significantly upon the nature rather than the strength of the two-body Hamiltonian interaction. For a variety of molecules we observe that this correction improves the 2-RDM energies in the equilibrium bonding region, while the 2-RDM energies at stretched or nearly dissociated geometries, already highly accurate, are not significantly changed. At equilibrium geometries the corrected 2-RDM energies are similar in accuracy to those from coupled-cluster singles and doubles (CCSD), but at nonequilibrium geometries the 2-RDM energies are often dramatically more accurate as shown in the bond stretching and dissociation data for water and nitrogen. (c) 2004 American Institute of Physics.
Electrically tunable spin polarization in silicene: A multi-terminal spin density matrix approach
International Nuclear Information System (INIS)
Chen, Son-Hsien
2016-01-01
Recent realized silicene field-effect transistor yields promising electronic applications. Using a multi-terminal spin density matrix approach, this paper presents an analysis of the spin polarizations in a silicene structure of the spin field-effect transistor by considering the intertwined intrinsic and Rashba spin–orbit couplings, gate voltage, Zeeman splitting, as well as disorder. Coexistence of the stagger potential and intrinsic spin–orbit coupling results in spin precession, making any in-plane polarization directions reachable by the gate voltage; specifically, the intrinsic coupling allows one to electrically adjust the in-plane components of the polarizations, while the Rashba coupling to adjust the out-of-plan polarizations. Larger electrically tunable ranges of in-plan polarizations are found in oppositely gated silicene than in the uniformly gated silicene. Polarizations in different phases behave distinguishably in weak disorder regime, while independent of the phases, stronger disorder leads to a saturation value. - Highlights: • Density matrix with spin rotations enables multi-terminal arbitrary spin injections. • Gate-voltage tunable in-plane polarizations require intrinsic SO coupling. • Gate-voltage tunable out-of-plane polarizations require Rashba SO coupling. • Oppositely gated silicene yields a large tunable range of in-plan polarizations. • Polarizations in different phases behave distinguishably only in weak disorder.
Energy Technology Data Exchange (ETDEWEB)
Hautmann, F. [Rutherford Appleton Laboratory, Chilton (United Kingdom); Oxford Univ. (United Kingdom). Dept. of Theoretical Physics; Antwerpen Univ. (Belgium). Elementaire Deeltjes Fysica; Jung, H.; Lelek, A.; Zlebcik, R. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Radescu, V. [European Organization for Nuclear Research (CERN), Geneva (Switzerland)
2017-08-15
We study parton-branching solutions of QCD evolution equations and present a method to construct both collinear and transverse momentum dependent (TMD) parton densities from this approach. We work with next-to-leading-order (NLO) accuracy in the strong coupling. Using the unitarity picture in terms of resolvable and non-resolvable branchings, we analyze the role of the soft-gluon resolution scale in the evolution equations. For longitudinal momentum distributions, we find agreement of our numerical calculations with existing evolution programs at the level of better than 1 percent over a range of five orders of magnitude both in evolution scale and in longitudinal momentum fraction. We make predictions for the evolution of transverse momentum distributions. We perform fits to the high-precision deep inelastic scattering (DIS) structure function measurements, and we present a set of NLO TMD distributions based on the parton branching approach.
Shamloo, Amir; Mohammadaliha, Negar; Heilshorn, Sarah C; Bauer, Amy L
2016-04-01
A thorough understanding of determining factors in angiogenesis is a necessary step to control the development of new blood vessels. Extracellular matrix density is known to have a significant influence on cellular behaviors and consequently can regulate vessel formation. The utilization of experimental platforms in combination with numerical models can be a powerful method to explore the mechanisms of new capillary sprout formation. In this study, using an integrative method, the interplay between the matrix density and angiogenesis was investigated. Owing the fact that the extracellular matrix density is a global parameter that can affect other parameters such as pore size, stiffness, cell-matrix adhesion and cross-linking, deeper understanding of the most important biomechanical or biochemical properties of the ECM causing changes in sprout morphogenesis is crucial. Here, we implemented both computational and experimental methods to analyze the mechanisms responsible for the influence of ECM density on the sprout formation that is difficult to be investigated comprehensively using each of these single methods. For this purpose, we first utilized an innovative approach to quantify the correspondence of the simulated collagen fibril density to the collagen density in the experimental part. Comparing the results of the experimental study and computational model led to some considerable achievements. First, we verified the results of the computational model using the experimental results. Then, we reported parameters such as the ratio of proliferating cells to migrating cells that was difficult to obtain from experimental study. Finally, this integrative system led to gain an understanding of the possible mechanisms responsible for the effect of ECM density on angiogenesis. The results showed that stable and long sprouts were observed at an intermediate collagen matrix density of 1.2 and 1.9 mg/ml due to a balance between the number of migrating and proliferating
International Nuclear Information System (INIS)
Migdal, A.A.; Polikarpov, M.I.; Veselov, A.I.; Yurov, V.P.
1983-01-01
The Langevin equation for the lattice theory with arbitrary gauge group is derived. The four-dimensional twisted Eguchi-Kawai model is investigated numerically. The results for the plaquette energy agree with those of the known Monte Carlo calculations. The new result is the distribution of eigenvalues of the plaquette matrix. In the strong coupling phase this distribution is smooth, whereas in the weak coupling phase a gap is clearly seen
Fractional equivalent Lagrangian densities for a fractional higher-order equation
International Nuclear Information System (INIS)
Fujioka, J
2014-01-01
In this communication we show that the equivalent Lagrangian densities (ELDs) of a fractional higher-order nonlinear Schrödinger equation with stable soliton-like solutions can be related in a hitherto unknown way. This new relationship is described in terms of a new fractional operator that includes both left- and right-sided fractional derivatives. Using this operator it is possible to generate new ELDs that contain different fractional parts, in addition to the already known ELDs, which only differ by a sum of first-order partial derivatives of two arbitrary functions. (fast track communications)
International Nuclear Information System (INIS)
Larson, N.M.; Perey, F.G.
1980-11-01
A method is described for determining the parameters of a model from experimental data based upon the utilization of Bayes' theorem. This method has several advantages over the least-squares method as it is commonly used; one important advantage is that the assumptions under which the parameter values have been determined are more clearly evident than in many results based upon least squares. Bayes' method has been used to develop a computer code which can be utilized to analyze neutron cross-section data by means of the R-matrix theory. The required formulae from the R-matrix theory are presented, and the computer implementation of both Bayes' equations and R-matrix theory is described. Details about the computer code and compelte input/output information are given
International Nuclear Information System (INIS)
Liebenberg, D.H.; Mills, R.L.; Bronson, J.C.
1977-01-01
Hydrogen isotopes play an important role in energy technologies, in particular, the compression to high densities for initiation of controlled thermonuclear fusion energy. At high densities the properties of the compressed hydrogen isotopes depart drastically from ideal thermodynamic predictions. The measurement of accurate data including the author's own recent measurements of n-H 2 and n-D 2 in the range 75 to 300 K and 0.2 to 2.0 GPa (2 to 20 kbar) is reviewed. An equation-of-state of the Benedict type is fit to these data with a double-process least-squares computer program. The results are reviewed and compared with existing data and with a variety of theoretical work reported for fluid hydrogens. A new heuristic correlation is presented for simplicity in predicting volumes and sound velocity at high pressures. 9 figures, 1 table
Kajzer-Bonk, Joanna; Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal
2016-01-01
The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011-12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales.
Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal
2016-01-01
The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011–12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales. PMID:28005942
Calculations with off-shell matrix elements, TMD parton densities and TMD parton showers
Energy Technology Data Exchange (ETDEWEB)
Bury, Marcin; Hameren, Andreas van; Kutak, Krzysztof; Sapeta, Sebastian [Polish Academy of Sciences, Institute of Nuclear Physics, Cracow (Poland); Jung, Hannes [Polish Academy of Sciences, Institute of Nuclear Physics, Cracow (Poland); DESY, Hamburg (Germany); Serino, Mirko [Polish Academy of Sciences, Institute of Nuclear Physics, Cracow (Poland); Ben Gurion University of the Negev, Department of Physics, Beersheba (Israel)
2018-02-15
A new calculation using off-shell matrix elements with TMD parton densities supplemented with a newly developed initial state TMD parton shower is described. The calculation is based on the KaTie package for an automated calculation of the partonic process in high-energy factorization, making use of TMD parton densities implemented in TMDlib. The partonic events are stored in an LHE file, similar to the conventional LHE files, but now containing the transverse momenta of the initial partons. The LHE files are read in by the Cascade package for the full TMD parton shower, final state shower and hadronization from Pythia where events in HEPMC format are produced. We have determined a full set of TMD parton densities and developed an initial state TMD parton shower, including all flavors following the TMD distribution. As an example of application we have calculated the azimuthal de-correlation of high p{sub t} dijets as measured at the LHC and found very good agreement with the measurement when including initial state TMD parton showers together with conventional final state parton showers and hadronization. (orig.)
Asymptotic densities from the modified Montroll-Weiss equation for coupled CTRWs
Aghion, Erez; Kessler, David A.; Barkai, Eli
2018-01-01
We examine the bi-scaling behavior of Lévy walks with nonlinear coupling, where χ, the particle displacement during each step, is coupled to the duration of the step, τ, by χ τβ. An example of such a process is regular Lévy walks, where β = 1. In recent years such processes were shown to be highly useful for analysis of a class of Langevin dynamics, in particular a system of Sisyphus laser-cooled atoms in an optical lattice, where β = 3/2. We discuss the well-known decoupling approximation used to describe the central part of the particles' position distribution, and use the recently introduced infinite-covariant density approach to study the large fluctuations. Since the density of the step displacements is fat-tailed, the last travel event must be treated with care for the latter. This effect requires a modification of the Montroll-Weiss equation, an equation which has proved important for the analysis of many microscopic models. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Zhang, Xing; Carter, Emily A.
2018-01-01
We revisit the static response function-based Kohn-Sham (KS) inversion procedure for determining the KS effective potential that corresponds to a given target electron density within finite atomic orbital basis sets. Instead of expanding the potential in an auxiliary basis set, we directly update the potential in its matrix representation. Through numerical examples, we show that the reconstructed density rapidly converges to the target density. Preliminary results are presented to illustrate the possibility of obtaining a local potential in real space from the optimized potential in its matrix representation. We have further applied this matrix-based KS inversion approach to density functional embedding theory. A proof-of-concept study of a solvated proton transfer reaction demonstrates the method's promise.
Ground states of linear rotor chains via the density matrix renormalization group
Iouchtchenko, Dmitri; Roy, Pierre-Nicholas
2018-04-01
In recent years, experimental techniques have enabled the creation of ultracold optical lattices of molecules and endofullerene peapod nanomolecular assemblies. It was previously suggested that the rotor model resulting from the placement of dipolar linear rotors in one-dimensional lattices at low temperature has a transition between ordered and disordered phases. We use the density matrix renormalization group (DMRG) to compute ground states of chains of up to 100 rotors and provide further evidence of the phase transition in the form of a diverging entanglement entropy. We also propose two methods and present some first steps toward rotational spectra of such molecular assemblies using DMRG. The present work showcases the power of DMRG in this new context of interacting molecular rotors and opens the door to the study of fundamental questions regarding criticality in systems with continuous degrees of freedom.
Density-matrix approach for the electroluminescence of molecules in a scanning tunneling microscope.
Tian, Guangjun; Liu, Ji-Cai; Luo, Yi
2011-04-29
The electroluminescence (EL) of molecules confined inside a nanocavity in the scanning tunneling microscope possesses many intriguing but unexplained features. We present here a general theoretical approach based on the density-matrix formalism to describe the EL from molecules near a metal surface induced by both electron tunneling and localized surface plasmon excitations simultaneously. It reveals the underlying physical mechanism for the external bias dependent EL. The important role played by the localized surface plasmon on the EL is highlighted. Calculations for porphyrin derivatives have reproduced corresponding experimental spectra and nicely explained the observed unusual large variation of emission spectral profiles. This general theoretical approach can find many applications in the design of molecular electronic and photonic devices.
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.)
International Nuclear Information System (INIS)
Luo, Da-Wei; Xu, Jing-Bo
2015-01-01
We use an alternative method to investigate the quantum criticality at zero and finite temperature using trace distance along with the density matrix renormalization group. It is shown that the average correlation measured by the trace distance between the system block and environment block in a DMRG sweep is able to detect the critical points of quantum phase transitions at finite temperature. As illustrative examples, we study spin-1 XXZ chains with uniaxial single-ion-type anisotropy and the Heisenberg spin chain with staggered coupling and external magnetic field. It is found that the trace distance shows discontinuity at the critical points of quantum phase transition and can be used as an indicator of QPTs
Quasi-particle entanglement: redefinition of the vacuum and reduced density matrix approach
International Nuclear Information System (INIS)
Samuelsson, P; Sukhorukov, E V; Buettiker, M
2005-01-01
A scattering approach to entanglement in mesoscopic conductors with independent fermionic quasi-particles is discussed. We focus on conductors in the tunnelling limit, where a redefinition of the quasi-particle vacuum transforms the wavefunction from a many-body product state of non-interacting particles to a state describing entangled two-particle excitations out of the new vacuum (Samuelsson, Sukhorukov and Buettiker 2003 Phys. Rev. Lett. 91 157002). The approach is illustrated with two examples: (i) a normal-superconducting system, where the transformation is made between Bogoliubov-de Gennes quasi-particles and Cooper pairs, and (ii) a normal system, where the transformation is made between electron quasi-particles and electron-hole pairs. This is compared to a scheme where an effective two-particle state is derived from the manybody scattering state by a reduced density matrix approach
Investigation of the alpha cluster model and the density matrix expansion in ion-ion collision
International Nuclear Information System (INIS)
Rashdan, M.B.M.
1986-01-01
This thesis deals with the investigation of the alpha cluster model (ACM) of brink and studies of the accuracy of the density matrix expansion (DME) approximation in deriving the real part of the ion-ion optical potential. the ACM is applied to calculate the inelastic 0 1 + →2 1 + charge form factor for electron scattering by 12 C to investigate the validity of this model for 12 C nucleus. it is found that the experimental curve can be fitted over the entire range of the momentum transfer by a generator - coordinate state for the 2 1 + state that consist of a superposition of two triangular ACM states with two different cluster separations and the same oscillator parameter
Lectures on light nonlinear and quantum optics using the density matrix
Rand, Stephen C.
2016-01-01
This book bridges the gap between introductory quantum mechanics and the research front of modern optics and scientific fields that make use of light. While suitable as a reference for the specialist in quantum optics, it also targets non-specialists from other disciplines who need to understand light and its uses in research. It introduces a single analytic tool, the density matrix, to analyze complex optical phenomena encountered in traditional as well as cross-disciplinary research. It moves swiftly in a tight sequence from elementary to sophisticated topics in quantum optics, including optical tweezers, laser cooling, coherent population transfer, optical magnetism, electromagnetically induced transparency, squeezed light, and cavity quantum electrodynamics. A systematic approach starts with the simplest systems—stationary two-level atoms—then introduces atomic motion, adds more energy levels, and moves on to discuss first-, second-, and third-order coherence effects that are the basis for analyzing n...
Low-density, high-strength intermetallic matrix composites by XD (trademark) synthesis
Kumar, K. S.; Dipietro, M. S.; Brown, S. A.; Whittenberger, J. D.
1991-01-01
A feasibility study was conducted to evaluate the potential of particulate composites based on low-density, L1(sub 2) trialuminide matrices for high-temperature applications. The compounds evaluated included Al22Fe3Ti8 (as a multiphase matrix), Al67Ti25Cr8, and Al66Ti25Mn9. The reinforcement consisted of TiB2 particulates. The TiB2 composites were processed by ingot and powder metallurgy techniques. Microstructural characterization and mechanical testing were performed in the hot-pressed and hot-isostatic-pressed condition. The casting were sectioned and isothermally forged into pancakes. All the materials were tested in compression as a function of temperature, and at high temperatures as a function of strain rate. The test results are discussed.
Heisenberg spin-one chain in staggered magnetic field: A density matrix renormalization group study
International Nuclear Information System (INIS)
Jizhong Lou; Xi Dai; Shaojin Qin; Zhaobin Su; Lu Yu
1999-04-01
Using the density matrix renormalization group technique, we calculate numerically the low energy excitation spectrum and magnetization curve of the spin-1 antiferromagnetic chain in a staggered magnetic field, which is expected to describe the physics of R 2 BaNiO 5 (R ≠ Y) family below the Neel temperature of the magnetic rare-earth (R) sublattice. These results are valid in the entire range of the staggered field, and agree with those given by the non-linear σ model study for small fields, but differ from the latter for large fields. They are consistent with the available experimental data. The correlation functions for this model are also calculated. The transverse correlations display the anticipated exponential decay with shorter correlation length, while the longitudinal correlations show explicitly the induced staggered magnetization. (author)
Evaluation of the thermodynamics of a four level system using canonical density matrix method
Directory of Open Access Journals (Sweden)
Awoga Oladunjoye A.
2013-02-01
Full Text Available We consider a four-level system with two subsystems coupled by weak interaction. The system is in thermal equilibrium. The thermodynamics of the system, namely internal energy, free energy, entropy and heat capacity, are evaluated using the canonical density matrix by two methods. First by Kronecker product method and later by treating the subsystems separately and then adding the evaluated thermodynamic properties of each subsystem. It is discovered that both methods yield the same result, the results obey the laws of thermodynamics and are the same as earlier obtained results. The results also show that each level of the subsystems introduces a new degree of freedom and increases the entropy of the entire system. We also found that the four-level system predicts a linear relationship between heat capacity and temperature at very low temperatures just as in metals. Our numerical results show the same trend.
Energy Technology Data Exchange (ETDEWEB)
Lloyd, S. A. M.; Ansbacher, W. [Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia V8W 3P6 (Canada); Department of Physics and Astronomy, University of Victoria, Victoria, British Columbia V8W 3P6 (Canada) and Department of Medical Physics, British Columbia Cancer Agency-Vancouver Island Centre, Victoria, British Columbia V8R 6V5 (Canada)
2013-01-15
Purpose: Acuros external beam (Acuros XB) is a novel dose calculation algorithm implemented through the ECLIPSE treatment planning system. The algorithm finds a deterministic solution to the linear Boltzmann transport equation, the same equation commonly solved stochastically by Monte Carlo methods. This work is an evaluation of Acuros XB, by comparison with Monte Carlo, for dose calculation applications involving high-density materials. Existing non-Monte Carlo clinical dose calculation algorithms, such as the analytic anisotropic algorithm (AAA), do not accurately model dose perturbations due to increased electron scatter within high-density volumes. Methods: Acuros XB, AAA, and EGSnrc based Monte Carlo are used to calculate dose distributions from 18 MV and 6 MV photon beams delivered to a cubic water phantom containing a rectangular high density (4.0-8.0 g/cm{sup 3}) volume at its center. The algorithms are also used to recalculate a clinical prostate treatment plan involving a unilateral hip prosthesis, originally evaluated using AAA. These results are compared graphically and numerically using gamma-index analysis. Radio-chromic film measurements are presented to augment Monte Carlo and Acuros XB dose perturbation data. Results: Using a 2% and 1 mm gamma-analysis, between 91.3% and 96.8% of Acuros XB dose voxels containing greater than 50% the normalized dose were in agreement with Monte Carlo data for virtual phantoms involving 18 MV and 6 MV photons, stainless steel and titanium alloy implants and for on-axis and oblique field delivery. A similar gamma-analysis of AAA against Monte Carlo data showed between 80.8% and 87.3% agreement. Comparing Acuros XB and AAA evaluations of a clinical prostate patient plan involving a unilateral hip prosthesis, Acuros XB showed good overall agreement with Monte Carlo while AAA underestimated dose on the upstream medial surface of the prosthesis due to electron scatter from the high-density material. Film measurements
The string difference equation of the D = 1 matrix model and W1+∞ symmetry of the KP hierarchy
International Nuclear Information System (INIS)
Awada, M.A.; Sin, S.J.
1992-01-01
In this paper, the authors give a connection between the D = 1 matrix model and the generalized KP hierarchy. First, the authors find a difference equation satisfied by F, the Legendre transformation of the free energy of the D = 1 matrix model on a circle of radius R. Then the authors show that it is a special case of the difference equation of the generalized KP hierarchy with its zero mode identified with the scaling variable of the D = 1 string theory. The authors propose that the massive D = 1 matrix model is described by the generalized KP hierarchy, which implies the manifest integrability of D = 1 string theory. The authors also show that the (generalized) KP hierarchy has an underlying W 1 + ∞ symmetry. By reduction, we prove that the generalized KdV hierarchy has a subalgebra of the above symmetry which again forms a W 1+ ∞ . The authors argue that there are no W constraints in D = 1 string theory, which is in contrast to D 1 + ∞ constraints
DEFF Research Database (Denmark)
Johnsen, Kristinn; Yngvason, Jakob
1996-01-01
We report on a numerical study of the density matrix functional introduced by Lieb, Solovej, and Yngvason for the investigation of heavy atoms in high magnetic fields. This functional describes exactly the quantum mechanical ground state of atoms and ions in the limit when the nuclear charge Z...... and the electron number N tend to infinity with N/Z fixed, and the magnetic field B tends to infinity in such a way that B/Z4/3→∞. We have calculated electronic density profiles and ground-state energies for values of the parameters that prevail on neutron star surfaces and compared them with results obtained...... by other methods. For iron at B=1012 G the ground-state energy differs by less than 2% from the Hartree-Fock value. We have also studied the maximal negative ionization of heavy atoms in this model at various field strengths. In contrast to Thomas-Fermi type theories atoms can bind excess negative charge...
International Nuclear Information System (INIS)
Sagmeister, S.
2009-01-01
The aim of this work is to compare two state-of-the-art methods for the investigation of excitonic effects in solids, namely Time-Dependent Density Functional Theory (TDDFT) and Many-Body Perturbation Theory (MBPT), for selected simple gap systems as well as semiconducting polymers. Within TDDFT, the linear response framework is used and the Dyson equation for the density-density response function is solved, whereas within MBPT, the Bethe-Salpeter equation (BSE) for the electron-hole correlation function is solved. The dielectric function is obtained as a last step. Both techniques take into account the excitonic effects caused by the interaction of electron-hole pairs. In the former these effects are included in the exchange-correlation (xc) kernel, whereas in the latter they are located in the interaction kernel of the BSE. Kohn-Sham single-particle wave functions obtained from Density Functional Theory within the linearized augmented planewave (LAPW) method are used to calculate all relevant quantities of the formalism. For the simple systems GaAs, Si and LiF are chosen. The role of several approximations to the xc kernel is studied and it is found that for GaAs and Si simple semi-empirical models provide a dielectric function in accordance with the BSE. For the case of LiF, being a system with a weak screening and a strongly bound exciton, only an xc kernel derived from MBPT yields reasonable results but still a slight discrepancy to the BSE is observed. Finally, the semiconducting polymers poly-acetylene and poly(phenylene-vinylene) (PPV) are studied. For both materials the concept of semi-empirical approximations to the xc kernel turns out to be ambiguous due to their low-dimensional character. In the case of poly-acetylene, the xc kernel derived from MBPT yields a dielectric function which is in close but not exact agreement with the one obtained from the BSE. (author) [de
Probability and Cumulative Density Function Methods for the Stochastic Advection-Reaction Equation
Energy Technology Data Exchange (ETDEWEB)
Barajas-Solano, David A.; Tartakovsky, Alexandre M.
2018-01-01
We present a cumulative density function (CDF) method for the probabilistic analysis of $d$-dimensional advection-dominated reactive transport in heterogeneous media. We employ a probabilistic approach in which epistemic uncertainty on the spatial heterogeneity of Darcy-scale transport coefficients is modeled in terms of random fields with given correlation structures. Our proposed CDF method employs a modified Large-Eddy-Diffusivity (LED) approach to close and localize the nonlocal equations governing the one-point PDF and CDF of the concentration field, resulting in a $(d + 1)$ dimensional PDE. Compared to the classsical LED localization, the proposed modified LED localization explicitly accounts for the mean-field advective dynamics over the phase space of the PDF and CDF. To illustrate the accuracy of the proposed closure, we apply our CDF method to one-dimensional single-species reactive transport with uncertain, heterogeneous advection velocities and reaction rates modeled as random fields.
Huang, Guanghui; Wan, Jianping; Chen, Hui
2013-02-01
Nonlinear stochastic differential equation models with unobservable state variables are now widely used in analysis of PK/PD data. Unobservable state variables are usually estimated with extended Kalman filter (EKF), and the unknown pharmacokinetic parameters are usually estimated by maximum likelihood estimator. However, EKF is inadequate for nonlinear PK/PD models, and MLE is known to be biased downwards. A density-based Monte Carlo filter (DMF) is proposed to estimate the unobservable state variables, and a simulation-based M estimator is proposed to estimate the unknown parameters in this paper, where a genetic algorithm is designed to search the optimal values of pharmacokinetic parameters. The performances of EKF and DMF are compared through simulations for discrete time and continuous time systems respectively, and it is found that the results based on DMF are more accurate than those given by EKF with respect to mean absolute error. Copyright © 2012 Elsevier Ltd. All rights reserved.
Burtyka, Filipp
2018-03-01
The paper firstly considers the problem of finding solvents for arbitrary unilateral polynomial matrix equations with second-order matrices over prime finite fields from the practical point of view: we implement the solver for this problem. The solver’s algorithm has two step: the first is finding solvents, having Jordan Normal Form (JNF), the second is finding solvents among the rest matrices. The first step reduces to the finding roots of usual polynomials over finite fields, the second is essentially exhaustive search. The first step’s algorithms essentially use the polynomial matrices theory. We estimate the practical duration of computations using our software implementation (for example that one can’t construct unilateral matrix polynomial over finite field, having any predefined number of solvents) and answer some theoretically-valued questions.
Bollhöfer, Matthias; Kressner, Daniel; Mehl, Christian; Stykel, Tatjana
2015-01-01
This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on ...
International Nuclear Information System (INIS)
Honda, Yasushi; Horiguchi, Tsuyoshi
2001-01-01
We investigate a uniformly frustrated 19-vertex model with an anisotropy parameter η by use of the density matrix renormalization group for the transfer matrix for 0.6≤η≤1.3. The scaling dimension x is calculated from eigenvalues of the transfer matrix for several values η. The finite-size scaling analyses with a logarithmic correction are carried out in order to determine transition temperatures. It is found that there are two kinds of phase transitions, although there is a possibility of a single transition. This result is not compatible with the result for the uniformly frustrated XY model
The equation of state package FEOS for high energy density matter
Faik, Steffen; Tauschwitz, Anna; Iosilevskiy, Igor
2018-06-01
Adequate equation of state (EOS) data is of high interest in the growing field of high energy density physics and especially essential for hydrodynamic simulation codes. The semi-analytical method used in the newly developed Frankfurt equation of state (FEOS) package provides an easy and fast access to the EOS of - in principle - arbitrary materials. The code is based on the well known QEOS model (More et al., 1988; Young and Corey, 1995) and is a further development of the MPQeos code (Kemp and Meyer-ter Vehn, 1988; Kemp and Meyer-ter Vehn, 1998) from Max-Planck-Institut für Quantenoptik (MPQ) in Garching Germany. The list of features contains the calculation of homogeneous mixtures of chemical elements and the description of the liquid-vapor two-phase region with or without a Maxwell construction. Full flexibility of the package is assured by its structure: A program library provides the EOS with an interface designed for Fortran or C/C++ codes. Two additional software tools allow for the generation of EOS tables in different file output formats and for the calculation and visualization of isolines and Hugoniot shock adiabats. As an example the EOS of fused silica (SiO2) is calculated and compared to experimental data and other EOS codes.
A numerical spectral approach to solve the dislocation density transport equation
International Nuclear Information System (INIS)
Djaka, K S; Taupin, V; Berbenni, S; Fressengeas, C
2015-01-01
A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme. (paper)
Nag, Abhinav; Kumari, Anuja; Kumar, Jagdish
2018-05-01
We have investigated structural, electronic and transport properties of the alkali metals using ab-initio density functional theory. The electron energy dispersions are found parabolic free electron like which is expected for alkali metals. The lattice constants for all the studied metals are also in good agreement within 98% with experiments. We have further computed their transport properties using semi-classical Boltzmann transport equations with special focus on electrical and thermal conductivity. Our objective was to obtain Wiedemann-Franz law and hence Lorenz number. The motivation to do these calculations is to see that how the incorporation of different interactions such as electron-lattice, electron-electron interaction affect the Wiedeman-Franz law. By solving Boltzmann transport equations, we have obtained electrical conductivity (σ/τ) and thermal conductivity (κ0 /τ) at different temperatures and then calculated Lorenz number using L = κ0 /(σT). The obtained value of Lorenz number has been found to match with value derived for free electron Fermi gas 2.44× 10-8 WΩK-2. Our results prove that the Wiedemann-Franz law as derived for free electron gas does not change much for alkali metals, even when one incorporates interaction of electrons with atomic nuclei and other electrons. However, at lower temperatures, the Lorenz number, was found to be deviating from its theoretical value.
International Nuclear Information System (INIS)
Kussmann, Jörg; Luenser, Arne; Beer, Matthias; Ochsenfeld, Christian
2015-01-01
An analytical method to calculate the molecular vibrational Hessian matrix at the self-consistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulomb-type two-electron integral contractions, we show that the effect of the perturbation on the electronic structure due to the displacement of nuclei decays at least as r −2 instead of r −1 . The perturbation is asymptotically local, and the computation of the Hessian matrix can, in principle, be performed with O(N) complexity. Our implementation exhibits linear scaling in all time-determining steps, with some rapid but quadratic-complexity steps remaining. Sample calculations illustrate linear or near-linear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably sub-quadratic to quadratic, depending on the density of the underlying electronic structure
International Nuclear Information System (INIS)
Nishiyama, Seiya; Morita, Hiroyuki; Ohnishi, Hiromasa
2004-01-01
The traditional Tamm-Dancoff (TD) method is one of the standard procedures for solving the Schroedinger equation of fermion many-body systems. However, it meets a serious difficulty when an instability occurs in the symmetry-adapted ground state of the independent particle approximation (IPA) and when the stable IPA ground state becomes of broken symmetry. If one uses the stable but broken symmetry IPA ground state as the starting approximation, TD wave functions also become of broken symmetry. On the contrary, if we start from a symmetry-adapted but unstable wave function, the convergence of the TD expansion becomes bad. Thus, the requirements of symmetry and rapid convergence are not in general compatible in the conventional TD expansion of the systems with strong collective correlations. Along the same line as Fukutome's, we give a group-theoretical deduction of a U(n) dyadic TD equation by using a matrix-valued generator coordinate
A Compact Numerical Implementation for Solving Stokes Equations Using Matrix-vector Operations
Zhang, Tao; Salama, Amgad; Sun, Shuyu; Zhong, Hua
2015-01-01
In this work, a numerical scheme is implemented to solve Stokes equations based on cell-centered finite difference over staggered grid. In this scheme, all the difference operations have been vectorized thereby eliminating loops. This is particularly important when using programming languages that require interpretations, e.g., MATLAB and Python. Using this scheme, the execution time becomes significantly smaller compared with non-vectorized operations and also become comparable with those languages that require no repeated interpretations like FORTRAN, C, etc. This technique has also been applied to Navier-Stokes equations under laminar flow conditions.
