Müller, Thomas
2009-11-12
The accurate prediction of the potential energy function of the X1Sigmag+ state of Cr2 is a remarkable challenge; large differential electron correlation effects, significant scalar relativistic contributions, the need for large flexible basis sets containing g functions, the importance of semicore valence electron correlation, and its multireference nature pose considerable obstacles. So far, the only reasonable successful approaches were based on multireference perturbation theory (MRPT). Recently, there was some controversy in the literature about the role of error compensation and systematic defects of various MRPT implementations that cannot be easily overcome. A detailed basis set study of the potential energy function is presented, adopting a variational method. The method of choice for this electron-rich target with up to 28 correlated electrons is fully uncontracted multireference-averaged quadratic coupled cluster (MR-AQCC), which shares the flexibility of the multireference configuration interaction (MRCI) approach and is, in addition, approximately size-extensive (0.02 eV in error as compared to the MRCI value of 1.37 eV for two noninteracting chromium atoms). The best estimate for De arrives at 1.48 eV and agrees well with the experimental data of 1.47 +/- 0.056 eV. At the estimated CBS limit, the equilibrium bond distance (1.685 A) and vibrational frequency (459 cm-1) are in agreement with experiment (1.679 A, 481 cm-1). Large basis sets and reference configuration spaces invariably result in huge wave function expansions (here, up to 2.8 billion configuration state functions), and efficient parallel implementations of the method are crucial. Hence, relevant details on implementation and general performance of the parallel program code are discussed as well.
Symmetric coupling of angular momenta, quadratic algebras and discrete polynomials
International Nuclear Information System (INIS)
Aquilanti, V; Marinelli, D; Marzuoli, A
2014-01-01
Eigenvalues and eigenfunctions of the volume operator, associated with the symmetric coupling of three SU(2) angular momentum operators, can be analyzed on the basis of a discrete Schrödinger–like equation which provides a semiclassical Hamiltonian picture of the evolution of a 'quantum of space', as shown by the authors in [1]. Emphasis is given here to the formalization in terms of a quadratic symmetry algebra and its automorphism group. This view is related to the Askey scheme, the hierarchical structure which includes all hypergeometric polynomials of one (discrete or continuous) variable. Key tool for this comparative analysis is the duality operation defined on the generators of the quadratic algebra and suitably extended to the various families of overlap functions (generalized recoupling coefficients). These families, recognized as lying at the top level of the Askey scheme, are classified and a few limiting cases are addressed
Bozkaya, Uǧur; Turney, Justin M.; Yamaguchi, Yukio; Schaefer, Henry F.; Sherrill, C. David
2011-09-01
Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the molecular orbitals (MOs) for the coupled-cluster doubles (CCD) method and second-order Møller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply "OD" and "OMP2" for short), respectively. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response density matrices, the MO gradient, and the MO Hessian are reported both in spin-orbital and closed-shell spin-adapted forms. The Newton-Raphson algorithm is used for the optimization procedure using the MO gradient and Hessian. Further, orbital stability analyses are also carried out at correlated levels. The OD and OMP2 approaches are compared with the standard MP2, CCD, CCSD, and CCSD(T) methods. All these methods are applied to H2O, three diatomics, and the O_4^+ molecule. Results demonstrate that the CCSD and OD methods give nearly identical results for H2O and diatomics; however, in symmetry-breaking problems as exemplified by O_4^+, the OD method provides better results for vibrational frequencies. The OD method has further advantages over CCSD: its analytic gradients are easier to compute since there is no need to solve the coupled-perturbed equations for the orbital response, the computation of one-electron properties are easier because there is no response contribution to the particle density matrices, the variational optimized orbitals can be readily extended to allow inactive orbitals, it avoids spurious second-order poles in its response function, and its transition dipole moments are gauge invariant. The OMP2 has these same advantages over canonical MP2, making it promising for excited state properties via linear response theory. The quadratically convergent orbital-optimization procedure converges quickly for OMP2, and provides molecular properties that
Projected coupled cluster theory.
Qiu, Yiheng; Henderson, Thomas M; Zhao, Jinmo; Scuseria, Gustavo E
2017-08-14
Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system or has to artificially break certain symmetries. On the other hand, projected Hartree-Fock theory captures the essential physics of many kinds of strong correlations via symmetry breaking and restoration. In this work, we combine and try to retain the merits of these two methods by applying symmetry projection to broken symmetry coupled cluster wave functions. The non-orthogonal nature of states resulting from the application of symmetry projection operators furnishes particle-hole excitations to all orders, thus creating an obstacle for the exact evaluation of overlaps. Here we provide a solution via a disentanglement framework theory that can be approximated rigorously and systematically. Results of projected coupled cluster theory are presented for molecules and the Hubbard model, showing that spin projection significantly improves unrestricted coupled cluster theory while restoring good quantum numbers. The energy of projected coupled cluster theory reduces to the unprojected one in the thermodynamic limit, albeit at a much slower rate than projected Hartree-Fock.
Photon–phonon parametric oscillation induced by quadratic coupling in an optomechanical resonator
International Nuclear Information System (INIS)
Zhang, Lin; Ji, Fengzhou; Zhang, Xu; Zhang, Weiping
2017-01-01
A direct photon–phonon parametric effect of quadratic coupling on the mean-field dynamics of an optomechanical resonator in the large-scale-movement regime is found and investigated. Under a weak pumping power, the mechanical resonator damps to a steady state with a nonlinear static response sensitively modified by the quadratic coupling. When the driving power increases beyond the static energy balance, the steady states lose their stabilities via Hopf bifurcations, and the resonator produces stable self-sustained oscillation (limit-circle behavior) of discrete energies with step-like amplitudes due to the parametric effect of quadratic coupling, which can be understood roughly by the power balance between gain and loss on the resonator. A further increase in the pumping power can induce a chaotic dynamic of the resonator via a typical routine of period-doubling bifurcation, but which can be stabilized by the parametric effect through an inversion-bifurcation process back to the limit-circle states. The bifurcation-to-inverse-bifurcation transitions are numerically verified by the maximal Lyapunov exponents of the dynamics, which indicate an efficient way of suppressing the chaotic behavior of the optomechanical resonator by quadratic coupling. Furthermore, the parametric effect of quadratic coupling on the dynamic transitions of an optomechanical resonator can be conveniently detected or traced by the output power spectrum of the cavity field. (paper)
Selective Linear or Quadratic Optomechanical Coupling via Measurement
Directory of Open Access Journals (Sweden)
Michael R. Vanner
2011-11-01
Full Text Available The ability to engineer both linear and nonlinear coupling with a mechanical resonator is an important goal for the preparation and investigation of macroscopic mechanical quantum behavior. In this work, a measurement based scheme is presented where linear or square mechanical-displacement coupling can be achieved using the optomechanical interaction that is linearly proportional to the mechanical position. The resulting square-displacement measurement strength is compared to that attainable in the dispersive case that has a direct interaction with the mechanical-displacement squared. An experimental protocol and parameter set are discussed for the generation and observation of non-Gaussian states of motion of the mechanical element.
Covariant quantization of Lagrangians with quadratic dependent fields and derivative couplings
International Nuclear Information System (INIS)
Lam, C.S.; Wang, K.
1977-01-01
A covariant path-integral formula is derived for Lagrangians with quadratic dependent fields and derivative couplings. It differs from the naive one by a factor which can be viewed graphically as due to the coupling with ghost fields. These path integrals can be shown to be unitary and to satisfy equations of motion if and only if this extra factor is present. Applications of this formula to gauge and other field theories are discussed
Inelastic scattering in a local polaron model with quadratic coupling to bosons
DEFF Research Database (Denmark)
Olsen, Thomas
2009-01-01
We calculate the inelastic scattering probabilities in the wide band limit of a local polaron model with quadratic coupling to bosons. The central object is a two-particle Green's function which is calculated exactly using a purely algebraic approach. Compared with the usual linear interaction term...... a quadratic interaction term gives higher probabilities for inelastic scattering involving a large number of bosons. As an application we consider the problem hot-electron-mediated energy transfer at surfaces and use the delta self-consistent field extension of density-functional theory to calculate...
Optical-response properties in hybrid optomechanical systems with quadratic coupling
Sun, Xue-Jian; Wang, Xin; Liu, Li-Na; Liu, Wen-Xiao; Fang, Ai-Ping; Li, Hong-Rong
2018-02-01
We theoretically investigate the optical-response properties of the four-mode quadratically coupled optomechanical system (OMS), in which two standard OMSs with quadratic coupling are coupled to each other via a common waveguide. In the presence of a strong control field applied to one cavity and a weak probe field applied to the other, we show that by suitably tuning the system parameters, there appears the normal mode splitting, optomechanically induced absorption, and double or triple electromagnetically induced transparency phenomena in the probe absorption spectrum. In particular, the explicit physical explanations for those fantastic phenomena are detailed discussed. Moreover, we also show that our proposal can be exploited to implement the optical switch as well as the slow and fast light effects.
Dynamical correlation functions of the quadratic coupling spin-Boson model
Zheng, Da-Chuan; Tong, Ning-Hua
2017-06-01
The spin-boson model with quadratic coupling is studied using the bosonic numerical renormalization group method. We focus on the dynamical auto-correlation functions {C}O(ω ), with the operator \\hat{O} taken as {\\hat{{{σ }}}}x, {\\hat{{{σ }}}}z, and \\hat{X}, respectively. In the weak-coupling regime α qualitatively, showing enhanced dephasing at the spin flip point. Project supported by the National Key Basic Research Program of China (Grant No. 2012CB921704), the National Natural Science Foundation of China (Grant No. 11374362), the Fundamental Research Funds for the Central Universities, China, and the Research Funds of Renmin University of China (Grant No. 15XNLQ03).
Optimal linear-quadratic control of coupled parabolic-hyperbolic PDEs
Aksikas, I.; Moghadam, A. Alizadeh; Forbes, J. F.
2017-10-01
This paper focuses on the optimal control design for a system of coupled parabolic-hypebolic partial differential equations by using the infinite-dimensional state-space description and the corresponding operator Riccati equation. Some dynamical properties of the coupled system of interest are analysed to guarantee the existence and uniqueness of the solution of the linear-quadratic (LQ)-optimal control problem. A state LQ-feedback operator is computed by solving the operator Riccati equation, which is converted into a set of algebraic and differential Riccati equations, thanks to the eigenvalues and the eigenvectors of the parabolic operator. The results are applied to a non-isothermal packed-bed catalytic reactor. The LQ-optimal controller designed in the early portion of the paper is implemented for the original nonlinear model. Numerical simulations are performed to show the controller performances.
BCS superconductivity for weakly coupled clusters
International Nuclear Information System (INIS)
Friedel, J.
1992-01-01
BCS superconductivity is expected to have fairly high critical temperatures when clusters of moderate sizes are weakly coupled to form a crystal. This remark extends to quasi zerodimensional cases, a remark initially made by Labbe for quasi one-dimensional ones and by Hirsch, Bok and Labbe for quasi twodimensional ones. Possible applications are envisaged for twodimensional clusters (fullerene) or threedimensional ones (metal clusters, Chevrel phases). Conditions for optimal applicability of the scheme are somewhat restricted. (orig.)
Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun
2018-01-01
In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.
Chen, Xin; Fan, Ruihua; Chen, Yiming; Zhai, Hui; Zhang, Pengfei
2017-11-17
The Sachdev-Ye-Kitaev (SYK) model is a concrete solvable model to study non-Fermi liquid properties, holographic duality, and maximally chaotic behavior. In this work, we consider a generalization of the SYK model that contains two SYK models with a different number of Majorana modes coupled by quadratic terms. This model is also solvable, and the solution shows a zero-temperature quantum phase transition between two non-Fermi liquid chaotic phases. This phase transition is driven by tuning the ratio of two mode numbers, and a nonchaotic Fermi liquid sits at the critical point with an equal number of modes. At a finite temperature, the Fermi liquid phase expands to a finite regime. More intriguingly, a different non-Fermi liquid phase emerges at a finite temperature. We characterize the phase diagram in terms of the spectral function, the Lyapunov exponent, and the entropy. Our results illustrate a concrete example of the quantum phase transition and critical behavior between two non-Fermi liquid phases.
Coupled Cluster Theory for Large Molecules
DEFF Research Database (Denmark)
Baudin, Pablo
This thesis describes the development of local approximations to coupled cluster (CC) theory for large molecules. Two different methods are presented, the divide–expand–consolidate scheme (DEC), for the calculation of ground state energies, and a local framework denoted LoFEx, for the calculation...
The polarizable embedding coupled cluster method
DEFF Research Database (Denmark)
Sneskov, Kristian; Schwabe, Tobias; Kongsted, Jacob
2011-01-01
We formulate a new combined quantum mechanics/molecular mechanics (QM/MM) method based on a self-consistent polarizable embedding (PE) scheme. For the description of the QM region, we apply the popular coupled cluster (CC) method detailing the inclusion of electrostatic and polarization effects...
Exponential quadratic operators and evolution of bosonic systems coupled to a heat bath
International Nuclear Information System (INIS)
Ni Xiaotong; Liu Yuxi; Kwek, L. C.; Wang Xiangbin
2010-01-01
Using exponential quadratic operators, we present a general framework for studying the exact dynamics of system-bath interaction in which the Hamiltonian is described by the quadratic form of bosonic operators. To demonstrate the versatility of the approach, we study how the environment affects the squeezing of quadrature components of the system. We further propose that the squeezing can be enhanced when parity kicks are applied to the system.
Stochastic coupled cluster theory: Efficient sampling of the coupled cluster expansion
Scott, Charles J. C.; Thom, Alex J. W.
2017-09-01
We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behavior of a coupled cluster wavefunction representation, we propose new approaches based on an intuitive, well-defined condition for sampling weights and on sampling the expansion in cluster operators of different excitation levels. We term these modifications even and truncated selections, respectively. Utilising both approaches demonstrates dramatically improved calculation stability as well as reduced computational and memory costs. These modifications are particularly effective at higher truncation levels owing to the large number of terms within the cluster expansion that can be neglected, as demonstrated by the reduction of the number of terms to be sampled when truncating at triple excitations by 77% and hextuple excitations by 98%.
Seniority-based coupled cluster theory
International Nuclear Information System (INIS)
Henderson, Thomas M.; Scuseria, Gustavo E.; Bulik, Ireneusz W.; Stein, Tamar
2014-01-01
Doubly occupied configuration interaction (DOCI) with optimized orbitals often accurately describes strong correlations while working in a Hilbert space much smaller than that needed for full configuration interaction. However, the scaling of such calculations remains combinatorial with system size. Pair coupled cluster doubles (pCCD) is very successful in reproducing DOCI energetically, but can do so with low polynomial scaling (N 3 , disregarding the two-electron integral transformation from atomic to molecular orbitals). We show here several examples illustrating the success of pCCD in reproducing both the DOCI energy and wave function and show how this success frequently comes about. What DOCI and pCCD lack are an effective treatment of dynamic correlations, which we here add by including higher-seniority cluster amplitudes which are excluded from pCCD. This frozen pair coupled cluster approach is comparable in cost to traditional closed-shell coupled cluster methods with results that are competitive for weakly correlated systems and often superior for the description of strongly correlated systems
Soudackov, Alexander V; Hammes-Schiffer, Sharon
2015-11-21
Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at high temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton
International Nuclear Information System (INIS)
Soudackov, Alexander V.; Hammes-Schiffer, Sharon
2015-01-01
Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at high temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton
Seniority zero pair coupled cluster doubles theory
International Nuclear Information System (INIS)
Stein, Tamar; Henderson, Thomas M.; Scuseria, Gustavo E.
2014-01-01
Coupled cluster theory with single and double excitations accurately describes weak electron correlation but is known to fail in cases of strong static correlation. Fascinatingly, however, pair coupled cluster doubles (p-CCD), a simplified version of the theory limited to pair excitations that preserve the seniority of the reference determinant (i.e., the number of unpaired electrons), has mean field computational cost and is an excellent approximation to the full configuration interaction (FCI) of the paired space provided that the orbital basis defining the pairing scheme is adequately optimized. In previous work, we have shown that optimization of the pairing scheme in the seniority zero FCI leads to a very accurate description of static correlation. The same conclusion extends to p-CCD if the orbitals are optimized to make the p-CCD energy stationary. We here demonstrate these results with numerous examples. We also explore the contributions of different seniority sectors to the coupled cluster doubles (CCD) correlation energy using different orbital bases. We consider both Hartree-Fock and Brueckner orbitals, and the role of orbital localization. We show how one can pair the orbitals so that the role of the Brueckner orbitals at the CCD level is retained at the p-CCD level. Moreover, we explore ways of extending CCD to accurately describe strongly correlated systems
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding.
Krause, Katharina; Klopper, Wim
2016-01-28
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian.
Communication: A simplified coupled-cluster Lagrangian for polarizable embedding
International Nuclear Information System (INIS)
Krause, Katharina; Klopper, Wim
2016-01-01
A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian
Landau, Arie
2013-07-07
This paper presents a new method for calculating spectroscopic properties in the framework of response theory utilizing a sequence of similarity transformations (STs). The STs are preformed using the coupled cluster (CC) and Fock-space coupled cluster operators. The linear and quadratic response functions of the new similarity transformed CC response (ST-CCR) method are derived. The poles of the linear response yield excitation-energy (EE) expressions identical to the ones in the similarity transformed equation-of-motion coupled cluster (STEOM-CC) approach. ST-CCR and STEOM-CC complement each other, in analogy to the complementarity of CC response (CCR) and equation-of-motion coupled cluster (EOM-CC). ST-CCR/STEOM-CC and CCR/EOM-CC yield size-extensive and size-intensive EEs, respectively. Other electronic-properties, e.g., transition dipole strengths, are also size-extensive within ST-CCR, in contrast to STEOM-CC. Moreover, analysis suggests that in comparison with CCR, the ST-CCR expressions may be confined to a smaller subspace, however, the precise scope of the truncation can only be determined numerically. In addition, reformulation of the time-independent STEOM-CC using the same parameterization as in ST-CCR, as well as an efficient truncation scheme, is presented. The shown convergence of the time-dependent and time-independent expressions displays the completeness of the presented formalism.