A Compact Numerical Implementation for Solving Stokes Equations Using Matrix-vector Operations
Zhang, Tao
2015-06-01
In this work, a numerical scheme is implemented to solve Stokes equations based on cell-centered finite difference over staggered grid. In this scheme, all the difference operations have been vectorized thereby eliminating loops. This is particularly important when using programming languages that require interpretations, e.g., MATLAB and Python. Using this scheme, the execution time becomes significantly smaller compared with non-vectorized operations and also become comparable with those languages that require no repeated interpretations like FORTRAN, C, etc. This technique has also been applied to Navier-Stokes equations under laminar flow conditions.
Changes in subchondral bone mineral density and collagen matrix organization in growing horses.
Holopainen, Jaakko T; Brama, Pieter A J; Halmesmäki, Esa; Harjula, Terhi; Tuukkanen, Juha; van Weeren, P René; Helminen, Heikki J; Hyttinen, Mika M
2008-12-01
The effects of growth and maturation on the mineral deposition and the collagen framework of equine subchondral bone (SCB) were studied. Osteochondral specimens (diameter 6 mm) from the left metacarpophalangeal joint of 5-(n=8), 11-(n=8) and 18-month-old (n=6) horses were investigated at two differently loaded sites (Site 1 (S1): intermittent peak loading; Site 2 (S2): habitual loading). The SCB mineral density (BMD) was measured with peripheral quantitative computer tomography (pQCT), and the data were adjusted against the volume fraction (Vv) of the bone extracellular matrix (ECM). Polarised light microscopy (PLM) was used to analyze the Vv, the collagen fibril parallelism index and the orientation angle distribution in two fractions (1 mm/fraction) beneath the osteochondral junction of the SCB. PLM analysis was made along two randomly selected perpendicularly oriented vertical sections to measure the tissue anisotropy in the x-, y-, and z-directions. The BMD of SCB at S1 and S2 increased significantly during maturation. At the same time, the Vv of the ECM increased even more. This meant that the Vv-adjusted BMD decreased. There were no significant differences between sites. The basic collagen fibril framework of SCB seems to be established already at the age of 5 months. During maturation, the extracellular matrix underwent a decrease in collagen fibril parallelism but no changes in collagen orientation. The variation was negligible in the collagen network estimates in the two section planes. Growth and maturation induce significant changes in the equine SCB. The BMD increase in SCB is primarily due to the growth of bone volume and not to any increase in mineral deposition. An increase in weight-bearing appears to greatly affect the BMD and the volume of the extracellular matrix. Growth and maturation induce a striking change in collagen fibril parallelism but not in fibril orientation. The structural anisotropy of the subchondral bone is significant along the
Numerical solution of matrix exponential in burn-up equation using mini-max polynomial approximation
International Nuclear Information System (INIS)
Kawamoto, Yosuke; Chiba, Go; Tsuji, Masashi; Narabayashi, Tadashi
2015-01-01
Highlights: • We propose a new numerical solution of matrix exponential in burn-up depletion calculations. • The depletion calculation with extremely short half-lived nuclides can be done numerically stable with this method. • The computational time is shorter than the other conventional methods. - Abstract: Nuclear fuel burn-up depletion calculations are essential to compute the nuclear fuel composition transition. In the burn-up calculations, the matrix exponential method has been widely used. In the present paper, we propose a new numerical solution of the matrix exponential, a Mini-Max Polynomial Approximation (MMPA) method. This method is numerically stable for burn-up matrices with extremely short half-lived nuclides as the Chebyshev Rational Approximation Method (CRAM), and it has several advantages over CRAM. We also propose a multi-step calculation, a computational time reduction scheme of the MMPA method, which can perform simultaneously burn-up calculations with several time periods. The applicability of these methods has been theoretically and numerically proved for general burn-up matrices. The numerical verification has been performed, and it has been shown that these methods have high precision equivalent to CRAM
Kanagawa, Tetsuya
2015-05-01
This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.
Wang, Huihui; Bokarev, Sergey I.; Aziz, Saadullah G.; Kühn, Oliver
2017-08-01
Recent developments in attosecond spectroscopy yield access to the correlated motion of electrons on their intrinsic timescales. Spin-flip dynamics is usually considered in the context of valence electronic states, where spin-orbit coupling is weak and processes related to the electron spin are usually driven by nuclear motion. However, for core-excited states, where the core-hole has a nonzero angular momentum, spin-orbit coupling is strong enough to drive spin-flips on a much shorter timescale. Using density matrix-based time-dependent restricted active space configuration interaction including spin-orbit coupling, we address an unprecedentedly short spin-crossover for the example of L-edge (2p→3d) excited states of a prototypical Fe(II) complex. This process occurs on a timescale, which is faster than that of Auger decay (∼4 fs) treated here explicitly. Modest variations of carrier frequency and pulse duration can lead to substantial changes in the spin-state yield, suggesting its control by soft X-ray light.
The Density Matrix for Single-mode Light after k-Photon Absorption
Voigt, H.; Bandilla, A.
In order to continue and generalize the studies of the density matrix of a light field undergoing k-photon absorption, in this paper we put the emphasis on the off-diagonal elements. The solution obtained earlier for the diagonal elements describing the photon statistics can be found as a special case but will not be discussed again. The general solution calculated by recursion shows an asymptotic behaviour if the initial photon number is sufficiently high. Only the initial phase information survives. Illustrating the solution we start with coherent light and a generalized coherent state.Translated AbstractDie Dichtematrix eines Lichtstrahls nach k-Photonen-Absorption aus einer ModeWir führen die Betrachtungen über das Verhalten der Dichtematrix eines Lichtfeldes nach k-Photonen-Absorption aus einer Mode verallgemeinernd weiter und konzentrieren uns auf die Nichtdiagonalelemente. Die im folgenden angegebene allgemeine Lösung, die durch Rekursion gefunden wurde, enthält die schon früher erhaltene, jedoch hier nicht weiter diskutierte Lösung für die Diagonalelemente als Spezialfall. Sie zeigt ferner, daß es einen asymptotischen Zustand gibt, der eine von der Ausgangsintensität unabhängige Information über die Ausgangsphase enthält. Zur Diskussion der Lösung werden verschiedene Anfangsbedingungen betrachtet, so z. B. kohärentes Licht und kohärentes Licht, das ein Medium mit nichtlinearem Brechungsindex durchlaufen hat (Kerr-Effekt).
Degree of conversion and cross-link density within a resin-matrix composite.
Al-Zain, Afnan O; Eckert, George J; Lukic, Henry; Megremis, Spiro J; Platt, Jeffrey A
2018-05-01
The aims of this study were to profile light radiated from two light-curing units (LCUs) and evaluate profile relationship to polymerization patterns within a resin-matrix composite (RMC). Beam profiles of one multiple emission peak light-emitting-diode and one quartz-tungsten-halogen curing-unit were measured using a beam profiler/spectrometer system. A camera-based profiler and an integrating sphere/spectrometer assembly were used to evaluate each LCU beam. Polymerization patterns within a nano-hybrid RMC were investigated using a mapping approach by assessing the degree of conversion utilizing micro-Raman spectroscopy and indirectly estimating cross-link-density by repeated microhardness testing before and after exposure to ethanol (%KH reduction, n = 3). The irradiance received on the top and bottom specimen surfaces from both LCUs was measured using a MARC-RC system. The investigated beam profile area from both LCUs was non-uniform and yielded localized discrepancies in DC (55.7-74.9%) and %KH reduction (26.7-54.1%). The LCU irradiance received at the bottom of the specimens was ∼10% of the top value. This study demonstrated that LCU beam profiles were non-uniform in the area explored. Localized differences in DC and %KH reduction existed throughout the RMC specimens but did not follow a specific pattern. © 2017 Wiley Periodicals, Inc. J Biomed Mater Res Part B: Appl Biomater, 106B: 1496-1504, 2018. © 2017 Wiley Periodicals, Inc.
Energy Technology Data Exchange (ETDEWEB)
Cwik, T. [California Institute of Technology, Pasadena, CA (United States); Katz, D.S. [Cray Research, El Segundo, CA (United States)
1996-12-31
Finite element modeling has proven useful for accurately simulating scattered or radiated electromagnetic fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of an electrical wavelength. An unstructured finite element model of realistic objects leads to a large, sparse, system of equations that needs to be solved efficiently with regard to machine memory and execution time. Both factorization and iterative solvers can be used to produce solutions to these systems of equations. Factorization leads to high memory requirements that limit the electrical problem size of three-dimensional objects that can be modeled. An iterative solver can be used to efficiently solve the system without excessive memory use and in a minimal amount of time if the convergence rate is controlled.
Connecting N-representability to Weyl's problem: the one-particle density matrix for N = 3 and R = 6
International Nuclear Information System (INIS)
Ruskai, Mary Beth
2007-01-01
An analytic proof of the necessity of the Borland-Dennis conditions for 3-representability of a one-particle density matrix with rank 6 is given. This may shed some light on Klyachko's recent use of Schubert calculus to find general conditions for N-representability. (fast track communication)
Akhundova, E. A.; Dodonov, V. V.; Manko, V. I.
1993-01-01
The exact expressions for density matrix and Wigner functions of quantum systems are known only in special cases. Corresponding Hamiltonians are quadratic forms of Euclidean coordinates and momenta. In this paper we consider the problem of one-dimensional free particle movement in the bounded region 0 is less than x is less than a (including the case a = infinity).
Westgate, Philip M
2013-07-20
Generalized estimating equations (GEEs) are routinely used for the marginal analysis of correlated data. The efficiency of GEE depends on how closely the working covariance structure resembles the true structure, and therefore accurate modeling of the working correlation of the data is important. A popular approach is the use of an unstructured working correlation matrix, as it is not as restrictive as simpler structures such as exchangeable and AR-1 and thus can theoretically improve efficiency. However, because of the potential for having to estimate a large number of correlation parameters, variances of regression parameter estimates can be larger than theoretically expected when utilizing the unstructured working correlation matrix. Therefore, standard error estimates can be negatively biased. To account for this additional finite-sample variability, we derive a bias correction that can be applied to typical estimators of the covariance matrix of parameter estimates. Via simulation and in application to a longitudinal study, we show that our proposed correction improves standard error estimation and statistical inference. Copyright © 2012 John Wiley & Sons, Ltd.
S-matrix approach to the equation of state of dilute nuclear matter
Indian Academy of Sciences (India)
2014-04-01
Apr 1, 2014 ... The result is a model-independent virial series for the pressure and density that systematically includes ... The calculated symmetry energy coefficients are found to be in fair agreement with the .... its empirical value. The prime ...
Updated users' guide for SAMMY: Multilevel R-matrix fits to neutron data using Bayes' equation
International Nuclear Information System (INIS)
Larson, N.M.
1989-06-01
In 1980 the multilevel multichannel R-matrix code SAMMY was released for use in analysis of neutron data at the Oak Ridge Electron Linear Accelerator. Since that time, SAMMY has undergone significant modifications: user-friendly options have been incorporated to streamline common operations and to protect a run from common user errors; the Reich-Moore formalism has been extended to include an optional logarithmic parameterization of the external R-matrix, for which any or all parameters may be varied; the ability to vary sample thickness, effective temperature, matching radius, and/or resolution-broadening parameters has been incorporated; to avoid loss of information (i.e., computer round-off errors) between runs, the ''covariance file'' now includes precise values for all variables; and unused but correlated variables may be included in the analysis. Because of these and earlier changes, the 1980 SAMMY manual is now hopelessly obsolete. This report is intended to be complete documentation for the current version of SAMMY. Its publication in looseleaf form will permit updates to the manual to be made concurrently with updates to the code itself, thus eliminating most of the time lag between update and documentation. 28 refs., 54 tabs
Updated user's guide for SAMMY: multilevel R-matrix fits to neutron data using Bayes' equation
International Nuclear Information System (INIS)
Larson, N.M.
1996-01-01
In 1980 the multilevel multichannel R-matrix code SAMMY was released for use in analysis of neutron data at the Oak Ridge Electron Linear Accelerator. Since that time, SAMMY has undergone significant modifications: (1) User-friendly options have been incorporated to streamline common operations and to protect a run from common user errors, (2) The Reich-Moore formalism has been extended to include an optional logarithmic parameterization of the external R-matrix, for which any or all parameters may be varied, (3) the ability to vary sample thickness, effective temperature, matching radius, and/or resolution-broadening parameters has been incorporated, (4) to avoid loss of information (i.e. computer round-off errors) between runs, the ''covariance file'' now includes precise values for al variables, (5) Unused but correlated variables may be included in the analysis. Because of these and earlier changes, the 1980 SAMMY manual is now hopelessly obsolete. This report is intended to be complete documentation for the current version of SAMMY. Its publication in looseleaf form will permit updates to the manual to be made concurrently with updates to the code itself, thus eliminating most of the time lag between update and documentation
International Nuclear Information System (INIS)
Dong, Jianping
2011-01-01
The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas-Fermi model, obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg-Kohn theorems in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics. -- Highlights: → Thomas-Fermi model under the framework of fractional quantum mechanics is studied. → We show the validity of the HK theorems in the space fractional quantum mechanics. → The density functional theory is generalized to the fractional quantum mechanics.
High Temperature, high pressure equation of state density correlations and viscosity correlations
Energy Technology Data Exchange (ETDEWEB)
Tapriyal, D.; Enick, R.; McHugh, M.; Gamwo, I.; Morreale, B.
2012-07-31
Global increase in oil demand and depleting reserves has derived a need to find new oil resources. To find these untapped reservoirs, oil companies are exploring various remote and harsh locations such as deep waters in Gulf of Mexico, remote arctic regions, unexplored deep deserts, etc. Further, the depth of new oil/gas wells being drilled has increased considerably to tap these new resources. With the increase in the well depth, the bottomhole temperature and pressure are also increasing to extreme values (i.e. up to 500 F and 35,000 psi). The density and viscosity of natural gas and crude oil at reservoir conditions are critical fundamental properties required for accurate assessment of the amount of recoverable petroleum within a reservoir and the modeling of the flow of these fluids within the porous media. These properties are also used to design appropriate drilling and production equipment such as blow out preventers, risers, etc. With the present state of art, there is no accurate database for these fluid properties at extreme conditions. As we have begun to expand this experimental database it has become apparent that there are neither equations of state for density or transport models for viscosity that can be used to predict these fundamental properties of multi-component hydrocarbon mixtures over a wide range of temperature and pressure. Presently, oil companies are using correlations based on lower temperature and pressure databases that exhibit an unsatisfactory predictive capability at extreme conditions (e.g. as great as {+-} 50%). From the perspective of these oil companies that are committed to safely producing these resources, accurately predicting flow rates, and assuring the integrity of the flow, the absence of an extensive experimental database at extreme conditions and models capable of predicting these properties over an extremely wide range of temperature and pressure (including extreme conditions) makes their task even more daunting.
Tabuchi, Mari; Seo, Makoto; Inoue, Takayuki; Ikeda, Takeshi; Kogure, Akinori; Inoue, Ikuo; Katayama, Shigehiro; Matsunaga, Toshiyuki; Hara, Akira; Komoda, Tsugikazu
2011-02-01
The increasing number of patients with metabolic syndrome is a critical global problem. In this study, we describe a novel geometrical electrophoretic separation method using a bioformulated-fiber matrix to analyze high-density lipoprotein (HDL) particles. HDL particles are generally considered to be a beneficial component of the cholesterol fraction. Conventional electrophoresis is widely used but is not necessarily suitable for analyzing HDL particles. Furthermore, a higher HDL density is generally believed to correlate with a smaller particle size. Here, we use a novel geometrical separation technique incorporating recently developed nanotechnology (Nata de Coco) to contradict this belief. A dyslipidemia patient given a 1-month treatment of fenofibrate showed an inverse relationship between HDL density and size. Direct microscopic observation and morphological observation of fractionated HDL particles confirmed a lack of relationship between particle density and size. This new technique may improve diagnostic accuracy and medical treatment for lipid related diseases.
International Nuclear Information System (INIS)
Luque, N.B.; Woelki, S.; Henderson, D.; Schmickler, W.
2011-01-01
Highlights: · We augment a double-layer model based on integral equations by calculating the interaction parameters with the electrode from quantum density functional theory · Explicit model calculations for Ag(1 1 1) in aqueous solutions give at least qualitatively good results for the particle profiles · Ours is the only method which allows the calculation of capacity-charge characteristics. · We obtain reasonable values for the Helmholtz (inner-layer) capacity. - Abstract: We have complemented the singlet reference interaction site model for the electric double layer by quantum chemical calculations for the interaction of ions and solvents with an electrode. Specific calculations have been performed for an aqueous solution of NaCl in contact with a Ag(1 1 1) electrode. The particle profiles near the electrode show the specific adsorption of Cl - ions, but not of Na + , and are at least in qualitative agreement with those obtained by molecular dynamics. Including the electronic response of the silver surface into the model results in reasonable capacity-charge characteristics.
Energy Technology Data Exchange (ETDEWEB)
Sari, Salih [Hacettepe University, Department of Nuclear Engineering, Beytepe, 06800 Ankara (Turkey); Erguen, Sule [Hacettepe University, Department of Nuclear Engineering, Beytepe, 06800 Ankara (Turkey); Barik, Muhammet; Kocar, Cemil; Soekmen, Cemal Niyazi [Hacettepe University, Department of Nuclear Engineering, Beytepe, 06800 Ankara (Turkey)
2009-03-15
In this study, isothermal turbulent bubbly flow is mechanistically modeled. For the modeling, Fluent version 6.3.26 is used as the computational fluid dynamics solver. First, the mechanistic models that simulate the interphase momentum transfer between the gas (bubbles) and liquid (continuous) phases are investigated, and proper models for the known flow conditions are selected. Second, an interfacial area transport equation (IATE) solution is added to Fluent's solution scheme in order to model the interphase momentum transfer mechanisms. In addition to solving IATE, bubble number density (BND) approach is also added to Fluent and this approach is also used in the simulations. Different source/sink models derived for the IATE and BND models are also investigated. The simulations of experiments based on the available data in literature are performed by using IATE and BND models in two and three-dimensions. The results show that the simulations performed by using IATE and BND models agree with each other and with the experimental data. The simulations performed in three-dimensions give better agreement with the experimental data.
International Nuclear Information System (INIS)
Sari, Salih; Erguen, Sule; Barik, Muhammet; Kocar, Cemil; Soekmen, Cemal Niyazi
2009-01-01
In this study, isothermal turbulent bubbly flow is mechanistically modeled. For the modeling, Fluent version 6.3.26 is used as the computational fluid dynamics solver. First, the mechanistic models that simulate the interphase momentum transfer between the gas (bubbles) and liquid (continuous) phases are investigated, and proper models for the known flow conditions are selected. Second, an interfacial area transport equation (IATE) solution is added to Fluent's solution scheme in order to model the interphase momentum transfer mechanisms. In addition to solving IATE, bubble number density (BND) approach is also added to Fluent and this approach is also used in the simulations. Different source/sink models derived for the IATE and BND models are also investigated. The simulations of experiments based on the available data in literature are performed by using IATE and BND models in two and three-dimensions. The results show that the simulations performed by using IATE and BND models agree with each other and with the experimental data. The simulations performed in three-dimensions give better agreement with the experimental data
A new baryonic equation of state at sub-nuclear densities for core-collapse simulations
Energy Technology Data Exchange (ETDEWEB)
Furusawa, Shun; Yamada, Shoichi; Sumiyoshi, Kohsuke; Suzuki, Hideyuki [Department of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555 (Japan); Department of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555 (Japan) and Advanced Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo 169-8555 (Japan); Numazu College of Technology, Ooka 3600, Numazu, Shizuoka 410-8501 (Japan); Faculty of Science and Technology, Tokyo University of Science, Yamazaki 2641, Noda, Chiba 278-8510 (Japan)
2012-11-12
We construct a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is based on the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by using relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to {approx} 1000. We have also taken into account the pasta phase. We find that the free energy and other thermodynamical quantities are not very different from those given in the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important effect to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent scattering rates on nuclei but has been unavailable so far.
A new baryonic equation of state at sub-nuclear densities for core-collapse simulations
International Nuclear Information System (INIS)
Furusawa, Shun; Yamada, Shoichi; Sumiyoshi, Kohsuke; Suzuki, Hideyuki
2012-01-01
We construct a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is based on the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by using relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to ∼ 1000. We have also taken into account the pasta phase. We find that the free energy and other thermodynamical quantities are not very different from those given in the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important effect to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent scattering rates on nuclei but has been unavailable so far.
A new baryonic equation of state at sub-nuclear densities for core-collapse simulations
Furusawa, Shun; Yamada, Shoichi; Sumiyoshi, Kohsuke; Suzuki, Hideyuki
2012-11-01
We construct a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is based on the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by using relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to ~ 1000. We have also taken into account the pasta phase. We find that the free energy and other thermodynamical quantities are not very different from those given in the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important effect to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent scattering rates on nuclei but has been unavailable so far.
Lance, Amanda; Yang, Chih-Chao; Swamydas, Muthulekha; Dean, Delphine; Deitch, Sandy; Burg, Karen J L; Dréau, Didier
2016-01-01
The extracellular matrix (ECM) contributes to the generation and dynamic of normal breast tissue, in particular to the generation of polarized acinar and ductal structures. In vitro 3D culture conditions, including variations in the composition of the ECM, have been shown to directly influence the formation and organization of acinus-like and duct-like structures. Furthermore, the density of the ECM appears to also play a role in the normal mammary tissue and tumour formation. Here we show that the density of the ECM directly influences the number, organization and function of breast acini. Briefly, non-malignant human breast MCF10A cells were incubated in increasing densities of a Matrigel®-collagen I matrix. Elastic moduli near and distant to the acinus structures were measured by atomic force microscopy, and the number of acinus structures was determined. Immunochemistry was used to investigate the expression levels of E-cadherin, laminin, matrix metalloproteinase-14 and ß-casein in MCF10A cells. The modulus of the ECM was significantly increased near the acinus structures and the number of acinus structures decreased with the increase in Matrigel-collagen I density. As evaluated by the expression of laminin, the organization of the acinus structures present was altered as the density of the ECM increased. Increases in both E-cadherin and MMP14 expression by MCF10A cells as ECM density increased were also observed. In contrast, MCF10A cells expressed lower ß-casein levels as the ECM density increased. Taken together, these observations highlight the key role of ECM density in modulating the number, organization and function of breast acini. Copyright © 2013 John Wiley & Sons, Ltd.
Streubel, A; Siepmann, J; Bodmeier, R
2003-01-01
The aim of this study was to develop and physicochemically characterize single unit, floating controlled drug delivery systems consisting of (i). polypropylene foam powder, (ii). matrix-forming polymer(s), (iii). drug, and (iv). filler (optional). The highly porous foam powder provided low density and, thus, excellent in vitro floating behavior of the tablets. All foam powder-containing tablets remained floating for at least 8 h in 0.1 N HCl at 37 degrees C. Different types of matrix-forming polymers were studied: hydroxypropyl methylcellulose (HPMC), polyacrylates, sodium alginate, corn starch, carrageenan, gum guar and gum arabic. The tablets eroded upon contact with the release medium, and the relative importance of drug diffusion, polymer swelling and tablet erosion for the resulting release patterns varied significantly with the type of matrix former. The release rate could effectively be modified by varying the "matrix-forming polymer/foam powder" ratio, the initial drug loading, the tablet geometry (radius and height), the type of matrix-forming polymer, the use of polymer blends and the addition of water-soluble or water-insoluble fillers (such as lactose or microcrystalline cellulose). The floating behavior of the low density drug delivery systems could successfully be combined with accurate control of the drug release patterns.
International Nuclear Information System (INIS)
Habershon, Scott
2013-01-01
We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency
Habershon, Scott
2013-09-14
We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency.
Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation
International Nuclear Information System (INIS)
Bonnet, M.; Meurant, G.
1978-01-01
Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr
Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation
International Nuclear Information System (INIS)
Bonnet, M.; Meurant, G.
1978-01-01
The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr
Energy Technology Data Exchange (ETDEWEB)
Mehta, M. L. [Institute of Fundamental Research Bombay (India); Gaudin, M. [Commissariat a l' energie atomique et aux energies alternatives - CEA, Centre d' Etudes Nucleaires de Saclay, Gif-sur-Yvette (France)
1960-07-01
An exact expression for the density of eigenvalues of a random- matrix is derived. When the order of the matrix becomes infinite, it can be seen very directly that it goes over to Wigner's 'semi-circle law'. Reprint of a paper published in 'Nuclear Physics' 18, 1960, p. 420-427 [French] On deduit une expression precise pour la densite des racines caracteristiques d'une matrice stochastique. Quand l'ordre de la matrice devient infini, on peut voir facilement qu'elle obeit a la loi dite 'semi-circulaire' de Wigner. Reproduction d'un article publie dans 'Nuclear Physics' 18, 1960, p. 420-427.
Chen, Meixiong; Yuan, Jie; Long, Xingwu; Kang, Zhenglong; Wang, Zhiguo; Li, Yingying
2013-12-01
A general beam position controlling method for 3D optical systems based on the method of solving ray matrix equations has been proposed in this paper. As a typical 3D optical system, nonplanar ring resonator of Zero-Lock Laser Gyroscopes has been chosen as an example to show its application. The total mismatching error induced by Faraday-wedge in nonplanar ring resonator has been defined and eliminated quite accurately with the error less than 1 μm. Compared with the method proposed in Ref. [14], the precision of the beam position controlling has been improved by two orders of magnitude. The novel method can be used to implement automatic beam position controlling in 3D optical systems with servo circuit. All those results have been confirmed by related alignment experiments. The results in this paper are important for beam controlling, ray tracing, cavity design and alignment in 3D optical systems.
Poelmans, Ward; Van Raemdonck, Mario; Verstichel, Brecht; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Alcoba, Diego R; Bultinck, Patrick; Van Neck, Dimitri
2015-09-08
We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N2, and CN(-)). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L(3), where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework.
Abbey, Colette A; Bayless, Kayla J
2014-09-01
This study was designed to determine the optimal conditions required for known pro-angiogenic stimuli to elicit successful endothelial sprouting responses. We used an established, quantifiable model of endothelial cell (EC) sprout initiation where ECs were tested for invasion in low (1 mg/mL) and high density (5 mg/mL) 3D collagen matrices. Sphingosine 1-phosphate (S1P) alone, or S1P combined with stromal derived factor-1α (SDF) and phorbol ester (TPA), elicited robust sprouting responses. The ability of these factors to stimulate sprouting was more effective in higher density collagen matrices. S1P stimulation resulted in a significant increase in invasion distance, and with the exception of treatment groups containing phorbol ester, invasion distance was longer in 1mg/mL compared to 5mg/mL collagen matrices. Closer examination of cell morphology revealed that increasing matrix density and supplementing with SDF and TPA enhanced the formation of multicellular structures more closely resembling capillaries. TPA enhanced the frequency and size of lumen formation and correlated with a robust increase in phosphorylation of p42/p44 Erk kinase, while S1P and SDF did not. Also, a higher number of significantly longer extended processes formed in 5mg/mL compared to 1mg/mL collagen matrices. Because collagen matrices at higher density have been reported to be stiffer, we tested for changes in the mechanosensitive protein, zyxin. Interestingly, zyxin phosphorylation levels inversely correlated with matrix density, while levels of total zyxin did not change significantly. Immunofluorescence and localization studies revealed that total zyxin was distributed evenly throughout invading structures, while phosphorylated zyxin was slightly more intense in extended peripheral processes. Silencing zyxin expression increased extended process length and number of processes, while increasing zyxin levels decreased extended process length. Altogether these data indicate that ECs
International Nuclear Information System (INIS)
Fischer, Tobias
2016-01-01
In this article the role of the supersaturation density equation of state (EOS) is explored in simulations of failed core-collapse supernova explosions. Therefore the nuclear EOS is extended via a one-parameter excluded-volume description for baryons, taking into account their finite and increasing volume with increasing density in excess of saturation density. Parameters are selected such that the resulting supernova EOS represent extreme cases, with high pressure variations at supersaturation density which feature extreme stiff and soft EOS variants of the reference case, i.e. without excluded-volume corrections. Unlike in the interior of neutron stars with central densities in excess of several times saturation density, central densities of core-collapse supernovae reach only slightly above saturation density. Hence, the impact of the supersaturation density EOS on the supernova dynamics as well as the neutrino signal is found to be negligible. It is mainly determined from the low- and intermediate-density domain, which is left unmodified within this generalized excluded volume approach. (orig.)
Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke
2018-02-01
In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.
Sun, Shuyu
2012-09-01
In this paper we introduce a new technique for the numerical solution of the various partial differential equations governing flow and transport phenomena in porous media. This method is proposed to be used in high level programming languages like MATLAB, Python, etc., which show to be more efficient for certain mathematical operations than for others. The proposed technique utilizes those operations in which these programming languages are efficient the most and keeps away as much as possible from those inefficient, time-consuming operations. In particular, this technique is based on the minimization of using multiple indices looping operations by reshaping the unknown variables into one-dimensional column vectors and performing the numerical operations using shifting matrices. The cell-centered information as well as the face-centered information are shifted to the adjacent face-center and cell-center, respectively. This enables the difference equations to be done for all the cells at once using matrix operations rather than within loops. Furthermore, for results post-processing, the face-center information can further be mapped to the physical grid nodes for contour plotting and stream lines constructions. In this work we apply this technique to flow and transport phenomena in porous media. © 2012 Elsevier Ltd.
International Nuclear Information System (INIS)
Cheng, Yi-Xin
1992-01-01
The Schwinger-Dyson loop equations for the hermitian multi-matrix chain models at finite N, are derived from the Ward identities of the partition functional under the infinitesimal field transformations. The constraint operators W n (m) satisfy the w 1+∞ -like algebra up to a linear combination of the lower spin operators. We find that the all the higher spin constraints are reducible to the Virasoro-type constraints for all the matrix chain models. (author)
Liu, Tao; Huang, Jie
2017-04-17
This paper presents a discrete-time recurrent neural network approach to solving systems of linear equations with two features. First, the system of linear equations may not have a unique solution. Second, the system matrix is not known precisely, but a sequence of matrices that converges to the unknown system matrix exponentially is known. The problem is motivated from solving the output regulation problem for linear systems. Thus, an application of our main result leads to an online solution to the output regulation problem for linear systems.
A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide
Allen, Rebecca; Reis, Tim; Sun, Shuyu
2013-01-01
-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE
Directory of Open Access Journals (Sweden)
Hrubý Jan
2012-04-01
Full Text Available The study presents some preliminary results of the density gradient theory (GT combined with two different equations of state (EoS: the classical cubic equation by van der Waals and a recent approach based on the statistical associating fluid theory (SAFT, namely its perturbed-chain (PC modification. The results showed that the cubic EoS predicted for a given surface tension the density profile with a noticeable defect. Bulk densities predicted by the cubic EoS differed as much as by 100 % from the reference data. On the other hand, the PC-SAFT EoS provided accurate results for density profile and both bulk densities in the large range of temperatures. It has been shown that PC-SAFT is a promising tool for accurate modeling of nucleation using the GT. Besides the basic case of a planar phase interface, the spherical interface was analyzed to model a critical cluster occurring either for nucleation of droplets (condensation or bubbles (boiling, cavitation. However, the general solution for the spherical interface will require some more attention due to its numerical difficulty.
Hao, Tian
2015-02-28
The tap density of a granular powder is often linked to the flowability via the Carr index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in the literature: the inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept under the assumption that particles will obey similar thermodynamic laws during the tapping process if the "granular temperature" is defined in a different way, we obtain the tap density equations, and they are reducible to the two empirical equations currently widely used in literature. Our equations could potentially fit experimental data better with an additional adjustable parameter. The tapping amplitude and frequency, the weight of the granular materials, and the environmental temperature are grouped into this parameter that weighs the pace of the packing process. The current results, in conjunction with our previous findings, may imply that both "dry" (granular) and "wet" (colloidal and polymeric) particle systems are governed by the same physical mechanisms in term of the role of the free volume and how particles behave (a rate controlled process).
International Nuclear Information System (INIS)
McCarthy, P.J.
1981-01-01
It is proved that normalised Stiefel manifolds admit a rational parametrisation which generalises Cayley's parametrisation of the unitary groups. Applying (the quaternionic case of) this parametrisation to the Atiyah-Drinfeld-Hitchin-Manin (ADHM) instanton matrix equations, large families of new explicit rational solutions emerge. In particular, new explicit non-'t Hooft solutions are presented. (orig.)
Gamow-Jordan vectors and non-reducible density operators from higher-order S-matrix poles
International Nuclear Information System (INIS)
Bohm, A.; Loewe, M.; Maxson, S.; Patuleanu, P.; Puentmann, C.; Gadella, M.
1997-01-01
In analogy to Gamow vectors that are obtained from first-order resonance poles of the S-matrix, one can also define higher-order Gamow vectors which are derived from higher-order poles of the S-matrix. An S-matrix pole of r-th order at z R =E R -iΓ/2 leads to r generalized eigenvectors of order k=0,1,hor-ellipsis,r-1, which are also Jordan vectors of degree (k+1) with generalized eigenvalue (E R -iΓ/2). The Gamow-Jordan vectors are elements of a generalized complex eigenvector expansion, whose form suggests the definition of a state operator (density matrix) for the microphysical decaying state of this higher-order pole. This microphysical state is a mixture of non-reducible components. In spite of the fact that the k-th order Gamow-Jordan vectors has the polynomial time-dependence which one always associates with higher-order poles, the microphysical state obeys a purely exponential decay law. copyright 1997 American Institute of Physics
Hu, S. X.; Gao, R.; Ding, Y.; Collins, L. A.; Kress, J. D.
2017-04-01
Using density-functional theory-based molecular-dynamics simulations, we have investigated the equation of state for silicon in a wide range of plasma density and temperature conditions of ρ =0.001 -500 g /c m3 and T =2000 -108K . With these calculations, we have established a first-principles equation-of-state (FPEOS) table of silicon for high-energy-density (HED) plasma simulations. When compared with the widely used SESAME-EOS model (Table 3810), we find that the FPEOS-predicted Hugoniot is ˜20% softer; for off-Hugoniot plasma conditions, the pressure and internal energy in FPEOS are lower than those of SESAME EOS for temperatures above T ≈ 1-10 eV (depending on density), while the former becomes higher in the low-T regime. The pressure difference between FPEOS and SESAME 3810 can reach to ˜50%, especially in the warm-dense-matter regime. Implementing the FPEOS table of silicon into our hydrocodes, we have studied its effects on Si-target implosions. When compared with the one-dimensional radiation-hydrodynamics simulation using the SESAME 3810 EOS model, the FPEOS simulation showed that (1) the shock speed in silicon is ˜10% slower; (2) the peak density of an in-flight Si shell during implosion is ˜20% higher than the SESAME 3810 simulation; (3) the maximum density reached in the FPEOS simulation is ˜40% higher at the peak compression; and (4) the final areal density and neutron yield are, respectively, ˜30% and ˜70% higher predicted by FPEOS versus the traditional simulation using SESAME 3810. All of these features can be attributed to the larger compressibility of silicon predicted by FPEOS. These results indicate that an accurate EOS table, like the FPEOS presented here, could be essential for the precise design of targets for HED experiments.
International Nuclear Information System (INIS)
Andrews, P.L.; Perkins, F.W.
1983-01-01
The investigation of the scattering of lower-hybrid waves by density fluctuations arising from drift waves in tokamaks is distinguished by the presence in the wave equation of a large, random, derivative-coupling term. The propagation of the lower-hybrid waves is well represented by a radiative transfer equation when the scale size of the density fluctuations is small compared to the overall plasma size. The radiative transfer equation is solved in two limits: first, the forward scattering limit, where the scale size of density fluctuations is large compared to the lower-hybrid perpendicular wavelength, and second, the large-angle scattering limit, where this inequality is reversed. The most important features of these solutions are well represented by analytical formulas derived by simple arguments. Based on conventional estimates for density fluctuations arising from drift waves and a parabolic density profile, the optical depth tau for scattering through a significant angle, is given by tauroughly-equal(2/N 2 /sub parallel/) (#betta#/sub p/i0/#betta#) 2 (m/sub e/c 2 /2T/sub i/)/sup 1/2/ [c/α(Ω/sub i/Ω/sub e/)/sup 1/2/ ], where #betta#/sub p/i0 is the central ion plasma frequency and T/sub i/ denotes the ion temperature near the edge of the plasma. Most of the scattering occurs near the surface. The transmission through the scattering region scales as tau - 1 and the emerging intensity has an angular spectrum proportional to cos theta, where sin theta = k/sub perpendicular/xB/sub p//(k/sub perpendicular/B/sub p/), and B/sub p/ is the poloidal field
Energy Technology Data Exchange (ETDEWEB)
Aoki, Sinya [Yukawa Institute for Theoretical Physics, Kyoto University,Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502 (Japan); Hanada, Masanori [Stanford Institute for Theoretical Physics, Stanford University,Stanford, CA 94305 (United States); Yukawa Institute for Theoretical Physics, Kyoto University,Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502 (Japan); The Hakubi Center for Advanced Research, Kyoto University,Yoshida Ushinomiyacho, Sakyo-ku, Kyoto 606-8501 (Japan); Nakamura, Atsushi [Research Institute for Information Science and Education, Hiroshima University,Higashi-Hiroshima 739-8527 (Japan)
2015-05-14
In the Monte Carlo study of QCD at finite baryon density based upon the phase reweighting method, the pion condensation in the phase-quenched theory and associated zero-mode prevent us from going to the low-temperature high-density region. We propose a method to circumvent them by a simple modification of the density of state method. We first argue that the standard version of the density of state method, which is invented to solve the overlapping problem, is effective only for a certain ‘good’ class of observables. We then modify it so as to solve the overlap problem for ‘bad’ observables as well. While, in the standard version of the density of state method, we usually constrain an observable we are interested in, we fix a different observable in our new method which has a sharp peak at some particular value characterizing the correct vacuum of the target theory. In the finite-density QCD, such an observable is the pion condensate. The average phase becomes vanishingly small as the value of the pion condensate becomes large, hence it is enough to consider configurations with π{sup +}≃0, where the zero mode does not appear. We demonstrate an effectiveness of our method by using a toy model (the chiral random matrix theory) which captures the properties of finite-density QCD qualitatively. We also argue how to apply our method to other theories including finite-density QCD. Although the example we study numerically is based on the phase reweighting method, the same idea can be applied to more general reweighting methods and we show how this idea can be applied to find a possible QCD critical point.
Energy Technology Data Exchange (ETDEWEB)
Roemelt, Michael, E-mail: michael.roemelt@theochem.rub.de [Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany and Max-Planck Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr (Germany)
2015-07-28
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
Ogarko, V.; Luding, Stefan
2012-01-01
We study bi- and polydisperse mixtures of hard sphere fluids with extreme size ratios up to 100. Simulation results are compared with previously found analytical equations of state by looking at the compressibility factor, Z, and agreement is found with much better than 1% deviation in the fluid
A generalized variational algebra and conserved densities for linear evolution equations
International Nuclear Information System (INIS)
Abellanas, L.; Galindo, A.
1978-01-01
The symbolic algebra of Gel'fand and Dikii is generalized to the case of n variables. Using this algebraic approach a rigorous characterization of the polynomial kernel of the variational derivative is given. This is applied to classify all the conservation laws for linear polynomial evolution equations of arbitrary order. (Auth.)
International Nuclear Information System (INIS)
Dimitrova, S.S.; Gaidarov, M.K.; Antonov, A.N.; Stoitsov, M.V.; Hodgson, P.E; Lukyanov, V.K.; Zemlyanaya, E.V.; Krumova, G.Z.
1997-01-01
Overlap functions and spectroscopic factors extracted from a model one-body density matrix (OBDM) accounting for short-range nucleon-nucleon correlations are used to calculate differential cross sections of (p, d) reactions and the momentum distributions of transitions to single-particle states in 16 O and 40 Ca. A comparison between the experimental (p, d) and (e, e'p) data, their DWBA and CDWIA analyses and the OBDM calculations is made. Our theoretical predictions for the spectroscopic factors are compared with the empirically extracted ones. It is shown that the overlap functions obtained within the Jastrow correlation method are applicable to the description of the quantities considered. (author)
Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic
2018-05-01
We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance g-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute g-tensors for the TiF3 and CuCl42 - complexes, a [2Fe-2S] model of the active center of ferredoxins, and a Mn4CaO5 model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining g-tensors in multireference calculations with a large number of open shells.
Prucker, V.; Bockstedte, M.; Thoss, M.; Coto, P. B.
2018-03-01
A single-particle density matrix approach is introduced to simulate the dynamics of heterogeneous electron transfer (ET) processes at interfaces. The characterization of the systems is based on a model Hamiltonian parametrized by electronic structure calculations and a partitioning method. The method is applied to investigate ET in a series of nitrile-substituted (poly)(p-phenylene)thiolate self-assembled monolayers adsorbed at the Au(111) surface. The results show a significant dependence of the ET on the orbital symmetry of the donor state and on the molecular and electronic structure of the spacer.
Prucker, V; Bockstedte, M; Thoss, M; Coto, P B
2018-03-28
A single-particle density matrix approach is introduced to simulate the dynamics of heterogeneous electron transfer (ET) processes at interfaces. The characterization of the systems is based on a model Hamiltonian parametrized by electronic structure calculations and a partitioning method. The method is applied to investigate ET in a series of nitrile-substituted (poly)(p-phenylene)thiolate self-assembled monolayers adsorbed at the Au(111) surface. The results show a significant dependence of the ET on the orbital symmetry of the donor state and on the molecular and electronic structure of the spacer.
Off-diagonal helicity density matrix elements for vector mesons produced in polarized e+e- processes
International Nuclear Information System (INIS)
Anselmino, M.; Murgia, F.; Quintairos, P.
1999-04-01
Final state q q-bar interactions give origin to non zero values of the off-diagonal element ρ 1,-1 of the helicity density matrix of vector mesons produced in e + e - annihilations, as confirmed by recent OPAL data on φ, D * and K * 's. New predictions are given for ρ 1,-1 of several mesons produced at large x E and small p T - i.e. collinear with the parent jet - in the annihilation of polarized 3 + and 3 - , the results depend strongly on the elementary dynamics and allow further non trivial tests of the standard model. (author)
Density induced phase transitions in the Schwinger model. A study with matrix product states
Energy Technology Data Exchange (ETDEWEB)
Banuls, Mari Carmen; Cirac, J. Ignacio; Kuehn, Stefan [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2017-02-15
We numerically study the zero temperature phase structure of the multiflavor Schwinger model at nonzero chemical potential. Using matrix product states, we reproduce analytical results for the phase structure for two flavors in the massless case and extend the computation to the massive case, where no analytical predictions are available. Our calculations allow us to locate phase transitions in the mass-chemical potential plane with great precision and provide a concrete example of tensor networks overcoming the sign problem in a lattice gauge theory calculation.
Raychaudhuri equation in the self-consistent Einstein-Cartan theory with spin-density
Fennelly, A. J.; Krisch, Jean P.; Ray, John R.; Smalley, Larry L.
1988-01-01
The physical implications of the Raychaudhuri equation for a spinning fluid in a Riemann-Cartan spacetime is developed and discussed using the self-consistent Lagrangian based formulation for the Einstein-Cartan theory. It was found that the spin-squared terms contribute to expansion (inflation) at early times and may lead to a bounce in the final collapse. The relationship between the fluid's vorticity and spin angular velocity is clarified and the effect of the interaction terms between the spin angular velocity and the spin in the Raychaudhuri equation investigated. These results should prove useful for studies of systems with an intrinsic spin angular momentum in extreme astrophysical or cosmological problems.
Density matrix of a quantum field in a particle-creating background
International Nuclear Information System (INIS)
Gavrilov, S.P.; Gitman, D.M.; Tomazelli, J.L.
2008-01-01
We examine the time evolution of a quantized field in external backgrounds that violate the stability of vacuum (particle-creating backgrounds). Our purpose is to study the exact form of the final quantum state (the density operator at the final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of evolution. We find a generating functional that allows one to obtain density operators for an arbitrary initial state. Averaging over states of the subsystem of antiparticles (particles), we obtain explicit forms of reduced density operators for the subsystem of particles (antiparticles). Analyzing one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g., gluons) in the initial state increases the creation rate of the same type of bosons. We discuss the question (and its relation to the initial stage of quark-gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not in thermal equilibrium. In this respect, we discuss some cases when pair-creation by an electric-like field can mimic the one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we analyze the time and temperature behavior of the mean numbers of created particles, provided that the effects of switching the external field on and off are negligible. It is demonstrated that at high temperatures and in slowly varying electric fields the rate of particle-creation is essentially time-dependent
Density matrix of a quantum field in a particle-creating background
Energy Technology Data Exchange (ETDEWEB)
Gavrilov, S.P. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05315-970 Sao Paulo, SP (Brazil)], E-mail: gavrilovsergeyp@yahoo.com; Gitman, D.M. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05315-970 Sao Paulo, SP (Brazil)], E-mail: gitman@dfn.if.usp.br; Tomazelli, J.L. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05315-970 Sao Paulo, SP (Brazil)], E-mail: tomazelli@fsc.ufsc.br
2008-06-01
We examine the time evolution of a quantized field in external backgrounds that violate the stability of vacuum (particle-creating backgrounds). Our purpose is to study the exact form of the final quantum state (the density operator at the final instant of time) that has emerged from a given arbitrary initial state (from a given arbitrary density operator at the initial time instant) in the course of evolution. We find a generating functional that allows one to obtain density operators for an arbitrary initial state. Averaging over states of the subsystem of antiparticles (particles), we obtain explicit forms of reduced density operators for the subsystem of particles (antiparticles). Analyzing one-particle correlation functions, we establish a one-to-one correspondence between these functions and the reduced density operators. It is shown that in the general case a presence of bosons (e.g., gluons) in the initial state increases the creation rate of the same type of bosons. We discuss the question (and its relation to the initial stage of quark-gluon plasma formation) whether a thermal form of one-particle distribution can appear even if the final state of the complete system is not in thermal equilibrium. In this respect, we discuss some cases when pair-creation by an electric-like field can mimic the one-particle thermal distribution. We apply our technics to some QFT problems in slowly varying electric-like backgrounds: electric, SU(3) chromoelectric, and metric. In particular, we analyze the time and temperature behavior of the mean numbers of created particles, provided that the effects of switching the external field on and off are negligible. It is demonstrated that at high temperatures and in slowly varying electric fields the rate of particle-creation is essentially time-dependent.
International Nuclear Information System (INIS)
March, N.H.
2002-08-01
In early work, Dawson and March [J. Chem. Phys. 81, 5850 (1984)] proposed a local energy method for treating both Hartree-Fock and correlated electron theory. Here, an exactly solvable model two-electron atom with pure harmonic interactions is treated in its ground state in the above context. A functional relation between the kinetic energy density t(r) at the origin r=0 and the electron density p(r) at the same point then emerges. The same approach is applied to the Hookean atom; in which the two electrons repel with Coulombic energy e 2 /r 12 , with r 12 the interelectronic separation, but are still harmonically confined. Again the kinetic energy density t(r) is the focal point, but now generalization away from r=0 is also effected. Finally, brief comments are added about He-like atomic ions in the limit of large atomic number. (author)
Analytical solution for the mode conversion equations with steep exponential density profiles
International Nuclear Information System (INIS)
Alava, M.J.; Heikkinen, J.A.
1992-01-01
A general analytical solution for the converted power from the fast magnetosonic wave to an ion Bernstein wave in a magnetized plasma with an exponential steeply increasing density profile is given in the closed form. The solution covers both the conversion at the lower-hybrid resonance and the conversion through the density gradient for small parallel wave numbers. As an application, the conversion coefficients at the scrape-off layer plasma are estimated in the context of ion cyclotron heating of a tokamak plasma
International Nuclear Information System (INIS)
Chen, Xin
2014-01-01
Understanding the roles of the temporary and spatial structures of quantum functional noise in open multilevel quantum molecular systems attracts a lot of theoretical interests. I want to establish a rigorous and general framework for functional quantum noises from the constructive and computational perspectives, i.e., how to generate the random trajectories to reproduce the kernel and path ordering of the influence functional with effective Monte Carlo methods for arbitrary spectral densities. This construction approach aims to unify the existing stochastic models to rigorously describe the temporary and spatial structure of Gaussian quantum noises. In this paper, I review the Euclidean imaginary time influence functional and propose the stochastic matrix multiplication scheme to calculate reduced equilibrium density matrices (REDM). In addition, I review and discuss the Feynman-Vernon influence functional according to the Gaussian quadratic integral, particularly its imaginary part which is critical to the rigorous description of the quantum detailed balance. As a result, I establish the conditions under which the influence functional can be interpreted as the average of exponential functional operator over real-valued Gaussian processes for open multilevel quantum systems. I also show the difference between the local and nonlocal phonons within this framework. With the stochastic matrix multiplication scheme, I compare the normalized REDM with the Boltzmann equilibrium distribution for open multilevel quantum systems
Theophilou, Iris; Lathiotakis, Nektarios N; Helbig, Nicole
2018-03-21
We investigate the structure of the one-body reduced density matrix of three electron systems, i.e., doublet and quadruplet spin configurations, corresponding to the smallest interacting system with an open-shell ground state. To this end, we use configuration interaction (CI) expansions of the exact wave function in Slater determinants built from natural orbitals in a finite dimensional Hilbert space. With the exception of maximally polarized systems, the natural orbitals of spin eigenstates are generally spin dependent, i.e., the spatial parts of the up and down natural orbitals form two different sets. A measure to quantify this spin dependence is introduced and it is shown that it varies by several orders of magnitude depending on the system. We also study the ordering issue of the spin-dependent occupation numbers which has practical implications in reduced density matrix functional theory minimization schemes, when generalized Pauli constraints (GPCs) are imposed and in the form of the CI expansion in terms of the natural orbitals. Finally, we discuss the aforementioned CI expansion when there are GPCs that are almost "pinned."
Theophilou, Iris; Lathiotakis, Nektarios N.; Helbig, Nicole
2018-03-01
We investigate the structure of the one-body reduced density matrix of three electron systems, i.e., doublet and quadruplet spin configurations, corresponding to the smallest interacting system with an open-shell ground state. To this end, we use configuration interaction (CI) expansions of the exact wave function in Slater determinants built from natural orbitals in a finite dimensional Hilbert space. With the exception of maximally polarized systems, the natural orbitals of spin eigenstates are generally spin dependent, i.e., the spatial parts of the up and down natural orbitals form two different sets. A measure to quantify this spin dependence is introduced and it is shown that it varies by several orders of magnitude depending on the system. We also study the ordering issue of the spin-dependent occupation numbers which has practical implications in reduced density matrix functional theory minimization schemes, when generalized Pauli constraints (GPCs) are imposed and in the form of the CI expansion in terms of the natural orbitals. Finally, we discuss the aforementioned CI expansion when there are GPCs that are almost "pinned."
International Nuclear Information System (INIS)
An, Hongli; Yuen, Manwai
2014-01-01
In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic symmetry for the Navier-Stokes model wherein the velocity components are governed by a generalized Emden dynamical system. In particular, when the viscosity variables are taken the same as Yuen [M. W. Yuen, “Analytical solutions to the Navier-Stokes equations,” J. Math. Phys. 49, 113102 (2008)], our solutions constitute a generalization of that obtained by Yuen. Interestingly, numerical simulations show that the analytical solutions can be used to explain the drifting phenomena of the propagation wave like Tsunamis in oceans
International Nuclear Information System (INIS)
Rabei, Eqab M.; Al-Jamel, A.; Widyan, H.; Baleanu, D.
2014-01-01
In a recent paper, Jaradat et al. [J. Math. Phys. 53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final results are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr. 72, 119 (2005)
Spin alignment and density matrix measurement in 28Si + 12C orbiting reaction
International Nuclear Information System (INIS)
Ray, A.; Shapira, D.; Halbert, M.L.; Gomez del Campo, J.; Kim, H.J.; Sullivan, J.P.; Shivakumar, B.; Mitchell, J.
1990-01-01
Gamma-ray angular correlations have been measured for the strongly damped reactions 12 C( 28 Si, 12 C) 28 Si between θ cm = (120 degree - 160 degree) for E cm = 43.5 and 48 MeV. We find that the density matrices for the 12 C(2 1 + ) and 28 Si states are almost diagonal with respect to the direction of motion of the outgoing particle. The measured density matrices and spin alignments are consistent with the picture of formation of a long-lived dinuclear complex undergoing orbiting, bending and wriggling motions, but not with those obtained from statistical compound nucleus or sticking model calculations. 17 refs., 2 figs., 1 tab
Shotorban, Babak
2010-04-01
The dynamic least-squares kernel density (LSQKD) model [C. Pantano and B. Shotorban, Phys. Rev. E 76, 066705 (2007)] is used to solve the Fokker-Planck equations. In this model the probability density function (PDF) is approximated by a linear combination of basis functions with unknown parameters whose governing equations are determined by a global least-squares approximation of the PDF in the phase space. In this work basis functions are set to be Gaussian for which the mean, variance, and covariances are governed by a set of partial differential equations (PDEs) or ordinary differential equations (ODEs) depending on what phase-space variables are approximated by Gaussian functions. Three sample problems of univariate double-well potential, bivariate bistable neurodynamical system [G. Deco and D. Martí, Phys. Rev. E 75, 031913 (2007)], and bivariate Brownian particles in a nonuniform gas are studied. The LSQKD is verified for these problems as its results are compared against the results of the method of characteristics in nondiffusive cases and the stochastic particle method in diffusive cases. For the double-well potential problem it is observed that for low to moderate diffusivity the dynamic LSQKD well predicts the stationary PDF for which there is an exact solution. A similar observation is made for the bistable neurodynamical system. In both these problems least-squares approximation is made on all phase-space variables resulting in a set of ODEs with time as the independent variable for the Gaussian function parameters. In the problem of Brownian particles in a nonuniform gas, this approximation is made only for the particle velocity variable leading to a set of PDEs with time and particle position as independent variables. Solving these PDEs, a very good performance by LSQKD is observed for a wide range of diffusivities.
Energy Technology Data Exchange (ETDEWEB)
Yunoki, Shunji [Life Science Group, Tokyo Metropolitan Industrial Technology Research Institute, 2-11-1 Fukasawa, Setagaya-ku, Tokyo 158-0081 (Japan); Sugiura, Hiroaki; Kondo, Eiji; Yasuda, Kazunori [Department of Sports Medicine and Joint Surgery, Graduate School of Medicine, Hokkaido University, Kita-15 Nishi-7, Sapporo, Hokkaido 060-8638 Japan (Japan); Ikoma, Toshiyuki; Tanaka, Junzo, E-mail: yunoki.shunji@iri-tokyo.jp [Department of Metallurgy and Ceramics Science, 2-12-1-S7-1, Ookayama, Meguro-ku, Tokyo 152-8550 (Japan)
2011-02-15
The aim of this study was to evaluate the effects of increased collagen-matrix density on the mechanical properties and in vivo absorbability of porous hydroxyapatite (HAp)-collagen composites as artificial bone materials. Seven types of porous HAp-collagen composites were prepared from HAp nanocrystals and dense collagen fibrils. Their densities and HAp/collagen weight ratios ranged from 122 to 331 mg cm{sup -3} and from 20/80 to 80/20, respectively. The flexural modulus and strength increased with an increase in density, reaching 2.46 {+-} 0.48 and 0.651 {+-} 0.103 MPa, respectively. The porous composites with a higher collagen-matrix density exhibited much higher mechanical properties at the same densities, suggesting that increasing the collagen-matrix density is an effective way of improving the mechanical properties. It was also suggested that other structural factors in addition to collagen-matrix density are required to achieve bone-like mechanical properties. The in vivo absorbability of the composites was investigated in bone defects of rabbit femurs, demonstrating that the absorption rate decreased with increases in the composite density. An exhaustive increase in density is probably limited by decreases in absorbability as artificial bones.
International Nuclear Information System (INIS)
Yunoki, Shunji; Sugiura, Hiroaki; Kondo, Eiji; Yasuda, Kazunori; Ikoma, Toshiyuki; Tanaka, Junzo
2011-01-01
The aim of this study was to evaluate the effects of increased collagen-matrix density on the mechanical properties and in vivo absorbability of porous hydroxyapatite (HAp)-collagen composites as artificial bone materials. Seven types of porous HAp-collagen composites were prepared from HAp nanocrystals and dense collagen fibrils. Their densities and HAp/collagen weight ratios ranged from 122 to 331 mg cm -3 and from 20/80 to 80/20, respectively. The flexural modulus and strength increased with an increase in density, reaching 2.46 ± 0.48 and 0.651 ± 0.103 MPa, respectively. The porous composites with a higher collagen-matrix density exhibited much higher mechanical properties at the same densities, suggesting that increasing the collagen-matrix density is an effective way of improving the mechanical properties. It was also suggested that other structural factors in addition to collagen-matrix density are required to achieve bone-like mechanical properties. The in vivo absorbability of the composites was investigated in bone defects of rabbit femurs, demonstrating that the absorption rate decreased with increases in the composite density. An exhaustive increase in density is probably limited by decreases in absorbability as artificial bones.
Timm, Matthew J; Matta, Chérif F; Massa, Lou; Huang, Lulu
2014-11-26
Bader's quantum theory of atoms in molecules (QTAIM) and chemical graph theory, merged in the localization-delocalization matrices (LDMs) and the electron-density-weighted connectivity matrices (EDWCM), are shown to benefit in computational speed from the kernel energy method (KEM). The LDM and EDWCM quantum chemical graph matrices of a 66-atom C46H20 hydrogen-terminated armchair graphene nanoribbon, in 14 (2×7) rings of C2v symmetry, are accurately reconstructed from kernel fragments. (This includes the full sets of electron densities at 84 bond critical points and 19 ring critical points, and the full sets of 66 localization and 4290 delocalization indices (LIs and DIs).) The average absolute deviations between KEM and directly calculated atomic electron populations, obtained from the sum of the LIs and half of the DIs of an atom, are 0.0012 ± 0.0018 e(-) (∼0.02 ± 0.03%) for carbon atoms and 0.0007 ± 0.0003 e(-) (∼0.01 ± 0.01%) for hydrogen atoms. The integration errors in the total electron population (296 electrons) are +0.0003 e(-) for the direct calculation (+0.0001%) and +0.0022 e(-) for KEM (+0.0007%). The accuracy of the KEM matrix elements is, thus, probably of the order of magnitude of the combined precision of the electronic structure calculation and the atomic integrations. KEM appears capable of delivering not only the total energies with chemical accuracy (which is well documented) but also local and nonlocal properties accurately, including the DIs between the fragments (crossing fragmentation lines). Matrices of the intact ribbon, the kernels, the KEM-reconstructed ribbon, and errors are available as Supporting Information .