Recent advances in coupled-cluster methods
Bartlett, Rodney J
1997-01-01
Today, coupled-cluster (CC) theory has emerged as the most accurate, widely applicable approach for the correlation problem in molecules. Furthermore, the correct scaling of the energy and wavefunction with size (i.e. extensivity) recommends it for studies of polymers and crystals as well as molecules. CC methods have also paid dividends for nuclei, and for certain strongly correlated systems of interest in field theory.In order for CC methods to have achieved this distinction, it has been necessary to formulate new, theoretical approaches for the treatment of a variety of essential quantities
Computational Aspects of Nuclear Coupled-Cluster Theory
International Nuclear Information System (INIS)
Dean, David Jarvis; Hagen, Gaute; Hjorth-Jensen, M.; Papenbrock, T.F.
2008-01-01
Coupled-cluster theory represents an important theoretical tool that we use to solve the quantum many-body problem. Coupled-cluster theory also lends itself to computation in a parallel computing environment. In this article, we present selected results from ab initio studies of stable and weakly bound nuclei utilizing computational techniques that we employ to solve coupled-cluster theory. We also outline several perspectives for future research directions in this area.
Collapsing spherical star in Scalar-Einstein-Gauss-Bonnet gravity with a quadratic coupling
Chakrabarti, Soumya
2018-04-01
We study the evolution of a self interacting scalar field in Einstein-Gauss-Bonnet theory in four dimension where the scalar field couples non minimally with the Gauss-Bonnet term. Considering a polynomial coupling of the scalar field with the Gauss-Bonnet term, a self-interaction potential and an additional perfect fluid distribution alongwith the scalar field, we investigate different possibilities regarding the outcome of the collapsing scalar field. The strength of the coupling and choice of the self-interaction potential serves as the pivotal initial conditions of the models presented. The high degree of non-linearity in the equation system is taken care off by using a method of invertibe point transformation of anharmonic oscillator equation, which has proven itself very useful in recent past while investigating dynamics of minimally coupled scalar fields.
Can Single-Reference Coupled Cluster Theory Describe Static Correlation?
Bulik, Ireneusz W; Henderson, Thomas M; Scuseria, Gustavo E
2015-07-14
While restricted single-reference coupled cluster theory truncated to singles and doubles (CCSD) provides very accurate results for weakly correlated systems, it usually fails in the presence of static or strong correlation. This failure is generally attributed to the qualitative breakdown of the reference, and can accordingly be corrected by using a multideterminant reference, including higher-body cluster operators in the ansatz, or allowing symmetry breaking in the reference. None of these solutions are ideal; multireference coupled cluster is not black box, including higher-body cluster operators is computationally demanding, and allowing symmetry breaking leads to the loss of good quantum numbers. It has long been recognized that quasidegeneracies can instead be treated by modifying the coupled cluster ansatz. The recently introduced pair coupled cluster doubles (pCCD) approach is one such example which avoids catastrophic failures and accurately models strong correlations in a symmetry-adapted framework. Here, we generalize pCCD to a singlet-paired coupled cluster model (CCD0) intermediate between coupled cluster doubles and pCCD, yielding a method that possesses the invariances of the former and much of the stability of the latter. Moreover, CCD0 retains the full structure of coupled cluster theory, including a fermionic wave function, antisymmetric cluster amplitudes, and well-defined response equations and density matrices.
Geometry and transport in a model of two coupled quadratic nonlinear waveguides
DEFF Research Database (Denmark)
Stirling, James R.; Bang, Ole; Christiansen, Peter Leth
2008-01-01
This paper applies geometric methods developed to understand chaos and transport in Hamiltonian systems to the study of power distribution in nonlinear waveguide arrays. The specific case of two linearly coupled X(2) waveguides is modeled and analyzed in terms of transport and geometry in the pha...
Cluster synchronization induced by one-node clusters in networks with asymmetric negative couplings
International Nuclear Information System (INIS)
Zhang, Jianbao; Ma, Zhongjun; Zhang, Gang
2013-01-01
This paper deals with the problem of cluster synchronization in networks with asymmetric negative couplings. By decomposing the coupling matrix into three matrices, and employing Lyapunov function method, sufficient conditions are derived for cluster synchronization. The conditions show that the couplings of multi-node clusters from one-node clusters have beneficial effects on cluster synchronization. Based on the effects of the one-node clusters, an effective and universal control scheme is put forward for the first time. The obtained results may help us better understand the relation between cluster synchronization and cluster structures of the networks. The validity of the control scheme is confirmed through two numerical simulations, in a network with no cluster structure and in a scale-free network
Cluster synchronization induced by one-node clusters in networks with asymmetric negative couplings
Zhang, Jianbao; Ma, Zhongjun; Zhang, Gang
2013-12-01
This paper deals with the problem of cluster synchronization in networks with asymmetric negative couplings. By decomposing the coupling matrix into three matrices, and employing Lyapunov function method, sufficient conditions are derived for cluster synchronization. The conditions show that the couplings of multi-node clusters from one-node clusters have beneficial effects on cluster synchronization. Based on the effects of the one-node clusters, an effective and universal control scheme is put forward for the first time. The obtained results may help us better understand the relation between cluster synchronization and cluster structures of the networks. The validity of the control scheme is confirmed through two numerical simulations, in a network with no cluster structure and in a scale-free network.
Singlet-paired coupled cluster theory for open shells
Gomez, John A.; Henderson, Thomas M.; Scuseria, Gustavo E.
2016-06-01
Restricted single-reference coupled cluster theory truncated to single and double excitations accurately describes weakly correlated systems, but often breaks down in the presence of static or strong correlation. Good coupled cluster energies in the presence of degeneracies can be obtained by using a symmetry-broken reference, such as unrestricted Hartree-Fock, but at the cost of good quantum numbers. A large body of work has shown that modifying the coupled cluster ansatz allows for the treatment of strong correlation within a single-reference, symmetry-adapted framework. The recently introduced singlet-paired coupled cluster doubles (CCD0) method is one such model, which recovers correct behavior for strong correlation without requiring symmetry breaking in the reference. Here, we extend singlet-paired coupled cluster for application to open shells via restricted open-shell singlet-paired coupled cluster singles and doubles (ROCCSD0). The ROCCSD0 approach retains the benefits of standard coupled cluster theory and recovers correct behavior for strongly correlated, open-shell systems using a spin-preserving ROHF reference.
Singlet-paired coupled cluster theory for open shells
International Nuclear Information System (INIS)
Gomez, John A.; Henderson, Thomas M.; Scuseria, Gustavo E.
2016-01-01
Restricted single-reference coupled cluster theory truncated to single and double excitations accurately describes weakly correlated systems, but often breaks down in the presence of static or strong correlation. Good coupled cluster energies in the presence of degeneracies can be obtained by using a symmetry-broken reference, such as unrestricted Hartree-Fock, but at the cost of good quantum numbers. A large body of work has shown that modifying the coupled cluster ansatz allows for the treatment of strong correlation within a single-reference, symmetry-adapted framework. The recently introduced singlet-paired coupled cluster doubles (CCD0) method is one such model, which recovers correct behavior for strong correlation without requiring symmetry breaking in the reference. Here, we extend singlet-paired coupled cluster for application to open shells via restricted open-shell singlet-paired coupled cluster singles and doubles (ROCCSD0). The ROCCSD0 approach retains the benefits of standard coupled cluster theory and recovers correct behavior for strongly correlated, open-shell systems using a spin-preserving ROHF reference.
Delay-induced cluster patterns in coupled Cayley tree networks
Singh, A.; Jalan, S.
2013-07-01
We study effects of delay in diffusively coupled logistic maps on the Cayley tree networks. We find that smaller coupling values exhibit sensitiveness to value of delay, and lead to different cluster patterns of self-organized and driven types. Whereas larger coupling strengths exhibit robustness against change in delay values, and lead to stable driven clusters comprising nodes from last generation of the Cayley tree. Furthermore, introduction of delay exhibits suppression as well as enhancement of synchronization depending upon coupling strength values. To the end we discuss the importance of results to understand conflicts and cooperations observed in family business.
Comparison of Cluster C personality disorders in couples with ...
African Journals Online (AJOL)
Comparison of Cluster C personality disorders in couples with normal divorce. ... Also purposeful sampling was used to select individuals. ... that the personality disorder group C, there is no significant difference between men and women.
Cluster synchronization modes in an ensemble of coupled chaotic oscillators
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Belykh, Igor V.; Mosekilde, Erik
2001-01-01
Considering systems of diffusively coupled identical chaotic oscillators, an effective method to determine the possible states of cluster synchronization and ensure their stability is presented. The method, which may find applications in communication engineering and other fields of science...
Fay, Temple H.
2012-01-01
Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…
Emergent organization of oscillator clusters in coupled self ...
Indian Academy of Sciences (India)
Additionally, the maps are coupled sequentially and unidirectionally, to their nearest neighbor, through the difference of their parametric variations. Interestingly we find that this model asymptotically yields clusters of superstable oscillators with different periods. We observe that the sizes of these oscillator clusters have a ...
Antiferromagnetic exchange coupling measurements on single Co clusters
Wernsdorfer, W.; Leroy, D.; Portemont, C.; Brenac, A.; Morel, R.; Notin, L.; Mailly, D.
2009-03-01
We report on single-cluster measurements of the angular dependence of the low-temperature ferromagnetic core magnetization switching field in exchange-coupled Co/CoO core-shell clusters (4 nm) using a micro-bridge DC superconducting quantum interference device (μ-SQUID). It is observed that the coupling with the antiferromagnetic shell induces modification in the switching field for clusters with intrinsic uniaxial anisotropy depending on the direction of the magnetic field applied during the cooling. Using a modified Stoner-Wohlfarth model, it is shown that the core interacts with two weakly coupled and asymmetrical antiferromagnetic sublattices. Ref.: C. Portemont, R. Morel, W. Wernsdorfer, D. Mailly, A. Brenac, and L. Notin, Phys. Rev. B 78, 144415 (2008)
Synchronization as Aggregation: Cluster Kinetics of Pulse-Coupled Oscillators.
O'Keeffe, Kevin P; Krapivsky, P L; Strogatz, Steven H
2015-08-07
We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators progressively coalesce into larger ones. Using tools from the study of aggregation phenomena, we obtain exact results for the time-dependent distribution of cluster sizes as the system evolves from disorder to synchrony.
Equation-of-motion coupled cluster perturbation theory revisited
DEFF Research Database (Denmark)
Eriksen, Janus Juul; Jørgensen, Poul; Olsen, Jeppe
2014-01-01
The equation-of-motion coupled cluster (EOM-CC) framework has been used for deriving a novel series of perturbative corrections to the coupled cluster singles and doubles energy that formally con- verges towards the full configuration interaction energy limit. The series is based on a Møller-Ples......-Plesset partitioning of the Hamiltonian and thus size extensive at any order in the perturbation, thereby rem- edying the major deficiency inherent to previous perturbation series based on the EOM-CC ansatz. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873138]...
Polishchuk, Alexander
2005-01-01
Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.
Computation of expectation values from vibrational coupled-cluster at the two-mode coupling level
DEFF Research Database (Denmark)
Zoccante, Alberto; Seidler, Peter; Christiansen, Ove
2011-01-01
In this work we show how the vibrational coupled-cluster method at the two-mode coupling level can be used to calculate zero-point vibrational averages of properties. A technique is presented, where any expectation value can be calculated using a single set of Lagrangian multipliers computed...
Cluster synchronization in community network with hybrid coupling
International Nuclear Information System (INIS)
Yang, Lixin; Jiang, Jun; Liu, Xiaojun
2016-01-01
Highlights: • A community network model with hybrid coupling is proposed. • Control scheme is designed via combining adaptive external coupling strength and feedback control. • The influence of topology structure on synchronization of community network is discussed. - Abstract: A general model of community network with hybrid coupling is proposed in this paper. In the community network model with hybrid coupling, the inner connections are in the same type of coupling within the same community and in different types of coupling in different communities. The connections between different pair of communities are also nonidentical. Cluster synchronization of community network with hybrid coupling is investigated via adaptive couplings control scheme. Effective controllers are designed for constructing an effective control scheme and adjusting automatically the adaptive external coupling strength by taking external coupling strength as adaptive variables on a small fraction of network edges. Moreover, the impact of the topology on the synchronizability of community network is investigated. The numerical results reveal that the number of links between communities and the degree of the connector nodes have significant effects on the synchronization performance.
Event-based cluster synchronization of coupled genetic regulatory networks
Yue, Dandan; Guan, Zhi-Hong; Li, Tao; Liao, Rui-Quan; Liu, Feng; Lai, Qiang
2017-09-01
In this paper, the cluster synchronization of coupled genetic regulatory networks with a directed topology is studied by using the event-based strategy and pinning control. An event-triggered condition with a threshold consisting of the neighbors' discrete states at their own event time instants and a state-independent exponential decay function is proposed. The intra-cluster states information and extra-cluster states information are involved in the threshold in different ways. By using the Lyapunov function approach and the theories of matrices and inequalities, we establish the cluster synchronization criterion. It is shown that both the avoidance of continuous transmission of information and the exclusion of the Zeno behavior are ensured under the presented triggering condition. Explicit conditions on the parameters in the threshold are obtained for synchronization. The stability criterion of a single GRN is also given under the reduced triggering condition. Numerical examples are provided to validate the theoretical results.
Application of a Light-Front Coupled Cluster Method
International Nuclear Information System (INIS)
Chabysheva, S.S.; Hiller, J.R.
2012-01-01
As a test of the new light-front coupled-cluster method in a gauge theory, we apply it to the nonperturbative construction of the dressed-electron state in QED, for an arbitrary covariant gauge, and compute the electron's anomalous magnetic moment. The construction illustrates the spectator and Fock-sector independence of vertex and self-energy contributions and indicates resolution of the difficulties with uncanceled divergences that plague methods based on Fock-space truncation. (author)
Coupled-cluster treatment of molecular strong-field ionization
Jagau, Thomas-C.
2018-05-01
Ionization rates and Stark shifts of H2, CO, O2, H2O, and CH4 in static electric fields have been computed with coupled-cluster methods in a basis set of atom-centered Gaussian functions with a complex-scaled exponent. Consideration of electron correlation is found to be of great importance even for a qualitatively correct description of the dependence of ionization rates and Stark shifts on the strength and orientation of the external field. The analysis of the second moments of the molecular charge distribution suggests a simple criterion for distinguishing tunnel and barrier suppression ionization in polyatomic molecules.
High-accuracy coupled cluster calculations of atomic properties
Energy Technology Data Exchange (ETDEWEB)
Borschevsky, A. [School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel and Centre for Theoretical Chemistry and Physics, The New Zealand Institute for Advanced Study, Massey University Auckland, Private Bag 102904, 0745 Auckland (New Zealand); Yakobi, H.; Eliav, E.; Kaldor, U. [School of Chemistry, Tel Aviv University, 69978 Tel Aviv (Israel)
2015-01-22
The four-component Fock-space coupled cluster and intermediate Hamiltonian methods are implemented to evaluate atomic properties. The latter include the spectra of nobelium and lawrencium (elements 102 and 103) in the range 20000-30000 cm{sup −1}, the polarizabilities of elements 112-114 and 118, required for estimating their adsorption enthalpies on surfaces used to separate them in accelerators, and the nuclear quadrupole moments of some heavy atoms. The calculations on superheavy elements are supported by the very good agreement with experiment obtained for the lighter homologues.
High-accuracy coupled cluster calculations of atomic properties
International Nuclear Information System (INIS)
Borschevsky, A.; Yakobi, H.; Eliav, E.; Kaldor, U.
2015-01-01
The four-component Fock-space coupled cluster and intermediate Hamiltonian methods are implemented to evaluate atomic properties. The latter include the spectra of nobelium and lawrencium (elements 102 and 103) in the range 20000-30000 cm −1 , the polarizabilities of elements 112-114 and 118, required for estimating their adsorption enthalpies on surfaces used to separate them in accelerators, and the nuclear quadrupole moments of some heavy atoms. The calculations on superheavy elements are supported by the very good agreement with experiment obtained for the lighter homologues
A coupled-cluster study of photodetachment cross sections of closed-shell anions
Cukras, Janusz; Decleva, Piero; Coriani, Sonia
2014-11-01
We investigate the performance of Stieltjes Imaging applied to Lanczos pseudo-spectra generated at the coupled cluster singles and doubles, coupled cluster singles and approximate iterative doubles and coupled cluster singles levels of theory in modeling the photodetachment cross sections of the closed shell anions H-, Li-, Na-, F-, Cl-, and OH-. The accurate description of double excitations is found to play a much more important role than in the case of photoionization of neutral species.
A coupled-cluster study of photodetachment cross sections of closed-shell anions
International Nuclear Information System (INIS)
Cukras, Janusz; Decleva, Piero; Coriani, Sonia
2014-01-01
We investigate the performance of Stieltjes Imaging applied to Lanczos pseudo-spectra generated at the coupled cluster singles and doubles, coupled cluster singles and approximate iterative doubles and coupled cluster singles levels of theory in modeling the photodetachment cross sections of the closed shell anions H − , Li − , Na − , F − , Cl − , and OH − . The accurate description of double excitations is found to play a much more important role than in the case of photoionization of neutral species
The coupled cluster theory of quantum lattice systems
International Nuclear Information System (INIS)
Bishop, R.; Xian, Yang
1994-01-01
The coupled cluster method is widely recognized nowadays as providing an ab initio method of great versatility, power, and accuracy for handling in a fully microscopic and systematic way the correlations between particles in quantum many-body systems. The number of successful applications made to date within both chemistry and physics is impressive. In this article, the authors review recent extensions of the method which now provide a unifying framework for also dealing with strongly interacting infinite quantum lattice systems described by a Hamiltonian. Such systems include both spin-lattice models (such as the anisotropic Heisenberg or XXZ model) exhibiting interesting magnetic properties, and electron lattice models (such as the tJ and Hubbard models), where the spins or fermions are localized on the sites of a regular lattice; as well as lattice gauge theories [such as the Abelian U(1) model of quantum electrodynamics and non-Abelian SU(n) models]. Illustrative results are given for both the XXZ spin lattice model and U(1) lattice gauge theory
Quadratically convergent MCSCF scheme using Fock operators
International Nuclear Information System (INIS)
Das, G.