Hoy, Erik P.; Mazziotti, David A.; Seideman, Tamar
2017-11-01
Can an electronic device be constructed using only a single molecule? Since this question was first asked by Aviram and Ratner in the 1970s [Chem. Phys. Lett. 29, 277 (1974)], the field of molecular electronics has exploded with significant experimental advancements in the understanding of the charge transport properties of single molecule devices. Efforts to explain the results of these experiments and identify promising new candidate molecules for molecular devices have led to the development of numerous new theoretical methods including the current standard theoretical approach for studying single molecule charge transport, i.e., the non-equilibrium Green's function formalism (NEGF). By pairing this formalism with density functional theory (DFT), a wide variety of transport problems in molecular junctions have been successfully treated. For some systems though, the conductance and current-voltage curves predicted by common DFT functionals can be several orders of magnitude above experimental results. In addition, since density functional theory relies on approximations to the exact exchange-correlation functional, the predicted transport properties can show significant variation depending on the functional chosen. As a first step to addressing this issue, the authors have replaced density functional theory in the NEGF formalism with a 2-electron reduced density matrix (2-RDM) method, creating a new approach known as the NEGF-RDM method. 2-RDM methods provide a more accurate description of electron correlation compared to density functional theory, and they have lower computational scaling compared to wavefunction based methods of similar accuracy. Additionally, 2-RDM methods are capable of capturing static electron correlation which is untreatable by existing NEGF-DFT methods. When studying dithiol alkane chains and dithiol benzene in model junctions, the authors found that the NEGF-RDM predicts conductances and currents that are 1-2 orders of magnitude below
International Nuclear Information System (INIS)
Fukuda, Ikuo; Nakamura, Haruki
2010-01-01
Several molecular dynamics techniques applying the Tsallis generalized distribution are presented. We have developed a deterministic dynamics to generate an arbitrary smooth density function ρ. It creates a measure-preserving flow with respect to the measure ρdω and realizes the density ρ under the assumption of the ergodicity. It can thus be used to investigate physical systems that obey such distribution density. Using this technique, the Tsallis distribution density based on a full energy function form along with the Tsallis index q ≥ 1 can be created. From the fact that an effective support of the Tsallis distribution in the phase space is broad, compared with that of the conventional Boltzmann-Gibbs (BG) distribution, and the fact that the corresponding energy-surface deformation does not change energy minimum points, the dynamics enhances the physical state sampling, in particular for a rugged energy surface spanned by a complicated system. Other feature of the Tsallis distribution is that it provides more degree of the nonlinearity, compared with the case of the BG distribution, in the deterministic dynamics equation, which is very useful to effectively gain the ergodicity of the dynamical system constructed according to the scheme. Combining such methods with the reconstruction technique of the BG distribution, we can obtain the information consistent with the BG ensemble and create the corresponding free energy surface. We demonstrate several sampling results obtained from the systems typical for benchmark tests in MD and from biomolecular systems.
Equation of state of fluid helium at high temperatures and densities
Cai, Lingcang; Chen, Qifeng; Gu, Yunjun; Zhang, Ying; Zhou, Xianming; Jing, Fuqian
2005-03-01
Hugoniot curves and shock temperatures of gas helium with initial temperature 293 K and three initial pressures 0.6, 1.2, and 5.0 MPa were measured up to 15000 K using a two-stage light-gas gun and transient radiation pyrometer. It was found that the calculated Hugoniot EOS of gas helium at the same initial pressure using Saha equation with Debye-Hückel correction was in good agreement with the experimental data. The curve of the calculated shock wave velocity with the particle velocity of gas helium which is shocked from the initial pressure 5 MPa and temperature 293 K, i.e., the D ≈ u relation, D= C 0+λ u ( uionization degree of the shocked gas helium reaches 10-3.
Progress on Complex Langevin simulations of a finite density matrix model for QCD
Energy Technology Data Exchange (ETDEWEB)
Bloch, Jacques [Univ. of Regensburg (Germany). Inst. for Theorectical Physics; Glesaan, Jonas [Swansea Univ., Swansea U.K.; Verbaarschot, Jacobus [Stony Brook Univ., NY (United States). Dept. of Physics and Astronomy; Zafeiropoulos, Savvas [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); College of William and Mary, Williamsburg, VA (United States); Heidelberg Univ. (Germany). Inst. for Theoretische Physik
2018-04-01
We study the Stephanov model, which is an RMT model for QCD at finite density, using the Complex Langevin algorithm. Naive implementation of the algorithm shows convergence towards the phase quenched or quenched theory rather than to intended theory with dynamical quarks. A detailed analysis of this issue and a potential resolution of the failure of this algorithm are discussed. We study the effect of gauge cooling on the Dirac eigenvalue distribution and time evolution of the norm for various cooling norms, which were specifically designed to remove the pathologies of the complex Langevin evolution. The cooling is further supplemented with a shifted representation for the random matrices. Unfortunately, none of these modifications generate a substantial improvement on the complex Langevin evolution and the final results still do not agree with the analytical predictions.
International Nuclear Information System (INIS)
Giambiagi, M.S. de; Giambiagi, M.
1982-01-01
Direct PPP-type calculations of self-consistent (SC) density matrices for excited states are described and the corresponding 'thawn' molecular orbitals (MO) are discussed. Special attention is addressed to particular solutions arising in conjugated systems of a certain symmetry, and to their chemical implications. The U(2) and U(3) algebras are applied respectively to the 4-electron and 6-electron cases: a natural separation of excited states in different cases follows. A simple approach to the convergence problem for excited states is given. The complementarity relations, an alternative formulation of the pairing theorem valid for heteromolecules and non-alternant systems, allow some fruitful experimental applications. Together with the extended pairing relations shown here, they may help to rationalize general trends. (Author) [pt
Density equation of bio-coal briquettes and quantity of maize cob in Phitsanulok, Thailand
Energy Technology Data Exchange (ETDEWEB)
Patomsok Wilaipon [Naresuan University, Phitsanulok (Thailand). Department of Mechanical Engineering
2008-07-01
One of the most important crops in Phitsanulok, a province in Northern Thailand, is maize. BaseD on the calculation, the quantity of maize cob produced in this region was approximately 220 kton year{sup -1}. The net heating value of maize cob was found to be 14.2 MJ kg{sup -1}. Therefore, the total energy over 874 TJ year-1 can be obtained from this agricultural waste. In the experiments, maize cob was utilized as the major ingredient for producing biomass-coal briquettes. The maize cob was treated with sodium hydroxide solution before mixing with coal fine. The ratios of coal:maize were 1:2 and 1:3, respectively. The range of briquetting pressures was from 4-8 MPa. The result showed that the density was strongly affected by both parameters. Finally, the relationship between biomass ratio, briquetting pressures and briquette density was developed and validated by using regression technique. 13 refs., 2 figs.
International Nuclear Information System (INIS)
Jeffcoat, David B.; DePrince, A. Eugene
2014-01-01
Propagating the equations of motion (EOM) for the one-electron reduced-density matrix (1-RDM) requires knowledge of the corresponding two-electron RDM (2-RDM). We show that the indeterminacy of this expression can be removed through a constrained optimization that resembles the variational optimization of the ground-state 2-RDM subject to a set of known N-representability conditions. Electronic excitation energies can then be obtained by propagating the EOM for the 1-RDM and following the dipole moment after the system interacts with an oscillating external electric field. For simple systems with well-separated excited states whose symmetry differs from that of the ground state, excitation energies obtained from this method are comparable to those obtained from full configuration interaction computations. Although the optimized 2-RDM satisfies necessary N-representability conditions, the procedure cannot guarantee a unique mapping from the 1-RDM to the 2-RDM. This deficiency is evident in the mean-field-quality description of transitions to states of the same symmetry as the ground state, as well as in the inability of the method to describe Rabi oscillations
Jeffcoat, David B.; DePrince, A. Eugene
2014-12-01
Propagating the equations of motion (EOM) for the one-electron reduced-density matrix (1-RDM) requires knowledge of the corresponding two-electron RDM (2-RDM). We show that the indeterminacy of this expression can be removed through a constrained optimization that resembles the variational optimization of the ground-state 2-RDM subject to a set of known N-representability conditions. Electronic excitation energies can then be obtained by propagating the EOM for the 1-RDM and following the dipole moment after the system interacts with an oscillating external electric field. For simple systems with well-separated excited states whose symmetry differs from that of the ground state, excitation energies obtained from this method are comparable to those obtained from full configuration interaction computations. Although the optimized 2-RDM satisfies necessary N-representability conditions, the procedure cannot guarantee a unique mapping from the 1-RDM to the 2-RDM. This deficiency is evident in the mean-field-quality description of transitions to states of the same symmetry as the ground state, as well as in the inability of the method to describe Rabi oscillations.
Nataf, Pierre; Mila, Frédéric
2018-04-01
We develop an efficient method to perform density matrix renormalization group simulations of the SU(N ) Heisenberg chain with open boundary conditions taking full advantage of the SU(N ) symmetry of the problem. This method is an extension of the method previously developed for exact diagonalizations and relies on a systematic use of the basis of standard Young tableaux. Concentrating on the model with the fundamental representation at each site (i.e., one particle per site in the fermionic formulation), we have benchmarked our results for the ground-state energy up to N =8 and up to 420 sites by comparing them with Bethe ansatz results on open chains, for which we have derived and solved the Bethe ansatz equations. The agreement for the ground-state energy is excellent for SU(3) (12 digits). It decreases with N , but it is still satisfactory for N =8 (six digits). Central charges c are also extracted from the entanglement entropy using the Calabrese-Cardy formula and agree with the theoretical values expected from the SU (N) 1 Wess-Zumino-Witten conformal field theories.
Kanharat, Nongnuch; Tuamsuk, Panya
2015-01-01
Prostate cancer is a major concern of public health. Microvascular density (MVD) is one of the prognostic markers for various solid cancers. Matrix metalloproteinase 11 (MMP11) plays an important role in angiogenesis and changes in its expression level are known to be associated with tumor progression and clinical outcome. To investigate the relationship between MVD and MMP11 expression in prostatic adenocarcinoma tissues. The expression levels of MMP11 and MVD were analyzed immunohistochemically for 50 specimens of prostatic adenocarcinoma. MMP11 was mainly expressed in stromal cells but rarely seen in epithelial cells. Mean MVD was 36/mm2, and it was correlated significantly only with bone metastases. MVD was also significantly correlated with MMP11 expression (r=0.29, p=0.044). MMP11 may alter the stromal microenvironment of prostate cancer to stimulate tumor angiogenesis.
Energy Technology Data Exchange (ETDEWEB)
Biplab Dey, Michael E. McCracken, David G. Ireland, Curtis A. Meyer
2011-05-01
The complete expression for the intensity in pseudo-scalar meson photoproduction with a polarized beam, target, and recoil baryon is derived using a density matrix approach that offers great economy of notation. A Cartesian basis with spins for all particles quantized along a single direction, the longitudinal beam direction, is used for consistency and clarity in interpretation. A single spin-quantization axis for all particles enables the amplitudes to be written in a manifestly covariant fashion with simple relations to those of the well-known CGLN formalism. Possible sign discrepancies between theoretical amplitude-level expressions and experimentally measurable intensity profiles are dealt with carefully. Our motivation is to provide a coherent framework for coupled-channel partial-wave analysis of several meson photoproduction reactions, incorporating recently published and forthcoming polarization data from Jefferson Lab.
International Nuclear Information System (INIS)
SivaRanjan, Uppala; Ramachandran, Ramesh
2014-01-01
A quantum-mechanical model integrating the concepts of reduced density matrix and effective Hamiltonians is proposed to explain the multi-spin effects observed in rotational resonance (R 2 ) nuclear magnetic resonance (NMR) experiments. Employing this approach, the spin system of interest is described in a reduced subspace inclusive of its coupling to the surroundings. Through suitable model systems, the utility of our theory is demonstrated and verified with simulations emerging from both analytic and numerical methods. The analytic results presented in this article provide an accurate description/interpretation of R 2 experimental results and could serve as a test-bed for distinguishing coherent/incoherent effects in solid-state NMR
Energy Technology Data Exchange (ETDEWEB)
Schmidt, David; Engel, Ralph; Roth, Markus [Karlsruhe Institute of Technology, Karlsruhe (Germany); Collaboration: Pierre Auger-Collaboration
2015-07-01
Event-by-event identification of cosmic ray primary composition lends itself to enhanced event selection in the search for anisotropic arrival directions. Principally, the number of muons reaching Earth's surface in an extensive air shower is indicative of composition. The Pierre Auger Observatory seeks to capitalize on this axiom by improving reconstructed muonic density estimates via an upgrade to its surface detector array. This upgrade, consisting of placing a scintillator on top of each existing water Cherenkov detector, exploits the differing response of two detectors to muonic and electromagnetic particles. Exploitation of this difference may be expressed in a matrix formalism whose application to simulated proton and iron showers is presented here.
Energy Technology Data Exchange (ETDEWEB)
SivaRanjan, Uppala; Ramachandran, Ramesh, E-mail: rramesh@iisermohali.ac.in [Department of Chemical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, Manauli, P.O. Box-140306, Mohali, Punjab (India)
2014-02-07
A quantum-mechanical model integrating the concepts of reduced density matrix and effective Hamiltonians is proposed to explain the multi-spin effects observed in rotational resonance (R{sup 2}) nuclear magnetic resonance (NMR) experiments. Employing this approach, the spin system of interest is described in a reduced subspace inclusive of its coupling to the surroundings. Through suitable model systems, the utility of our theory is demonstrated and verified with simulations emerging from both analytic and numerical methods. The analytic results presented in this article provide an accurate description/interpretation of R{sup 2} experimental results and could serve as a test-bed for distinguishing coherent/incoherent effects in solid-state NMR.
Shenvi, Neil; van Aggelen, Helen; Yang, Yang; Yang, Weitao; Schwerdtfeger, Christine; Mazziotti, David
2013-08-07
Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r(4)), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the standard p2RDM algorithm, somewhere between that of CCSD and CCSD(T).
Bischoff, Jan-Moritz; Jeckelmann, Eric
2017-11-01
We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems. The dynamical DMRG is used to compute the linear response of a finite system to an applied ac source-drain voltage; then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the dc conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in a homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.
International Nuclear Information System (INIS)
Smeyers, Y.G.; Delgado-Barrio, G.
1976-01-01
The half-projected Hartree--Fock function for singlet states (HPHF) is analyzed in terms of natural electronic configurations. For this purpose the HPHF spinless density matrix and its natural orbitals are first deduced. It is found that the HPHF function does not contain any contribution from odd-times excited configurations. It is seen in addition, in the case of the singlet ground states, this function is approximately equivalent to two closed-shell configurations, although the nature of the excited one depends on the nuclear geometry. An example is given in the case of the LiH ground state. Finally, the application of this model for studying systems of more than two atoms is criticized
Kumar, Manoranjan
2016-02-03
An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N=3n+1≈500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with NA≠NB. The ground state (GS) and spin densities ρr=⟨Szr⟩ at site r are quite different for junctions with S=1/2, 1, 3/2, and 2. The GS has finite total spin SG=2S(S) for even (odd) N and for MG=SG in the SG spin manifold, ρr>0(<0) at sites of the larger (smaller) sublattice. S=1/2 junctions have delocalized states and decreasing spin densities with increasing N. S=1 junctions have four localized Sz=1/2 states at the end of each arm and centered on the junction, consistent with localized states in S=1 chains with finite Haldane gap. The GS of S=3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S=1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S=3/2 or 2 junctions.
Kumar, Manoranjan; Parvej, Aslam; Thomas, Simil; Ramasesha, S.; Soos, Z. G.
2016-01-01
An efficient density matrix renormalization group (DMRG) algorithm is presented and applied to Y junctions, systems with three arms of n sites that meet at a central site. The accuracy is comparable to DMRG of chains. As in chains, new sites are always bonded to the most recently added sites and the superblock Hamiltonian contains only new or once renormalized operators. Junctions of up to N=3n+1≈500 sites are studied with antiferromagnetic (AF) Heisenberg exchange J between nearest-neighbor spins S or electron transfer t between nearest neighbors in half-filled Hubbard models. Exchange or electron transfer is exclusively between sites in two sublattices with NA≠NB. The ground state (GS) and spin densities ρr=⟨Szr⟩ at site r are quite different for junctions with S=1/2, 1, 3/2, and 2. The GS has finite total spin SG=2S(S) for even (odd) N and for MG=SG in the SG spin manifold, ρr>0(<0) at sites of the larger (smaller) sublattice. S=1/2 junctions have delocalized states and decreasing spin densities with increasing N. S=1 junctions have four localized Sz=1/2 states at the end of each arm and centered on the junction, consistent with localized states in S=1 chains with finite Haldane gap. The GS of S=3/2 or 2 junctions of up to 500 spins is a spin density wave with increased amplitude at the ends of arms or near the junction. Quantum fluctuations completely suppress AF order in S=1/2 or 1 junctions, as well as in half-filled Hubbard junctions, but reduce rather than suppress AF order in S=3/2 or 2 junctions.
Rothman, Adam E.; Mazziotti, David A.
2010-03-01
We study molecular conductivity for a one-electron, bath-molecule-bath model Hamiltonian. The primary quantum-mechanical variable is the one-electron reduced density matrix (1-RDM). By identifying similarities between the steady-state Liouville equation and the anti-Hermitian contracted Schrödinger equation (ACSE) [D. A. Mazziotti, Phys. Rev. A 75, 022505 (2007)], we develop a way of enforcing nonequilibrium, steady-state behavior in a time-independent theory. Our results illustrate the relationship between current and voltage in molecular junctions assuming that the total number of electrons under consideration can be fixed across all driving potentials. The impetus for this work is a recent study by Subotnik et al. that also uses the 1-RDM to study molecular conductivity under different assumptions regarding the total number of electrons [J. E. Subotnik et al., J. Chem. Phys. 130, 144105 (2009)]. Unlike calculations in the previous study, our calculations result in 1-RDMs that are fully N-representable. The present work maintains N-representability through a bath-bath mixing that is related to a time-independent relaxation of the baths in the absence of the molecule, as governed by the ACSE. A lack of N-representability can be important since it corresponds to occupying energy states in the molecule or baths with more than one electron or hole (the absence of an electron) in violation of the Pauli principle. For this reason the present work may serve as an important, albeit preliminary, step in designing a 2-RDM/ACSE method for studying steady-state molecular conductivity with an explicit treatment of electron correlation.
International Nuclear Information System (INIS)
Ryder, E.E.
1992-08-01
Historical and projected inventories of spent fuel from commercial light-water nuclear reactors exhibit diverse decay characteristics and ages. This report summarizes a preliminary reexamination of a method for determining equivalent thermal loads for the range of spent fuel expected at a potential underground repository. The method, known at the Equivalent Energy Density (EED) concept, bases its equivalence criteria on the assumption that a given waste will produce worst-case thermomechanical effects equal to worst-case thermomechanical effects produced by a baseline waste, provided that the thermal energy deposited in the host rock over a specified deposition period is the same for both waste descriptions. To test this assumption, temperature histories at representative locations within the host rock were calculated using layouts defined by the EED concept and four deposition periods (20, 50, 100, and 300 years). It was found that the peak temperatures at near-field locations were best matched by the shorter deposition periods of 20 and 50 years. However, due to the sensitivity of the near-field environment to short-term canister-to-canister interactions, caution,should be used when choosing a near-field deposition period. At the location chosen to represent the far-field, a 300-year deposition period provided reasonable correspondence of peak temperature responses for all waste descriptions examined
Institute of Scientific and Technical Information of China (English)
周彬; 段广仁
2006-01-01
A complete, general and explicit solution to the generalized Sylvester matrix equation AX-XF = BY, with F being an arbitrary square matrix, is investigated. The proposed solution is in an extremely neat form represented by a controllability matrix of the matrix pair (A,B), a symmetric operator and an observability matrix of the matrix pair (Z,F), where Z is an arbitrary matrix used to denote the degree of freedom in the solution. Furthermore, based on the Faddeev - Leverrier algorithm, an equivalent form of the proposed solution is established. At the same time, an equivalent form of the solutions proposed in [ 13 ] is also induced. These results provide great convenience to the analysis and design problems in control systems. The results proposed in this note is a further discussion of the results proposed in [ 13 ].%给出了广义Sylvester矩阵方程AX-XF=BY当F为任意矩阵时的一种完全的解析通解.该通解由矩阵对(A,B)构成的能控性矩阵,一个对称算子矩阵和矩阵对(Z,F)构成的能观性矩阵组成,这里Z是一个任意的参数矩阵,用来表征该方程的解的自由度.利用著名的Levverrier算法,该解析解的一个等价形式被给出.给出的结果是参考文献[13]的推广,在[13]中F被假设为友矩阵.
Murphy, E; FitzGerald, O; Saxne, T; Bresnihan, B
2002-11-01
Chondromalacia patellae is a potentially disabling disorder characterised by features of patellar cartilage degradation. To evaluate markers of cartilage and bone turnover in patients with chondromalacia patellae. 18 patients with chondromalacia patellae were studied. Serum cartilage oligomeric matrix protein (s-COMP) and bone sialoprotein (s-BSP) levels were measured by enzyme linked immunosorbent assay (ELISA) and compared with those of age and sex matched healthy control subjects. Periarticular bone mineral density (BMD) of both knee joints was assessed by dual energy x ray absorptiometry (DXA). s-COMP levels were significantly raised in all patients with chondromalacia patellae compared with healthy control subjects (p=0.0001). s-BSP levels did not differ significantly between the groups (p=0.41). BMD of the patella was significantly reduced in patients with chondromalacia patellae compared with the control subjects (p=0.016). In patients with bilateral chondromalacia patellae, BMD of the patella was lower in the more symptomatic knee joint (p=0.005). Changes in periarticular BMD were localised to the patella and were not present in femoral regions. Neither s-COMP (p=0.18) nor s-BSP (p=0.40) levels correlated with patellar BMD. Increased s-COMP levels, reflecting cartilage degradation, and reduced BMD localised to the patella may represent clinically useful markers in the diagnosis and monitoring of patients with chondromalacia patellae. Measures of cartilage degradation did not correlate with loss of patellar bone density, suggesting dissociated pathophysiological mechanisms.
International Nuclear Information System (INIS)
Leal A, B.; Mireles G, F.; Quirino T, L.; Pinedo, J.L.
2005-01-01
In the area of the Radiological Safety it is required of a calibrated detection system in energy and efficiency for the determination of the concentration in activity in samples that vary in chemical composition and by this in density. The area of Nuclear Engineering requires to find the grade of isotopic enrichment of the uranium of the Sub-critic Nuclear Chicago 9000 Mark. Given the experimental importance that has the determination from the curves of efficiency to the effects of establishing the quantitative results, is appealed to the simulation of the response function of the detector used in the Regional Center of Nuclear Studies inside the range of energy of 80 keV to 1400 keV varying the density of the matrix and the chemical composition by means of the application of the Monte Carlo code MCNP-4A. The obtained results in the simulation of the response function of the detector show a grade of acceptance in the range from 500 to 1400 keV energy, with a smaller percentage discrepancy to 10%, in the range of low energy that its go from 59 to 400 keV, the percentage discrepancy varies from 17% until 30%, which is manifested in the opposing isotopic relationship for 5 fuel rods of the Sub critic nuclear assemble. (Author)
Jensen, Kevin L.; Finkenstadt, Daniel; Shabaev, Andrew; Lambrakos, Samuel G.; Moody, Nathan A.; Petillo, John J.; Yamaguchi, Hisato; Liu, Fangze
2018-01-01
Recent experimental measurements of a bulk material covered with a small number of graphene layers reported by Yamaguchi et al. [NPJ 2D Mater. Appl. 1, 12 (2017)] (on bialkali) and Liu et al. [Appl. Phys. Lett. 110, 041607 (2017)] (on copper) and the needs of emission models in beam optics codes have lead to substantial changes in a Moments model of photoemission. The changes account for (i) a barrier profile and density of states factor based on density functional theory (DFT) evaluations, (ii) a Drude-Lorentz model of the optical constants and laser penetration depth, and (iii) a transmission probability evaluated by an Airy Transfer Matrix Approach. Importantly, the DFT results lead to a surface barrier profile of a shape similar to both resonant barriers and reflectionless wells: the associated quantum mechanical transmission probabilities are shown to be comparable to those recently required to enable the Moments (and Three Step) model to match experimental data but for reasons very different than the assumption by conventional wisdom that a barrier is responsible. The substantial modifications of the Moments model components, motivated by computational materials methods, are developed. The results prepare the Moments model for use in treating heterostructures and discrete energy level systems (e.g., quantum dots) proposed for decoupling the opposing metrics of performance that undermine the performance of advanced light sources like the x-ray Free Electron Laser. The consequences of the modified components on quantum yield, emittance, and emission models needed by beam optics codes are discussed.
Yan, YiJing
2014-02-07
This work establishes a strongly correlated system-and-bath dynamics theory, the many-dissipaton density operators formalism. It puts forward a quasi-particle picture for environmental influences. This picture unifies the physical descriptions and algebraic treatments on three distinct classes of quantum environments, electron bath, phonon bath, and two-level spin or exciton bath, as their participating in quantum dissipation processes. Dynamical variables for theoretical description are no longer just the reduced density matrix for system, but remarkably also those for quasi-particles of bath. The present theoretical formalism offers efficient and accurate means for the study of steady-state (nonequilibrium and equilibrium) and real-time dynamical properties of both systems and hybridizing environments. It further provides universal evaluations, exact in principle, on various correlation functions, including even those of environmental degrees of freedom in coupling with systems. Induced environmental dynamics could be reflected directly in experimentally measurable quantities, such as Fano resonances and quantum transport current shot noise statistics.
International Nuclear Information System (INIS)
Donolato, C
2005-01-01
A relation between the gradient of the electric field and mean curvature of equipotential surfaces (Green's differential equation) is applied to a two-dimensional free-boundary problem arising in the study of ion sheaths around wedge-shaped cathodes. With the assumption that the equipotential lines are hyperbolae, this relation leads to a nonlinear ordinary differential equation for the potential along the bisector line of the wedge. An approximate solution is found, which yields, in particular, the sheath width along this line as a function of the wedge angle. The resulting values are in good agreement with published results obtained by numerically solving Poisson's equation
Gueddida, Saber; Yan, Zeyin; Kibalin, Iurii; Voufack, Ariste Bolivard; Claiser, Nicolas; Souhassou, Mohamed; Lecomte, Claude; Gillon, Béatrice; Gillet, Jean-Michel
2018-04-28
In this paper, we propose a simple cluster model with limited basis sets to reproduce the unpaired electron distributions in a YTiO 3 ferromagnetic crystal. The spin-resolved one-electron-reduced density matrix is reconstructed simultaneously from theoretical magnetic structure factors and directional magnetic Compton profiles using our joint refinement algorithm. This algorithm is guided by the rescaling of basis functions and the adjustment of the spin population matrix. The resulting spin electron density in both position and momentum spaces from the joint refinement model is in agreement with theoretical and experimental results. Benefits brought from magnetic Compton profiles to the entire spin density matrix are illustrated. We studied the magnetic properties of the YTiO 3 crystal along the Ti-O 1 -Ti bonding. We found that the basis functions are mostly rescaled by means of magnetic Compton profiles, while the molecular occupation numbers are mainly modified by the magnetic structure factors.
Xiong, Yuan
2014-04-28
Spurious current emerging in the vicinity of phase interfaces is a well-known disadvantage of the lattice Boltzmann equation (LBE) for two-phase flows. Previous analysis shows that this unphysical phenomenon comes from the force imbalance at discrete level inherited in LBE (Guo et al 2011 Phys. Rev. E 83 036707). Based on the analysis of the LBE free of checkerboard effects, in this work we further show that the force imbalance is caused by the different discretization stencils: the implicit one from the streaming process and the explicit one from the discretization of the force term. Particularly, the total contribution includes two parts, one from the difference between the intrinsically discretized density (or ideal gas pressure) gradient and the explicit ones in the force term, and the other from the explicit discretized chemical potential gradients in the intrinsically discretized force term. The former contribution is a special feature of LBE which was not realized previously.
Sun, Shuyu; Salama, Amgad; El-Amin, Mohamed
2012-01-01
In this paper we introduce a new technique for the numerical solution of the various partial differential equations governing flow and transport phenomena in porous media. This method is proposed to be used in high level programming languages like
International Nuclear Information System (INIS)
Ridder, Barbara; Foertsch, Tobias C.; Welle, Alexander; Mattes, Daniela S.; Bojnicic-Kninski, Clemens M. von; Loeffler, Felix F.; Nesterov-Mueller, Alexander; Meier, Michael A.R.; Breitling, Frank
2016-01-01
Highlights: • New matrix material for peptide array synthesis from a ‘solid solvent’. • Resolution was increased with possible spot densities of up to 20.000 spots per cm"2. • The coupling depth and the effectiveness of washing steps analyzed by ToF-SIMS. • Adaptations and custom changes of the matrix material are possible. - Abstract: Poly(dimethylacrylamide) (PDMA) based matrix materials were developed for laser-based in situ solid phase peptide synthesis to produce high density arrays. In this specific array synthesis approach, amino acid derivatives are embedded into a matrix material, serving as a “solid” solvent material at room temperature. Then, a laser pulse transfers this mixture to the target position on a synthesis slide, where the peptide array is synthesized. Upon heating above the glass transition temperature of the matrix material, it softens, allowing diffusion of the amino acid derivatives to the synthesis surface and serving as a solvent for peptide bond formation. Here, we synthesized PDMA six-arm star polymers, offering the desired matrix material properties, using atom transfer radical polymerization. With the synthesized polymers as matrix material, we structured and synthesized arrays with combinatorial laser transfer. With densities of up to 20,000 peptide spots per cm"2, the resolution could be increased compared to the commercially available standard matrix material. Time-of-Flight Secondary Ion Mass Spectrometry experiments revealed the penetration behavior of an amino acid derivative into the prepared acceptor synthesis surface and the effectiveness of the washing protocols.