1981-01-01
A quadratically convergent formulation of the MCSCF method using Fock operators is presented. Among its advantages the present formulation is quadratically convergent unlike the earlier ones based on Fock operators. In contrast to other quadratically convergent schemes as well as the one based on generalized Brillouin's theorem, this method leads easily to a hybrid scheme where the weakly coupled orbitals (such as the core) are handled purely by Fock equations, while the rest of the orbitals are treated by a quadratically convergent approach with a truncated virtual space obtained by the use of the corresponding Fock equations
One- and two-cluster synchronized dynamics of non-diffusively coupled Tchebycheff map networks
International Nuclear Information System (INIS)
Schäfer, Mirko; Greiner, Martin
2012-01-01
We use the master stability formalism to discuss one- and two-cluster synchronization of coupled Tchebycheff map networks. For diffusively coupled map systems, the one-cluster synchronized dynamics is given by the behaviour of the individual maps, and the coupling only determines the stability of the coherent state. For the case of non-diffusive coupling and for two-cluster synchronization, the synchronized dynamics on networks is different from the behaviour of the single individual map. Depending on the coupling, we study numerically the characteristics of various forms of the resulting synchronized dynamics. The stability properties of the respective one-cluster synchronized states are discussed for arbitrary network structures. For the case of two-cluster synchronization on bipartite networks we also present analytical expressions for fixed points and zig-zag patterns, and explicitly determine the linear stability of these orbits for the special case of ring-networks.
Photoionization cross section by Stieltjes imaging applied to coupled cluster Lanczos pseudo-spectra
Energy Technology Data Exchange (ETDEWEB)
Cukras, Janusz; Coriani, Sonia; Decleva, Piero [Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, via L. Giorgieri 1, I-34127 Trieste (Italy); Christiansen, Ove [Department of Chemistry, Aarhus University, DK-8000 Aarhus C (Denmark); Norman, Patrick [Department of Physics, Chemistry and Biology, Linköping University, SE-581 83 Linköping (Sweden)
2013-09-07
A recently implemented asymmetric Lanczos algorithm for computing (complex) linear response functions within the coupled cluster singles (CCS), coupled cluster singles and iterative approximate doubles (CC2), and coupled cluster singles and doubles (CCSD) is coupled to a Stieltjes imaging technique in order to describe the photoionization cross section of atoms and molecules, in the spirit of a similar procedure recently proposed by Averbukh and co-workers within the Algebraic Diagrammatic Construction approach. Pilot results are reported for the atoms He, Ne, and Ar and for the molecules H{sub 2}, H{sub 2}O, NH{sub 3}, HF, CO, and CO{sub 2}.
Photoionization cross section by Stieltjes imaging applied to coupled cluster Lanczos pseudo-spectra
Cukras, Janusz; Coriani, Sonia; Decleva, Piero; Christiansen, Ove; Norman, Patrick
2013-09-01
A recently implemented asymmetric Lanczos algorithm for computing (complex) linear response functions within the coupled cluster singles (CCS), coupled cluster singles and iterative approximate doubles (CC2), and coupled cluster singles and doubles (CCSD) is coupled to a Stieltjes imaging technique in order to describe the photoionization cross section of atoms and molecules, in the spirit of a similar procedure recently proposed by Averbukh and co-workers within the Algebraic Diagrammatic Construction approach. Pilot results are reported for the atoms He, Ne, and Ar and for the molecules H2, H2O, NH3, HF, CO, and CO2.
Photoionization cross section by Stieltjes imaging applied to coupled cluster Lanczos pseudo-spectra
International Nuclear Information System (INIS)
Cukras, Janusz; Coriani, Sonia; Decleva, Piero; Christiansen, Ove; Norman, Patrick
2013-01-01
A recently implemented asymmetric Lanczos algorithm for computing (complex) linear response functions within the coupled cluster singles (CCS), coupled cluster singles and iterative approximate doubles (CC2), and coupled cluster singles and doubles (CCSD) is coupled to a Stieltjes imaging technique in order to describe the photoionization cross section of atoms and molecules, in the spirit of a similar procedure recently proposed by Averbukh and co-workers within the Algebraic Diagrammatic Construction approach. Pilot results are reported for the atoms He, Ne, and Ar and for the molecules H 2 , H 2 O, NH 3 , HF, CO, and CO 2
International Nuclear Information System (INIS)
Badreddine, Houssem; Saanouni, Khemaies; Dogui, Abdelwaheb
2007-01-01
In this work an improved material model is proposed that shows good agreement with experimental data for both hardening curves and plastic strain ratios in uniaxial and equibiaxial proportional loading paths for steel metal until the final fracture. This model is based on non associative and non normal flow rule using two different orthotropic equivalent stresses in both yield criterion and plastic potential functions. For the plastic potential the classical Hill 1948 quadratic equivalent stress is considered while for the yield criterion the Karafillis and Boyce 1993 non quadratic equivalent stress is used taking into account the non linear mixed (kinematic and isotropic) hardening. Applications are made to hydro bulging tests using both circular and elliptical dies. The results obtained with different particular cases of the model such as the normal quadratic and the non normal non quadratic cases are compared and discussed with respect to the experimental results
Quadratic Functionals with General Boundary Conditions
International Nuclear Information System (INIS)
Dosla, Z.; Dosly, O.
1997-01-01
The purpose of this paper is to give the Reid 'Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in terms of Riccati equation solutions
Optimal Quadratic Programming Algorithms
Dostal, Zdenek
2009-01-01
Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This title presents various algorithms for solving large QP problems. It is suitable as an introductory text on quadratic programming for graduate students and researchers
Withers, Christopher S.; Nadarajah, Saralees
2012-01-01
We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…
A coupled-cluster study of photodetachment cross sections of closed-shell anions
Energy Technology Data Exchange (ETDEWEB)
Cukras, Janusz; Decleva, Piero; Coriani, Sonia, E-mail: coriani@units.it [Dipartimento di Scienze Chimiche e Farmaceutiche, Università degli Studi di Trieste, via L. Giorgieri 1, I-34127, Trieste (Italy)
2014-11-07
We investigate the performance of Stieltjes Imaging applied to Lanczos pseudo-spectra generated at the coupled cluster singles and doubles, coupled cluster singles and approximate iterative doubles and coupled cluster singles levels of theory in modeling the photodetachment cross sections of the closed shell anions H{sup −}, Li{sup −}, Na{sup −}, F{sup −}, Cl{sup −}, and OH{sup −}. The accurate description of double excitations is found to play a much more important role than in the case of photoionization of neutral species.
Simulation of circularly polarized luminescence spectra using coupled cluster theory
Energy Technology Data Exchange (ETDEWEB)
McAlexander, Harley R.; Crawford, T. Daniel, E-mail: crawdad@vt.edu [Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061 (United States)
2015-04-21
We report the first computations of circularly polarized luminescence (CPL) rotatory strengths at the equation-of-motion coupled cluster singles and doubles (EOM-CCSD) level of theory. Using a test set of eight chiral ketones, we compare both dipole and rotatory strengths for absorption (electronic circular dichroism) and emission to the results from time-dependent density-functional theory (TD-DFT) and available experimental data for both valence and Rydberg transitions. For two of the compounds, we obtained optimized geometries of the lowest several excited states using both EOM-CCSD and TD-DFT and determined that structures and EOM-CCSD transition properties obtained with each structure were sufficiently similar that TD-DFT optimizations were acceptable for the remaining test cases. Agreement between EOM-CCSD and the Becke three-parameter exchange function and Lee-Yang-Parr correlation functional (B3LYP) corrected using the Coulomb attenuating method (CAM-B3LYP) is typically good for most of the transitions, though agreement with the uncorrected B3LYP functional is significantly worse for all reported properties. The choice of length vs. velocity representation of the electric dipole operator has little impact on the EOM-CCSD transition strengths for nearly all of the states we examined. For a pair of closely related β, γ-enones, (1R)-7-methylenebicyclo[2.2.1]heptan-2-one and (1S)-2-methylenebicyclo[2.2.1]heptan-7-one, we find that EOM-CCSD and CAM-B3LYP agree with the energetic ordering of the two possible excited-state conformations, resulting in good agreement with experimental rotatory strengths in both absorption and emission, whereas B3LYP yields a qualitatively incorrect result for the CPL signal of (1S)-2-methylenebicyclo[2.2.1]heptan-7-one. Finally, we predict that one of the compounds considered here, trans-bicyclo[3.3.0]octane-3,7-dione, is unique in that it exhibits an achiral ground state and a chiral first excited state, leading to a strong CPL
Application of Bibliographic Coupling versus Cited Titles Words in Patent Fuzzy Clustering
Directory of Open Access Journals (Sweden)
Anahita Kermani
2013-03-01
Full Text Available Attribute selection is one of the steps before patent clustering. Various attributes can be used for clustering. In this study, the effect of using citation and citation title words, respectively, in form of bibliographic coupling and citation title words sharing, were measured and compared with each other, as patent attributes. This study was done in an experimental method, on a collection of 717 US Patent cited in the patents belong to 977/774 subclass of US Patent Classification. Fuzzy C-means was used for patent clustering and extended BCubed precision and extended BCubed recall were used as evaluation measure. The results showed that the clustering produced by bibliographic coupling had better performance than clustering used citation title words and existence of cluster structure were in a wider range of exhaustivity than citation title words.
Black, Joshua A.; Knowles, Peter J.
2018-06-01
The performance of quasi-variational coupled-cluster (QV) theory applied to the calculation of activation and reaction energies has been investigated. A statistical analysis of results obtained for six different sets of reactions has been carried out, and the results have been compared to those from standard single-reference methods. In general, the QV methods lead to increased activation energies and larger absolute reaction energies compared to those obtained with traditional coupled-cluster theory.
Lai, Yi Ming
2013-07-09
We study ensembles of globally coupled, nonidentical phase oscillators subject to correlated noise, and we identify several important factors that cause noise and coupling to synchronize or desynchronize a system. By introducing noise in various ways, we find an estimate for the onset of synchrony of a system in terms of the coupling strength, noise strength, and width of the frequency distribution of its natural oscillations. We also demonstrate that noise alone can be sufficient to synchronize nonidentical oscillators. However, this synchrony depends on the first Fourier mode of a phase-sensitivity function, through which we introduce common noise into the system. We show that higher Fourier modes can cause desynchronization due to clustering effects, and that this can reinforce clustering caused by different forms of coupling. Finally, we discuss the effects of noise on an ensemble in which antiferromagnetic coupling causes oscillators to form two clusters in the absence of noise. © 2013 American Physical Society.
Gravitation and quadratic forms
International Nuclear Information System (INIS)
Ananth, Sudarshan; Brink, Lars; Majumdar, Sucheta; Mali, Mahendra; Shah, Nabha
2017-01-01
The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.
Gravitation and quadratic forms
Energy Technology Data Exchange (ETDEWEB)
Ananth, Sudarshan [Indian Institute of Science Education and Research,Pune 411008 (India); Brink, Lars [Department of Physics, Chalmers University of Technology,S-41296 Göteborg (Sweden); Institute of Advanced Studies and Department of Physics & Applied Physics,Nanyang Technological University,Singapore 637371 (Singapore); Majumdar, Sucheta [Indian Institute of Science Education and Research,Pune 411008 (India); Mali, Mahendra [School of Physics, Indian Institute of Science Education and Research,Thiruvananthapuram, Trivandrum 695016 (India); Shah, Nabha [Indian Institute of Science Education and Research,Pune 411008 (India)
2017-03-31
The light-cone Hamiltonians describing both pure (N=0) Yang-Mills and N=4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N=8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.
A Coupled Hidden Markov Random Field Model for Simultaneous Face Clustering and Tracking in Videos
Wu, Baoyuan
2016-10-25
Face clustering and face tracking are two areas of active research in automatic facial video processing. They, however, have long been studied separately, despite the inherent link between them. In this paper, we propose to perform simultaneous face clustering and face tracking from real world videos. The motivation for the proposed research is that face clustering and face tracking can provide useful information and constraints to each other, thus can bootstrap and improve the performances of each other. To this end, we introduce a Coupled Hidden Markov Random Field (CHMRF) to simultaneously model face clustering, face tracking, and their interactions. We provide an effective algorithm based on constrained clustering and optimal tracking for the joint optimization of cluster labels and face tracking. We demonstrate significant improvements over state-of-the-art results in face clustering and tracking on several videos.
Emergent organization of oscillator clusters in coupled self ...
Indian Academy of Sciences (India)
dynamics, whereby at fixed intervals of time the nonlinearity parameter at each site ... The function g is the feedback adjustment function introduced in ref. ..... cluster of size c − 1) and the probability distribution of P(c), it also has power law.
Communication: A Jastrow factor coupled cluster theory for weak and strong electron correlation
International Nuclear Information System (INIS)
Neuscamman, Eric
2013-01-01
We present a Jastrow-factor-inspired variant of coupled cluster theory that accurately describes both weak and strong electron correlation. Compatibility with quantum Monte Carlo allows for variational energy evaluations and an antisymmetric geminal power reference, two features not present in traditional coupled cluster that facilitate a nearly exact description of the strong electron correlations in minimal-basis N 2 bond breaking. In double-ζ treatments of the HF and H 2 O bond dissociations, where both weak and strong correlations are important, this polynomial cost method proves more accurate than either traditional coupled cluster or complete active space perturbation theory. These preliminary successes suggest a deep connection between the ways in which cluster operators and Jastrow factors encode correlation
Phase correlation and clustering of a nearest neighbour coupled oscillators system
International Nuclear Information System (INIS)
EI-Nashar, Hassan F.
2002-09-01
We investigated the phases in a system of nearest neighbour coupled oscillators before complete synchronization in frequency occurs. We found that when oscillators under the influence of coupling form a cluster of the same time-average frequency, their phases start to correlate. An order parameter, which measures this correlation, starts to grow at this stage until it reaches maximum. This means that a time-average phase locked state is reached between the oscillators inside the cluster of the same time- average frequency. At this strength the cluster attracts individual oscillators or a cluster to join in. We also observe that clustering in averaged frequencies orders the phases of the oscillators. This behavior is found at all the transition points studied. (author)
Phase correlation and clustering of a nearest neighbour coupled oscillators system
Ei-Nashar, H F
2002-01-01
We investigated the phases in a system of nearest neighbour coupled oscillators before complete synchronization in frequency occurs. We found that when oscillators under the influence of coupling form a cluster of the same time-average frequency, their phases start to correlate. An order parameter, which measures this correlation, starts to grow at this stage until it reaches maximum. This means that a time-average phase locked state is reached between the oscillators inside the cluster of the same time- average frequency. At this strength the cluster attracts individual oscillators or a cluster to join in. We also observe that clustering in averaged frequencies orders the phases of the oscillators. This behavior is found at all the transition points studied.
Energy Technology Data Exchange (ETDEWEB)
Wahlen-Strothman, J. M. [Rice Univ., Houston, TX (United States); Henderson, T. H. [Rice Univ., Houston, TX (United States); Hermes, M. R. [Rice Univ., Houston, TX (United States); Degroote, M. [Rice Univ., Houston, TX (United States); Qiu, Y. [Rice Univ., Houston, TX (United States); Zhao, J. [Rice Univ., Houston, TX (United States); Dukelsky, J. [Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Inst. de Estructura de la Materia; Scuseria, G. E. [Rice Univ., Houston, TX (United States)
2018-01-03
Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems, but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories. We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime.
Hermes, Matthew R.; Dukelsky, Jorge; Scuseria, Gustavo E.
2017-06-01
The failures of single-reference coupled-cluster theory for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled-cluster theory fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled-cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a test bed [J. Chem. Phys. 146, 054110 (2017), 10.1063/1.4974989]. We generalize the concept of a symmetry-projected mean-field wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled-cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled-cluster theory is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram.
Dickmann, M
2015-01-01
In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where -1 is not a sum of squares and 2 is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of T-isometry, where T is a preorder of the given ring, A, or T = A^2. (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in
Ellis, John; Sueiro, Maria
2014-01-01
Inflationary models based on a single scalar field $\\phi$ with a quadratic potential $V = \\frac{1}{2} m^2 \\phi^2$ are disfavoured by the recent Planck constraints on the scalar index, $n_s$, and the tensor-to-scalar ratio for cosmological density perturbations, $r_T$. In this paper we study how such a quadratic inflationary model can be rescued by postulating additional fields with quadratic potentials, such as might occur in sneutrino models, which might serve as either curvatons or supplementary inflatons. Introducing a second scalar field reduces but does not remove the pressure on quadratic inflation, but we find a sample of three-field models that are highly compatible with the Planck data on $n_s$ and $r_T$. We exhibit a specific three-sneutrino example that is also compatible with the data on neutrino mass difference and mixing angles.
Separable quadratic stochastic operators
International Nuclear Information System (INIS)
Rozikov, U.A.; Nazir, S.
2009-04-01
We consider quadratic stochastic operators, which are separable as a product of two linear operators. Depending on properties of these linear operators we classify the set of the separable quadratic stochastic operators: first class of constant operators, second class of linear and third class of nonlinear (separable) quadratic stochastic operators. Since the properties of operators from the first and second classes are well known, we mainly study the properties of the operators of the third class. We describe some Lyapunov functions of the operators and apply them to study ω-limit sets of the trajectories generated by the operators. We also compare our results with known results of the theory of quadratic operators and give some open problems. (author)
Near-Edge X-ray Absorption Fine Structure within Multilevel Coupled Cluster Theory.
Myhre, Rolf H; Coriani, Sonia; Koch, Henrik
2016-06-14
Core excited states are challenging to calculate, mainly because they are embedded in a manifold of high-energy valence-excited states. However, their locality makes their determination ideal for local correlation methods. In this paper, we demonstrate the performance of multilevel coupled cluster theory in computing core spectra both within the core-valence separated and the asymmetric Lanczos implementations of coupled cluster linear response theory. We also propose a visualization tool to analyze the excitations using the difference between the ground-state and excited-state electron densities.
International Nuclear Information System (INIS)
Mani, B. K.; Angom, D.; Latha, K. V. P.
2009-01-01
We have carried out a detailed and systematic study of the correlation energies of inert gas atoms Ne, Ar, Kr, and Xe using relativistic many-body perturbation theory and relativistic coupled-cluster theory. In the relativistic coupled-cluster calculations, we implement perturbative triples and include these in the correlation energy calculations. We then calculate the dipole polarizability of the ground states using perturbed coupled-cluster theory.