Energy Technology Data Exchange (ETDEWEB)
Ridder, Barbara [Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Institute of Organic Chemistry (IOC), Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76131 Karlsruhe (Germany); Foertsch, Tobias C. [Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Welle, Alexander [Karlsruhe Nano Micro Facility (KNMF), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Mattes, Daniela S. [Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Institute of Organic Chemistry (IOC), Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76131 Karlsruhe (Germany); Bojnicic-Kninski, Clemens M. von; Loeffler, Felix F.; Nesterov-Mueller, Alexander [Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Meier, Michael A.R., E-mail: m.a.r.meier@kit.edu [Institute of Organic Chemistry (IOC), Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 6, 76131 Karlsruhe (Germany); Breitling, Frank, E-mail: frank.breitling@kit.edu [Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany)
2016-12-15
Highlights: • New matrix material for peptide array synthesis from a ‘solid solvent’. • Resolution was increased with possible spot densities of up to 20.000 spots per cm{sup 2}. • The coupling depth and the effectiveness of washing steps analyzed by ToF-SIMS. • Adaptations and custom changes of the matrix material are possible. - Abstract: Poly(dimethylacrylamide) (PDMA) based matrix materials were developed for laser-based in situ solid phase peptide synthesis to produce high density arrays. In this specific array synthesis approach, amino acid derivatives are embedded into a matrix material, serving as a “solid” solvent material at room temperature. Then, a laser pulse transfers this mixture to the target position on a synthesis slide, where the peptide array is synthesized. Upon heating above the glass transition temperature of the matrix material, it softens, allowing diffusion of the amino acid derivatives to the synthesis surface and serving as a solvent for peptide bond formation. Here, we synthesized PDMA six-arm star polymers, offering the desired matrix material properties, using atom transfer radical polymerization. With the synthesized polymers as matrix material, we structured and synthesized arrays with combinatorial laser transfer. With densities of up to 20,000 peptide spots per cm{sup 2}, the resolution could be increased compared to the commercially available standard matrix material. Time-of-Flight Secondary Ion Mass Spectrometry experiments revealed the penetration behavior of an amino acid derivative into the prepared acceptor synthesis surface and the effectiveness of the washing protocols.
Energy Technology Data Exchange (ETDEWEB)
Banik, Sarmistha [BITS Pilani, Hyderabad Campus, Hyderabad-500078 (India); Hempel, Matthias [Departement Physik, Universität Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland); Bandyopadhyay, Debades [Astroparticle Physics and Cosmology Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata-700064 (India)
2014-10-01
We develop new hyperon equation of state (EoS) tables for core-collapse supernova simulations and neutron stars. These EoS tables are based on a density-dependent relativistic hadron field theory where baryon-baryon interaction is mediated by mesons, using the parameter set DD2 for nucleons. Furthermore, light and heavy nuclei along with interacting nucleons are treated in the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich which includes excluded volume effects. Of all possible hyperons, we consider only the contribution of Λs. We have developed two variants of hyperonic EoS tables: in the npΛφ case the repulsive hyperon-hyperon interaction mediated by the strange φ meson is taken into account, and in the npΛ case it is not. The EoS tables for the two cases encompass a wide range of densities (10{sup –12} to ∼1 fm{sup –3}), temperatures (0.1 to 158.48 MeV), and proton fractions (0.01 to 0.60). The effects of Λ hyperons on thermodynamic quantities such as free energy per baryon, pressure, or entropy per baryon are investigated and found to be significant at higher densities. The cold, β-equilibrated EoS (with the crust included self-consistently) results in a 2.1 M {sub ☉} maximum mass neutron star for the npΛφ case, whereas that for the npΛ case is 1.95 M {sub ☉}. The npΛφ EoS represents the first supernova EoS table involving hyperons that is directly compatible with the recently measured 2 M {sub ☉} neutron stars.
Chavez, Gustavo Ivan
2017-07-10
This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic partial differential equations on a Cartesian product mesh, such as the variable-coefficient Poisson equation, the convection-diffusion equation, and the wave Helmholtz equation in heterogeneous media. The algorithm extends the traditional cyclic reduction method with hierarchical matrix techniques. The resulting method exposes substantial concurrency, and its arithmetic operations and memory consumption grow only log-linearly with problem size, assuming bounded rank of off-diagonal matrix blocks, even for problems with arbitrary coefficient structure. The method can be used as a standalone direct solver with tunable accuracy, or as a black-box preconditioner in conjunction with Krylov methods. The challenges that distinguish this work from other thrusts in this active field are the hybrid distributed-shared parallelism that can demonstrate the algorithm at large-scale, full three-dimensionality, and the three stressors of the current state-of-the-art multigrid technology: high wavenumber Helmholtz (indefiniteness), high Reynolds convection (nonsymmetry), and high contrast diffusion (inhomogeneity). Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST\\'s Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption.
Bone Mineral 31P and Matrix-Bound Water Densities Measured by Solid-State 1H and 31P MRI
Seifert, Alan C.; Li, Cheng; Rajapakse, Chamith S.; Bashoor- Zadeh, Mahdieh; Bhagat, Yusuf A.; Wright, Alexander C.; Zemel, Babette S.; Zavaliangos, Antonios; Wehrli, Felix W.
2014-01-01
Bone is a composite material consisting of mineral and hydrated collagen fractions. MRI of bone is challenging due to extremely short transverse relaxation times, but solid-state imaging sequences exist that can acquire the short-lived signal from bone tissue. Previous work to quantify bone density via MRI used powerful experimental scanners. This work seeks to establish the feasibility of MRI-based measurement on clinical scanners of bone mineral and collagen-bound water densities, the latter as a surrogate of matrix density, and to examine the associations of these parameters with porosity and donors’ age. Mineral and matrix-bound water images of reference phantoms and cortical bone from 16 human donors, ages 27-97 years, were acquired by zero-echo-time 31P and 1H MRI on whole body 7T and 3T scanners, respectively. Images were corrected for relaxation and RF inhomogeneity to obtain density maps. Cortical porosity was measured by micro-CT, and apparent mineral density by pQCT. MRI-derived densities were compared to x-ray-based measurements by least-squares regression. Mean bone mineral 31P density was 6.74±1.22 mol/L (corresponding to 1129±204 mg/cc mineral), and mean bound water 1H density was 31.3±4.2 mol/L (corresponding to 28.3±3.7 %v/v). Both 31P and bound water (BW) densities were correlated negatively with porosity (31P: R2 = 0.32, p bone mineralization ratio (expressed here as the ratio of 31P density to bound water density), which is proportional to true bone mineralization, was found to be uncorrelated with porosity, age, or pQCT density. This work establishes the feasibility of image-based quantification of bone mineral and bound water densities using clinical hardware. PMID:24846186
International Nuclear Information System (INIS)
Yamada, Susumu; Igarashi, Ryo; Machida, Masahiko; Imamura, Toshiyuki; Okumura, Masahiko; Onishi, Hiroaki
2010-01-01
We parallelize the density matrix renormalization group (DMRG) method, which is a ground-state solver for one-dimensional quantum lattice systems. The parallelization allows us to extend the applicable range of the DMRG to n-leg ladders i.e., quasi two-dimension cases. Such an extension is regarded to bring about several breakthroughs in e.g., quantum-physics, chemistry, and nano-engineering. However, the straightforward parallelization requires all-to-all communications between all processes which are unsuitable for multi-core systems, which is a mainstream of current parallel computers. Therefore, we optimize the all-to-all communications by the following two steps. The first one is the elimination of the communications between all processes by only rearranging data distribution with the communication data amount kept. The second one is the avoidance of the communication conflict by rescheduling the calculation and the communication. We evaluate the performance of the DMRG method on multi-core supercomputers and confirm that our two-steps tuning is quite effective. (author)
Energy Technology Data Exchange (ETDEWEB)
Afzali, R., E-mail: afzali@kntu.ac.ir [Department of Physics, K. N. Toosi University of Technology, Tehran, 15418 (Iran, Islamic Republic of); Ebrahimian, N., E-mail: n.ebrahimian@shahed.ac.ir [Department of Physics, Faculty of Basic Sciences, Shahed University, Tehran, 18155-159 (Iran, Islamic Republic of); Eghbalifar, B., E-mail: b.eghbali2011@yahoo.com [Department of Agricultural Management, Marvdasht Branch, Azad University, Marvdasht (Iran, Islamic Republic of)
2016-10-07
Highlights: • In contrast to a s-wave superconductor, the quantum correlation of the d-wave superconductor is sensitive to the change of the gap magnitude. • Quantum discord of the d-wave superconductor oscillates. • Quantum discord becomes zero at a characteristic length of the d-wave superconductor. • Quantum correlation strongly depends on the length of grain. Length of the superconductor lower, the quantum correlation length higher. • Quantum tripartite entanglement for a nano-scale d-wave superconductor is better than for a bulk d-wave superconductor. - Abstract: By approximating the energy gap, entering nano-size effect via gap fluctuation and calculating the Green's functions and the space-spin density matrix, the dependence of quantum correlation (entanglement, discord and tripartite entanglement) on the relative distance of two electron spins forming Cooper pairs, the energy gap and the length of bulk and nano interacting Fermi system (a nodal d-wave superconductor) is determined. In contrast to a s-wave superconductor, quantum correlation of the system is sensitive to the change of the gap magnitude and strongly depends on the length of the grain. Also, quantum discord oscillates. Furthermore, the entanglement length and the correlation length are investigated. Discord becomes zero at a characteristic length of the d-wave superconductor.
Yao, Yao; Sun, Ke-Wei; Luo, Zhen; Ma, Haibo
2018-01-18
The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.
Energy Technology Data Exchange (ETDEWEB)
Wald, R M [Chicago Univ., Ill. (USA). Lab. for Astrophysics and Space Research
1975-11-01
Hawking's analysis of particle creation by black holes is extended by explicity obtaining the expression for the quantum mechanical state vector PSI which results from particle creation starting from the vacuum during gravitational collapse. We first discuss the quantum field theory of a Hermitian scalar field in an external potential or in a curved but asymptotically flat spacetime with no horizon present. Making the necessary modification for the case when a horizon is present, we apply this theory for a massless Hermitian scalar field to get the state vector describing the steady state emission at late times for particle creation during gravitational collapse to a Schwarzschild black hole. We find that the state vector describing particle creation from the vacuum decomposes into a simple product of state vectors for each individual mode. The density matrix describing emission of particles to infinity by this particle creation process is found to be identical to that of black body emission. Thus, black hole emission agrees in complete detail with black body emission (orig./BJ).
International Nuclear Information System (INIS)
Mazziotti, David A.
2002-01-01
Atomic and molecular ground-state energies are variationally determined by constraining the two-particle reduced density matrix (2-RDM) to satisfy positivity conditions. Because each positivity condition corresponds to correcting the ground-state energies for a class of Hamiltonians with two-particle interactions, these conditions collectively provide a new approach to many-body theory that, unlike perturbation theory, can capture significantly correlated phenomena including the multireference effects of potential-energy surfaces. The D, Q, and G conditions for the 2-RDM are extended through generalized lifting operators inspired from the formal solution of N-representability. These lifted conditions agree with the hierarchy of positivity conditions presented by Mazziotti and Erdahl [Phys. Rev. A 63, 042113 (2001)]. The connection between positivity and the formal solution explains how constraining higher RDMs to be positive semidefinite improves the N representability of the 2-RDM and suggests using pieces of higher positivity conditions that computationally scale like the D condition. With the D, Q, and G conditions as well as pieces of higher positivity the electronic energies for Be, LiH, H 2 O, and BH are computed through a primal-dual interior-point algorithm for positive semidefinite programming. The variational method produces potential-energy surfaces that are highly accurate even far from the equilibrium geometry where single-reference perturbation-based methods often fail to produce realistic energies
MAVRI, J; BERENDSEN, HJC
1995-01-01
The methodology for treatment of proton transfer processes by density matrix evolution (DME) with inclusion of many excited states is presented. The DME method (Berendsen, H. J. C.; Mavri, J. J. Phys. Chem. 1993, 97, 13464) that simulates the dynamics of quantum systems embedded in a classical
De Nardis, J.; Caux, J.-S.
2014-01-01
We apply the logic of the quench action to give an exact analytical expression for the time evolution of the one-body density matrix after an interaction quench in the Lieb-Liniger model from the ground state of the free theory (BEC state) to the infinitely repulsive regime. In this limit there
International Nuclear Information System (INIS)
Larson, N.M.
1985-04-01
In 1980 the multilevel multichannel R-matrix code SAMMY was released for use in analysis of neutron data at the Oak Ridge Electron Linear Accelerator. Since that time, SAMMY has undergone significant modifications: (1) User-friendly options have been incorporated to streamline common operations and to protect a run from common user errors. (2) The Reich-Moore formalism has been extended to include an optional logarithmic parameterization of the external R-matrix, for which any or all parameters may be varied. (3) The ability to vary sample thickness, effective temperature, matching radius, and/or resolution-broadening parameters has been incorporated. (4) To avoid loss of information (i.e., computer round-off errors) between runs, the ''covariance file'' now includes precise values for all variables. (5) Unused but correlated variables may be included in the analysis. Because of these and earlier changes, the 1980 SAMMY manual is now obsolete. This report is intended to be complete documentation for the current version of SAMMY. In August of 1984 the users' guide for version P of the multilevel multichannel R-matrix code SAMMY was published. Recently, major changes within SAMMY have led to the creation of version O, which is documented in this report. Among these changes are: (1) an alternative matrix-manipulation method for use in certain special cases; (2) division of theoretical cross-section generation and broadening operations into separate segments of the code; (3) an option to use the multilevel Breit-Wigner approximation to generate theoretical cross sections; (4) new input options; (5) renaming all temporary files as SAM...DAT; (6) more sophisticated use of temporary files to maximize the number of data points that may be analyzed in a single run; and (7) significant internal restructing of the code in preparation for changes described here and for planned future changes
Rashid, M.
2011-01-01
Considering the Lagrangian density of the electromagnetic field, a 4 × 4 transformation matrix is found which can be used to include two of the symmetrized Maxwell’s equations as one of the Euler-Lagrange equations of the complete Lagrangian density. The 4 × 4 transformation matrix introduces newly
Moraes Rêgo, Patrícia Helena; Viana da Fonseca Neto, João; Ferreira, Ernesto M.
2015-08-01
The main focus of this article is to present a proposal to solve, via UDUT factorisation, the convergence and numerical stability problems that are related to the covariance matrix ill-conditioning of the recursive least squares (RLS) approach for online approximations of the algebraic Riccati equation (ARE) solution associated with the discrete linear quadratic regulator (DLQR) problem formulated in the actor-critic reinforcement learning and approximate dynamic programming context. The parameterisations of the Bellman equation, utility function and dynamic system as well as the algebra of Kronecker product assemble a framework for the solution of the DLQR problem. The condition number and the positivity parameter of the covariance matrix are associated with statistical metrics for evaluating the approximation performance of the ARE solution via RLS-based estimators. The performance of RLS approximators is also evaluated in terms of consistence and polarisation when associated with reinforcement learning methods. The used methodology contemplates realisations of online designs for DLQR controllers that is evaluated in a multivariable dynamic system model.
Directory of Open Access Journals (Sweden)
D. Jabari Sabeg
2016-10-01
Full Text Available In this paper, we present a new computational method for solving nonlinear singular boundary value problems of fractional order arising in biology. To this end, we apply the operational matrices of derivatives of shifted Legendre polynomials to reduce such problems to a system of nonlinear algebraic equations. To demonstrate the validity and applicability of the presented method, we present some numerical examples.
Lü, Boqiang; Shi, Xiaoding; Zhong, Xin
2018-06-01
We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier–Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D Cauchy problem of the density-dependent Navier–Stokes equations on the whole space admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Furthermore, we also obtain the large time decay rates of the spatial gradients of the velocity and the pressure, which are the same as those of the homogeneous case.
Flavored quantum Boltzmann equations
International Nuclear Information System (INIS)
Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean
2010-01-01
We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.
International Nuclear Information System (INIS)
Larson, Nancy M.
2007-01-01
1 - Description of problem or function: The purpose of the code is to analyze time-of-flight cross section data in the resolved and unresolved resonance regions, where the incident particle is either a neutron or a charged particle (p, alpha, d,...). Energy-differential cross sections and angular-distribution data are treated, as are certain forms of energy-integrated data. In the resolved resonance region (RRR), theoretical cross sections are generated using the Reich-Moore approximation to R-matrix theory (and extensions thereof). Sophisticated models are used to describe the experimental situation: Data-reduction parameters (e.g. normalization, background, sample thickness) are included. Several options are available for both resolution and Doppler broadening, including a crystal-lattice model for Doppler broadening. Self-shielding and multiple-scattering correction options are available for analysis of capture cross sections. Multiple isotopes and impurities within a sample are handled accurately. Cross sections in the unresolved resonance region (URR) can also be analyzed using SAMMY. The capability was borrowed from Froehner's FITACS code; SAMMY modifications for the URR include more exact calculation of partial derivatives, normalization options for the experimental data, increased flexibility for input of experimental data, introduction of user-friendly input options. In both energy regions, values for resonance parameters and for data-related parameters (such as normalization, sample thickness, effective temperature, resolution parameters) are determined via fits to the experimental data using Bayes' method (see below). Final results may be reported in ENDF format for inclusion in the evaluated nuclear data files. The manner in which SAMMY 7 (released in 2006) differs from the previous version (SAMMY-M6) is itemized in Section I.A of the SAMMY users' manual. Details of the 7.0.1 update are documented in an errata SAMMY 7.0.1 Errata (http://www.ornl.gov/sci
Energy Technology Data Exchange (ETDEWEB)
Abdulagatov, I.M. E-mail: ilmutdin@boulder.nist.govmangur@datacom.ru; Azizov, N.D. E-mail: Nazim_Azizov@yahoo.com
2004-01-01
(p,V{sub m},T,x) properties of four aqueous LiNO{sub 3} solutions (0.181, 0.526, 0.963, and 1.728) mol {center_dot} kg{sup -1} H{sub 2}O were measured in the liquid phase with a constant-volume piezometer immersed in a precision liquid thermostat. Measurements were made for 10 isotherms between (298 and 573) K. The range of pressure was from (2 to 40) MPa. The total uncertainty of density, pressure, temperature, and concentration measurements were estimated to be less than 0.06 %, 0.05 %, 10 mK, and 0.014 %, respectively. The values of saturated density were determined by extrapolating experimental (p,{rho}) data to the vapor-pressure at fixed temperature and composition using an interpolating equation. A polynomial type of equation of state for specific volume was obtained as a function of temperature, pressure, and composition by a least-squares method from the experimental data. The average absolute deviation (AAD) between measured and calculated values from this polynomial equation for density was 0.02 %. Measured values of solution density were compared with values calculated from Pitzer's ion-interaction equation. The agreement is within (0.2 to 0.4) % depending of concentration range.
Gravitational lensing by eigenvalue distributions of random matrix models
Martínez Alonso, Luis; Medina, Elena
2018-05-01
We propose to use eigenvalue densities of unitary random matrix ensembles as mass distributions in gravitational lensing. The corresponding lens equations reduce to algebraic equations in the complex plane which can be treated analytically. We prove that these models can be applied to describe lensing by systems of edge-on galaxies. We illustrate our analysis with the Gaussian and the quartic unitary matrix ensembles.
International Nuclear Information System (INIS)
Wu, Ru-Shan; Wang, Benfeng; Hu, Chunhua
2015-01-01
We derived the renormalized nonlinear sensitivity operator and the related inverse thin-slab propagator (ITSP) for nonlinear tomographic waveform inversion based on the theory of nonlinear partial derivative operator and its De Wolf approximation. The inverse propagator is based on a renormalization procedure to the forward and inverse transition matrix scattering series. The ITSP eliminates the divergence of the inverse Born series for strong perturbations by stepwise partial summation (renormalization). Numerical tests showed that the inverse Born T-series starts to diverge at moderate perturbation (20% for the given model of Gaussian ball with a radius of 5 wavelength), while the ITSP has no divergence problem for any strong perturbations (up to 100% perturbation for test model). In addition, the ITSP is a non-iterative, marching algorithm with only one sweep, and therefore very efficient in comparison with the iterative inversion based on the inverse-Born scattering series. This convergence and efficiency improvement has potential applications to the iterative procedure of waveform inversion. (paper)
Directory of Open Access Journals (Sweden)
Ichitaro Yamazaki
2015-01-01
of their low-rank properties. To compute a low-rank approximation of a dense matrix, in this paper, we study the performance of QR factorization with column pivoting or with restricted pivoting on multicore CPUs with a GPU. We first propose several techniques to reduce the postprocessing time, which is required for restricted pivoting, on a modern CPU. We then examine the potential of using a GPU to accelerate the factorization process with both column and restricted pivoting. Our performance results on two eight-core Intel Sandy Bridge CPUs with one NVIDIA Kepler GPU demonstrate that using the GPU, the factorization time can be reduced by a factor of more than two. In addition, to study the performance of our implementations in practice, we integrate them into a recently developed software StruMF which algebraically exploits such low-rank structures for solving a general sparse linear system of equations. Our performance results for solving Poisson's equations demonstrate that the proposed techniques can significantly reduce the preconditioner construction time of StruMF on the CPUs, and the construction time can be further reduced by 10%–50% using the GPU.
Venturi, D.; Karniadakis, G. E.
2012-08-01
By using functional integral methods we determine new evolution equations satisfied by the joint response-excitation probability density function (PDF) associated with the stochastic solution to first-order nonlinear partial differential equations (PDEs). The theory is presented for both fully nonlinear and for quasilinear scalar PDEs subject to random boundary conditions, random initial conditions or random forcing terms. Particular applications are discussed for the classical linear and nonlinear advection equations and for the advection-reaction equation. By using a Fourier-Galerkin spectral method we obtain numerical solutions of the proposed response-excitation PDF equations. These numerical solutions are compared against those obtained by using more conventional statistical approaches such as probabilistic collocation and multi-element probabilistic collocation methods. It is found that the response-excitation approach yields accurate predictions of the statistical properties of the system. In addition, it allows to directly ascertain the tails of probabilistic distributions, thus facilitating the assessment of rare events and associated risks. The computational cost of the response-excitation method is order magnitudes smaller than the one of more conventional statistical approaches if the PDE is subject to high-dimensional random boundary or initial conditions. The question of high-dimensionality for evolution equations involving multidimensional joint response-excitation PDFs is also addressed.
Bodewig, E
1959-01-01
Matrix Calculus, Second Revised and Enlarged Edition focuses on systematic calculation with the building blocks of a matrix and rows and columns, shunning the use of individual elements. The publication first offers information on vectors, matrices, further applications, measures of the magnitude of a matrix, and forms. The text then examines eigenvalues and exact solutions, including the characteristic equation, eigenrows, extremum properties of the eigenvalues, bounds for the eigenvalues, elementary divisors, and bounds for the determinant. The text ponders on approximate solutions, as well
Chen, Zhenhua; Chen, Xun; Wu, Wei
2013-04-01
In this series, the n-body reduced density matrix (n-RDM) approach for nonorthogonal orbitals and their applications to ab initio valence bond (VB) methods are presented. As the first paper of this series, Hamiltonian matrix elements between internally contracted VB wave functions are explicitly provided by means of nonorthogonal orbital based RDM approach. To this end, a more generalized Wick's theorem, called enhanced Wick's theorem, is presented both in arithmetical and in graphical forms, by which the deduction of expressions for the matrix elements between internally contracted VB wave functions is dramatically simplified, and the matrix elements are finally expressed in terms of tensor contractions of electronic integrals and n-RDMs of the reference VB self-consistent field wave function. A string-based algorithm is developed for the purpose of evaluating n-RDMs in an efficient way. Using the techniques presented in this paper, one is able to develop new methods and efficient algorithms for nonorthogonal orbital based many-electron theory much easier than by use of the first quantized formulism.
Putting density back into the habitat-quality equation: case study of an open-nesting forest bird.
Pérot, Aurore; Villard, Marc-André
2009-12-01
Ecological traps and other cases of apparently maladaptive habitat selection cast doubt on the relevance of density as an indicator of habitat quality. Nevertheless, the prevalence of these phenomena remains poorly known, and density may still reflect habitat quality in most systems. We examined the relationship between density and two other parameters of habitat quality in an open-nesting passerine species: the Ovenbird (Seiurus aurocapilla). We hypothesized that the average individual bird makes a good decision when selecting its breeding territory and that territory spacing reflects site productivity or predation risk. Therefore, we predicted that density would be positively correlated with productivity (number of young fledged per unit area). Because individual performance is sensitive to events partly determined by chance, such as nest predation, we further predicted density would be weakly correlated or uncorrelated with the proportion of territories fledging young. We collected data in 23 study sites (25 ha each), 16 of which were located in untreated mature northern hardwood forest and seven in stands partially harvested (treated) 1-7 years prior to the survey. Density explained most of the variability in productivity (R(2)= 0.73), and there was no apparent decoupling between density and productivity in treated plots. In contrast, there was no significant relationship between density and the proportion of territories fledging >or=1 young over the entire breeding season. These results suggest that density reflects habitat quality at the plot scale in this study system. To our knowledge this is one of the few studies testing the value of territory density as an indicator of habitat quality in an open-nesting bird species on the basis of a relatively large number of sizeable study plots.
Akemann, G; Bittner, E; Lombardo, M; Markum, H; Pullirsch, R
2004-01-01
We investigate the eigenvalue spectrum of the staggered Dirac matrix in two color QCD at finite chemical potential. The profiles of complex eigenvalues close to the origin are compared to a complex generalization of the chiral Gaussian Symplectic Ensemble, confirming its predictions for weak and strong non-Hermiticity. They differ from the QCD symmetry class with three colors by a level repulsion from both the real and imaginary axis.
International Nuclear Information System (INIS)
Akemann, Gernot; Bittner, Elmar; Lombardo, Maria-Paola; Markum, Harald; Pullirsch, Rainer
2005-01-01
We investigate the eigenvalue spectrum of the staggered Dirac matrix in two color QCD at finite chemical potential. The profiles of complex eigenvalues close to the origin are compared to a complex generalization of the chiral Gaussian Symplectic Ensemble, confirming its predictions for weak and strong non-Hermiticity. They differ from the QCD symmetry class with three colors by a level repulsion from both the real and imaginary axis
International Nuclear Information System (INIS)
Meer, R. van; Gritsenko, O. V.; Baerends, E. J.
2014-01-01
Time dependent density matrix functional theory in its adiabatic linear response formulation delivers exact excitation energies ω α and oscillator strengths f α for two-electron systems if extended to the so-called phase including natural orbital (PINO) theory. The Löwdin-Shull expression for the energy of two-electron systems in terms of the natural orbitals and their phases affords in this case an exact phase-including natural orbital functional (PILS), which is non-primitive (contains other than just J and K integrals). In this paper, the extension of the PILS functional to N-electron systems is investigated. With the example of an elementary primitive NO functional (BBC1) it is shown that current density matrix functional theory ground state functionals, which were designed to produce decent approximations to the total energy, fail to deliver a qualitatively correct structure of the (inverse) response function, due to essential deficiencies in the reconstruction of the two-body reduced density matrix (2RDM). We now deduce essential features of an N-electron functional from a wavefunction Ansatz: The extension of the two-electron Löwdin-Shull wavefunction to the N-electron case informs about the phase information. In this paper, applications of this extended Löwdin-Shull (ELS) functional are considered for the simplest case, ELS(1): one (dissociating) two-electron bond in the field of occupied (including core) orbitals. ELS(1) produces high quality ω α (R) curves along the bond dissociation coordinate R for the molecules LiH, Li 2 , and BH with the two outer valence electrons correlated. All of these results indicate that response properties are much more sensitive to deficiencies in the reconstruction of the 2RDM than the ground state energy, since derivatives of the functional with respect to both the NOs and the occupation numbers need to be accurate
Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.
2018-04-01
The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.
Miao, Jian-Jian; Jin, Hui-Ke; Zhang, Fu-Chun; Zhou, Yi
2018-01-11
We study Kitaev model in one-dimension with open boundary condition by using exact analytic methods for non-interacting system at zero chemical potential as well as in the symmetric case of Δ = t, and by using density-matrix-renormalization-group method for interacting system with nearest neighbor repulsion interaction. We suggest and examine an edge correlation function of Majorana fermions to characterize the long range order in the topological superconducting states and study the phase diagram of the interating Kitaev chain.
Bates, Kevin R.; Daniels, Andrew D.; Scuseria, Gustavo E.
1998-01-01
We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
International Nuclear Information System (INIS)
Barber, D.P.
2015-10-01
I extend and update earlier work, summarised in an earlier paper (D.P. Barber, M. Voigt, AIP Conference Proceedings 1149 (28)), whereby the invariant polarisation-tensor field (ITF) for deuterons in storage rings was introduced to complement the invariant spin field (ISF). Taken together, the ITF and the ISF provide a definition of the equilibrium spin density-matrix field which, in turn, offers a clean framework for describing equilibrium spin-1 ensembles in storage rings. I show how to construct the ITF by stroboscopic averaging, I give examples, I discuss adiabatic invariance and I introduce a formalism for describing the effect of noise and damping.
Willige, van R.W.G.; Linssen, J.P.H.; Voragen, A.G.J.
2000-01-01
The influence of oil and food components in real food products on the absorption of four flavour compounds (limonene, decanal, linalool and ethyl 2-methyl butyrate) into linear low-density polyethylene (LLDPE) was studied using a large volume injection GC in vial extraction method. Model food
Directory of Open Access Journals (Sweden)
Weigelt C.
2012-08-01
Full Text Available Two designs of square-celled metallic honeycomb structures fabricated by a modified extrusion technology based on a powder feedstock were investigated. The strength and ductility of these cellular materials are achieved by an austenitic CrNi (AISI 304 steel matrix particle reinforced by an MgO partially-stabilized zirconia building up their cell wall microstructure. Similar to the mechanical behaviour of the bulk materials, the strengthening mechanism and the martensitic phase transformations in the cell walls are affected by the deformation temperature and the nominal strain rate. The microstructure evolution during quasi-static and dynamic impact compression up to high strain rates of 103 1/s influences the buckling and failure behaviour of the honeycomb structures. In contrast to bending-dominated quasi-isotropic networks like open-celled metal foams, axial compressive loading to the honeycomb’s channels causes membrane stretching as well as crushing of the vertical cell node elements and cell walls. The presented honeycomb materials differ geometrically in their cell wall thickness-to-cell size-ratio. Therefore, the failure behaviour is predominantly controlled by global buckling and torsional-flexural buckling, respectively, accompanied by plastic matrix flow and strengthening of the cell wall microstructure.
Keiser, Dennis D.; Jue, Jan-Fong; Miller, Brandon D.; Gan, Jian; Robinson, Adam B.; Medvedev, Pavel G.; Madden, James W.; Moore, Glenn A.