Phase models and clustering in networks of oscillators with delayed coupling
Campbell, Sue Ann; Wang, Zhen
2018-01-01
We consider a general model for a network of oscillators with time delayed coupling where the coupling matrix is circulant. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay enters as a phase shift. We use the phase model to determine model independent existence and stability results for symmetric cluster solutions. Our results extend previous work to systems with time delay and a more general coupling matrix. We show that the presence of the time delay can lead to the coexistence of multiple stable clustering solutions. We apply our analytical results to a network of Morris Lecar neurons and compare these results with numerical continuation and simulation studies.
Entangled states decoherence in coupled molecular spin clusters
Troiani, Filippo; Szallas, Attila; Bellini, Valerio; Affronte, Marco
2010-03-01
Localized electron spins in solid-state systems are widely investigated as potential building blocks of quantum devices and computers. While most efforts in the field have been focused on semiconductor low-dimensional structures, molecular antiferromagnets were recently recognized as alternative implementations of effective few-level spin systems. Heterometallic, Cr-based spin rings behave as effective spin-1/2 systems at low temperature and show long decoherence times [1]; besides, they can be chemically linked and magnetically coupled in a controllable fascion [2]. Here, we theoretically investigate the decoherence of the Bell states in such ring dimers, resulting from hyperfine interactions with nuclear spins. Based on a microscopic description of the molecules [3], we simulate the effect of inhomogeneous broadening, spectral diffusion and electron-nuclear entanglement on the electron-spin coherence, estimating the role of the different nuclei (and of possible chemical substitutions), as well as the effect of simple spin-echo sequences. References: [1] F. Troiani, et al., Phys. Rev. Lett. 94, 207208 (2005). [2] G. A. Timco, S: Carretta, F. Troiani et al., Nature Nanotech. 4, 173 (2009). [3] F. Troiani, V. Bellini, and M. Affronte, Phys. Rev. B 77, 054428 (2008).
Maitra, Rahul; Nakajima, Takahito
2017-11-28
We present an accurate single reference coupled cluster theory in which the conventional Fock operator matrix is suitably dressed to simulate the effect of triple and higher excitations within a singles and doubles framework. The dressing thus invoked originates from a second-order perturbative approximation of a similarity transformed Hamiltonian and induces higher rank excitations through local renormalization of individual occupied and unoccupied orbital lines. Such a dressing is able to recover a significant amount of correlation effects beyond singles and doubles approximation, but only with an economic n 5 additional cost. Due to the inclusion of higher rank excitations via the Fock matrix dressing, this method is a natural improvement over conventional coupled cluster theory with singles and doubles approximation, and this method would be demonstrated via applications on some challenging systems. This highly promising scheme has a conceptually simple structure which is also easily generalizable to a multi-reference coupled cluster scheme for treating strong degeneracy. We shall demonstrate that this method is a natural lowest order perturbative approximation to the recently developed iterative n-body excitation inclusive coupled cluster singles and doubles scheme [R. Maitra et al., J. Chem. Phys. 147, 074103 (2017)].
Czech Academy of Sciences Publication Activity Database
Demel, Ondřej; Kedžuch, S.; Noga, J.; Pittner, Jiří
2013-01-01
Roč. 111, 16-17 (2013), s. 2477-2488 ISSN 0026-8976 R&D Projects: GA ČR GPP208/10/P041; GA ČR GAP208/11/2222 Institutional support: RVO:61388955 Keywords : explicitly correlated * coupled cluster * multireference Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 1.642, year: 2013
Czech Academy of Sciences Publication Activity Database
Brabec, Jiří; Bhaskaran-Neir, K.; Govind, N.; Pittner, Jiří
2012-01-01
Roč. 137, č. 17 (2012), s. 171101 ISSN 0021-9606 R&D Projects: GA ČR GAP208/11/2222 Institutional support: RVO:61388955 Keywords : coupled cluster calculations * electron correlations * excited states Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.164, year: 2012
A Coupled User Clustering Algorithm Based on Mixed Data for Web-Based Learning Systems
Directory of Open Access Journals (Sweden)
Ke Niu
2015-01-01
Full Text Available In traditional Web-based learning systems, due to insufficient learning behaviors analysis and personalized study guides, a few user clustering algorithms are introduced. While analyzing the behaviors with these algorithms, researchers generally focus on continuous data but easily neglect discrete data, each of which is generated from online learning actions. Moreover, there are implicit coupled interactions among the data but are frequently ignored in the introduced algorithms. Therefore, a mass of significant information which can positively affect clustering accuracy is neglected. To solve the above issues, we proposed a coupled user clustering algorithm for Wed-based learning systems by taking into account both discrete and continuous data, as well as intracoupled and intercoupled interactions of the data. The experiment result in this paper demonstrates the outperformance of the proposed algorithm.
Experimental observation of chimera and cluster states in a minimal globally coupled network
Energy Technology Data Exchange (ETDEWEB)
Hart, Joseph D. [Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742 (United States); Department of Physics, University of Maryland, College Park, Maryland 20742 (United States); Bansal, Kanika [Department of Mathematics, University at Buffalo, SUNY Buffalo, New York 14260 (United States); US Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005 (United States); Murphy, Thomas E. [Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742 (United States); Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742 (United States); Roy, Rajarshi [Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742 (United States); Department of Physics, University of Maryland, College Park, Maryland 20742 (United States); Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)
2016-09-15
A “chimera state” is a dynamical pattern that occurs in a network of coupled identical oscillators when the symmetry of the oscillator population is broken into synchronous and asynchronous parts. We report the experimental observation of chimera and cluster states in a network of four globally coupled chaotic opto-electronic oscillators. This is the minimal network that can support chimera states, and our study provides new insight into the fundamental mechanisms underlying their formation. We use a unified approach to determine the stability of all the observed partially synchronous patterns, highlighting the close relationship between chimera and cluster states as belonging to the broader phenomenon of partial synchronization. Our approach is general in terms of network size and connectivity. We also find that chimera states often appear in regions of multistability between global, cluster, and desynchronized states.
Energy Technology Data Exchange (ETDEWEB)
Byrd, Jason N., E-mail: byrd.jason@ensco.com [Quantum Theory Project, University of Florida, Gainesville, Florida 32611 (United States); ENSCO, Inc., 4849 North Wickham Road, Melbourne, Florida 32940 (United States); Lutz, Jesse J., E-mail: jesse.lutz.ctr@afit.edu; Jin, Yifan; Ranasinghe, Duminda S.; Perera, Ajith; Bartlett, Rodney J., E-mail: rodbartl@ufl.edu [Quantum Theory Project, University of Florida, Gainesville, Florida 32611 (United States); Montgomery, John A. [Department of Physics, University of Connecticut, Storrs, Connecticut 06269 (United States); Duan, Xiaofeng F. [Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio 45433 (United States); Air Force Research Laboratory DoD Supercomputing Resource Center, Wright-Patterson Air Force Base, Ohio 45433 (United States); Burggraf, Larry W. [Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio 45433 (United States); Sanders, Beverly A. [Quantum Theory Project, University of Florida, Gainesville, Florida 32611 (United States); Department of Computer and Information Science and Engineering, University of Florida, Gainesville, Florida 32611 (United States)
2016-07-14
The accurate determination of the preferred Si{sub 12}C{sub 12} isomer is important to guide experimental efforts directed towards synthesizing SiC nano-wires and related polymer structures which are anticipated to be highly efficient exciton materials for the opto-electronic devices. In order to definitively identify preferred isomeric structures for silicon carbon nano-clusters, highly accurate geometries, energies, and harmonic zero point energies have been computed using coupled-cluster theory with systematic extrapolation to the complete basis limit for set of silicon carbon clusters ranging in size from SiC{sub 3} to Si{sub 12}C{sub 12}. It is found that post-MBPT(2) correlation energy plays a significant role in obtaining converged relative isomer energies, suggesting that predictions using low rung density functional methods will not have adequate accuracy. Utilizing the best composite coupled-cluster energy that is still computationally feasible, entailing a 3-4 SCF and coupled-cluster theory with singles and doubles extrapolation with triple-ζ (T) correlation, the closo Si{sub 12}C{sub 12} isomer is identified to be the preferred isomer in the support of previous calculations [X. F. Duan and L. W. Burggraf, J. Chem. Phys. 142, 034303 (2015)]. Additionally we have investigated more pragmatic approaches to obtaining accurate silicon carbide isomer energies, including the use of frozen natural orbital coupled-cluster theory and several rungs of standard and double-hybrid density functional theory. Frozen natural orbitals as a way to compute post-MBPT(2) correlation energy are found to be an excellent balance between efficiency and accuracy.
International Nuclear Information System (INIS)
Byrd, Jason N.; Lutz, Jesse J.; Jin, Yifan; Ranasinghe, Duminda S.; Perera, Ajith; Bartlett, Rodney J.; Montgomery, John A.; Duan, Xiaofeng F.; Burggraf, Larry W.; Sanders, Beverly A.
2016-01-01
The accurate determination of the preferred Si 12 C 12 isomer is important to guide experimental efforts directed towards synthesizing SiC nano-wires and related polymer structures which are anticipated to be highly efficient exciton materials for the opto-electronic devices. In order to definitively identify preferred isomeric structures for silicon carbon nano-clusters, highly accurate geometries, energies, and harmonic zero point energies have been computed using coupled-cluster theory with systematic extrapolation to the complete basis limit for set of silicon carbon clusters ranging in size from SiC 3 to Si 12 C 12 . It is found that post-MBPT(2) correlation energy plays a significant role in obtaining converged relative isomer energies, suggesting that predictions using low rung density functional methods will not have adequate accuracy. Utilizing the best composite coupled-cluster energy that is still computationally feasible, entailing a 3-4 SCF and coupled-cluster theory with singles and doubles extrapolation with triple-ζ (T) correlation, the closo Si 12 C 12 isomer is identified to be the preferred isomer in the support of previous calculations [X. F. Duan and L. W. Burggraf, J. Chem. Phys. 142, 034303 (2015)]. Additionally we have investigated more pragmatic approaches to obtaining accurate silicon carbide isomer energies, including the use of frozen natural orbital coupled-cluster theory and several rungs of standard and double-hybrid density functional theory. Frozen natural orbitals as a way to compute post-MBPT(2) correlation energy are found to be an excellent balance between efficiency and accuracy.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio
2016-01-01
We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Indirect quantum tomography of quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Burgarth, Daniel [Institute for Mathematical Sciences, Imperial College London, London SW7 2PG (United Kingdom); Maruyama, Koji; Nori, Franco, E-mail: daniel@burgarth.de, E-mail: kmaruyama@riken.jp [Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198 (Japan)
2011-01-15
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few resources. We found that almost all the properties of the Hamiltonian are determined by its surface and that these properties can be measured even if the system can only be initialized to a mixed state. Therefore, our method can be applied to various physical models, with important examples including coupled nano-mechanical oscillators, hopping fermions in optical lattices and transverse Ising chains.
Pulse-coupled mixed-mode oscillators: Cluster states and extreme noise sensitivity
Karamchandani, Avinash J.; Graham, James N.; Riecke, Hermann
2018-04-01
Motivated by rhythms in the olfactory system of the brain, we investigate the synchronization of all-to-all pulse-coupled neuronal oscillators exhibiting various types of mixed-mode oscillations (MMOs) composed of sub-threshold oscillations (STOs) and action potentials ("spikes"). We focus particularly on the impact of the delay in the interaction. In the weak-coupling regime, we reduce the system to a Kuramoto-type equation with non-sinusoidal phase coupling and the associated Fokker-Planck equation. Its linear stability analysis identifies the appearance of various cluster states. Their type depends sensitively on the delay and the width of the pulses. Interestingly, long delays do not imply slow population rhythms, and the number of emerging clusters only loosely depends on the number of STOs. Direct simulations of the oscillator equations reveal that for quantitative agreement of the weak-coupling theory the coupling strength and the noise have to be extremely small. Even moderate noise leads to significant skipping of STO cycles, which can enhance the diffusion coefficient in the Fokker-Planck equation by two orders of magnitude. Introducing an effective diffusion coefficient extends the range of agreement significantly. Numerical simulations of the Fokker-Planck equation reveal bistability and solutions with oscillatory order parameters that result from nonlinear mode interactions. These are confirmed in simulations of the full spiking model.
International Nuclear Information System (INIS)
Tecmer, Paweł; Visscher, Lucas; Severo Pereira Gomes, André; Knecht, Stefan
2014-01-01
We present a study of the electronic structure of the [UO 2 ] + , [UO 2 ] 2 + , [UO 2 ] 3 + , NUO, [NUO] + , [NUO] 2 + , [NUN] − , NUN, and [NUN] + molecules with the intermediate Hamiltonian Fock-space coupled cluster method. The accuracy of mean-field approaches based on the eXact-2-Component Hamiltonian to incorporate spin–orbit coupling and Gaunt interactions are compared to results obtained with the Dirac–Coulomb Hamiltonian. Furthermore, we assess the reliability of calculations employing approximate density functionals in describing electronic spectra and quantities useful in rationalizing Uranium (VI) species reactivity (hardness, electronegativity, and electrophilicity)
Tecmer, Paweł; Severo Pereira Gomes, André; Knecht, Stefan; Visscher, Lucas
2014-07-01
We present a study of the electronic structure of the [UO2]+, [UO2]2 +, [UO2]3 +, NUO, [NUO]+, [NUO]2 +, [NUN]-, NUN, and [NUN]+ molecules with the intermediate Hamiltonian Fock-space coupled cluster method. The accuracy of mean-field approaches based on the eXact-2-Component Hamiltonian to incorporate spin-orbit coupling and Gaunt interactions are compared to results obtained with the Dirac-Coulomb Hamiltonian. Furthermore, we assess the reliability of calculations employing approximate density functionals in describing electronic spectra and quantities useful in rationalizing Uranium (VI) species reactivity (hardness, electronegativity, and electrophilicity).
Quantum optics meets quantum many-body theory: coupled cluster studies of the Rabi Hamiltonian
International Nuclear Information System (INIS)
Davidson, N.J.; Quick, R.M.; Bishop, R.F.; Van der Walt, D.M.
1998-01-01
The Rabi Hamiltonian, which describes the interaction of a single mode of electromagnetic radiation with a two level system, is one of the fundamental models of quantum optics. It is also of wider interest as it provides a generic model for the interaction of bosons and fermions. To allow for a systematic analysis of the strong-coupling behaviour, we have applied the coupled cluster method (CCM) to the Rabi Hamiltonian to calculate its spectrum. We find strong evidence for the existence of a somewhat subtle quantum phase transition. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)
Nonequilibrium dynamics of polariton entanglement in a cluster of coupled traps
Energy Technology Data Exchange (ETDEWEB)
Quiroga, L [Departamento de Fisica, Universidad de Los Andes, A.A.4976, Bogota D.C. (Colombia); Tejedor, C, E-mail: lquiroga@uniandes.edu.c [Departamento de Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid, Cantoblanco, E-28049, Madrid (Spain)
2009-05-01
We study in detail the generation and relaxation of quantum coherences (entanglement) in a system of coupled polariton traps. By exploiting a Lie algebraic based super-operator technique we provide an analytical exact solution for the Markovian dissipative dynamics (Master equation) of such system which is valid for arbitrary cluster size, polariton-polariton interaction strength, temperature and initial state. Based on the exact solution of the Master equation at T = OK, we discuss how dissipation affects the quantum entanglement dynamics of coupled polariton systems.
Energy Technology Data Exchange (ETDEWEB)
Peng, Bo; Govind, Niranjan; Apra, Edoardo; Klemm, Michael; Hammond, Jeff R.; Kowalski, Karol
2017-02-03
In this paper we apply equation-of-motion coupled cluster (EOMCC) methods in studies of vertical ionization potentials (IP) and electron affinities (EA) for sin- gled walled carbon nanotubes. EOMCC formulations for ionization potentials and electron affinities employing excitation manifolds spanned by single and double ex- citations (IP/EA-EOMCCSD) are used to study IPs and EAs of nanotubes as a function of nanotube length. Several armchair nanotubes corresponding to C20nH20 models with n = 2 - 6 have been used in benchmark calculations. In agreement with previous studies, we demonstrate that the electronegativity of C20nH20 systems remains, to a large extent, independent of nanotube length. We also compare IP/EA- EOMCCSD results with those obtained with the coupled cluster models with single and double excitations corrected by perturbative triples, CCSD(T), and density func- tional theory (DFT) using global and range-separated hybrid exchange-correlation functionals.
Fourth-order perturbative extension of the single-double excitation coupled-cluster method
International Nuclear Information System (INIS)
Derevianko, Andrei; Emmons, Erik D.
2002-01-01
Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the lowest-order wave function. The complete set of fourth-order diagrams involves only connected single, double, and triple excitations and disconnected quadruple excitations. Approximately half of the fourth-order diagrams are not accounted for by the popular coupled-cluster method truncated at single and double excitations (CCSD). Explicit formulas are tabulated for the entire set of fourth-order diagrams missed by the CCSD method and its linearized version, i.e., contributions from connected triple and disconnected quadruple excitations. A partial summation scheme of the derived fourth-order contributions to all orders of perturbation theory is proposed
Communication: Time-dependent optimized coupled-cluster method for multielectron dynamics
Sato, Takeshi; Pathak, Himadri; Orimo, Yuki; Ishikawa, Kenichi L.
2018-02-01
Time-dependent coupled-cluster method with time-varying orbital functions, called time-dependent optimized coupled-cluster (TD-OCC) method, is formulated for multielectron dynamics in an intense laser field. We have successfully derived the equations of motion for CC amplitudes and orthonormal orbital functions based on the real action functional, and implemented the method including double excitations (TD-OCCD) and double and triple excitations (TD-OCCDT) within the optimized active orbitals. The present method is size extensive and gauge invariant, a polynomial cost-scaling alternative to the time-dependent multiconfiguration self-consistent-field method. The first application of the TD-OCC method of intense-laser driven correlated electron dynamics in Ar atom is reported.
Communication: Biological applications of coupled-cluster frozen-density embedding
Heuser, Johannes; Höfener, Sebastian
2018-04-01
We report the implementation of the Laplace-transform scaled opposite-spin (LT-SOS) resolution-of-the-identity second-order approximate coupled-cluster singles and doubles (RICC2) combined with frozen-density embedding for excitation energies and molecular properties. In the present work, we furthermore employ the Hartree-Fock density for the interaction energy leading to a simplified Lagrangian which is linear in the Lagrangian multipliers. This approximation has the key advantage of a decoupling of the coupled-cluster amplitude and multipliers, leading also to a significant reduction in computation time. Using the new simplified Lagrangian in combination with efficient wavefunction models such as RICC2 or LT-SOS-RICC2 and density-functional theory (DFT) for the environment molecules (CC2-in-DFT) enables the efficient study of biological applications such as the rhodopsin and visual cone pigments using ab initio methods as routine applications.