2016-06-01
Low-enriched (U-235 RERTR-8 experiment at high temperature, high fission rate, and high power, up to high fission density. This paper describes the results of the scanning electron microscopy (SEM) analysis of an irradiated fuel plate using polished samples and those produced with a focused ion beam. A follow-up paper will discuss the results of transmission electron microscopy (TEM) analysis. Using SEM, it was observed that even at very aggressive irradiation conditions, negligible chemical interaction occurred between the irradiated U-7Mo fuel particles and Mg matrix; no interconnection of fission gas bubbles from fuel particle to fuel particle was observed; the interconnected fission gas bubbles that were observed in the irradiated U-7Mo particles resulted in some transport of solid fission products to the U-7Mo/Mg interface; the presence of microstructural pathways in some U-9.1 Mo particles that could allow for transport of fission gases did not result in the apparent presence of large porosity at the U-7Mo/Mg interface; and, the Mg-Al interaction layers that were present at the Mg matrix/Al 6061 cladding interface exhibited good radiation stability, i.e. no large pores.
Abreu, P; Adye, T; Alekseev, G D; Alemany, R; Allport, P P; Almehed, S; Amaldi, Ugo; Amato, S; Andersson, P; Andreazza, A; Antilogus, P; Apel, W D; Arnoud, Y; Åsman, B; Augustin, J E; Augustinus, A; Baillon, Paul; Bambade, P; Barão, F; Barbi, M S; Barbiellini, Guido; Bardin, Dimitri Yuri; Barker, G; Baroncelli, A; Bärring, O; Bates, M J; Battaglia, Marco; Baubillier, M; Baudot, J; Becks, K H; Begalli, M; Beillière, P; Belokopytov, Yu A; Benvenuti, Alberto C; Bérat, C; Berggren, M; Bertini, D; Bertrand, D; Besançon, M; Bianchi, F; Bigi, M; Bilenky, S M; Billoir, P; Bizouard, M A; Bloch, D; Blume, M; Bonesini, M; Bonivento, W; Booth, P S L; Borgland, A W; Borisov, G; Bosio, C; Botner, O; Boudinov, E; Bouquet, B; Bourdarios, C; Bowcock, T J V; Bozzo, M; Branchini, P; Brand, K D; Brenke, T; Brenner, R A; Bricman, C; Brown, R C A; Brückman, P; Brunet, J M; Bugge, L; Buran, T; Burgsmüller, T; Buschmann, P; Cabrera, S; Caccia, M; Calvi, M; Camacho-Rozas, A J; Camporesi, T; Canale, V; Canepa, M; Cao, F; Carena, F; Carroll, L; Caso, Carlo; Castillo-Gimenez, M V; Cattai, A; Cavallo, F R; Chabaud, V; Chapkin, M M; Charpentier, P; Chaussard, L; Checchia, P; Chelkov, G A; Chen, M; Chierici, R; Chliapnikov, P V; Chochula, P; Chorowicz, V; Chudoba, J; Cindro, V; Collins, P; Contri, R; Cortina, E; Cosme, G; Cossutti, F; Cowell, J H; Crawley, H B; Crennell, D J; Crosetti, G; Cuevas-Maestro, J; Czellar, S; Dahm, J; D'Almagne, B; Dam, M; Damgaard, G; Dauncey, P D; Davenport, Martyn; Da Silva, W; Deghorain, A; Della Ricca, G; Delpierre, P A; Demaria, N; De Angelis, A; de Boer, Wim; De Brabandere, S; De Clercq, C; La Vaissière, C de; De Lotto, B; De Min, A; De Paula, L S; Dijkstra, H; Di Ciaccio, Lucia; Di Diodato, A; Djannati, A; Dolbeau, J; Doroba, K; Dracos, M; Drees, J; Drees, K A; Dris, M; Durand, J D; Edsall, D M; Ehret, R; Eigen, G; Ekelöf, T J C; Ekspong, Gösta; Elsing, M; Engel, J P; Erzen, B; Espirito-Santo, M C; Falk, E; Fanourakis, G K; Fassouliotis, D; Feindt, Michael; Fenyuk, A; Ferrari, P; Ferrer, A; Fichet, S; Filippas-Tassos, A; Firestone, A; Fischer, P A; Föth, H; Fokitis, E; Fontanelli, F; Formenti, F; Franek, B J; Frodesen, A G; Frühwirth, R; Fulda-Quenzer, F; Fuster, J A; Galloni, A; Gamba, D; Gandelman, M; García, C; García, J; Gaspar, C; Gasparini, U; Gavillet, P; Gazis, E N; Gelé, D; Gerber, J P; Gerdyukov, L N; Gokieli, R; Golob, B; Gonçalves, P; Gopal, Gian P; Gorn, L; Górski, M; Guz, Yu; Gracco, Valerio; Graziani, E; Green, C; Grefrath, A; Gris, P; Grosdidier, G; Grzelak, K; Günther, M; Guy, J; Hahn, F; Hahn, S; Hajduk, Z; Hallgren, A; Hamacher, K; Harris, F J; Hedberg, V; Henriques, R P; Hernández, J J; Herquet, P; Herr, H; Hessing, T L; Heuser, J M; Higón, E; Holmgren, S O; Holt, P J; Holthuizen, D J; Hoorelbeke, S; Houlden, M A; Hrubec, Josef; Huet, K; Hultqvist, K; Jackson, J N; Jacobsson, R; Jalocha, P; Janik, R; Jarlskog, C; Jarlskog, G; Jarry, P; Jean-Marie, B; Johansson, E K; Jönsson, L B; Jönsson, P E; Joram, Christian; Juillot, P; Kaiser, M; Kapusta, F; Karafasoulis, K; Katsanevas, S; Katsoufis, E C; Keränen, R; Khokhlov, Yu A; Khomenko, B A; Khovanskii, N N; King, B J; Kjaer, N J; Klapp, O; Klein, H; Kluit, P M; Knoblauch, D; Kokkinias, P; Koratzinos, M; Korcyl, K; Kostyukhin, V; Kourkoumelis, C; Kuznetsov, O; Krammer, Manfred; Kreuter, C; Kronkvist, I J; Krstic, J; Krumshtein, Z; Krupinski, W; Kubinec, P; Kucewicz, W; Kurvinen, K L; Lacasta, C; Laktineh, I; Lamsa, J; Lanceri, L; Lane, D W; Langefeld, P; Laugier, J P; Lauhakangas, R; Leder, Gerhard; Ledroit, F; Lefébure, V; Legan, C K; Leisos, A; Leitner, R; Lemonne, J; Lenzen, Georg; Lepeltier, V; Lesiak, T; Libby, J; Liko, D; Lipniacka, A; Lippi, I; Lörstad, B; Loken, J G; López, J M; Loukas, D; Lutz, P; Lyons, L; MacNaughton, J N; Maehlum, G; Mahon, J R; Maio, A; Malmgren, T G M; Malychev, V; Mandl, F; Marco, J; Marco, R P; Maréchal, B; Margoni, M; Marin, J C; Mariotti, C; Markou, A; Martínez-Rivero, C; Martínez-Vidal, F; Martí i García, S; Masik, J; Matorras, F; Matteuzzi, C; Matthiae, Giorgio; Mazzucato, M; McCubbin, M L; McKay, R; McNulty, R; McPherson, G; Medbo, J; Meroni, C; Meyer, S; Meyer, W T; Myagkov, A; Michelotto, M; Migliore, E; Mirabito, L; Mitaroff, Winfried A; Mjörnmark, U; Moa, T; Møller, R; Mönig, K; Monge, M R; Morettini, P; Müller, H; Münich, K; Mulders, M; Mundim, L M; Murray, W J; Muryn, B; Myatt, Gerald; Myklebust, T; Naraghi, F; Navarria, Francesco Luigi; Navas, S; Nawrocki, K; Negri, P; Némécek, S; Neumann, W; Neumeister, N; Nicolaidou, R; Nielsen, B S; Nieuwenhuizen, M; Nikolaenko, V; Nikolenko, M; Niss, P; Nomerotski, A; Normand, Ainsley; Nygren, A; Oberschulte-Beckmann, W; Obraztsov, V F; Olshevskii, A G; Onofre, A; Orava, Risto; Orazi, G; Österberg, K; Ouraou, A; Paganini, P; Paganoni, M; Pain, R; Palka, H; Papadopoulou, T D; Papageorgiou, K; Pape, L; Parkes, C; Parodi, F; Parzefall, U; Passeri, A; Pegoraro, M; Peralta, L; Pernegger, H; Pernicka, Manfred; Perrotta, A; Petridou, C; Petrolini, A; Phillips, H T; Piana, G; Pierre, F; Pimenta, M; Podobnik, T; Podobrin, O; Pol, M E; Polok, G; Poropat, P; Pozdnyakov, V; Privitera, P; Pukhaeva, N; Pullia, Antonio; Radojicic, D; Ragazzi, S; Rahmani, H; Ratoff, P N; Read, A L; Reale, M; Rebecchi, P; Redaelli, N G; Regler, Meinhard; Reid, D; Reinhardt, R; Renton, P B; Resvanis, L K; Richard, F; Rídky, J; Rinaudo, G; Røhne, O M; Romero, A; Ronchese, P; Roos, L; Rosenberg, E I; Rosinsky, P; Roudeau, Patrick; Rovelli, T; Ruhlmann-Kleider, V; Ruiz, A; Rybicki, K; Saarikko, H; Sacquin, Yu; Sadovskii, A; Sajot, G; Salt, J; Sannino, M; Schneider, H; Schwickerath, U; Schyns, M A E; Sciolla, G; Scuri, F; Seager, P; Sedykh, Yu; Segar, A M; Seitz, A; Sekulin, R L; Serbelloni, L; Shellard, R C; Sheridan, A; Siegrist, P; Silvestre, R; Simonetto, F; Sissakian, A N; Skaali, T B; Smadja, G; Smirnov, N; Smirnova, O G; Smith, G R; Sokolov, A; Solovyanov, O; Sosnowski, R; Souza-Santos, D; Spassoff, Tz; Spiriti, E; Sponholz, P; Squarcia, S; Stampfer, D; Stanescu, C; Stanic, S; Stapnes, Steinar; Stavitski, I; Stevenson, K; Stocchi, A; Strauss, J; Strub, R; Stugu, B; Szczekowski, M; Szeptycka, M; Tabarelli de Fatis, T; Tavernet, J P; Tegenfeldt, F; Terranova, F; Thomas, J; Tilquin, A; Timmermans, J; Tkatchev, L G; Todorov, T; Todorova, S; Toet, D Z; Tomaradze, A G; Tonazzo, A; Tortora, L; Tranströmer, G; Treille, D; Tristram, G; Trombini, A; Troncon, C; Tsirou, A L; Turluer, M L; Tyapkin, I A; Tyndel, M; Tzamarias, S; Überschär, B; Ullaland, O; Uvarov, V; Valenti, G; Vallazza, E; van Apeldoorn, G W; van Dam, P; Van Eldik, J; Van Lysebetten, A; Vassilopoulos, N; Vegni, G; Ventura, L; Venus, W A; Verbeure, F; Verlato, M; Vertogradov, L S; Vilanova, D; Vincent, P; Vitale, L; Vlasov, E; Vodopyanov, A S; Vrba, V; Wahlen, H; Walck, C; Weiser, C; Wetherell, Alan M; Wicke, D; Wickens, J H; Wielers, M; Wilkinson, G R; Williams, W S C; Winter, M; Witek, M; Wlodek, T; Yi, J; Yip, K; Yushchenko, O P; Zach, F; Zaitsev, A; Zalewska-Bak, A; Zalewski, Piotr; Zavrtanik, D; Zevgolatakos, E; Zimin, N I; Zucchelli, G C; Zumerle, G
1997-01-01
The spin density matrix elements for the $\\rho^0$, K$^{*0}(892)$ and $\\phi$ produced in hadronic Z$^0$ decays are measured in the DELPHI detector. There is no evidence for spin alignment of the K$^{*0}(892)$ and $\\phi$ in the region $x_p \\leq 0.3$ ($x_p = p/p_{beam}$), where $\\rho_{00} = 0.33 \\pm 0.05$ and $\\rho_{00} = 0.30 \\pm 0.04$, respectively. In the fragmentation region, $x_p \\geq 0.4$, there is some indication for spin alignment of the $\\rho^0$ and K$^{*0}(892)$, since $\\rho_{00} = 0.43 \\pm 0.05$ and $\\rho_{00} = 0.46 \\pm 0.08$, respectively. These values are compared with those found in meson-induced hadronic reactions. For the $\\phi$, $\\rho_{00} = 0.30 \\pm 0.04$ for $x_p \\geq 0.4$ and $0.55 \\pm 0.10$ for $x_p \\geq 0.7$. The off-diagonal spin density matrix element $\\rho_{1-1}$ is consistent with zero in all cases.
International Nuclear Information System (INIS)
Hopper, M.A.; Robinson, P.; Grainger, A.J.
2011-01-01
Aim: To determine the sensitivities, specificities, and receiver-operating characteristics (ROCs) for sagittal conventional spin-echo proton density (SE-PD) and fast spin-echo proton density (FSE-PD) sequences in the diagnosis of meniscal tears when compared to arthroscopic findings utilizing increased FSE matrix acquisition size. Method and materials: Magnetic resonance imaging (MRI) studies of 97 knees (194 menisci) were independently and prospectively interpreted by two experienced musculoskeletal radiologists over four separate readings at least 3 weeks apart. Readings 1 and 2 included images in all three planes in accordance with the standard protocol with either a SE or FSE sagittal PD, at readings 3 and 4 just the SE or FSE sagittal PD sequences were reported. The FSE sequence was acquired with an increased matrix size, compared to the SE sequence, to provide increased resolution. Menisci were graded for the presence of a tear and statistical analysis to calculate sensitivity and specificity was performed comparing to arthroscopy as the reference standard. ROC analysis for the diagnosis of meniscal tears on the SE and FSE sagittal sequences was also evaluated. Reader concordance for the SE and FSE sequences was calculated. Results: Sixty-seven tears were noted at arthroscopy; 60 were detected on SE and 56 on FSE. The sensitivity and specificity for SE was 90 and 90%, and for FSE was 84 and 94%, respectively, with no significant difference. ROC analysis showed no significant difference between the two sequences and kappa values demonstrated a higher level of reader agreement for the FSE than for the SE reading. Conclusion: Use of a FSE sagittal PD sequence with an increased matrix size provides comparable performance to conventional SE sagittal PD when evaluating meniscal disease with a modern system. The present study indicates an increased level of concordance between readers for the FSE sagittal sequence compared to the conventional SE.
Energy Technology Data Exchange (ETDEWEB)
Hopper, M.A.; Robinson, P. [Leeds Teaching Hospitals NHS Trust, Leeds (United Kingdom); Grainger, A.J., E-mail: andrew.grainger@leedsth.nhs.u [Leeds Teaching Hospitals NHS Trust, Leeds (United Kingdom)
2011-04-15
Aim: To determine the sensitivities, specificities, and receiver-operating characteristics (ROCs) for sagittal conventional spin-echo proton density (SE-PD) and fast spin-echo proton density (FSE-PD) sequences in the diagnosis of meniscal tears when compared to arthroscopic findings utilizing increased FSE matrix acquisition size. Method and materials: Magnetic resonance imaging (MRI) studies of 97 knees (194 menisci) were independently and prospectively interpreted by two experienced musculoskeletal radiologists over four separate readings at least 3 weeks apart. Readings 1 and 2 included images in all three planes in accordance with the standard protocol with either a SE or FSE sagittal PD, at readings 3 and 4 just the SE or FSE sagittal PD sequences were reported. The FSE sequence was acquired with an increased matrix size, compared to the SE sequence, to provide increased resolution. Menisci were graded for the presence of a tear and statistical analysis to calculate sensitivity and specificity was performed comparing to arthroscopy as the reference standard. ROC analysis for the diagnosis of meniscal tears on the SE and FSE sagittal sequences was also evaluated. Reader concordance for the SE and FSE sequences was calculated. Results: Sixty-seven tears were noted at arthroscopy; 60 were detected on SE and 56 on FSE. The sensitivity and specificity for SE was 90 and 90%, and for FSE was 84 and 94%, respectively, with no significant difference. ROC analysis showed no significant difference between the two sequences and kappa values demonstrated a higher level of reader agreement for the FSE than for the SE reading. Conclusion: Use of a FSE sagittal PD sequence with an increased matrix size provides comparable performance to conventional SE sagittal PD when evaluating meniscal disease with a modern system. The present study indicates an increased level of concordance between readers for the FSE sagittal sequence compared to the conventional SE.
Chiang, Cherie Y; Zebaze, Roger; Wang, Xiao-Fang; Ghasem-Zadeh, Ali; Zajac, Jeffrey D; Seeman, Ego
2018-02-28
Reduced bone mineral density (BMD) may be due to reduced mineralized bone matrix volume, incomplete secondary mineralization or reduced primary mineralization. As bone biopsy is invasive, we hypothesized that non-invasive image acquisition at high resolution can accurately quantify matrix mineral density (MMD). Quantification of MMD was confined to voxels attenuation photons above 80% of that produced by fully mineralized bone matrix because attenuation at this level is due to variation in mineralization not porosity. To assess accuracy, 9 cadaveric distal radii were imaged at a voxel size of 82 microns using high resolution peripheral quantitative computed tomography (HR-pQCT, XtremeCT, Scanco Medical AG, Switzerland) and compared with VivaCT 40 (µCT) at 19 microns voxel size. Associations between MMD and porosity were studied in 94 heathy vitamin D replete pre-menopausal, 77 post-menopausal women, and in a 27 year-old woman with vitamin-D Dependent Rickets (VDDR). Microstructure and MMD were quantified using StrAx (StraxCorp, Melbourne, Australia). MMD measured by HR-pQCT and µCT correlated (R = 0.87; p woman with VDDR, MMD was 5.6 SD lower, and porosity was 5.6 SD higher, than the respective trait means in premenopausal women. BMD was reduced (Z scores femoral neck - 4.3 SD, lumbar spine - 3.8 SD). Low radiation HR-pQCT may facilitate non-invasive quantification of bone's MMD and microstructure in health, disease and during treatment. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.
International Nuclear Information System (INIS)
Efimov, V.N.; Schulz, H.
1976-01-01
It is shown that in the framework of the boundary condition models (BCM) for the two-particle interaction the Schroedinger equation for the system of three identical bosons can be reduced to the one-dimensional integral equation in an exact way. The method used for obtaining such an equation is based on a special consideration of the two-particle off-shell wave functions. The binding energy of the simple three-particle system is calculated. It is indicated that by means of the equation obtained it is possible to change the off-shell behaviour of the two-particle t-matrix and therefore to simulate three particle effects. (Auth.)
International Nuclear Information System (INIS)
Lago, S.; Giuliano Albo, P.A.
2013-01-01
Highlights: ► A novel method for calculating the isobaric specific heat capacity is presented. ► Heat capacity (C p ) was determined only by speed-of-sound and density measurements. ► (C p ) temperature dependence has been related to speed-of-sound by a new expression. ► Heat capacity for water, nonane, undecane, and rapeseed oil methyl ester are obtained. -- Abstract: The determination of thermal quantities from mechanical properties is still a challenge in the thermodynamic field. In this work, the authors suggest a preliminary numerical calculation which allows to determine the constant pressure specific heat capacity, starting from density and speed-of-sound experimental values, as input data. This method is a variant of the well characterized Recursive Equation Method (REM) [1] and permits to develop empirical equations of state for single phase fluids. In particular, the isobaric specific heat capacity has been obtained, in a wide range of temperatures and pressures, for pure water, n-nonane, n-undecane, and rapeseed oil methyl ester. The results have been compared with those available in the literature, when it was possible. Moreover, the typical uncertainty of heat capacity has been estimated to be in the order of 1.5%; however it has been shown that it can be improved when proper distributions of the experimental points are available
International Nuclear Information System (INIS)
Sudarshan, E.C.G.; Mukunda, N.
1978-03-01
A systematic structure analysis of the correlation functions of statistical quantum optics is carried out. From a suitably defined auxiliary two-point function identification of the excited modes in the wave field is found. The relative simplicity of the higher order correlation functions emerges as a by-product and the conditions under which these are made pure are derived. These results depend in a crucial manner on the notion of coherence indices aand of unimodular coherence indices. A new class of approximate expressions for the density operator of a statistical wave field is worked out based on discrete characteristic sets. These are even more economical than the diagonal coherent state representations. An appreciation of the subtleties of quantum theory obtains. Certain implications for the physics of light beams are cited. 28 references
Energy Technology Data Exchange (ETDEWEB)
Brandenburg, G W; Dunwoodie, W M; Lasinski, T A; Leith, D W.G.S.; Williams, S H [Stanford Linear Accelerator Center, Calif. (USA); Carnegie, R K [Carleton Univ., Ottawa, Ontario (Canada). Dept. of Physics; Cashmore, R J [Oxford Univ. (UK). Dept. of Physics; Davier, M [Lab. de l' Accelerateur Lineaire, Orsay, France; Matthews, J A.J. [Michigan State Univ., East Lansing (USA). Dept. of Physics; Walden, P [British Columbia Univ., Vancouver (Canada). TRIUMF Facility
1975-11-24
The results of a wire chamber spectrometer experiment studying anti K*(890) production in the reaction K/sup -/p..-->..K/sup -/..pi../sup +/n at 13 GeV are presented. Strong forward structure is observed for mod(t)
Hine, N D M; Haynes, P D; Mostofi, A A; Payne, M C
2010-09-21
We present calculations of formation energies of defects in an ionic solid (Al(2)O(3)) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.
Energy Technology Data Exchange (ETDEWEB)
Kozlowski, K.K.
2010-12-15
Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear Schroedinger model. This representation allows one to read-off straightforwardly the long-time/large-distance asymptotic behavior of this correlator. Our method of analysis reduces the complexity of the computation of the asymptotic behavior of correlation functions in the so-called interacting integrable models, to the one appearing in free fermion equivalent models. We compute explicitly the first few terms appearing in the asymptotic expansion. Part of these terms stems from excitations lying away from the Fermi boundary, and hence go beyond what can be obtained by using the CFT/Luttinger liquid based predictions. (orig.)
On the Efficiency of Algorithms for Solving Hartree–Fock and Kohn–Sham Response Equations
DEFF Research Database (Denmark)
Kauczor, Joanna; Jørgensen, Poul; Norman, Patrick
2011-01-01
The response equations as occurring in the Hartree–Fock, multiconfigurational self-consistent field, and Kohn–Sham density functional theory have identical matrix structures. The algorithms that are used for solving these equations are discussed, and new algorithms are proposed where trial vectors...
Prodhan, Suryoday; Ramasesha, S.
2018-05-01
The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry (C2) , electron-hole symmetry (J ) , and parity or spin-flip symmetry (P ) in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.
Pelzer, Kenley; Greenman, Loren; Gidofalvi, Gergely; Mazziotti, David A
2011-06-09
Polyaromatic hydrocarbons (PAHs) are a class of organic molecules with importance in several branches of science, including medicine, combustion chemistry, and materials science. The delocalized π-orbital systems in PAHs require highly accurate electronic structure methods to capture strong electron correlation. Treating correlation in PAHs has been challenging because (i) traditional wave function methods for strong correlation have not been applicable since they scale exponentially in the number of strongly correlated orbitals, and (ii) alternative methods such as the density-matrix renormalization group and variational two-electron reduced density matrix (2-RDM) methods have not been applied beyond linear acene chains. In this paper we extend the earlier results from active-space variational 2-RDM theory [Gidofalvi, G.; Mazziotti, D. A. J. Chem. Phys. 2008, 129, 134108] to the more general two-dimensional arrangement of rings--acene sheets--to study the relationship between geometry and electron correlation in PAHs. The acene-sheet calculations, if performed with conventional wave function methods, would require wave function expansions with as many as 1.5 × 10(17) configuration state functions. To measure electron correlation, we employ several RDM-based metrics: (i) natural-orbital occupation numbers, (ii) the 1-RDM von Neumann entropy, (iii) the correlation energy per carbon atom, and (iv) the squared Frobenius norm of the cumulant 2-RDM. The results confirm a trend of increasing polyradical character with increasing molecular size previously observed in linear PAHs and reveal a corresponding trend in two-dimensional (arch-shaped) PAHs. Furthermore, in PAHs of similar size they show significant variations in correlation with geometry. PAHs with the strictly linear geometry (chains) exhibit more electron correlation than PAHs with nonlinear geometries (sheets).
van Meer, R; Gritsenko, O V; Baerends, E J
2018-03-14
Almost all functionals that are currently used in density matrix functional theory have been created by some a priori ansatz that generates approximations to the second-order reduced density matrix (2RDM). In this paper, a more consistent approach is used: we analyze the 2RDMs (in the natural orbital basis) of rather accurate multi-reference configuration interaction expansions for several small molecules (CH 4 , NH 3 , H 2 O, FH, and N 2 ) and use the knowledge gained to generate new functionals. The analysis shows that a geminal-like structure is present in the 2RDMs, even though no geminal theory has been applied from the onset. It is also shown that the leading non-geminal dynamical correlation contributions are generated by a specific set of double excitations. The corresponding determinants give rise to non-JKL (non Coulomb/Exchange like) multipole-multipole dispersive attractive terms between geminals. Due to the proximity of the geminals, these dispersion terms are large and cannot be omitted, proving pure JKL functionals to be essentially deficient. A second correction emerges from the observation that the "normal" geminal-like exchange between geminals breaks down when one breaks multiple bonds. This problem can be fixed by doubling the exchange between bond broken geminals, effectively restoring the often physically correct high-spin configurations on the bond broken fragments. Both of these corrections have been added to the commonly used antisymmetrized product of strongly orthogonal geminals functional. The resulting non-JKL functional Extended Löwdin-Shull Dynamical-Multibond is capable of reproducing complete active space self-consistent field curves, in which one active orbital is used for each valence electron.
van Meer, R.; Gritsenko, O. V.; Baerends, E. J.
2018-03-01
Almost all functionals that are currently used in density matrix functional theory have been created by some a priori ansatz that generates approximations to the second-order reduced density matrix (2RDM). In this paper, a more consistent approach is used: we analyze the 2RDMs (in the natural orbital basis) of rather accurate multi-reference configuration interaction expansions for several small molecules (CH4, NH3, H2O, FH, and N2) and use the knowledge gained to generate new functionals. The analysis shows that a geminal-like structure is present in the 2RDMs, even though no geminal theory has been applied from the onset. It is also shown that the leading non-geminal dynamical correlation contributions are generated by a specific set of double excitations. The corresponding determinants give rise to non-JKL (non Coulomb/Exchange like) multipole-multipole dispersive attractive terms between geminals. Due to the proximity of the geminals, these dispersion terms are large and cannot be omitted, proving pure JKL functionals to be essentially deficient. A second correction emerges from the observation that the "normal" geminal-like exchange between geminals breaks down when one breaks multiple bonds. This problem can be fixed by doubling the exchange between bond broken geminals, effectively restoring the often physically correct high-spin configurations on the bond broken fragments. Both of these corrections have been added to the commonly used antisymmetrized product of strongly orthogonal geminals functional. The resulting non-JKL functional Extended Löwdin-Shull Dynamical-Multibond is capable of reproducing complete active space self-consistent field curves, in which one active orbital is used for each valence electron.
International Nuclear Information System (INIS)
Piattella, O.F.; Rodrigues, D.C.; Fabris, J.C.; Pacheco, J.A. de Freitas
2013-01-01
We discuss solutions of Vlasov-Einstein equation for collisionless dark matter particles in the context of a flat Friedmann universe. We show that, after decoupling from the primordial plasma, the dark matter phase-space density indicator Q = ρ/(σ 1D 2 ) 3/2 remains constant during the expansion of the universe, prior to structure formation. This well known result is valid for non-relativistic particles and is not ''observer dependent'' as in solutions derived from the Vlasov-Poisson system. In the linear regime, the inclusion of velocity dispersion effects permits to define a physical Jeans length for collisionless matter as function of the primordial phase-space density indicator: λ J = (5π/G) 1/2 Q −1/3 ρ dm −1/6 . The comoving Jeans wavenumber at matter-radiation equality is smaller by a factor of 2-3 than the comoving wavenumber due to free-streaming, contributing to the cut-off of the density fluctuation power spectrum at the lowest scales. We discuss the physical differences between these two scales. For dark matter particles of mass equal to 200 GeV, the derived Jeans mass is 4.3 × 10 −6 M ⊙
International Nuclear Information System (INIS)
Guo, Z.; Lin, P.; Lowengrub, J.S.
2014-01-01
In this paper, we investigate numerically a diffuse interface model for the Navier–Stokes equation with fluid–fluid interface when the fluids have different densities [48]. Under minor reformulation of the system, we show that there is a continuous energy law underlying the system, assuming that all variables have reasonable regularities. It is shown in the literature that an energy law preserving method will perform better for multiphase problems. Thus for the reformulated system, we design a C 0 finite element method and a special temporal scheme where the energy law is preserved at the discrete level. Such a discrete energy law (almost the same as the continuous energy law) for this variable density two-phase flow model has never been established before with C 0 finite element. A Newton method is introduced to linearise the highly non-linear system of our discretization scheme. Some numerical experiments are carried out using the adaptive mesh to investigate the scenario of coalescing and rising drops with differing density ratio. The snapshots for the evolution of the interface together with the adaptive mesh at different times are presented to show that the evolution, including the break-up/pinch-off of the drop, can be handled smoothly by our numerical scheme. The discrete energy functional for the system is examined to show that the energy law at the discrete level is preserved by our scheme
Kishi, Ryohei; Nakano, Masayoshi
2011-04-21
A novel method for the calculation of the dynamic polarizability (α) of open-shell molecular systems is developed based on the quantum master equation combined with the broken-symmetry (BS) time-dependent density functional theory within the Tamm-Dancoff approximation, referred to as the BS-DFTQME method. We investigate the dynamic α density distribution obtained from BS-DFTQME calculations in order to analyze the spatial contributions of electrons to the field-induced polarization and clarify the contributions of the frontier orbital pair to α and its density. To demonstrate the performance of this method, we examine the real part of dynamic α of singlet 1,3-dipole systems having a variety of diradical characters (y). The frequency dispersion of α, in particular in the resonant region, is shown to strongly depend on the exchange-correlation functional as well as on the diradical character. Under sufficiently off-resonant condition, the dynamic α is found to decrease with increasing y and/or the fraction of Hartree-Fock exchange in the exchange-correlation functional, which enhances the spin polarization, due to the decrease in the delocalization effects of π-diradical electrons in the frontier orbital pair. The BS-DFTQME method with the BHandHLYP exchange-correlation functional also turns out to semiquantitatively reproduce the α spectra calculated by a strongly correlated ab initio molecular orbital method, i.e., the spin-unrestricted coupled-cluster singles and doubles.