Applying the Coupled-Cluster Ansatz to Solids and Surfaces in the Thermodynamic Limit
Gruber, Thomas; Liao, Ke; Tsatsoulis, Theodoros; Hummel, Felix; Grüneis, Andreas
2018-04-01
Modern electronic structure theories can predict and simulate a wealth of phenomena in surface science and solid-state physics. In order to allow for a direct comparison with experiment, such ab initio predictions have to be made in the thermodynamic limit, substantially increasing the computational cost of many-electron wave-function theories. Here, we present a method that achieves thermodynamic limit results for solids and surfaces using the "gold standard" coupled cluster ansatz of quantum chemistry with unprecedented efficiency. We study the energy difference between carbon diamond and graphite crystals, adsorption energies of water on h -BN, as well as the cohesive energy of the Ne solid, demonstrating the increased efficiency and accuracy of coupled cluster theory for solids and surfaces.
Hidden conic quadratic representation of some nonconvex quadratic optimization problems
Ben-Tal, A.; den Hertog, D.
The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated
Binary classification posed as a quadratically constrained quadratic ...
Indian Academy of Sciences (India)
Binary classification is posed as a quadratically constrained quadratic problem and solved using the proposed method. Each class in the binary classification problem is modeled as a multidimensional ellipsoid to forma quadratic constraint in the problem. Particle swarms help in determining the optimal hyperplane or ...
Coupled-Cluster and Configuration-Interaction Calculations for Heavy Nuclei
International Nuclear Information System (INIS)
Horoi, M.; Gour, J. R.; Wloch, M.; Lodriguito, M. D.; Brown, B. A.; Piecuch, P.
2007-01-01
We compare coupled-cluster (CC) and configuration-interaction (CI) results for 56 Ni obtained in the pf-shell basis, focusing on practical CC approximations that can be applied to systems with dozens or hundreds of correlated fermions. The weight of the reference state and the strength of correlation effects are controlled by the gap between the f 7/2 orbit and the f 5/2 , p 3/2 , p 1/2 orbits. Independent of the gap, the CC method with 1p-1h and 2p-2h clusters and a noniterative treatment of 3p-3h clusters is as accurate as the more demanding CI approach truncated at the 4p-4h level
International Nuclear Information System (INIS)
Pal, Sourav; Sajeev, Y.; Vaval, Nayana
2006-01-01
The Fock space multi-reference coupled-cluster (FSMRCC) method is used for the study of the shape resonance energy and width in an electron-atom/molecule collision. The procedure is based upon combining a complex absorbing potential (CAP) with FSMRCC theory. Accurate resonance parameters are obtained by solving a small non-Hermitian eigen-value problem. We study the shape resonances in e - -C 2 H 4 and e - -Mg
Coupled Hartree-Fock calculation of {sup 13} C shielding tensors in acetylene clusters
Energy Technology Data Exchange (ETDEWEB)
Craw, John Simon; Nascimento, Marco Antonio Chaer [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Quimica
1992-12-31
The coupled Hartree Fock method has been used to calculate ab-initio carbon magnetic shielding tensors for small clusters of acetylene molecules. The chemical shift increases from the monomer to the dimer and trimer. This is mainly due increased diamagnetism, which is imperfectly cancelled by increased paramagnetism due to loss of axial symmetry. Anisotropic effects are shown to be small in both the dimer the and trimer. (author) 21 refs., 2 tabs.
A quasiparticle-based multi-reference coupled-cluster method.
Rolik, Zoltán; Kállay, Mihály
2014-10-07
The purpose of this paper is to introduce a quasiparticle-based multi-reference coupled-cluster (MRCC) approach. The quasiparticles are introduced via a unitary transformation which allows us to represent a complete active space reference function and other elements of an orthonormal multi-reference (MR) basis in a determinant-like form. The quasiparticle creation and annihilation operators satisfy the fermion anti-commutation relations. On the basis of these quasiparticles, a generalization of the normal-ordered operator products for the MR case can be introduced as an alternative to the approach of Mukherjee and Kutzelnigg [Recent Prog. Many-Body Theor. 4, 127 (1995); Mukherjee and Kutzelnigg, J. Chem. Phys. 107, 432 (1997)]. Based on the new normal ordering any quasiparticle-based theory can be formulated using the well-known diagram techniques. Beyond the general quasiparticle framework we also present a possible realization of the unitary transformation. The suggested transformation has an exponential form where the parameters, holding exclusively active indices, are defined in a form similar to the wave operator of the unitary coupled-cluster approach. The definition of our quasiparticle-based MRCC approach strictly follows the form of the single-reference coupled-cluster method and retains several of its beneficial properties. Test results for small systems are presented using a pilot implementation of the new approach and compared to those obtained by other MR methods.
Quadratic Diophantine equations
Andreescu, Titu
2015-01-01
This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.
Indian Academy of Sciences (India)
V. Suresh University Of Hyderabad Hyderabad
2008-10-31
Oct 31, 2008 ... We say that (a1,··· ,an) is a zero of the polynomial f if f (a1,··· ,an) = 0. One of the main problems in Mathematics is to determine whether the given polynomial has a (non-trivial) zero or not. For example, let us recall the Fermat's last theorem: V. Suresh University Of Hyderabad Hyderabad. Isotropy of quadratic ...
Xu, Enhua; Li, Shuhua
2015-03-07
An externally corrected CCSDt (coupled cluster with singles, doubles, and active triples) approach employing four- and five-body clusters from the complete active space self-consistent field (CASSCF) wave function (denoted as ecCCSDt-CASSCF) is presented. The quadruple and quintuple excitation amplitudes within the active space are extracted from the CASSCF wave function and then fed into the CCSDt-like equations, which can be solved in an iterative way as the standard CCSDt equations. With a size-extensive CASSCF reference function, the ecCCSDt-CASSCF method is size-extensive. When the CASSCF wave function is readily available, the computational cost of the ecCCSDt-CASSCF method scales as the popular CCSD method (if the number of active orbitals is small compared to the total number of orbitals). The ecCCSDt-CASSCF approach has been applied to investigate the potential energy surface for the simultaneous dissociation of two O-H bonds in H2O, the equilibrium distances and spectroscopic constants of 4 diatomic molecules (F2(+), O2(+), Be2, and NiC), and the reaction barriers for the automerization reaction of cyclobutadiene and the Cl + O3 → ClO + O2 reaction. In most cases, the ecCCSDt-CASSCF approach can provide better results than the CASPT2 (second order perturbation theory with a CASSCF reference function) and CCSDT methods.
Linked cluster expansion in the SU(2) lattice Higgs model at strong gauge coupling
International Nuclear Information System (INIS)
Wagner, C.E.M.
1989-01-01
A linked cluster expansion is developed for the β=0 limit of the SU(2) Higgs model. This method, when combined with strong gauge coupling expansions, is used to obtain the phase transition surface and the behaviour of scalar and vector masses in the lattice regularized theory. The method, in spite of the low order of truncation of the series applied, gives a reasonable agreement with Monte Carlo data for the phase transition surface and a qualitatively good picture of the behaviour of Higgs, glueball and gauge vector boson masses, in the strong coupling limit. Some limitations of the method are discussed, and an intuitive picture of the different behaviour for small and large bare self-coupling λ is given. (orig.)
Wang, Jong-Yi; Liang, Yia-Wen; Yeh, Chun-Chen; Liu, Chiu-Shong; Wang, Chen-Yu
2018-02-21
Spousal clustering of cancer warrants attention. Whether the common environment or high-age vulnerability determines cancer clustering is unclear. The risk of clustering in couples versus non-couples is undetermined. The time to cancer clustering after the first cancer diagnosis is yet to be reported. This study investigated cancer clustering over time among couples by using nationwide data. A cohort of 5643 married couples in the 2002-2013 Taiwan National Health Insurance Research Database was identified and randomly matched with 5643 non-couple pairs through dual propensity score matching. Factors associated with clustering (both spouses with tumours) were analysed by using the Cox proportional hazard model. Propensity-matched analysis revealed that the risk of clustering of all tumours among couples (13.70%) was significantly higher than that among non-couples (11.84%) (OR=1.182, 95% CI 1.058 to 1.321, P=0.0031). The median time to clustering of all tumours and of malignant tumours was 2.92 and 2.32 years, respectively. Risk characteristics associated with clustering included high age and comorbidity. Shared environmental factors among spouses might be linked to a high incidence of cancer clustering. Cancer incidence in one spouse may signal cancer vulnerability in the other spouse. Promoting family-oriented cancer care in vulnerable families and preventing shared lifestyle risk factors for cancer are suggested. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2018. All rights reserved. No commercial use is permitted unless otherwise expressly granted.
International Nuclear Information System (INIS)
Zhu Yun; Zheng Zhi-Gang; Yang Jun-Zhong
2013-01-01
Dynamics of a one-dimensional array of non-locally coupled Kuramoto phase oscillators with an external potential is studied. A four-cluster chimera state is observed for the moderate strength of the external potential. Different from the clustered chimera states studied before, the instantaneous frequencies of the oscillators in a synchronized cluster are different in the presence of the external potential. As the strength of the external potential increases, a bifurcation from the two-cluster chimera state to the four-cluster chimera states can be found. These phenomena are well predicted analytically with the help of the Ott—Antonsen ansatz. (general)
Hydrodynamical simulations of coupled and uncoupled quintessence models - II. Galaxy clusters
Carlesi, Edoardo; Knebe, Alexander; Lewis, Geraint F.; Yepes, Gustavo
2014-04-01
We study the z = 0 properties of clusters (and large groups) of galaxies within the context of interacting and non-interacting quintessence cosmological models, using a series of adiabatic SPH simulations. Initially, we examine the average properties of groups and clusters, quantifying their differences in ΛCold Dark Matter (ΛCDM), uncoupled Dark Energy (uDE) and coupled Dark Energy (cDE) cosmologies. In particular, we focus upon radial profiles of the gas density, temperature and pressure, and we also investigate how the standard hydrodynamic equilibrium hypothesis holds in quintessence cosmologies. While we are able to confirm previous results about the distribution of baryons, we also find that the main discrepancy (with differences up to 20 per cent) can be seen in cluster pressure profiles. We then switch attention to individual structures, mapping each halo in quintessence cosmology to its ΛCDM counterpart. We are able to identify a series of small correlations between the coupling in the dark sector and halo spin, triaxiality and virialization ratio. When looking at spin and virialization of dark matter haloes, we find a weak (5 per cent) but systematic deviation in fifth force scenarios from ΛCDM.
Zhang, Yifan
2016-08-18
For face naming in TV series or movies, a typical way is using subtitles/script alignment to get the time stamps of the names, and tagging them to the faces. We study the problem of face naming in videos when subtitles are not available. To this end, we divide the problem into two tasks: face clustering which groups the faces depicting a certain person into a cluster, and name assignment which associates a name to each face. Each task is formulated as a structured prediction problem and modeled by a hidden conditional random field (HCRF) model. We argue that the two tasks are correlated problems whose outputs can provide prior knowledge of the target prediction for each other. The two HCRFs are coupled in a unified graphical model called coupled HCRF where the joint dependence of the cluster labels and face name association is naturally embedded in the correlation between the two HCRFs. We provide an effective algorithm to optimize the two HCRFs iteratively and the performance of the two tasks on real-world data set can be both improved.
Wave failure at strong coupling in intracellular C a2 + signaling system with clustered channels
Li, Xiang; Wu, Yuning; Gao, Xuejuan; Cai, Meichun; Shuai, Jianwei
2018-01-01
As an important intracellular signal, C a2 + ions control diverse cellular functions. In this paper, we discuss the C a2 + signaling with a two-dimensional model in which the inositol 1,4,5-trisphosphate (I P3 ) receptor channels are distributed in clusters on the endoplasmic reticulum membrane. The wave failure at large C a2 + diffusion coupling is discussed in detail in the model. We show that with varying model parameters the wave failure is a robust behavior with either deterministic or stochastic channel dynamics. We suggest that the wave failure should be a general behavior in inhomogeneous diffusing systems with clustered excitable regions and may occur in biological C a2 + signaling systems.
Cluster synchronization in networks of identical oscillators with α-function pulse coupling.
Chen, Bolun; Engelbrecht, Jan R; Mirollo, Renato
2017-02-01
We study a network of N identical leaky integrate-and-fire model neurons coupled by α-function pulses, weighted by a coupling parameter K. Studies of the dynamics of this system have mostly focused on the stability of the fully synchronized and the fully asynchronous splay states, which naturally depends on the sign of K, i.e., excitation vs inhibition. We find that there is also a rich set of attractors consisting of clusters of fully synchronized oscillators, such as fixed (N-1,1) states, which have synchronized clusters of sizes N-1 and 1, as well as splay states of clusters with equal sizes greater than 1. Additionally, we find limit cycles that clarify the stability of previously observed quasiperiodic behavior. Our framework exploits the neutrality of the dynamics for K=0 which allows us to implement a dimensional reduction strategy that simplifies the dynamics to a continuous flow on a codimension 3 subspace with the sign of K determining the flow direction. This reduction framework naturally incorporates a hierarchy of partially synchronized subspaces in which the new attracting states lie. Using high-precision numerical simulations, we describe completely the sequence of bifurcations and the stability of all fixed points and limit cycles for N=2-4. The set of possible attracting states can be used to distinguish different classes of neuron models. For instance from our previous work [Chaos 24, 013114 (2014)CHAOEH1054-150010.1063/1.4858458] we know that of the types of partially synchronized states discussed here, only the (N-1,1) states can be stable in systems of identical coupled sinusoidal (i.e., Kuramoto type) oscillators, such as θ-neuron models. Upon introducing a small variation in individual neuron parameters, the attracting fixed points we discuss here generalize to equivalent fixed points in which neurons need not fire coincidently.
Accelerating the coupled-cluster singles and doubles method using the chain-of-sphere approximation
Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert
2018-06-01
In this paper, we present a chain-of-sphere implementation of the external exchange term, the computational bottleneck of coupled-cluster calculations at the singles and doubles level. This implementation is compared to standard molecular orbital, atomic orbital and resolution of identity implementations of the same term within the ORCA package and turns out to be the most efficient one for larger molecules, with a better accuracy than the resolution-of-identity approximation. Furthermore, it becomes possible to perform a canonical CC calculation on a tetramer of nucleobases in 17 days, 20 hours.
Aprà, E; Kowalski, K
2016-03-08
In this paper we discuss the implementation of multireference coupled-cluster formalism with singles, doubles, and noniterative triples (MRCCSD(T)), which is capable of taking advantage of the processing power of the Intel Xeon Phi coprocessor. We discuss the integration of two levels of parallelism underlying the MRCCSD(T) implementation with computational kernels designed to offload the computationally intensive parts of the MRCCSD(T) formalism to Intel Xeon Phi coprocessors. Special attention is given to the enhancement of the parallel performance by task reordering that has improved load balancing in the noniterative part of the MRCCSD(T) calculations. We also discuss aspects regarding efficient optimization and vectorization strategies.
International Nuclear Information System (INIS)
Bhowmik, Anal; Majumder, Sonjoy; Roy, Sourav; Dutta, Narendra Nath
2017-01-01
This work presents precise calculations of important electromagnetic transition amplitudes along with details of their many-body correlations using the relativistic coupled-cluster method. Studies of hyperfine interaction constants, useful for plasma diagnostics, with this correlation exhaustive many-body approach, are another important area of this work. The calculated oscillator strengths of allowed transitions, amplitudes of forbidden transitions and lifetimes are compared with the other theoretical results wherever available and they show a good agreement. Hyperfine constants of different isotopes of W VI, presented in this paper, will be helpful in gaining an accurate picture of the abundances of this element in different astronomical bodies. (paper)
Quadratic spatial soliton interactions
Jankovic, Ladislav
Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO 3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30
Cluster Synchronization of Diffusively Coupled Nonlinear Systems: A Contraction-Based Approach
Aminzare, Zahra; Dey, Biswadip; Davison, Elizabeth N.; Leonard, Naomi Ehrich
2018-04-01
Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with FitzHugh-Nagumo dynamics, we show that our new sufficient condition is tighter than those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex networked systems.
Analytical Energy Gradients for Excited-State Coupled-Cluster Methods
Wladyslawski, Mark; Nooijen, Marcel
The equation-of-motion coupled-cluster (EOM-CC) and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) methods have been firmly established as accurate and routinely applicable extensions of single-reference coupled-cluster theory to describe electronically excited states. An overview of these methods is provided, with emphasis on the many-body similarity transform concept that is the key to a rationalization of their accuracy. The main topic of the paper is the derivation of analytical energy gradients for such non-variational electronic structure approaches, with an ultimate focus on obtaining their detailed algebraic working equations. A general theoretical framework using Lagrange's method of undetermined multipliers is presented, and the method is applied to formulate the EOM-CC and STEOM-CC gradients in abstract operator terms, following the previous work in [P.G. Szalay, Int. J. Quantum Chem. 55 (1995) 151] and [S.R. Gwaltney, R.J. Bartlett, M. Nooijen, J. Chem. Phys. 111 (1999) 58]. Moreover, the systematics of the Lagrange multiplier approach is suitable for automation by computer, enabling the derivation of the detailed derivative equations through a standardized and direct procedure. To this end, we have developed the SMART (Symbolic Manipulation and Regrouping of Tensors) package of automated symbolic algebra routines, written in the Mathematica programming language. The SMART toolkit provides the means to expand, differentiate, and simplify equations by manipulation of the detailed algebraic tensor expressions directly. The Lagrangian multiplier formulation establishes a uniform strategy to perform the automated derivation in a standardized manner: A Lagrange multiplier functional is constructed from the explicit algebraic equations that define the energy in the electronic method; the energy functional is then made fully variational with respect to all of its parameters, and the symbolic differentiations directly yield the explicit
Energy Technology Data Exchange (ETDEWEB)
Epifanovsky, Evgeny [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States); Department of Chemistry, University of California, Berkeley, California 94720 (United States); Q-Chem Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588 (United States); Klein, Kerstin; Gauss, Jürgen [Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz (Germany); Stopkowicz, Stella [Department of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, N-0315 Oslo (Norway); Krylov, Anna I. [Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 (United States)
2015-08-14
We present a formalism and an implementation for calculating spin-orbit couplings (SOCs) within the EOM-CCSD (equation-of-motion coupled-cluster with single and double substitutions) approach. The following variants of EOM-CCSD are considered: EOM-CCSD for excitation energies (EOM-EE-CCSD), EOM-CCSD with spin-flip (EOM-SF-CCSD), EOM-CCSD for ionization potentials (EOM-IP-CCSD) and electron attachment (EOM-EA-CCSD). We employ a perturbative approach in which the SOCs are computed as matrix elements of the respective part of the Breit-Pauli Hamiltonian using zeroth-order non-relativistic wave functions. We follow the expectation-value approach rather than the response-theory formulation for property calculations. Both the full two-electron treatment and the mean-field approximation (a partial account of the two-electron contributions) have been implemented and benchmarked using several small molecules containing elements up to the fourth row of the periodic table. The benchmark results show the excellent performance of the perturbative treatment and the mean-field approximation. When used with an appropriate basis set, the errors with respect to experiment are below 5% for the considered examples. The findings regarding basis-set requirements are in agreement with previous studies. The impact of different correlation treatment in zeroth-order wave functions is analyzed. Overall, the EOM-IP-CCSD, EOM-EA-CCSD, EOM-EE-CCSD, and EOM-SF-CCSD wave functions yield SOCs that agree well with each other (and with the experimental values when available). Using an EOM-CCSD approach that provides a more balanced description of the target states yields more accurate results.
Quadratic soliton self-reflection at a quadratically nonlinear interface
Jankovic, Ladislav; Kim, Hongki; Stegeman, George; Carrasco, Silvia; Torner, Lluis; Katz, Mordechai
2003-11-01
The reflection of bulk quadratic solutions incident onto a quadratically nonlinear interface in periodically poled potassium titanyl phosphate was observed. The interface consisted of the boundary between two quasi-phase-matched regions displaced from each other by a half-period. At high intensities and small angles of incidence the soliton is reflected.
International Nuclear Information System (INIS)
Shen Jun; Piecuch, Piotr
2012-01-01
Graphical abstract: The key ideas behind biorthogonal moment expansions in coupled-cluster theory are discussed. Methods that enable merging active-space and renormalized coupled-cluster approaches are proposed and tested. Abstract: After reviewing recent progress in the area of the development of coupled-cluster (CC) methods for quasi-degenerate electronic states that are characterized by stronger non-dynamical correlation effects, including new generations of single- and multi-reference approaches that can handle bond breaking and excited states dominated by many-electron transitions, and after discussing the key elements of the left-eigenstate completely renormalized (CR) CC and equation-of-motion (EOM) CC methods, and the underlying biorthogonal method of moments of CC (MMCC) equations [P. Piecuch, M. Włoch, J. Chem. Phys. 123 (2005) 224105; P. Piecuch, M. Włoch, J.R. Gour, A. Kinal, Chem. Phys. Lett. 418 (2006) 467; M. Włoch, M.D. Lodriguito, P. Piecuch, J.R. Gour, Mol. Phys. 104 (2006) 2149], it is argued that it is beneficial to merge the CR-CC/EOMCC and active-space CC/EOMCC [P. Piecuch, Mol. Phys. 108 (2010) 2987, and references therein] theories into a single formalism. In order to accomplish this goal, the biorthogonal MMCC theory, which provides compact many-body expansions for the differences between the full configuration interaction and CC or, in the case of excited states, EOMCC energies, obtained using conventional truncation schemes in the cluster operator T and excitation operator R μ , is generalized, so that one can correct the CC/EOMCC energies obtained with arbitrary truncations in T and R μ for the selected many-electron correlation effects of interest. The resulting moment expansions, defining the new, Flexible MMCC (Flex-MMCC) formalism, and the ensuing CC(P; Q) hierarchy, proposed in the present work, enable one to correct energies obtained in the active-space CC and EOMCC calculations, in which one selects higher many
Quadratic brackets from symplectic forms
International Nuclear Information System (INIS)
Alekseev, Anton Yu.; Todorov, Ivan T.
1994-01-01
We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite-dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is the appearance of quadratic Poisson brackets for group-like variables. It is believed that upon quantization they lead to quadratic exchange algebras. ((orig.))
Students' Understanding of Quadratic Equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
International Nuclear Information System (INIS)
Rogers, Simon; Girolami, Mark; Kolch, Walter; Waters, Katrina M.; Liu, Tao; Thrall, Brian D.; Wiley, H. S.
2008-01-01
Modern transcriptomics and proteomics enable us to survey the expression of RNAs and proteins at large scales. While these data are usually generated and analyzed separately, there is an increasing interest in comparing and co-analyzing transcriptome and proteome expression data. A major open question is whether transcriptome and proteome expression is linked and how it is coordinated. Results: Here we have developed a probabilistic clustering model that permits analysis of the links between transcriptomic and proteomic profiles in a sensible and flexible manner. Our coupled mixture model defines a prior probability distribution over the component to which a protein profile should be assigned conditioned on which component the associated mRNA profile belongs to. By providing probabilistic assignments this approach sits between the two extremes of concatenating the data on the assumption that mRNA and protein clusters would have a one-to-one relationship, and independent clustering where the mRNA profile provides no information on the protein profile and vice-versa. We apply this approach to a large dataset of quantitative transcriptomic and proteomic expression data obtained from a human breast epithelial cell line (HMEC) stimulated by epidermal growth factor (EGF) over a series of timepoints corresponding to one cell cycle. The results reveal a complex relationship between transcriptome and proteome with most mRNA clusters linked to at least two protein clusters, and vice versa. A more detailed analysis incorporating information on gene function from the gene ontology database shows that a high correlation of mRNA and protein expression is limited to the components of some molecular machines, such as the ribosome, cell adhesion complexes and the TCP-1 chaperonin involved in protein folding. Conclusions: The dynamic regulation of the transcriptome and proteome in mammalian cells in response to an acute mitogenic stimulus appears largely independent with very little
Optimization of the Coupled Cluster Implementation in NWChem on Petascale Parallel Architectures
Energy Technology Data Exchange (ETDEWEB)
Anisimov, Victor; Bauer, Gregory H.; Chadalavada, Kalyana; Olson, Ryan M.; Glenski, Joseph W.; Kramer, William T.; Apra, Edoardo; Kowalski, Karol
2014-09-04
Coupled cluster singles and doubles (CCSD) algorithm has been optimized in NWChem software package. This modification alleviated the communication bottleneck and provided from 2- to 5-fold speedup in the CCSD iteration time depending on the problem size and available memory. Sustained 0.60 petaflop/sec performance on CCSD(T) calculation has been obtained on NCSA Blue Waters. This number included all stages of the calculation from initialization till termination, iterative computation of single and double excitations, and perturbative accounting for triple excitations. In the section of perturbative triples alone, the computation maintained 1.18 petaflop/sec performance level. CCSD computations have been performed on Guanine-Cytosine deoxydinucleotide monophosphate (GC-dDMP) to probe the conformational energy difference in DNA single strand in A- and B-conformations. The computation revealed significant discrepancy between CCSD and classical force fields in prediction of relative energy of A- and B-conformations of GC-dDMP.
Noniterative Multireference Coupled Cluster Methods on Heterogeneous CPU-GPU Systems
Energy Technology Data Exchange (ETDEWEB)
Bhaskaran-Nair, Kiran; Ma, Wenjing; Krishnamoorthy, Sriram; Villa, Oreste; van Dam, Hubertus JJ; Apra, Edoardo; Kowalski, Karol
2013-04-09
A novel parallel algorithm for non-iterative multireference coupled cluster (MRCC) theories, which merges recently introduced reference-level parallelism (RLP) [K. Bhaskaran-Nair, J.Brabec, E. Aprà, H.J.J. van Dam, J. Pittner, K. Kowalski, J. Chem. Phys. 137, 094112 (2012)] with the possibility of accelerating numerical calculations using graphics processing unit (GPU) is presented. We discuss the performance of this algorithm on the example of the MRCCSD(T) method (iterative singles and doubles and perturbative triples), where the corrections due to triples are added to the diagonal elements of the MRCCSD (iterative singles and doubles) effective Hamiltonian matrix. The performance of the combined RLP/GPU algorithm is illustrated on the example of the Brillouin-Wigner (BW) and Mukherjee (Mk) state-specific MRCCSD(T) formulations.
Low rank factorization of the Coulomb integrals for periodic coupled cluster theory.
Hummel, Felix; Tsatsoulis, Theodoros; Grüneis, Andreas
2017-03-28
We study a tensor hypercontraction decomposition of the Coulomb integrals of periodic systems where the integrals are factorized into a contraction of six matrices of which only two are distinct. We find that the Coulomb integrals can be well approximated in this form already with small matrices compared to the number of real space grid points. The cost of computing the matrices scales as O(N 4 ) using a regularized form of the alternating least squares algorithm. The studied factorization of the Coulomb integrals can be exploited to reduce the scaling of the computational cost of expensive tensor contractions appearing in the amplitude equations of coupled cluster methods with respect to system size. We apply the developed methodologies to calculate the adsorption energy of a single water molecule on a hexagonal boron nitride monolayer in a plane wave basis set and periodic boundary conditions.
DEFF Research Database (Denmark)
List, Nanna Holmgaard; Coriani, Sonia; Kongsted, Jacob
2014-01-01
are specifically motivated by a twofold aim: (i) computation of core excitations in realistic surroundings and (ii) examination of the effect of the differential response of the environment upon excitation solely related to the CC multipliers (herein denoted the J matrix) in computations of excitation energies......We present an extension of a previously reported implementation of a Lanczos-driven coupled-cluster (CC) damped linear response approach to molecules in condensed phases, where the effects of a surrounding environment are incorporated by means of the polarizable embedding formalism. We...... and transition moments of polarizable-embedded molecules. Numerical calculations demonstrate that the differential polarization of the environment due to the first-order CC multipliers provides only minor contributions to the solvatochromic shift for all transitions considered. We thus complement previous works...
Garza, Alejandro J.; Sousa Alencar, Ana G.; Scuseria, Gustavo E.
2015-12-01
Singlet-paired coupled cluster doubles (CCD0) is a simplification of CCD that relinquishes a fraction of dynamic correlation in order to be able to describe static correlation. Combinations of CCD0 with density functionals that recover specifically the dynamic correlation missing in the former have also been developed recently. Here, we assess the accuracy of CCD0 and CCD0+DFT (and variants of these using Brueckner orbitals) as compared to well-established quantum chemical methods for describing ground-state properties of singlet actinide molecules. The f0 actinyl series (UO22+, NpO23+, PuO24+), the isoelectronic NUN, and thorium (ThO, ThO2+) and nobelium (NoO, NoO2) oxides are studied.
Coupled cluster calculations for static and dynamic polarizabilities of C60
Kowalski, Karol; Hammond, Jeff R.; de Jong, Wibe A.; Sadlej, Andrzej J.
2008-12-01
New theoretical predictions for the static and frequency dependent polarizabilities of C60 are reported. Using the linear response coupled cluster approach with singles and doubles and a basis set especially designed to treat the molecular properties in external electric field, we obtained 82.20 and 83.62 Å3 for static and dynamic (λ =1064 nm) polarizabilities. These numbers are in a good agreement with experimentally inferred data of 76.5±8 and 79±4 Å3 [R. Antoine et al., J. Chem. Phys.110, 9771 (1999); A. Ballard et al., J. Chem. Phys.113, 5732 (2000)]. The reported results were obtained with the highest wave function-based level of theory ever applied to the C60 system.
Equation-of-motion coupled cluster method for high spin double electron attachment calculations
Energy Technology Data Exchange (ETDEWEB)
Musiał, Monika, E-mail: musial@ich.us.edu.pl; Lupa, Łukasz; Kucharski, Stanisław A. [Institute of Chemistry, University of Silesia, Szkolna 9, 40-006 Katowice (Poland)
2014-03-21
The new formulation of the equation-of-motion (EOM) coupled cluster (CC) approach applicable to the calculations of the double electron attachment (DEA) states for the high spin components is proposed. The new EOM equations are derived for the high spin triplet and quintet states. In both cases the new equations are easier to solve but the substantial simplification is observed in the case of quintets. Out of 21 diagrammatic terms contributing to the standard DEA-EOM-CCSDT equations for the R{sub 2} and R{sub 3} amplitudes only four terms survive contributing to the R{sub 3} part. The implemented method has been applied to the calculations of the excited states (singlets, triplets, and quintets) energies of the carbon and silicon atoms and potential energy curves for selected states of the Na{sub 2} (triplets) and B{sub 2} (quintets) molecules.
Novel strategy to implement active-space coupled-cluster methods
Rolik, Zoltán; Kállay, Mihály
2018-03-01
A new approach is presented for the efficient implementation of coupled-cluster (CC) methods including higher excitations based on a molecular orbital space partitioned into active and inactive orbitals. In the new framework, the string representation of amplitudes and intermediates is used as long as it is beneficial, but the contractions are evaluated as matrix products. Using a new diagrammatic technique, the CC equations are represented in a compact form due to the string notations we introduced. As an application of these ideas, a new automated implementation of the single-reference-based multi-reference CC equations is presented for arbitrary excitation levels. The new program can be considered as an improvement over the previous implementations in many respects; e.g., diagram contributions are evaluated by efficient vectorized subroutines. Timings for test calculations for various complete active-space problems are presented. As an application of the new code, the weak interactions in the Be dimer were studied.
Synergy between pair coupled cluster doubles and pair density functional theory
Energy Technology Data Exchange (ETDEWEB)
Garza, Alejandro J.; Bulik, Ireneusz W. [Department of Chemistry, Rice University, Houston, Texas 77251-1892 (United States); Henderson, Thomas M. [Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892 (United States); Scuseria, Gustavo E. [Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892 (United States); Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)
2015-01-28
Pair coupled cluster doubles (pCCD) has been recently studied as a method capable of accounting for static correlation with low polynomial cost. We present three combinations of pCCD with Kohn–Sham functionals of the density and on-top pair density (the probability of finding two electrons on top of each other) to add dynamic correlation to pCCD without double counting. With a negligible increase in computational cost, these pCCD+DFT blends greatly improve upon pCCD in the description of typical problems where static and dynamic correlations are both important. We argue that—as a black-box method with low scaling, size-extensivity, size-consistency, and a simple quasidiagonal two-particle density matrix—pCCD is an excellent match for pair density functionals in this type of fusion of multireference wavefunctions with DFT.
State-selective multireference coupled-cluster theory: In pursuit of property calculation
International Nuclear Information System (INIS)
Ghose, K.B.; Piecuch, P.; Pal, S.; Adamowicz, L.
1996-01-01
In this work, we examine the efficiency of the recently developed [P. Piecuch et al., J. Chem. Phys. 99, 6732 (1993)] state-selective (SS) multi-reference (MR) coupled-cluster (CC) method for calculation of molecular properties. In our earlier papers, we demonstrated that the SSMRCC method with inclusion of single, double, and internal and semi-internal triple excitations [SSCCSD(T) approach] is capable of providing an accurate description of the ground-state potential energy surfaces. In this paper, we present the dipole moment and polarizability values of the HF molecule at equilibrium and stretched geometries calculated using finite field technique and SSCCSD(T) ansatz. The calculations use double zeta quality basis sets with and without polarization functions. Molecular orbital basis sets include both relaxed and nonrelaxed orbitals. copyright 1996 American Institute of Physics
Alexander, Nathan; Woetzel, Nils; Meiler, Jens
2011-02-01
Clustering algorithms are used as data analysis tools in a wide variety of applications in Biology. Clustering has become especially important in protein structure prediction and virtual high throughput screening methods. In protein structure prediction, clustering is used to structure the conformational space of thousands of protein models. In virtual high throughput screening, databases with millions of drug-like molecules are organized by structural similarity, e.g. common scaffolds. The tree-like dendrogram structure obtained from hierarchical clustering can provide a qualitative overview of the results, which is important for focusing detailed analysis. However, in practice it is difficult to relate specific components of the dendrogram directly back to the objects of which it is comprised and to display all desired information within the two dimensions of the dendrogram. The current work presents a hierarchical agglomerative clustering method termed bcl::Cluster. bcl::Cluster utilizes the Pymol Molecular Graphics System to graphically depict dendrograms in three dimensions. This allows simultaneous display of relevant biological molecules as well as additional information about the clusters and the members comprising them.
Similarity-transformed equation-of-motion vibrational coupled-cluster theory
Faucheaux, Jacob A.; Nooijen, Marcel; Hirata, So
2018-02-01
A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. The first transformation uses an exponential excitation operator, defining the equation-of-motion vibrational coupled-cluster (EOM-XVCC) method, and the second uses an exponential excitation-deexcitation operator. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. We furthermore elucidate the similarities and differences between electronic and vibrational STEOM methods and between STEOM-XVCC and vibrational many-body Green's function theory based on the Dyson equation, which is also an anharmonic one-mode theory. The latter comparison inspires three approximate STEOM-XVCC methods utilizing the common approximations made in the Dyson equation: the diagonal approximation, a perturbative expansion of the Dyson self-energy, and the frequency-independent approximation. The STEOM-XVCC method including up to the simultaneous four-mode excitation operator in a quartic force field and its three approximate variants are formulated and implemented in computer codes with the aid of computer algebra, and they are applied to small test cases with varied degrees of anharmonicity.
Properties of coupled-cluster equations originating in excitation sub-algebras
Kowalski, Karol
2018-03-01
In this paper, we discuss properties of single-reference coupled cluster (CC) equations associated with the existence of sub-algebras of excitations that allow one to represent CC equations in a hybrid fashion where the cluster amplitudes associated with these sub-algebras can be obtained by solving the corresponding eigenvalue problem. For closed-shell formulations analyzed in this paper, the hybrid representation of CC equations provides a natural way for extending active-space and seniority number concepts to provide an accurate description of electron correlation effects. Moreover, a new representation can be utilized to re-define iterative algorithms used to solve CC equations, especially for tough cases defined by the presence of strong static and dynamical correlation effects. We will also explore invariance properties associated with excitation sub-algebras to define a new class of CC approximations referred to in this paper as the sub-algebra-flow-based CC methods. We illustrate the performance of these methods on the example of ground- and excited-state calculations for commonly used small benchmark systems.