Güssregen, Stefan; Matter, Hans; Hessler, Gerhard; Lionta, Evanthia; Heil, Jochen; Kast, Stefan M
2017-07-24
Water molecules play an essential role for mediating interactions between ligands and protein binding sites. Displacement of specific water molecules can favorably modulate the free energy of binding of protein-ligand complexes. Here, the nature of water interactions in protein binding sites is investigated by 3D RISM (three-dimensional reference interaction site model) integral equation theory to understand and exploit local thermodynamic features of water molecules by ranking their possible displacement in structure-based design. Unlike molecular dynamics-based approaches, 3D RISM theory allows for fast and noise-free calculations using the same detailed level of solute-solvent interaction description. Here we correlate molecular water entities instead of mere site density maxima with local contributions to the solvation free energy using novel algorithms. Distinct water molecules and hydration sites are investigated in multiple protein-ligand X-ray structures, namely streptavidin, factor Xa, and factor VIIa, based on 3D RISM-derived free energy density fields. Our approach allows the semiquantitative assessment of whether a given structural water molecule can potentially be targeted for replacement in structure-based design. Finally, PLS-based regression models from free energy density fields used within a 3D-QSAR approach (CARMa - comparative analysis of 3D RISM Maps) are shown to be able to extract relevant information for the interpretation of structure-activity relationship (SAR) trends, as demonstrated for a series of serine protease inhibitors.
Energy Technology Data Exchange (ETDEWEB)
Nagata, Keitaro [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba 305-0801 (Japan); Nishimura, Jun [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba 305-0801 (Japan); Department of Particle and Nuclear Physics, School of High Energy Accelerator Science,Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba 305-0801 (Japan); Shimasaki, Shinji [KEK Theory Center, High Energy Accelerator Research Organization,1-1 Oho, Tsukuba 305-0801 (Japan); Research and Education Center for Natural Sciences, Keio University,Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan)
2016-07-14
Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a generalized Banks-Casher relation as we confirm explicitly.
Danel, J.-F.; Kazandjian, L.
2018-06-01
It is shown that the equation of state (EOS) and the radial distribution functions obtained by density-functional theory molecular dynamics (DFT-MD) obey a simple scaling law. At given temperature, the thermodynamic properties and the radial distribution functions given by a DFT-MD simulation remain unchanged if the mole fractions of nuclei of given charge and the average volume per atom remain unchanged. A practical interest of this scaling law is to obtain an EOS table for a fluid from that already obtained for another fluid if it has the right characteristics. Another practical interest of this result is that an asymmetric mixture made up of light and heavy atoms requiring very different time steps can be replaced by a mixture of atoms of equal mass, which facilitates the exploration of the configuration space in a DFT-MD simulation. The scaling law is illustrated by numerical results.
A random matrix model of relaxation
International Nuclear Information System (INIS)
Lebowitz, J L; Pastur, L
2004-01-01
We consider a two-level system, S 2 , coupled to a general n level system, S n , via a random matrix. We derive an integral representation for the mean reduced density matrix ρ(t) of S 2 in the limit n → ∞, and we identify a model of S n which possesses some of the properties expected for macroscopic thermal reservoirs. In particular, it yields the Gibbs form for ρ(∞). We also consider an analog of the van Hove limit and obtain a master equation (Markov dynamics) for the evolution of ρ(t) on an appropriate time scale
Extended biorthogonal matrix polynomials
Directory of Open Access Journals (Sweden)
Ayman Shehata
2017-01-01
Full Text Available The pair of biorthogonal matrix polynomials for commutative matrices were first introduced by Varma and Tasdelen in [22]. The main aim of this paper is to extend the properties of the pair of biorthogonal matrix polynomials of Varma and Tasdelen and certain generating matrix functions, finite series, some matrix recurrence relations, several important properties of matrix differential recurrence relations, biorthogonality relations and matrix differential equation for the pair of biorthogonal matrix polynomials J(A,B n (x, k and K(A,B n (x, k are discussed. For the matrix polynomials J(A,B n (x, k, various families of bilinear and bilateral generating matrix functions are constructed in the sequel.
International Nuclear Information System (INIS)
Klaehn, T.; Blaschke, D.; Typel, S.; Dalen, E. N. E. van; Faessler, A.; Fuchs, C.; Gaitanos, T.; Wolter, H. H.; Grigorian, H.; Ho, A.; Weber, F.; Kolomeitsev, E. E.; Miller, M. C.; Roepke, G.; Truemper, J.; Voskresensky, D. N.
2006-01-01
A new scheme for testing nuclear matter equations of state (EoSs) at high densities using constraints from neutron star (NS) phenomenology and a flow data analysis of heavy-ion collisions is suggested. An acceptable EoS shall not allow the direct Urca process to occur in NSs with masses below 1.5M · , and also shall not contradict flow and kaon production data of heavy-ion collisions. Compact star constraints include the mass measurements of 2.1±0.2M · (1σ level) for PSR J0751+1807 and of 2.0±0.1M · from the innermost stable circular orbit for 4U 1636-536, the baryon mass--gravitational mass relationships from Pulsar B in J0737-3039 and the mass-radius relationships from quasiperiodic brightness oscillations in 4U 0614+09 and from the thermal emission of RX J1856-3754. This scheme is applied to a set of relativistic EoSs which are constrained otherwise from nuclear matter saturation properties. We demonstrate on the given examples that the test scheme due to the quality of the newly emerging astrophysical data leads to useful selection criteria for the high-density behavior of nuclear EoSs
Kurashige, Yuki; Yanai, Takeshi
2011-09-07
We present a second-order perturbation theory based on a density matrix renormalization group self-consistent field (DMRG-SCF) reference function. The method reproduces the solution of the complete active space with second-order perturbation theory (CASPT2) when the DMRG reference function is represented by a sufficiently large number of renormalized many-body basis, thereby being named DMRG-CASPT2 method. The DMRG-SCF is able to describe non-dynamical correlation with large active space that is insurmountable to the conventional CASSCF method, while the second-order perturbation theory provides an efficient description of dynamical correlation effects. The capability of our implementation is demonstrated for an application to the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems that require best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets. The DMRG-CASPT2/cc-pwCV5Z calculations were performed with a large (3d double-shell) active space consisting of 28 orbitals. Our approach using large-size DMRG reference addressed the problems of why the dissociation energy is largely overestimated by CASPT2 with the small active space consisting of 12 orbitals (3d4s), and also is oversensitive to the choice of the zeroth-order Hamiltonian. © 2011 American Institute of Physics
Raney Distributions and Random Matrix Theory
Forrester, Peter J.; Liu, Dang-Zheng
2015-03-01
Recent works have shown that the family of probability distributions with moments given by the Fuss-Catalan numbers permit a simple parameterized form for their density. We extend this result to the Raney distribution which by definition has its moments given by a generalization of the Fuss-Catalan numbers. Such computations begin with an algebraic equation satisfied by the Stieltjes transform, which we show can be derived from the linear differential equation satisfied by the characteristic polynomial of random matrix realizations of the Raney distribution. For the Fuss-Catalan distribution, an equilibrium problem characterizing the density is identified. The Stieltjes transform for the limiting spectral density of the singular values squared of the matrix product formed from inverse standard Gaussian matrices, and standard Gaussian matrices, is shown to satisfy a variant of the algebraic equation relating to the Raney distribution. Supported on , we show that it too permits a simple functional form upon the introduction of an appropriate choice of parameterization. As an application, the leading asymptotic form of the density as the endpoints of the support are approached is computed, and is shown to have some universal features.
International Nuclear Information System (INIS)
Silva, Milena Wollmann da
2013-01-01
In this work, we report a genuine analytical representation for the solution of the neutron point kinetics equation free of the stiffness character, assuming that the reactivity is a continuous and sectionally continuous function of time. To this end, we initially cast the point kinetics equation in a first order linear differential equation. Next, we split the corresponding matrix as a sum of a diagonal matrix with a matrix, whose components contain the off-diagonal elements. Next, expanding the neutron density and the delayed neutron precursors concentrations in a truncated series, and replacing these expansions in the matrix equation, we come out with an equation, which allows to construct a recursive system, a first order matrix differential equation with source. The fundamental characteristic of this system relies on the fact that the corresponding matrix is diagonal, meanwhile the source term is written in terms of the matrix with the off-diagonal components. Further, the first equation of the recursive system has no source and satisfies the initial conditions. On the other hand, the remaining equations satisfy the null initial condition. Due to the diagonal feature of the matrix, we attain analytical solutions for these recursive equations. We also mention that we evaluate the results for any time value, without the analytical continuity because the purposed solution is free on the stiffness character. Finally, we present numerical simulations and comparisons against literature results, considering specific the applications for the following reactivity functions: constant, step, ramp, and sine. (author)
Energy Technology Data Exchange (ETDEWEB)
Barnes, Alexander E. [Carnegie Mellon Univ., Pittsburgh, PA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2017-05-31
The quark model has been successful in classifying the spectrum of mesons observed since the 1960s, however, it fails to explain some of the measured bound states. Lattice QCD predictions have shown that an excited gluonic field may contribute to the quantum numbers of the bound state and form hybrid mesons, qq-bar-g, where g is a constituent gluon. It is possible for some hybrids to possess quantum numbers forbidden by the quark model and are known as \\smoking gun" hybrids due to their lack of mixing with conventional qq-bar states. The GlueX photoproduction experiment at Jefferson Lab in Newport News, VA is designed to study hybrid mesons and to map their spectrum. A 12 GeV electron beam produces 9 GeV linearly polarized photons via coherent bremsstrahlung in a diamond radiator which are incident on a liquid H2 target. In order to determine the photon energy, the use of a tagging spectrometer which measures the energy of the post-bremsstrahlung electron is required. The tagger microscope is a scintillating fiber detector designed to measure the energy of electrons corresponding to the polarized photons. The main focus of this work is the design and construction of the tagger microscope electronics as well as the calibration of the microscope within the experiment. Additionally, the analysis of the reaction gamma-p -> phi-p, where phi (1020) -> K+K-, is discussed. This analysis provides a high-level calibration for GlueX in regards to understanding the acceptance and sensitivity of the detectors to mesons with strange quark content. By studying the phi with linearly polarized photons, information on the production mechanism can be extracted. The measurement of the phi spin-density matrix elements are shown and compared with past data which are found to be in agreement.
Roemelt, Michael; Krewald, Vera; Pantazis, Dimitrios A
2018-01-09
The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed.
Dey, B.; Meyer, C. A.; Bellis, M.; Williams, M.; Adhikari, K. P.; Adikaram, D.; Aghasyan, M.; Amaryan, M. J.; Anderson, M. D.; Anefalos Pereira, S.; Ball, J.; Baltzell, N. A.; Battaglieri, M.; Bedlinskiy, I.; Biselli, A. S.; Bono, J.; Boiarinov, S.; Briscoe, W. J.; Brooks, W. K.; Burkert, V. D.; Carman, D. S.; Celentano, A.; Chandavar, S.; Colaneri, L.; Cole, P. L.; Contalbrigo, M.; Cortes, O.; Crede, V.; D'Angelo, A.; Dashyan, N.; De Vita, R.; De Sanctis, E.; Deur, A.; Djalali, C.; Doughty, D.; Dugger, M.; Dupre, R.; El Alaoui, A.; El Fassi, L.; Elouadrhiri, L.; Fedotov, G.; Fegan, S.; Fleming, J. A.; Garçon, M.; Gevorgyan, N.; Ghandilyan, Y.; Gilfoyle, G. P.; Giovanetti, K. L.; Girod, F. X.; Glazier, D. I.; Goetz, J. T.; Gothe, R. W.; Griffioen, K. A.; Guidal, M.; Hafidi, K.; Hanretty, C.; Harrison, N.; Hattawy, M.; Hicks, K.; Ho, D.; Holtrop, M.; Hyde, C. E.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Jenkins, D.; Jo, H. S.; Joo, K.; Keller, D.; Khandaker, M.; Kim, A.; Kim, W.; Klein, A.; Klein, F. J.; Koirala, S.; Kubarovsky, V.; Kuhn, S. E.; Kuleshov, S. V.; Lenisa, P.; Livingston, K.; Lu, H.; MacGregor, I. J. D.; Markov, N.; Mayer, M.; McCracken, M. E.; McKinnon, B.; Mineeva, T.; Mirazita, M.; Mokeev, V.; Montgomery, R. A.; Moriya, K.; Moutarde, H.; Munevar, E.; Munoz Camacho, C.; Nadel-Turonski, P.; Niccolai, S.; Niculescu, G.; Niculescu, I.; Osipenko, M.; Pappalardo, L. L.; Paremuzyan, R.; Park, K.; Pasyuk, E.; Peng, P.; Phillips, J. J.; Pisano, S.; Pogorelko, O.; Pozdniakov, S.; Price, J. W.; Procureur, S.; Protopopescu, D.; Puckett, A. J. R.; Rimal, D.; Ripani, M.; Ritchie, B. G.; Rizzo, A.; Rossi, P.; Roy, P.; Sabatié, F.; Saini, M. S.; Schott, D.; Schumacher, R. A.; Seder, E.; Senderovich, I.; Sharabian, Y. G.; Simonyan, A.; Smith, E. S.; Sober, D. I.; Sokhan, D.; Stepanyan, S. S.; Stoler, P.; Strakovsky, I. I.; Strauch, S.; Sytnik, V.; Taiuti, M.; Tang, W.; Tkachenko, S.; Ungaro, M.; Vernarsky, B.; Vlassov, A. V.; Voskanyan, H.; Voutier, E.; Walford, N. K.; Watts, D. P.; Zachariou, N.; Zana, L.; Zhang, J.; Zhao, Z. W.; Zonta, I.; CLAS Collaboration
2014-05-01
High-statistics measurements of differential cross sections and spin density matrix elements for the reaction γp →ϕp have been made using the CLAS detector at Jefferson Lab. We cover center-of-mass energies (√s ) from 1.97 to 2.84 GeV, with an extensive coverage in the ϕ production angle. The high statistics of the data sample made it necessary to carefully account for the interplay between the ϕ natural lineshape and effects of the detector resolution, that are found to be comparable in magnitude. We study both the charged- (ϕ →K+K-) and neutral- (ϕ →KS0KL0) KK ¯ decay modes of the ϕ. Further, for the charged mode, we differentiate between the cases where the final K- track is directly detected or its momentum reconstructed as the total missing momentum in the event. The two charged-mode topologies and the neutral-mode have different resolutions and are calibrated against each other. Extensive usage is made of kinematic fitting to improve the reconstructed ϕ mass resolution. Our final results are reported in 10- and mostly 30-MeV-wide √s bins for the charged- and the neutral-modes, respectively. Possible effects from K+Λ* channels with pKK ¯ final states are discussed. These present results constitute the most precise and extensive ϕ photoproduction measurements to date and in conjunction with the ω photoproduction results recently published by CLAS, will greatly improve our understanding of low energy vector meson photoproduction.
Liouville equation of relativistic charged fermion
International Nuclear Information System (INIS)
Wang Renchuan; Zhu Dongpei; Huang Zhuoran; Ko Che-ming
1991-01-01
As a form of density martrix, the Wigner function is the distribution in quantum phase space. It is a 2 X 2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4 x 4 matrix function. In this paper authors obtain a Wigner function for the relativistic fermion in the form of 2 x 2 matrix, and the Liouville equation satisfied by the Wigner function. this equivalent to the Dirac equation of changed fermion in QED. The equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). Authors prove that the 2 x 2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with above Wigner function
Gozem, Samer; Melaccio, Federico; Valentini, Alessio; Filatov, Michael; Huix-Rotllant, Miquel; Ferré, Nicolas; Frutos, Luis Manuel; Angeli, Celestino; Krylov, Anna I; Granovsky, Alexander A; Lindh, Roland; Olivucci, Massimo
2014-08-12
We report and characterize ground-state and excited-state potential energy profiles using a variety of electronic structure methods along a loop lying on the branching plane associated with a conical intersection (CI) of a reduced retinal model, the penta-2,4-dieniminium cation (PSB3). Whereas the performance of the equation-of-motion coupled-cluster, density functional theory, and multireference methods had been tested along the excited- and ground-state paths of PSB3 in our earlier work, the ability of these methods to correctly describe the potential energy surface shape along a CI branching plane has not yet been investigated. This is the focus of the present contribution. We find, in agreement with earlier studies by others, that standard time-dependent DFT (TDDFT) does not yield the correct two-dimensional (i.e., conical) crossing along the branching plane but rather a one-dimensional (i.e., linear) crossing along the same plane. The same type of behavior is found for SS-CASPT2(IPEA=0), SS-CASPT2(IPEA=0.25), spin-projected SF-TDDFT, EOM-SF-CCSD, and, finally, for the reference MRCISD+Q method. In contrast, we found that MRCISD, CASSCF, MS-CASPT2(IPEA=0), MS-CASPT2(IPEA=0.25), XMCQDPT2, QD-NEVPT2, non-spin-projected SF-TDDFT, and SI-SA-REKS yield the expected conical crossing. To assess the effect of the different crossing topologies (i.e., linear or conical) on the PSB3 photoisomerization efficiency, we discuss the results of 100 semiclassical trajectories computed by CASSCF and SS-CASPT2(IPEA=0.25) for a PSB3 derivative. We show that for the same initial conditions, the two methods yield similar dynamics leading to isomerization quantum yields that differ by only a few percent.
Adebesin, B. O.; Rabiu, A. B.; Obrou, O. K.; Adeniyi, J. O.
2018-03-01
The F2 layer peak electron density (NmF2) was investigated over Korhogo (Geomagnetic: 1.26°S, 67.38°E), a station near the magnetic equator in the African sector. Data for 1996 and 2000 were, respectively, categorized into low solar quiet and disturbed and high solar quiet and disturbed. NmF2 prenoon peak was higher than the postnoon peak during high solar activity irrespective of magnetic activity condition, while the postnoon peak was higher for low solar activity. Higher NmF2 peak amplitude characterizes disturbed magnetic activity than quiet magnetic condition for any solar activity. The maximum peaks appeared in equinox. June solstice noontime bite out lagged other seasons by 1-2 h. For any condition of solar and magnetic activities, the daytime NmF2 percentage variability (%VR) measured by the relative standard deviation maximizes/minimizes in June solstice/equinox. Daytime variability increases with increasing magnetic activity. The highest peak in the morning time NmF2 variability occurs in equinox, while the highest evening/nighttime variability appeared in June solstice for all solar/magnetic conditions. The nighttime annual variability amplitude is higher during disturbed than quiet condition regardless of solar activity period. At daytime, variability is similar for all conditions of solar activities. NmF2 at Korhogo is well represented on the International Reference Ionosphere-International Radio Consultative Committee (IRI-CCIR) option. The model/observation relationship performed best between local midnight and postmidnight period (00-08 LT). The noontime trough characteristics is not prominent in the IRI pattern during high solar activity but evident during low solar conditions when compared with Korhogo observations. The Nash-Sutcliffe coefficients revealed better model performance during disturbed activities.
Nuclear reaction matrix and nuclear forces
International Nuclear Information System (INIS)
Nagata, Sinobu; Bando, Hiroharu; Akaishi, Yoshinori.
1979-01-01
An essentially exact method of solution is presented for the reaction- matrix (G-matrix) equation defined with the orthogonalized plane-wave intermediate spectrum for high-lying two-particle states. The accuracy is examined for introduced truncations and also in comparison with the Tsai-Kuo and Sauer methods. Properties of the G-matrix are discussed with emphasis on the relation with the saturation mechanism, especially overall saturation from light to heavy nuclei. Density and starting-energy dependences of the G-matrix are separately extracted and discussed. It is demonstrated that the triplet-even tensor component of the nuclear force is principally responsible for these dependences and hence for the saturation mechanism. In this context different nuclear potentials are used in the renormalized Brueckner calculation for energies of closed-shell nuclei in the harmonic oscillator basis. A semi-phenomenological ''two-body potential'' is devised so that it can reproduce the saturation energies and densities of nuclear matter and finite nuclei in the lowest-order Brueckner treatment. It is composed of a realistic N-N potential and two additional parts; one incorporates the three-body force effect and the other is assumed to embody higher-cluster correlations in G. The tensor component in the triplet-even state of this potential is enhanced by the three-body force effect. The G-matrix is represented in the effective local form and decomposed into central, LS and tensor components. (author)
Fractional Schroedinger equation
International Nuclear Information System (INIS)
Laskin, Nick
2002-01-01
Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations
Belitsky, A. V.
2017-10-01
The Operator Product Expansion for null polygonal Wilson loop in planar maximally supersymmetric Yang-Mills theory runs systematically in terms of multi-particle pentagon transitions which encode the physics of excitations propagating on the color flux tube ending on the sides of the four-dimensional contour. Their dynamics was unraveled in the past several years and culminated in a complete description of pentagons as an exact function of the 't Hooft coupling. In this paper we provide a solution for the last building block in this program, the SU(4) matrix structure arising from internal symmetry indices of scalars and fermions. This is achieved by a recursive solution of the Mirror and Watson equations obeyed by the so-called singlet pentagons and fixing the form of the twisted component in their tensor decomposition. The non-singlet, or charged, pentagons are deduced from these by a limiting procedure.
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A.V. Belitsky
2017-10-01
Full Text Available The Operator Product Expansion for null polygonal Wilson loop in planar maximally supersymmetric Yang–Mills theory runs systematically in terms of multi-particle pentagon transitions which encode the physics of excitations propagating on the color flux tube ending on the sides of the four-dimensional contour. Their dynamics was unraveled in the past several years and culminated in a complete description of pentagons as an exact function of the 't Hooft coupling. In this paper we provide a solution for the last building block in this program, the SU(4 matrix structure arising from internal symmetry indices of scalars and fermions. This is achieved by a recursive solution of the Mirror and Watson equations obeyed by the so-called singlet pentagons and fixing the form of the twisted component in their tensor decomposition. The non-singlet, or charged, pentagons are deduced from these by a limiting procedure.
Updated User's Guide for Sammy: Multilevel R-Matrix Fits to Neutron Data Using Bayes' Equations
Energy Technology Data Exchange (ETDEWEB)
Larson, Nancy M [ORNL
2008-10-01
In 1980 the multilevel multichannel R-matrix code SAMMY was released for use in analysis of neutron-induced cross section data at the Oak Ridge Electron Linear Accelerator. Since that time, SAMMY has evolved to the point where it is now in use around the world for analysis of many different types of data. SAMMY is not limited to incident neutrons but can also be used for incident protons, alpha particles, or other charged particles; likewise, Coulomb exit hannels can be included. Corrections for a wide variety of experimental conditions are available in the code: Doppler and resolution broadening, multiple-scattering corrections for capture or reaction yields, normalizations and backgrounds, to name but a few. The fitting procedure is Bayes' method, and data and parameter covariance matrices are properly treated within the code. Pre- and post-processing capabilities are also available, including (but not limited to) connections with the Evaluated Nuclear Data Files. Though originally designed for use in the resolved resonance region, SAMMY also includes a treatment for data analysis in the unresolved resonance region.
Energy Technology Data Exchange (ETDEWEB)
Silva, Milena Wollmann da
2013-08-01
In this work, we report a genuine analytical representation for the solution of the neutron point kinetics equation free of the stiffness character, assuming that the reactivity is a continuous and sectionally continuous function of time. To this end, we initially cast the point kinetics equation in a first order linear differential equation. Next, we split the corresponding matrix as a sum of a diagonal matrix with a matrix, whose components contain the off-diagonal elements. Next, expanding the neutron density and the delayed neutron precursors concentrations in a truncated series, and replacing these expansions in the matrix equation, we come out with an equation, which allows to construct a recursive system, a first order matrix differential equation with source. The fundamental characteristic of this system relies on the fact that the corresponding matrix is diagonal, meanwhile the source term is written in terms of the matrix with the off-diagonal components. Further, the first equation of the recursive system has no source and satisfies the initial conditions. On the other hand, the remaining equations satisfy the null initial condition. Due to the diagonal feature of the matrix, we attain analytical solutions for these recursive equations. We also mention that we evaluate the results for any time value, without the analytical continuity because the purposed solution is free on the stiffness character. Finally, we present numerical simulations and comparisons against literature results, considering specific the applications for the following reactivity functions: constant, step, ramp, and sine. (author)
Notes on Mayer expansions and matrix models
International Nuclear Information System (INIS)
Bourgine, Jean-Emile
2014-01-01
Mayer cluster expansion is an important tool in statistical physics to evaluate grand canonical partition functions. It has recently been applied to the Nekrasov instanton partition function of N=2 4d gauge theories. The associated canonical model involves coupled integrations that take the form of a generalized matrix model. It can be studied with the standard techniques of matrix models, in particular collective field theory and loop equations. In the first part of these notes, we explain how the results of collective field theory can be derived from the cluster expansion. The equalities between free energies at first orders is explained by the discrete Laplace transform relating canonical and grand canonical models. In a second part, we study the canonical loop equations and associate them with similar relations on the grand canonical side. It leads to relate the multi-point densities, fundamental objects of the matrix model, to the generating functions of multi-rooted clusters. Finally, a method is proposed to derive loop equations directly on the grand canonical model
arXiv GeV-scale hot sterile neutrino oscillations: a derivation of evolution equations
Ghiglieri, J.
2017-05-23
Starting from operator equations of motion and making arguments based on a separation of time scales, a set of equations is derived which govern the non-equilibrium time evolution of a GeV-scale sterile neutrino density matrix and active lepton number densities at temperatures T > 130 GeV. The density matrix possesses generation and helicity indices; we demonstrate how helicity permits for a classification of various sources for leptogenesis. The coefficients parametrizing the equations are determined to leading order in Standard Model couplings, accounting for the LPM resummation of 1+n 2+n scatterings and for all 2 2 scatterings. The regime in which sphaleron processes gradually decouple so that baryon plus lepton number becomes a separate non-equilibrium variable is also considered.
Non-markovian boltzmann equation
International Nuclear Information System (INIS)
Kremp, D.; Bonitz, M.; Kraeft, W.D.; Schlanges, M.
1997-01-01
A quantum kinetic equation for strongly interacting particles (generalized binary collision approximation, ladder or T-matrix approximation) is derived in the framework of the density operator technique. In contrast to conventional kinetic theory, which is valid on large time scales as compared to the collision (correlation) time only, our approach retains the full time dependencies, especially also on short time scales. This means retardation and memory effects resulting from the dynamics of binary correlations and initial correlations are included. Furthermore, the resulting kinetic equation conserves total energy (the sum of kinetic and potential energy). The second aspect of generalization is the inclusion of many-body effects, such as self-energy, i.e., renormalization of single-particle energies and damping. To this end we introduce an improved closure relation to the Bogolyubov endash Born endash Green endash Kirkwood endash Yvon hierarchy. Furthermore, in order to express the collision integrals in terms of familiar scattering quantities (Mo/ller operator, T-matrix), we generalize the methods of quantum scattering theory by the inclusion of medium effects. To illustrate the effects of memory and damping, the results of numerical simulations are presented. copyright 1997 Academic Press, Inc
Density and starting-energy dependent effective interaction
International Nuclear Information System (INIS)
Yamaguchi, Norio; Nagata, Sinobu; Kasuga, Teruo
1979-01-01
A new effective potential constructed from the reaction matrix calculation of nuclear matters is proposed, taking three-body effects into account. Starting from the two-body scattering equation for nuclear matters, an equation with averaged momentum is introduced as the definition of effective interaction. The parameters in the equation are the Fermi momentum and the starting energy. The nuclear density dependence and the starting energy dependence are independently treated in the potential. The effective interactions including three-body effects were calculated. The dependence on the starting energy is large. The effective interaction is more attractive in the triplet E state, and assures overall saturation without any artificial renormalization. The reaction matrix calculation can be well reproduced by the calculation with this effective potential. The results of calculation for the binding energy of He-4 and O-16 and the shell model matrix elements of O-16 are represented. (Kato, T.)
Two derivations of the master equation of quantum Brownian motion
Energy Technology Data Exchange (ETDEWEB)
Halliwell, J J [Blackett Laboratory, Imperial College, London SW7 2BZ (United Kingdom)
2007-03-23
Central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment, such as that of Joos and Zeh. Such master equations enjoy a close relationship with spontaneous localization models, like the GRW model. The aim of this paper is to present two derivations of the master equation. The first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible, focusing on physical principles and without the complications of S-matrix theory. This derivation may serve as a useful tutorial example for students attempting to learn this subject area. The second is the opposite: a very general derivation using non-relativistic many-body field theory. It reduces to the equation of the type given by Joos and Zeh in the one-particle sector, but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence. This master equation also emphasizes the role of local number density as the 'preferred basis' for decoherence in this model.
Two derivations of the master equation of quantum Brownian motion
International Nuclear Information System (INIS)
Halliwell, J J
2007-01-01
Central to many discussion of decoherence is a master equation for the reduced density matrix of a massive particle experiencing scattering from its surrounding environment, such as that of Joos and Zeh. Such master equations enjoy a close relationship with spontaneous localization models, like the GRW model. The aim of this paper is to present two derivations of the master equation. The first derivation is a pedagogical model designed to illustrate the origins of the master equation as simply as possible, focusing on physical principles and without the complications of S-matrix theory. This derivation may serve as a useful tutorial example for students attempting to learn this subject area. The second is the opposite: a very general derivation using non-relativistic many-body field theory. It reduces to the equation of the type given by Joos and Zeh in the one-particle sector, but correcting certain numerical factors which have recently become significant in connection with experimental tests of decoherence. This master equation also emphasizes the role of local number density as the 'preferred basis' for decoherence in this model
Green's matrix for a second-order self-adjoint matrix differential operator
International Nuclear Information System (INIS)
Sisman, Tahsin Cagri; Tekin, Bayram
2010-01-01
A systematic construction of the Green's matrix for a second-order self-adjoint matrix differential operator from the linearly independent solutions of the corresponding homogeneous differential equation set is carried out. We follow the general approach of extracting the Green's matrix from the Green's matrix of the corresponding first-order system. This construction is required in the cases where the differential equation set cannot be turned to an algebraic equation set via transform techniques.