A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions
International Nuclear Information System (INIS)
Jian Jinbao; Hu Qingjie; Tang Chunming; Zheng Haiyan
2007-01-01
In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported
On Characterization of Quadratic Splines
DEFF Research Database (Denmark)
Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong
2005-01-01
that the representation can be refined in a neighborhood of a non-degenerate point and a set of non-degenerate minimizers. Based on these characterizations, many existing algorithms for specific convex quadratic splines are also finite convergent for a general convex quadratic spline. Finally, we study the relationship...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general....
Energy Technology Data Exchange (ETDEWEB)
Kowalski, K., E-mail: karol.kowalski@pnnl.gov; Bhaskaran-Nair, K.; Shelton, W. A. [William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352 (United States)
2014-09-07
In this paper we discuss a new formalism for producing an analytic coupled-cluster (CC) Green's function for an N-electron system by shifting the poles of similarity transformed Hamiltonians represented in N − 1 and N + 1 electron Hilbert spaces. Simple criteria are derived for the states in N − 1 and N + 1 electron spaces that are then corrected in the spectral resolution of the corresponding matrix representations of the similarity transformed Hamiltonian. The accurate description of excited state processes within a Green's function formalism would be of significant importance to a number of scientific communities ranging from physics and chemistry to engineering and the biological sciences. This is because the Green's function methodology provides a direct path for not only calculating properties whose underlying origins come from coupled many-body interactions but also provides a straightforward path for calculating electron transport, response, and correlation functions that allows for a direct link with experiment. As a special case of this general formulation, we discuss the application of this technique for Green's function defined by the CC with singles and doubles representation of the ground-state wave function.
Energy Technology Data Exchange (ETDEWEB)
Kowalski, K. [William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA; Bhaskaran-Nair, K. [William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA; Shelton, W. A. [William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O. Box 999, Richland, Washington 99352, USA
2014-09-07
In this paper we discuss a new formalism for producing an analytic coupled-cluster (CC) Green's function for an N-electron system by shifting the poles of similarity transformed Hamiltonians represented in N - 1 and N + 1 electron Hilbert spaces. Simple criteria are derived for the states in N - 1 and N + 1 electron spaces that are then corrected in the spectral resolution of the corresponding matrix representations of the similarity transformed Hamiltonian. The accurate description of excited state processes within a Green's function formalism would be of significant importance to a number of scientific communities ranging from physics and chemistry to engineering and the biological sciences. This is because the Green's function methodology provides a direct path for not only calculating properties whose underlying origins come from coupled many-body interactions but also provides a straightforward path for calculating electron transport, response, and correlation functions that allows for a direct link with experiment. Finally, as a special case of this general formulation, we discuss the application of this technique for Green's function defined by the CC with singles and doubles representation of the ground-state wave function.
International Nuclear Information System (INIS)
Kowalski, K.; Bhaskaran-Nair, K.; Shelton, W. A.
2014-01-01
In this paper we discuss a new formalism for producing an analytic coupled-cluster (CC) Green's function for an N-electron system by shifting the poles of similarity transformed Hamiltonians represented in N − 1 and N + 1 electron Hilbert spaces. Simple criteria are derived for the states in N − 1 and N + 1 electron spaces that are then corrected in the spectral resolution of the corresponding matrix representations of the similarity transformed Hamiltonian. The accurate description of excited state processes within a Green's function formalism would be of significant importance to a number of scientific communities ranging from physics and chemistry to engineering and the biological sciences. This is because the Green's function methodology provides a direct path for not only calculating properties whose underlying origins come from coupled many-body interactions but also provides a straightforward path for calculating electron transport, response, and correlation functions that allows for a direct link with experiment. As a special case of this general formulation, we discuss the application of this technique for Green's function defined by the CC with singles and doubles representation of the ground-state wave function
Solving Coupled Gross--Pitaevskii Equations on a Cluster of PlayStation 3 Computers
Edwards, Mark; Heward, Jeffrey; Clark, C. W.
2009-05-01
At Georgia Southern University we have constructed an 8+1--node cluster of Sony PlayStation 3 (PS3) computers with the intention of using this computing resource to solve problems related to the behavior of ultra--cold atoms in general with a particular emphasis on studying bose--bose and bose--fermi mixtures confined in optical lattices. As a first project that uses this computing resource, we have implemented a parallel solver of the coupled time--dependent, one--dimensional Gross--Pitaevskii (TDGP) equations. These equations govern the behavior of dual-- species bosonic mixtures. We chose the split--operator/FFT to solve the coupled 1D TDGP equations. The fast Fourier transform component of this solver can be readily parallelized on the PS3 cpu known as the Cell Broadband Engine (CellBE). Each CellBE chip contains a single 64--bit PowerPC Processor Element known as the PPE and eight ``Synergistic Processor Element'' identified as the SPE's. We report on this algorithm and compare its performance to a non--parallel solver as applied to modeling evaporative cooling in dual--species bosonic mixtures.
On the Coupling Time of the Heat-Bath Process for the Fortuin-Kasteleyn Random-Cluster Model
Collevecchio, Andrea; Elçi, Eren Metin; Garoni, Timothy M.; Weigel, Martin
2018-01-01
We consider the coupling from the past implementation of the random-cluster heat-bath process, and study its random running time, or coupling time. We focus on hypercubic lattices embedded on tori, in dimensions one to three, with cluster fugacity at least one. We make a number of conjectures regarding the asymptotic behaviour of the coupling time, motivated by rigorous results in one dimension and Monte Carlo simulations in dimensions two and three. Amongst our findings, we observe that, for generic parameter values, the distribution of the appropriately standardized coupling time converges to a Gumbel distribution, and that the standard deviation of the coupling time is asymptotic to an explicit universal constant multiple of the relaxation time. Perhaps surprisingly, we observe these results to hold both off criticality, where the coupling time closely mimics the coupon collector's problem, and also at the critical point, provided the cluster fugacity is below the value at which the transition becomes discontinuous. Finally, we consider analogous questions for the single-spin Ising heat-bath process.
Energy Technology Data Exchange (ETDEWEB)
Hehn, Anna-Sophia; Holzer, Christof; Klopper, Wim, E-mail: klopper@kit.edu
2016-11-10
Highlights: • Ring-coupled-cluster-doubles approach now implemented with exchange terms. • Ring-coupled-cluster-doubles approach now implemented with F12 functions. • Szabo–Ostlund scheme (SO2) implemented for use in SAPT. • Fast convergence to the limit of a complete basis. • Implementation in the TURBOMOLE program system. - Abstract: Random-phase-approximation (RPA) methods have proven to be powerful tools in electronic-structure theory, being non-empirical, computationally efficient and broadly applicable to a variety of molecular systems including small-gap systems, transition-metal compounds and dispersion-dominated complexes. Applications are however hindered due to the slow basis-set convergence of the electron-correlation energy with the one-electron basis. As a remedy, we present approximate explicitly-correlated RPA approaches based on the ring-coupled-cluster-doubles formulation including exchange contributions. Test calculations demonstrate that the basis-set convergence of correlation energies is drastically accelerated through the explicitly-correlated approach, reaching 99% of the basis-set limit with triple-zeta basis sets. When implemented in close analogy to early work by Szabo and Ostlund [36], the new explicitly-correlated ring-coupled-cluster-doubles approach including exchange has the perspective to become a valuable tool in the framework of symmetry-adapted perturbation theory (SAPT) for the computation of dispersion energies of molecular complexes of weakly interacting closed-shell systems.
Lee, Timothy J.; Arnold, James O. (Technical Monitor)
1994-01-01
A new spin orbital basis is employed in the development of efficient open-shell coupled-cluster and perturbation theories that are based on a restricted Hartree-Fock (RHF) reference function. The spin orbital basis differs from the standard one in the spin functions that are associated with the singly occupied spatial orbital. The occupied orbital (in the spin orbital basis) is assigned the delta(+) = 1/square root of 2(alpha+Beta) spin function while the unoccupied orbital is assigned the delta(-) = 1/square root of 2(alpha-Beta) spin function. The doubly occupied and unoccupied orbitals (in the reference function) are assigned the standard alpha and Beta spin functions. The coupled-cluster and perturbation theory wave functions based on this set of "symmetric spin orbitals" exhibit much more symmetry than those based on the standard spin orbital basis. This, together with interacting space arguments, leads to a dramatic reduction in the computational cost for both coupled-cluster and perturbation theory. Additionally, perturbation theory based on "symmetric spin orbitals" obeys Brillouin's theorem provided that spin and spatial excitations are both considered. Other properties of the coupled-cluster and perturbation theory wave functions and models will be discussed.
Lee, Timothy J.; Langhoff, Stephen R. (Technical Monitor)
1997-01-01
Recent work on the development of single-reference perturbation theories for the study of excited electronic states will be discussed. The utility of these methods will be demonstrated by comparison to linear-response coupled-cluster excitation energies. Results for some halogen molecules of interest in stratospheric chemistry will be presented.
International Nuclear Information System (INIS)
Piecuch, Piotr; Wloch, Marta; Gour, Jeffrey R.; Dean, David J.; Papenbrock, Thomas; Hjorth-Jensen, Morten
2005-01-01
We review basic elements of the single-reference coupled-cluster theory and discuss large scale ab initio calculations of ground and excited states of 15O, 16O, and 17O using coupled-cluster methods and algorithms developed in quantum chemistry. By using realistic two-body interactions and the renormalized form of the Hamiltonian obtained with a no-core G-matrix approach, we obtain the converged results for 16O and promising preliminary results for 15O and 17O at the level of two-body interactions. The calculated properties other than energies include matter density, charge radius, and charge form factor. The relatively low costs of coupled-cluster calculations, which are characterized by the low-order polynomial scaling with the system size, enable us to probe large model spaces with up to 7 or 8 major oscillator shells, for which non-truncated shell-model calculations for nuclei with A = 15 17 active particles are presently not possible. We argue that the use of coupled-cluster methods and computer algorithms developed by quantum chemists to calculate properties of nuclei is an important step toward the development of accurate and affordable many-body theories that cross the boundaries of various physical sciences
Cremer, Dieter; Kraka, Elfi; Filatov, Michael
2008-01-01
Bond dissociation energies (BDEs) of neutral HgX and cationic HgX(+) molecules range from less than a kcal mol(-1) to as much as 60 kcal mol(-1). Using NESCICCCSD(T) [normalized elimination of the small component and coupled-cluster theory with all single and double excitations and a perturbative
Czech Academy of Sciences Publication Activity Database
Brabec, Jiří; Bhaskaran-Neir, K.; Kowalski, K.; Pittner, Jiří; van Dam, H. J. J.
2012-01-01
Roč. 542, 23 July (2012), s. 128-133 ISSN 0009-2614 R&D Projects: GA ČR GAP208/11/2222 Institutional support: RVO:61388955 Keywords : multireference Coupled Cluster (MRCC) methods * molecular systems * polycarbenes Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.145, year: 2012
DEFF Research Database (Denmark)
Paidarová, Ivana; Sauer, Stephan P. A.
2012-01-01
We have compared the performance of density functional theory (DFT) using five different exchange-correlation functionals with four coupled cluster theory based wave function methods in the calculation of geometrical derivatives of the polarizability tensor of methane. The polarizability gradient...
Spectroscopic factors with coupled-cluster connecting ab initio nuclear structure to reactions
International Nuclear Information System (INIS)
Jensen, Oeyvind
2011-02-01
This thesis has two parts. Tools and theory are presented in the first part, and papers with specific applications to nuclear physics are collected in the second part. A synopsis of theoretical foundations and basic techniques for many body quantum physics is presented in the context of a computer implementation of Wick's theorem for the symbolic algebra system SymPy. A pedagogical introduction to the implemented Python module is presented, and non-trivial aspects of the implemented simplification algorithms are discussed. Computer aided manipulations of second quantization expressions relieves practitioners of laborious and error-prone hand calculations necessary for the derivation of programmable equations. Theoretical developments of the Coupled-Cluster method (CCM) at Singles- and-Doubles level (CCSD) for the calculation of spectroscopic factors (SF) and radial overlap functions are presented. Algebraic expressions are derived from novel diagram techniques. CCM is one of the most successful methods for accurate numerical quantum mechanical simulations of medium sized many-body systems studied within Chemistry and Nuclear Physics. The recently developed spherical formulation of CCM is presented and alternative coupling schemes of quantum mechanical angular momentum are discussed in the context of a computer implementation for Racah algebra with SymPy. A pedagogical introduction to this functionality is given and it is used to derive angular momentum coupled expressions for efficient calculation of the spectroscopic factor diagrams. The first research paper presents a calculation of spectroscopic factors with CCSD. Details of the calculation is presented and convergence properties, as well as the dependence on various model parameters are discussed. Interactions with different cut-offs are employed and the dependence of the SF on the interactions are studied. In the second paper we employ the angular momentum coupled SF expressions and the spherical formulation
Energy Technology Data Exchange (ETDEWEB)
Azar, Richard Julian, E-mail: julianazar2323@berkeley.edu; Head-Gordon, Martin, E-mail: mhg@cchem.berkeley.edu [Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)
2015-05-28
Your correspondents develop and apply fully nonorthogonal, local-reference perturbation theories describing non-covalent interactions. Our formulations are based on a Löwdin partitioning of the similarity-transformed Hamiltonian into a zeroth-order intramonomer piece (taking local CCSD solutions as its zeroth-order eigenfunction) plus a first-order piece coupling the fragments. If considerations are limited to a single molecule, the proposed intermolecular similarity-transformed perturbation theory represents a frozen-orbital variant of the “(2)”-type theories shown to be competitive with CCSD(T) and of similar cost if all terms are retained. Different restrictions on the zeroth- and first-order amplitudes are explored in the context of large-computation tractability and elucidation of non-local effects in the space of singles and doubles. To accurately approximate CCSD intermolecular interaction energies, a quadratically growing number of variables must be included at zeroth-order.
Speeding up equation of motion coupled cluster theory with the chain of spheres approximation
International Nuclear Information System (INIS)
Dutta, Achintya Kumar; Neese, Frank; Izsák, Róbert
2016-01-01
In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel’s test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm −1 (59 μHartree) for excitation energies and 6.799 cm −1 (31 μHartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core
Speeding up equation of motion coupled cluster theory with the chain of spheres approximation
Energy Technology Data Exchange (ETDEWEB)
Dutta, Achintya Kumar; Neese, Frank, E-mail: frank.neese@cec.mpg.de; Izsák, Róbert, E-mail: robert.izsak@cec.mpg.de [Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, 45470 Mülheim an der Ruhr (Germany)
2016-01-21
In the present paper, the chain of spheres exchange (COSX) approximation is applied to the highest scaling terms in the equation of motion (EOM) coupled cluster equations with single and double excitations, in particular, the terms involving integrals with four virtual labels. It is found that even the acceleration of this single term yields significant computational gains without compromising the desired accuracy of the method. For an excitation energy calculation on a cluster of five water molecules using 585 basis functions, the four virtual term is 9.4 times faster using COSX with a loose grid than using the canonical implementation, which yields a 2.6 fold acceleration for the whole of the EOM calculation. For electron attachment calculations, the four virtual term is 15 times and the total EOM calculation is 10 times faster than the canonical calculation for the same system. The accuracy of the new method was tested using Thiel’s test set for excited states using the same settings and the maximum absolute deviation over the whole test set was found to be 12.945 cm{sup −1} (59 μHartree) for excitation energies and 6.799 cm{sup −1} (31 μHartree) for electron attachments. Using MP2 amplitudes for the ground state in combination with the parallel evaluation of the full EOM equations in the manner discussed in this paper enabled us to perform calculations for large systems. Electron affinity values for the two lowest states of a Zn protoporphyrine model compound (224 correlated electrons and 1120 basis functions) were obtained in 3 days 19 h using 4 cores of a Xeon E5-2670 processor allocating 10 GB memory per core. Calculating the lowest two excitation energies for trans-retinal (114 correlated electrons and 539 basis functions) took 1 day 21 h using eight cores of the same processor and identical memory allocation per core.
Holguín-Gallego, Fernando José; Chávez-Calvillo, Rodrigo; García-Revilla, Marco; Francisco, Evelio; Pendás, Ángel Martín; Rocha-Rinza, Tomás
2016-07-15
The electronic energy partition established by the Interacting Quantum Atoms (IQA) approach is an important method of wavefunction analyses which has yielded valuable insights about different phenomena in physical chemistry. Most of the IQA applications have relied upon approximations, which do not include either dynamical correlation (DC) such as Hartree-Fock (HF) or external DC like CASSCF theory. Recently, DC was included in the IQA method by means of HF/Coupled-Cluster (CC) transition densities (Chávez-Calvillo et al., Comput. Theory Chem. 2015, 1053, 90). Despite the potential utility of this approach, it has a few drawbacks, for example, it is not consistent with the calculation of CC properties different from the total electronic energy. To improve this situation, we have implemented the IQA energy partition based on CC Lagrangian one- and two-electron orbital density matrices. The development presented in this article is tested and illustrated with the H2 , LiH, H2 O, H2 S, N2 , and CO molecules for which the IQA results obtained under the consideration of (i) the CC Lagrangian, (ii) HF/CC transition densities, and (iii) HF are critically analyzed and compared. Additionally, the effect of the DC in the different components of the electronic energy in the formation of the T-shaped (H2 )2 van der Waals cluster and the bimolecular nucleophilic substitution between F(-) and CH3 F is examined. We anticipate that the approach put forward in this article will provide new understandings on subjects in physical chemistry wherein DC plays a crucial role like molecular interactions along with chemical bonding and reactivity. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
Higher-order equation-of-motion coupled-cluster methods for ionization processes.