Quantum statistics of stimulated Raman and hyper-Raman scattering by master equation approach
International Nuclear Information System (INIS)
Gupta, P.S.; Dash, J.
1991-01-01
A quantum theoretical density matrix formalism of stimulated Raman and hyper-Raman scattering using master equation approach is presented. The atomic system is described by two energy levels. The effects of upper level population and the cavity loss are incorporated. The photon statistics, coherence characteristics and the building up of the Stokes field are investigated. (author). 8 figs., 5 refs
International Nuclear Information System (INIS)
Marziliano, P.A.; Menguzzato, G.; Scuderi, A.; Scalise, C.; Coletta, V.
2017-01-01
Aim of study: We built biomass expansion factors (BCEFs) from Douglas-fir felled trees planted with different planting densities to evaluate the differences according tree size and planting density. Area of study: The Douglas-fir plantation under study is located on the northern coastal chain of Calabria (Tyrrhenian side) south Italy. Materials and methods: We derived tree level BCEFs, relative to crown (BCEFc), to stem (BCEFst = basic density, BD) and total above-ground (BCEFt) from destructive measurements carried out in a Douglas-fir plantation where four study plots were selected according to different planting densities (from 833 to 2500 trees per hectare). The measured BCEFs were regressed against diameter at breast height and total height, planting density, site productivity (SP) and their interactions to test the variation of BCEFs. Analysis of variance (ANOVA) and the post hoc Tukey comparison test were used to test differences in BCEFt, BCEFc and in BD between plots with different planting density. Main results: BCEFs decreased with increasing total height and DBH, but large dispersion measures were obtained for any of the compartments in the analysis. An increasing trend with planting density was found for all the analyzed BCEFs, but together with planting density, BCEFs also resulted dependent upon site productivity. BCEFt average values ranged between 1.40 Mg m-3 in planting density with 833 trees/ha (PD833) to 2.09 Mg m-3 in planting density with 2500 trees/ha (PD2500), which are in the range of IPCC prescribed values for Douglas-fir trees. Research highlights: Our results showed that the application of BCEF to estimate forest biomass in stands with different planting densities should explicitly account for the effect of planting density and site productivity.
Energy Technology Data Exchange (ETDEWEB)
Marziliano, P.A.; Menguzzato, G.; Scuderi, A.; Scalise, C.; Coletta, V.
2017-11-01
Aim of study: We built biomass expansion factors (BCEFs) from Douglas-fir felled trees planted with different planting densities to evaluate the differences according tree size and planting density. Area of study: The Douglas-fir plantation under study is located on the northern coastal chain of Calabria (Tyrrhenian side) south Italy. Materials and methods: We derived tree level BCEFs, relative to crown (BCEFc), to stem (BCEFst = basic density, BD) and total above-ground (BCEFt) from destructive measurements carried out in a Douglas-fir plantation where four study plots were selected according to different planting densities (from 833 to 2500 trees per hectare). The measured BCEFs were regressed against diameter at breast height and total height, planting density, site productivity (SP) and their interactions to test the variation of BCEFs. Analysis of variance (ANOVA) and the post hoc Tukey comparison test were used to test differences in BCEFt, BCEFc and in BD between plots with different planting density. Main results: BCEFs decreased with increasing total height and DBH, but large dispersion measures were obtained for any of the compartments in the analysis. An increasing trend with planting density was found for all the analyzed BCEFs, but together with planting density, BCEFs also resulted dependent upon site productivity. BCEFt average values ranged between 1.40 Mg m-3 in planting density with 833 trees/ha (PD833) to 2.09 Mg m-3 in planting density with 2500 trees/ha (PD2500), which are in the range of IPCC prescribed values for Douglas-fir trees. Research highlights: Our results showed that the application of BCEF to estimate forest biomass in stands with different planting densities should explicitly account for the effect of planting density and site productivity.
Matrix product approach for the asymmetric random average process
International Nuclear Information System (INIS)
Zielen, F; Schadschneider, A
2003-01-01
We consider the asymmetric random average process which is a one-dimensional stochastic lattice model with nearest-neighbour interaction but continuous and unbounded state variables. First, the explicit functional representations, so-called beta densities, of all local interactions leading to steady states of product measure form are rigorously derived. This also completes an outstanding proof given in a previous publication. Then we present an alternative solution for the processes with factorized stationary states by using a matrix product ansatz. Due to continuous state variables we obtain a matrix algebra in the form of a functional equation which can be solved exactly
Yamashita, Shizuya; Kawase, Ryota; Nakaoka, Hajime; Nakatani, Kazuhiro; Inagaki, Miwako; Yuasa-Kawase, Miyako; Tsubakio-Yamamoto, Kazumi; Sandoval, Jose C; Masuda, Daisaku; Ohama, Tohru; Nakagawa-Toyama, Yumiko; Matsuyama, Akifumi; Nishida, Makoto; Ishigami, Masato
2009-12-01
In routine clinical laboratory testing and numerous epidemiological studies, LDL-cholesterol (LDL-C) has been estimated commonly using the Friedewald equation. We investigated the relationship between the Friedewald equation and 4 homogeneous assays for LDL-C. LDL-C was determined by 4 homogeneous assays [liquid selective detergent method: LDL-C (L), selective solubilization method: LDL-C (S), elimination method: LDL-C (E), and enzyme selective protecting method: LDL-C (P)]. Samples with discrepancies between the Friedewald equation and the 4 homogeneous assays for LDL-C were subjected to polyacrylamide gel electrophoresis and the beta-quantification method. The correlations between the Friedewald equation and the 4 homogeneous LDL-C assays were as follows: LDL-C (L) (r=0.962), LDL-C (S) (r=0.986), LDL-C (E) (r=0.946) and LDL-C (P) (r=0.963). Discrepancies were observed in sera from type III hyperlipoproteinemia patients and in sera containing large amounts of midband and small dense LDL on polyacrylamide gel electrophoresis. LDL-C (S) was most strongly correlated with the beta-quantification method even in sera from patients with type III hyperlipoproteinemia. Of the 4 homogeneous assays for LDL-C, LDL-C (S) exhibited the closest correlation with the Friedewald equation and the beta-quantification method, thus reflecting the current clinical databases for coronary heart disease.
Kaneko, Ai; Sankai, Yoshiyuki
2014-01-01
The primary culture of neuronal cells plays an important role in neuroscience. There has long been a need for methods enabling the long-term culture of primary neurons at low density, in defined serum-free medium. However, the lower the cell density, the more difficult it is to maintain the cells in culture. Therefore, we aimed to develop a method for long-term culture of neurons at low density, in serum-free medium, without the need for a glial feeder layer. Here, we describe the work leading to our determination of a protocol for long-term (>2 months) primary culture of rat hippocampal neurons in serum-free medium at the low density of 3×10(4) cells/mL (8.9×10(3) cells/cm2) without a glial feeder layer. Neurons were cultured on a three-dimensional nanofibrous hydrogel, PuraMatrix, and sandwiched under a coverslip to reproduce the in vivo environment, including the three-dimensional extracellular matrix, low-oxygen conditions, and exposure to concentrated paracrine factors. We examined the effects of varying PuraMatrix concentrations, the timing and presence or absence of a coverslip, the timing of neuronal isolation from embryos, cell density at plating, medium components, and changing the medium or not on parameters such as developmental pattern, cell viability, neuronal ratio, and neurite length. Using our method of combining the sandwich culture technique with PuraMatrix in Neurobasal medium/B27/L-glutamine for primary neuron culture, we achieved longer neurites (≥3,000 µm), greater cell viability (≥30%) for 2 months, and uniform culture across the wells. We also achieved an average neuronal ratio of 97%, showing a nearly pure culture of neurons without astrocytes. Our method is considerably better than techniques for the primary culture of neurons, and eliminates the need for a glial feeder layer. It also exhibits continued support for axonal elongation and synaptic activity for long periods (>6 weeks).
Directory of Open Access Journals (Sweden)
Ai Kaneko
Full Text Available The primary culture of neuronal cells plays an important role in neuroscience. There has long been a need for methods enabling the long-term culture of primary neurons at low density, in defined serum-free medium. However, the lower the cell density, the more difficult it is to maintain the cells in culture. Therefore, we aimed to develop a method for long-term culture of neurons at low density, in serum-free medium, without the need for a glial feeder layer. Here, we describe the work leading to our determination of a protocol for long-term (>2 months primary culture of rat hippocampal neurons in serum-free medium at the low density of 3×10(4 cells/mL (8.9×10(3 cells/cm2 without a glial feeder layer. Neurons were cultured on a three-dimensional nanofibrous hydrogel, PuraMatrix, and sandwiched under a coverslip to reproduce the in vivo environment, including the three-dimensional extracellular matrix, low-oxygen conditions, and exposure to concentrated paracrine factors. We examined the effects of varying PuraMatrix concentrations, the timing and presence or absence of a coverslip, the timing of neuronal isolation from embryos, cell density at plating, medium components, and changing the medium or not on parameters such as developmental pattern, cell viability, neuronal ratio, and neurite length. Using our method of combining the sandwich culture technique with PuraMatrix in Neurobasal medium/B27/L-glutamine for primary neuron culture, we achieved longer neurites (≥3,000 µm, greater cell viability (≥30% for 2 months, and uniform culture across the wells. We also achieved an average neuronal ratio of 97%, showing a nearly pure culture of neurons without astrocytes. Our method is considerably better than techniques for the primary culture of neurons, and eliminates the need for a glial feeder layer. It also exhibits continued support for axonal elongation and synaptic activity for long periods (>6 weeks.
The transfer matrix approach to circular graphene quantum dots
International Nuclear Information System (INIS)
Nguyen, H Chau; Nguyen, Nhung T T; Nguyen, V Lien
2016-01-01
We adapt the transfer matrix (T -matrix) method originally designed for one-dimensional quantum mechanical problems to solve the circularly symmetric two-dimensional problem of graphene quantum dots. Similar to one-dimensional problems, we show that the generalized T -matrix contains rich information about the physical properties of these quantum dots. In particular, it is shown that the spectral equations for bound states as well as quasi-bound states of a circular graphene quantum dot and related quantities such as the local density of states and the scattering coefficients are all expressed exactly in terms of the T -matrix for the radial confinement potential. As an example, we use the developed formalism to analyse physical aspects of a graphene quantum dot induced by a trapezoidal radial potential. Among the obtained results, it is in particular suggested that the thermal fluctuations and electrostatic disorders may appear as an obstacle to controlling the valley polarization of Dirac electrons. (paper)
Milovanovic, Petar; Djuric, Marija; Rakocevic, Zlatko
2012-11-01
There is an increasing interest in bone nano-structure, the ultimate goal being to reveal the basis of age-related bone fragility. In this study, power spectral density (PSD) data and fractal dimensions of the mineralized bone matrix were extracted from atomic force microscope topography images of the femoral neck trabeculae. The aim was to evaluate age-dependent differences in the mineralized matrix of human bone and to consider whether these advanced nano-descriptors might be linked to decreased bone remodeling observed by some authors and age-related decline in bone mechanical competence. The investigated bone specimens belonged to a group of young adult women (n = 5, age: 20-40 years) and a group of elderly women (n = 5, age: 70-95 years) without bone diseases. PSD graphs showed the roughness density distribution in relation to spatial frequency. In all cases, there was a fairly linear decrease in magnitude of the power spectra with increasing spatial frequencies. The PSD slope was steeper in elderly individuals (-2.374 vs. -2.066), suggesting the dominance of larger surface morphological features. Fractal dimension of the mineralized bone matrix showed a significant negative trend with advanced age, declining from 2.467 in young individuals to 2.313 in the elderly (r = 0.65, P = 0.04). Higher fractal dimension in young women reflects domination of smaller mineral grains, which is compatible with the more freshly remodeled structure. In contrast, the surface patterns in elderly individuals were indicative of older tissue age. Lower roughness and reduced structural complexity (decreased fractal dimension) of the interfibrillar bone matrix in the elderly suggest a decline in bone toughness, which explains why aged bone is more brittle and prone to fractures. © 2012 The Authors Journal of Anatomy © 2012 Anatomical Society.
Directory of Open Access Journals (Sweden)
K. Banoo
1998-01-01
equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.
Structure and properties of Hughston's stochastic extension of the Schroedinger equation
International Nuclear Information System (INIS)
Adler, Stephen L.; Horwitz, Lawrence P.
2000-01-01
Hughston has recently proposed a stochastic extension of the Schroedinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston's equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston's equation to earlier work on norm-preserving stochastic equations, and show that Hughston's equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston's, suffices to give an objective interpretation of the measurement process in quantum mechanics. (c) 2000 American Institute of Physics
A density tensor hierarchy for open system dynamics: retrieving the noise
International Nuclear Information System (INIS)
Adler, Stephen L
2007-01-01
We develop a density tensor hierarchy for open system dynamics that recovers information about fluctuations (or 'noise') lost in passing to the reduced density matrix. For the case of fluctuations arising from a classical probability distribution, the hierarchy is formed from expectations of products of pure state density matrix elements and can be compactly summarized by a simple generating function. For the case of quantum fluctuations arising when a quantum system interacts with a quantum environment in an overall pure state, the corresponding hierarchy is defined as the environmental trace of products of system matrix elements of the full density matrix. Whereas all members of the classical noise hierarchy are system observables, only the lowest member of the quantum noise hierarchy is directly experimentally measurable. The unit trace and idempotence properties of the pure state density matrix imply descent relations for the tensor hierarchies, that relate the order n tensor, under contraction of appropriate pairs of tensor indices, to the order n - 1 tensor. As examples to illustrate the classical probability distribution formalism, we consider a spatially isotropic ensemble of spin-1/2 pure states, a quantum system evolving by an Ito stochastic Schroedinger equation and a quantum system evolving by a jump process Schroedinger equation. As examples to illustrate the corresponding trace formalism in the quantum fluctuation case, we consider the tensor hierarchies for collisional Brownian motion of an infinite mass Brownian particle and for the weak coupling Born-Markov master equation. In different specializations, the latter gives the hierarchies generalizing the quantum optical master equation and the Caldeira-Leggett master equation. As a further application of the density tensor, we contrast stochastic Schroedinger equations that reduce and that do not reduce the state vector, and discuss why a quantum system coupled to a quantum environment behaves like
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Directory of Open Access Journals (Sweden)
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
DEFF Research Database (Denmark)
de Lasson, Jakob Rosenkrantz; Mørk, Jesper; Kristensen, Philip Trøst
2013-01-01
We present a numerical formalism for solving the Lippmann–Schwinger equation for the electric field in three dimensions. The formalism may be applied to scatterers of different shapes and embedded in different background media, and we develop it in detail for the specific case of spherical scatte...
Directory of Open Access Journals (Sweden)
Hao Li
2016-01-01
Full Text Available 1,1,1,2,3,3,3-Heptafluoropropane (R227ea is a good refrigerant that reduces greenhouse effects and ozone depletion. In practical applications, we usually have to know the compressed liquid densities at different temperatures and pressures. However, the measurement requires a series of complex apparatus and operations, wasting too much manpower and resources. To solve these problems, here, Song and Mason equation, support vector machine (SVM, and artificial neural networks (ANNs were used to develop theoretical and machine learning models, respectively, in order to predict the compressed liquid densities of R227ea with only the inputs of temperatures and pressures. Results show that compared with the Song and Mason equation, appropriate machine learning models trained with precise experimental samples have better predicted results, with lower root mean square errors (RMSEs (e.g., the RMSE of the SVM trained with data provided by Fedele et al. [1] is 0.11, while the RMSE of the Song and Mason equation is 196.26. Compared to advanced conventional measurements, knowledge-based machine learning models are proved to be more time-saving and user-friendly.
International Nuclear Information System (INIS)
Zhalij, Alexander
2002-01-01
We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field
Head-Marsden, Kade; Mazziotti, David A
2015-02-07
For an open, time-dependent quantum system, Lindblad derived the most general modification of the quantum Liouville equation in the Markovian approximation that models environmental effects while preserving the non-negativity of the system's density matrix. While Lindblad's modification is correct for N-electron density matrices, solution of the Liouville equation with a Lindblad operator causes the one-electron reduced density matrix (1-RDM) to violate the Pauli exclusion principle. Consequently, after a short time, the 1-RDM is not representable by an ensemble N-electron density matrix (not ensemble N-representable). In this communication, we derive the necessary and sufficient constraints on the Lindbladian matrix within the Lindblad operator to ensure that the 1-RDM remains N-representable for all time. The theory is illustrated by considering the relaxation of an excitation in several molecules F2, N2, CO, and BeH2 subject to environmental noise.
Directory of Open Access Journals (Sweden)
Geoff Recktenwald
2013-04-01
Full Text Available Zirconium dioxide has received particular attention as a fuel matrix because of its ability to form a solid solution with transuranic elements, natural radiation stability and desirable mechanical properties. However, zirconium dioxide has a lower coefficient of thermal conductivity than uranium dioxide and this presents an obstacle to the deployment of these fuels in commercial reactors. Here we show that axial doping of a zirconium dioxide based fuel with erbium reduces power peaking and fuel temperature. Full core simulations of a modified AP1000 core were done using MCNPX 2.7.0. The inert matrix fuel contained 15 w/o transuranics at its beginning of life and constituted 28% of the assemblies in the core. Axial doping reduced power peaking at startup by more than ~23% in the axial direction and reduced the peak to average power within the core from 1.80 to 1.44. The core was able to remain critical between refueling while running at a simulated 2000 MWth on an 18 month refueling cycle. The results show that the reactor would maintain negative core average reactivity and void coefficients during operation. This type of fuel cycle would reduce the overall production of transuranics in a pressurized water reactor by 86%.
Ziegler, Tom; Krykunov, Mykhaylo; Autschbach, Jochen
2014-09-09
The random phase approximation (RPA) equation of adiabatic time dependent density functional ground state response theory (ATDDFT) has been used extensively in studies of excited states. It extracts information about excited states from frequency dependent ground state response properties and avoids, thus, in an elegant way, direct Kohn-Sham calculations on excited states in accordance with the status of DFT as a ground state theory. Thus, excitation energies can be found as resonance poles of frequency dependent ground state polarizability from the eigenvalues of the RPA equation. ATDDFT is approximate in that it makes use of a frequency independent energy kernel derived from the ground state functional. It is shown in this study that one can derive the RPA equation of ATDDFT from a purely variational approach in which stationary states above the ground state are located using our constricted variational DFT (CV-DFT) method and the ground state functional. Thus, locating stationary states above the ground state due to one-electron excitations with a ground state functional is completely equivalent to solving the RPA equation of TDDFT employing the same functional. The present study is an extension of a previous work in which we demonstrated the equivalence between ATDDFT and CV-DFT within the Tamm-Dancoff approximation.
Tveito, Aslak; Lines, Glenn T; Edwards, Andrew G; McCulloch, Andrew
2016-07-01
Markov models are ubiquitously used to represent the function of single ion channels. However, solving the inverse problem to construct a Markov model of single channel dynamics from bilayer or patch-clamp recordings remains challenging, particularly for channels involving complex gating processes. Methods for solving the inverse problem are generally based on data from voltage clamp measurements. Here, we describe an alternative approach to this problem based on measurements of voltage traces. The voltage traces define probability density functions of the functional states of an ion channel. These probability density functions can also be computed by solving a deterministic system of partial differential equations. The inversion is based on tuning the rates of the Markov models used in the deterministic system of partial differential equations such that the solution mimics the properties of the probability density function gathered from (pseudo) experimental data as well as possible. The optimization is done by defining a cost function to measure the difference between the deterministic solution and the solution based on experimental data. By evoking the properties of this function, it is possible to infer whether the rates of the Markov model are identifiable by our method. We present applications to Markov model well-known from the literature. Copyright © 2016 The Authors. Published by Elsevier Inc. All rights reserved.
On the dilute gas two particle density matrices of p--H2 and He4
International Nuclear Information System (INIS)
Weres, O.
1976-01-01
In the preceding paper we demonstrated that the reduced two- particle density matrix of simple quantum liquids could profitably be re-expressed in terms of a Taylor expansion of its logarithm about the diagonal. In the present publication we examine the Taylor coefficients which arise when the dilute gas two particle density matrix is expanded in this way. In particular, we evaluate the leading coefficients of p-H 2 and He 4 exactly and extend the Wigner--Kirkwood approximation to provided approximate expressions for them. We demonstrate how these approximate expressions may be applied to yield results superior to those yielded by the ordinary Wigner--Kirkwood approximation. In an appendix we demonstrate how the Block equation for the dilute gas two particle density matrix may be reduced to an equivalent closed set of equations for the leading Taylor coefficients
Octonionic matrix representation and electromagnetism
Energy Technology Data Exchange (ETDEWEB)
Chanyal, B. C. [Kumaun University, S. S. J. Campus, Almora (India)
2014-12-15
Keeping in mind the important role of octonion algebra, we have obtained the electromagnetic field equations of dyons with an octonionic 8 x 8 matrix representation. In this paper, we consider the eight - dimensional octonionic space as a combination of two (external and internal) four-dimensional spaces for the existence of magnetic monopoles (dyons) in a higher-dimensional formalism. As such, we describe the octonion wave equations in terms of eight components from the 8 x 8 matrix representation. The octonion forms of the generalized potential, fields and current source of dyons in terms of 8 x 8 matrix are discussed in a consistent manner. Thus, we have obtained the generalized Dirac-Maxwell equations of dyons from an 8x8 matrix representation of the octonion wave equations in a compact and consistent manner. The generalized Dirac-Maxwell equations are fully symmetric Maxwell equations and allow for the possibility of magnetic charges and currents, analogous to electric charges and currents. Accordingly, we have obtained the octonionic Dirac wave equations in an external field from the matrix representation of the octonion-valued potentials of dyons.
International Nuclear Information System (INIS)
Laenen, E.
1995-01-01
We propose a new evolution equation for the gluon density relevant for the region of small x B . It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multigluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed α s . We find that the effects of multigluon correlations on the deep-inelastic structure function are small. (orig.)
International Nuclear Information System (INIS)
Seifert, N.; Gibson, N.D.; Risley, J.S.
1995-01-01
In continuation of our previous work, charge transfer processes occurring in protons on rare-gas-atom collisions have been investigated. Diagonal and real off-diagonal coherence elements of the density matrix for H(n=3) atoms produced in 20--100-keV electron-capture collisions with Kr atoms are experimentally determined by analyzing the Balmer-α light from the decay of H atoms from the (n=3) state to the (n=2) state. The intensity and polarization of the emitted light are measured as functions of an axially symmetric electric field in the collision region. These data are fitted to a numerical model of the H atom in an electric field in order to extract density-matrix elements. The results are compared to previous studies of H + on He and Ar. The collisionally produced dipole moment of the H(n=3) atom decreases for increasing atomic number of the rare-gas target atoms, which indicates that the final phase of the collision process is not essential for the formation of the dipole moment. This physical picture is further supported by our alignment data. Absolute cross sections for charge transfer to the 3s, 3p, and 3d levels are presented as well
Energy Technology Data Exchange (ETDEWEB)
Brandenburg, G W; Carnegie, R K; Cashmore, R J; Davier, M; Lasinski, T A; Leith, D W.G.S.; Mathews, J A.J.; Walden, P; Williams, S H [Stanford Linear Accelerator Center, Calif. (USA)
1976-03-01
The differential cross sections and density matrix elements for the phi and rho/sup 0/ mesons have been measured in the reactions K/sup -/p..-->..K/sup -/K/sup +/(..lambda..,..sigma../sup 0/) and K/sup -/p..--> pi../sup -/..pi../sup +/(..lambda..,..sigma../sup 0/) at 13 GeV using a wire chamber spectrometer. The analysis shows that while the vector meson production is dominated by the natural parity exchange amplitude, some unnatural parity exchange is also required. Furthermore the phi and rho natural exchange cross sections are identical in shape and have the 2:1 relative strength expected in the quark model with K* and K** exchange degeneracy. The analysis of the clear peak-dip rho/sup 0/-..omega.. interference pattern observed in the ..pi../sup -/..pi../sup +/ data indicates that the ..omega.. production is in phase with the rho and of similar magnitude. Both the S* and f' meson are clearly observed in this experiment. The S* data are found to be consistent with S* parameters deduced from ..pi pi.. scattering analyses. The f' density matrix elements and a new limit on the f'..--> pi../sup -/..pi../sup +/ branching ratio are presented.
DEFF Research Database (Denmark)
Yang, Q.; Goding, S.; Hagenaars, M.
2006-01-01
. Analyses of tumors for extracellular matrix (ECM) components and PECAM-1(+) vasculature, revealed that the I-R lesions are hypovascularized and contain very little laminin, collagen and fibronectin. In contrast, the I-P loose tumors are well-vascularized and they contain high amounts of ECM components....... Interestingly, the distribution pattern of ECM components in the I-P loose tumors is almost identical to that of the normal lung tissue, indicating that these tumors develop around the alveolar walls which provide the loose tumors with both a supporting tissue and a rich blood supply. In conclusion, tumor...... infiltration by activated NK and T cells correlates with the presence of ECM components and PECAM-1(+) vasculature in the malignant tissue. Thus, analysis of the distribution of ECM and vasculature in tumor biopsies may help select patients most likely to benefit from cellular adoptive immunotherapy....
Franklin, Joel N
2003-01-01
Mathematically rigorous introduction covers vector and matrix norms, the condition-number of a matrix, positive and irreducible matrices, much more. Only elementary algebra and calculus required. Includes problem-solving exercises. 1968 edition.
DEFF Research Database (Denmark)
Yan, Jun; Jacobsen, Karsten W.; Thygesen, Kristian S.
2012-01-01
-dimensional systems of graphene and hexagonal boron-nitride (h-BN) we find good agreement with previous many-body calculations. For the graphene/h-BN interface we find that the fundamental and optical gaps of the h-BN layer are reduced by 2.0 and 0.7 eV, respectively, compared to freestanding h-BN. This reduction......We present an efficient implementation of the Bethe-Salpeter equation (BSE) for optical properties of materials in the projector augmented wave method Grid-based projector-augmented wave method (GPAW). Single-particle energies and wave functions are obtained from the Gritsenko, Leeuwen, Lenthe...
Two-mode Gaussian density matrices and squeezing of photons
International Nuclear Information System (INIS)
Tucci, R.R.
1992-01-01
In this paper, the authors generalize to 2-mode states the 1-mode state results obtained in a previous paper. The authors study 2-mode Gaussian density matrices. The authors find a linear transformation which maps the two annihilation operators, one for each mode, into two new annihilation operators that are uncorrelated and unsqueezed. This allows the authors to express the density matrix as a product of two 1-mode density matrices. The authors find general conditions under which 2-mode Gaussian density matrices become pure states. Possible pure states include the 2-mode squeezed pure states commonly mentioned in the literature, plus other pure states never mentioned before. The authors discuss the entropy and thermodynamic laws (Second Law, Fundamental Equation, and Gibbs-Duhem Equation) for the 2-mode states being considered
Hohn, Franz E
2012-01-01
This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics. The work starts with the most basic laws of matrix algebra and progresses to the sweep-out process for obtaining the complete solution of any given system of linear equations - homogeneous or nonhomogeneous - and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology.Other subjects include the complete treatment of the structur
Decoherence, discord, and the quantum master equation for cosmological perturbations
Hollowood, Timothy J.; McDonald, Jamie I.
2017-05-01
We examine environmental decoherence of cosmological perturbations in order to study the quantum-to-classical transition and the impact of noise on entanglement during inflation. Given an explicit interaction between the system and environment, we derive a quantum master equation for the reduced density matrix of perturbations, drawing parallels with quantum Brownian motion, where we see the emergence of fluctuation and dissipation terms. Although the master equation is not in Lindblad form, we see how typical solutions exhibit positivity on super-horizon scales, leading to a physically meaningful density matrix. This allows us to write down a Langevin equation with stochastic noise for the classical trajectories which emerge from the quantum system on super-horizon scales. In particular, we find that environmental decoherence increases in strength as modes exit the horizon, with the growth driven essentially by white noise coming from local contributions to environmental correlations. Finally, we use our master equation to quantify the strength of quantum correlations as captured by discord. We show that environmental interactions have a tendency to decrease the size of the discord and that these effects are determined by the relative strength of the expansion rate and interaction rate of the environment. We interpret this in terms of the competing effects of particle creation versus environmental fluctuations, which tend to increase and decrease the discord respectively.
Variational principles for particles and fields in Heisenberg matrix mechanics
International Nuclear Information System (INIS)
Klein, A.; Li, C.T.; Vassanji, M.
1980-01-01
For many years we have advocated a form of quantum mechanics based on the application of sum rule methods (completeness) to the equations of motion and to the commutation relations, i.e., to Heisenberg matrix mechanics. Sporadically we have discussed or alluded to a variational foundation for this method. In this paper we present a series of variational principles applicable to a range of systems from one-dimensional quantum mechanics to quantum fields. The common thread is that the stationary quantity is the trace of the Hamiltonian over Hilbert space (or over a subspace of interest in an approximation) expressed as a functional of matrix elements of the elementary operators of the theory. These parameters are constrained by the kinematical relations of the theory introduced by the method of Lagrange multipliers. For the field theories, variational principles in which matrix elements of the density operators are chosen as fundamental are also developed. A qualitative discussion of applications is presented
Quantum mechanics in matrix form
Ludyk, Günter
2018-01-01
This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matrix calculus. Only a brief description of Schrödinger's wave mechanics is given (in most books exclusively treated), to show their equivalence to Heisenberg's matrix method. In the first part the historical development of Quantum theory by Planck, Bohr and Sommerfeld is sketched, followed by the ideas and methods of Heisenberg, Born and Jordan. Then Pauli's spin and exclusion principles are treated. Pauli's exclusion principle leads to the structure of atoms. Finally, Dirac´s relativistic quantum mechanics is shortly presented. Matrices and matrix equations are today easy to handle when implementing numerical algorithms using standard software as MAPLE and Mathematica.
Semiconductor spintronics: The full matrix approach
Rossani, A.
2015-12-01
A new model, based on an asymptotic procedure for solving the spinor kinetic equations of electrons and phonons is proposed, which gives naturally the displaced Fermi-Dirac distribution function at the leading order. The balance equations for the electron number, energy density and momentum, plus the Poisson’s equation, constitute now a system of six equations. Moreover, two equations for the evolution of the spin densities are added, which account for a general dispersion relation.