Kamiya, Muneaki; Hirata, So
2006-08-21
Compact algebraic equations defining the equation-of-motion coupled-cluster (EOM-CC) methods for ionization potentials (IP-EOM-CC) have been derived and computer implemented by virtue of a symbolic algebra system largely automating these processes. Models with connected cluster excitation operators truncated after double, triple, or quadruple level and with linear ionization operators truncated after two-hole-one-particle (2h1p), three-hole-two-particle (3h2p), or four-hole-three-particle (4h3p) level (abbreviated as IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively) have been realized into parallel algorithms taking advantage of spin, spatial, and permutation symmetries with optimal size dependence of the computational costs. They are based on spin-orbital formalisms and can describe both alpha and beta ionizations from open-shell (doublet, triplet, etc.) reference states into ionized states with various spin magnetic quantum numbers. The application of these methods to Koopmans and satellite ionizations of N2 and CO (with the ambiguity due to finite basis sets eliminated by extrapolation) has shown that IP-EOM-CCSD frequently accounts for orbital relaxation inadequately and displays errors exceeding a couple of eV. However, these errors can be systematically reduced to tenths or even hundredths of an eV by IP-EOM-CCSDT or CCSDTQ. Comparison of spectroscopic parameters of the FH+ and NH+ radicals between IP-EOM-CC and experiments has also underscored the importance of higher-order IP-EOM-CC treatments. For instance, the harmonic frequencies of the A 2Sigma- state of NH+ are predicted to be 1285, 1723, and 1705 cm(-1) by IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively, as compared to the observed value of 1707 cm(-1). The small adiabatic energy separation (observed 0.04 eV) between the X 2Pi and a 4Sigma- states of NH+ also requires IP-EOM-CCSDTQ for a quantitative prediction (0.06 eV) when the a 4Sigma- state has the low-spin magnetic quantum number (s(z) = 1/2). When the
Shen, Jun; Piecuch, Piotr
2012-06-01
After reviewing recent progress in the area of the development of coupled-cluster (CC) methods for quasi-degenerate electronic states that are characterized by stronger non-dynamical correlation effects, including new generations of single- and multi-reference approaches that can handle bond breaking and excited states dominated by many-electron transitions, and after discussing the key elements of the left-eigenstate completely renormalized (CR) CC and equation-of-motion (EOM) CC methods, and the underlying biorthogonal method of moments of CC (MMCC) equations [P. Piecuch, M. Włoch, J. Chem. Phys. 123 (2005) 224105; P. Piecuch, M. Włoch, J.R. Gour, A. Kinal, Chem. Phys. Lett. 418 (2006) 467; M. Włoch, M.D. Lodriguito, P. Piecuch, J.R. Gour, Mol. Phys. 104 (2006) 2149], it is argued that it is beneficial to merge the CR-CC/EOMCC and active-space CC/EOMCC [P. Piecuch, Mol. Phys. 108 (2010) 2987, and references therein] theories into a single formalism. In order to accomplish this goal, the biorthogonal MMCC theory, which provides compact many-body expansions for the differences between the full configuration interaction and CC or, in the case of excited states, EOMCC energies, obtained using conventional truncation schemes in the cluster operator T and excitation operator Rμ, is generalized, so that one can correct the CC/EOMCC energies obtained with arbitrary truncations in T and Rμ for the selected many-electron correlation effects of interest. The resulting moment expansions, defining the new, Flexible MMCC (Flex-MMCC) formalism, and the ensuing CC(P; Q) hierarchy, proposed in the present work, enable one to correct energies obtained in the active-space CC and EOMCC calculations, in which one selects higher many-body components of T and Rμ via active orbitals and which recover much of the relevant non-dynamical and some dynamical electron correlation effects in applications involving potential energy surfaces (PESs) along bond breaking coordinates, for the
Energy Technology Data Exchange (ETDEWEB)
Brabec, Jiri; Pittner, Jiri; van Dam, Hubertus JJ; Apra, Edoardo; Kowalski, Karol
2012-02-01
A novel algorithm for implementing general type of multireference coupled-cluster (MRCC) theory based on the Jeziorski-Monkhorst exponential Ansatz [B. Jeziorski, H.J. Monkhorst, Phys. Rev. A 24, 1668 (1981)] is introduced. The proposed algorithm utilizes processor groups to calculate the equations for the MRCC amplitudes. In the basic formulation each processor group constructs the equations related to a specific subset of references. By flexible choice of processor groups and subset of reference-specific sufficiency conditions designated to a given group one can assure optimum utilization of available computing resources. The performance of this algorithm is illustrated on the examples of the Brillouin-Wigner and Mukherjee MRCC methods with singles and doubles (BW-MRCCSD and Mk-MRCCSD). A significant improvement in scalability and in reduction of time to solution is reported with respect to recently reported parallel implementation of the BW-MRCCSD formalism [J.Brabec, H.J.J. van Dam, K. Kowalski, J. Pittner, Chem. Phys. Lett. 514, 347 (2011)].
Simulation of the photodetachment spectrum of HHfO- using coupled-cluster calculations
Mok, Daniel K. W.; Dyke, John M.; Lee, Edmond P. F.
2016-12-01
The photodetachment spectrum of HHfO- was simulated using restricted-spin coupled-cluster single-double plus perturbative triple {RCCSD(T)} calculations performed on the ground electronic states of HHfO and HHfO-, employing basis sets of up to quintuple-zeta quality. The computed RCCSD(T) electron affinity of 1.67 ± 0.02 eV at the complete basis set limit, including Hf 5s25p6 core correlation and zero-point energy corrections, agrees well with the experimental value of 1.70 ± 0.05 eV from a recent photodetachment study [X. Li et al., J. Chem. Phys. 136, 154306 (2012)]. For the simulation, Franck-Condon factors were computed which included allowances for anharmonicity and Duschinsky rotation. Comparisons between simulated and experimental spectra confirm the assignments of the molecular carrier and electronic states involved but suggest that the experimental vibrational structure has suffered from poor signal-to-noise ratio. An alternative assignment of the vibrational structure to that suggested in the experimental work is presented.
Symmetry broken and restored coupled-cluster theory: I. Rotational symmetry and angular momentum
International Nuclear Information System (INIS)
Duguet, T
2015-01-01
We extend coupled-cluster (CC) theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of near-degenerate finite quantum systems with an open-shell character. As such, the newly developed many-body formalism offers a wealth of potential applications and further extensions dedicated to the ab initio description of, e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism, which encompasses both single-reference CC theory and projected Hartree–Fock theory as particular cases, permits the computation of usual sets of connected diagrams while consistently incorporating static correlations through the highly non-perturbative restoration of rotational symmetry. Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy associated with each angular momentum, is accessed within a single calculation. A key difficulty presently overcome relates to the necessity to handle generalized energy and norm kernels for which naturally terminating CC expansions could be eventually obtained. The present work focuses on SU(2) but can be extended to any (locally) compact Lie group and to discrete groups, such as most point groups. In particular, the formalism will be soon generalized to U(1) symmetry associated with particle number conservation. This is relevant to Bogoliubov CC theory that was recently applied to singly open-shell nuclei. (paper)
Energy Technology Data Exchange (ETDEWEB)
Ibrahim, Khaled Z. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Epifanovsky, Evgeny [Q-Chem, Inc., Pleasanton, CA (United States); Williams, Samuel W. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Krylov, Anna I. [Univ. of Southern California, Los Angeles, CA (United States). Dept. of Chemistry
2016-07-26
Coupled-cluster methods provide highly accurate models of molecular structure by explicit numerical calculation of tensors representing the correlation between electrons. These calculations are dominated by a sequence of tensor contractions, motivating the development of numerical libraries for such operations. While based on matrix-matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the tensor representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts to extend the Libtensor framework to work in the distributed memory environment in a scalable and energy efficient manner. We achieve up to 240 speedup compared with the best optimized shared memory implementation. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures, (Cray XC30&XC40, BlueGene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance. Nevertheless, we preserve a uni ed interface to both programming models to maintain the productivity of computational quantum chemists.
Diagonal Born-Oppenheimer correction for coupled-cluster wave-functions
Shamasundar, K. R.
2018-06-01
We examine how geometry-dependent normalisation freedom of electronic wave-functions affects extraction of a meaningful diagonal Born-Oppenheimer correction (DBOC) to the ground-state Born-Oppenheimer potential energy surface (PES). By viewing this freedom as a kind of gauge-freedom, it is shown that DBOC and the resulting associated mass-dependent adiabatic PES are gauge-invariant quantities. A sum-over-states (SOS) formula for DBOC which explicitly exhibits this invariance is derived. A biorthogonal formulation suitable for DBOC computations using standard unnormalised coupled-cluster (CC) wave-functions is presented. This is shown to lead to a biorthogonal version of SOS formula with similar properties. On this basis, different computational schemes for evaluating DBOC using approximate CC wave-functions are derived. One of this agrees with the formula used in the current literature. The connection to adiabatic-to-diabatic transformations in non-adiabatic dynamics is explored and complications arising from biorthogonal nature of CC theory are identified.
Convergence of the Light-Front Coupled-Cluster Method in Scalar Yukawa Theory
Usselman, Austin
We use Fock-state expansions and the Light-Front Coupled-Cluster (LFCC) method to study mass eigenvalue problems in quantum field theory. Specifically, we study convergence of the method in scalar Yukawa theory. In this theory, a single charged particle is surrounded by a cloud of neutral particles. The charged particle can create or annihilate neutral particles, causing the n-particle state to depend on the n + 1 and n - 1-particle state. Fock state expansion leads to an infinite set of coupled equations where truncation is required. The wave functions for the particle states are expanded in a basis of symmetric polynomials and a generalized eigenvalue problem is solved for the mass eigenvalue. The mass eigenvalue problem is solved for multiple values for the coupling strength while the number of particle states and polynomial basis order are increased. Convergence of the mass eigenvalue solutions is then obtained. Three mass ratios between the charged particle and neutral particles were studied. This includes a massive charged particle, equal masses and massive neutral particles. Relative probability between states can also be explored for more detailed understanding of the process of convergence with respect to the number of Fock sectors. The reliance on higher order particle states depended on how large the mass of the charge particle was. The higher the mass of the charged particle, the more the system depended on higher order particle states. The LFCC method solves this same mass eigenvalue problem using an exponential operator. This exponential operator can then be truncated instead to form a finite system of equations that can be solved using a built in system solver provided in most computational environments, such as MatLab and Mathematica. First approximation in the LFCC method allows for only one particle to be created by the new operator and proved to be not powerful enough to match the Fock state expansion. The second order approximation allowed one
Mück, Leonie Anna; Gauss, Jürgen
2012-03-21
We propose a generally applicable scheme for the computation of spin-orbit (SO) splittings in degenerate open-shell systems using multireference coupled-cluster (MRCC) theory. As a specific method, Mukherjee's version of MRCC (Mk-MRCC) in conjunction with an effective mean-field SO operator is adapted for this purpose. An expression for the SO splittings is derived and implemented using Mk-MRCC analytic derivative techniques. The computed SO splittings are found to be in satisfactory agreement with experimental data. Due to the symmetry properties of the SO operator, SO splittings can be considered a quality measure for the coupling between reference determinants in Jeziorski-Monkhorst based MRCC methods. We thus provide numerical insights into the coupling problem of Mk-MRCC theory. © 2012 American Institute of Physics
Stability in quadratic torsion theories
Energy Technology Data Exchange (ETDEWEB)
Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2017-11-15
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)
Stability in quadratic torsion theories
International Nuclear Information System (INIS)
Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado
2017-01-01
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)
A pair natural orbital implementation of the coupled cluster model CC2 for excitation energies.
Helmich, Benjamin; Hättig, Christof
2013-08-28
We demonstrate how to extend the pair natural orbital (PNO) methodology for excited states, presented in a previous work for the perturbative doubles correction to configuration interaction singles (CIS(D)), to iterative coupled cluster methods such as the approximate singles and doubles model CC2. The original O(N(5)) scaling of the PNO construction is reduced by using orbital-specific virtuals (OSVs) as an intermediate step without spoiling the initial accuracy of the PNO method. Furthermore, a slower error convergence for charge-transfer states is analyzed and resolved by a numerical Laplace transformation during the PNO construction, so that an equally accurate treatment of local and charge-transfer excitations is achieved. With state-specific truncated PNO expansions, the eigenvalue problem is solved by combining the Davidson algorithm with deflation to project out roots that have already been determined and an automated refresh with a generation of new PNOs to achieve self-consistency of the PNO space. For a large test set, we found that truncation errors for PNO-CC2 excitation energies are only slightly larger than for PNO-CIS(D). The computational efficiency of PNO-CC2 is demonstrated for a large organic dye, where a reduction of the doubles space by a factor of more than 1000 is obtained compared to the canonical calculation. A compression of the doubles space by a factor 30 is achieved by a unified OSV space only. Moreover, calculations with the still preliminary PNO-CC2 implementation on a series of glycine oligomers revealed an early break even point with a canonical RI-CC2 implementation between 100 and 300 basis functions.
Theoretical characterization of the F(2)O(3) molecule by coupled-cluster methods.
Huang, Ming-Ju; Watts, John D
2010-09-23
Coupled-cluster calculations with extended basis sets that include noniterative connected triple excitations (CCSD(T)) have been used to study the FOOOF isomer of F(2)O(3). Second-order Moller-Plessett perturbation theory (MP2) and density-functional theory (B3LYP functional) calculations have also been performed for comparison. Two local minima of similar energy, namely, conformers of C(2) and C(s) symmetry have been located. Structures, harmonic vibrational frequencies, and standard enthalpies and free energies of formation have been calculated. The calculated bond lengths of F(2)O(3) are more characteristic of those in F(2)O and a "normal" peroxide than the unusual bond lengths in F(2)O(2). Both conformers have equal F-O and O-O bond lengths, contrary to a recent suggestion of an unsymmetrical structure. The harmonic vibrational frequencies can aid possible identification of gaseous F(2)O(3). The calculated Δ(f)H° and Δ(f)G° are 110 and 173 kJ mol(-1), respectively. These values are based on extrapolation of CCSD(T) results with augmented triple- and quadruple-ζ basis sets and are expected to be within chemical accuracy (i.e., 1 kcal mol(-1) or 4 kJ mol(-1)). F(2)O(3) is calculated to be stable to decomposition to either FO + FOO or F(2) + O(3), but unstable to decomposition to its elements, to F(2)O(2) + (1)/(2)O(2), and to F(2)O + O(2).
Lupinetti, Concetta; Thakkar, Ajit J
2005-01-22
Accurate static dipole polarizabilities and hyperpolarizabilities are calculated for the ground states of the Al, Si, P, S, Cl, and Ar atoms. The finite-field computations use energies obtained with various ab initio methods including Moller-Plesset perturbation theory and the coupled cluster approach. Excellent agreement with experiment is found for argon. The experimental alpha for Al is likely to be in error. Only limited comparisons are possible for the other atoms because hyperpolarizabilities have not been reported previously for most of these atoms. Our recommended values of the mean dipole polarizability (in the order Al-Ar) are alpha/e(2)a(0) (2)E(h) (-1)=57.74, 37.17, 24.93, 19.37, 14.57, and 11.085 with an error estimate of +/-0.5%. The recommended values of the mean second dipole hyperpolarizability (in the order Al-Ar) are gamma/e(4)a(0) (4)E(h) (-3)=2.02 x 10(5), 4.31 x 10(4), 1.14 x 10(4), 6.51 x 10(3), 2.73 x 10(3), and 1.18 x 10(3) with an error estimate of +/-2%. Our recommended polarizability anisotropy values are Deltaalpha/e(2)a(0) (2)E(h) (-1)=-25.60, 8.41, -3.63, and 1.71 for Al, Si, S, and Cl respectively, with an error estimate of +/-1%. The recommended hyperpolarizability anisotropies are Deltagamma/e(4)a(0) (4)E(h) (-3)=-3.88 x 10(5), 4.16 x 10(4), -7.00 x 10(3), and 1.65 x 10(3) for Al, Si, S, and Cl, respectively, with an error estimate of +/-4%. (c) 2005 American Institute of Physics.
A view on coupled cluster perturbation theory using a bivariational Lagrangian formulation.
Kristensen, Kasper; Eriksen, Janus J; Matthews, Devin A; Olsen, Jeppe; Jørgensen, Poul
2016-02-14
We consider two distinct coupled cluster (CC) perturbation series that both expand the difference between the energies of the CCSD (CC with single and double excitations) and CCSDT (CC with single, double, and triple excitations) models in orders of the Møller-Plesset fluctuation potential. We initially introduce the E-CCSD(T-n) series, in which the CCSD amplitude equations are satisfied at the expansion point, and compare it to the recently developed CCSD(T-n) series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)], in which not only the CCSD amplitude, but also the CCSD multiplier equations are satisfied at the expansion point. The computational scaling is similar for the two series, and both are term-wise size extensive with a formal convergence towards the CCSDT target energy. However, the two series are different, and the CCSD(T-n) series is found to exhibit a more rapid convergence up through the series, which we trace back to the fact that more information at the expansion point is utilized than for the E-CCSD(T-n) series. The present analysis can be generalized to any perturbation expansion representing the difference between a parent CC model and a higher-level target CC model. In general, we demonstrate that, whenever the parent parameters depend upon the perturbation operator, a perturbation expansion of the CC energy (where only parent amplitudes are used) differs from a perturbation expansion of the CC Lagrangian (where both parent amplitudes and parent multipliers are used). For the latter case, the bivariational Lagrangian formulation becomes more than a convenient mathematical tool, since it facilitates a different and faster convergent perturbation series than the simpler energy-based expansion.
Quadratic prediction of factor scores
Wansbeek, T
1999-01-01
Factor scores are naturally predicted by means of their conditional expectation given the indicators y. Under normality this expectation is linear in y but in general it is an unknown function of y. II is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic
On quadratic variation of martingales
Indian Academy of Sciences (India)
On quadratic variation of martingales. 459. The proof relied on the theory of stochastic integration. Subsequently, in Karandikar. [4], the formula was derived using only Doob's maximal inequality. Thus this could be the starting point for the development of stochastic calculus for continuous semimartingales without bringing in ...
Impurity solitons with quadratic nonlinearities
DEFF Research Database (Denmark)
Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis
1998-01-01
We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...
Quadratic divergences and dimensional regularisation
International Nuclear Information System (INIS)
Jack, I.; Jones, D.R.T.
1990-01-01
We present a detailed analysis of quadratic and quartic divergences in dimensionally regulated renormalisable theories. We perform explicit three-loop calculations for a general theory of scalars and fermions. We find that the higher-order quartic divergences are related to the lower-order ones by the renormalisation group β-functions. (orig.)
Indian Academy of Sciences (India)
2017-09-27
Sep 27, 2017 ... Author for correspondence (zh4403701@126.com). MS received 15 ... lic clusters using density functional theory (DFT)-GGA of the DMOL3 package. ... In the process of geometric optimization, con- vergence thresholds ..... and Postgraduate Research & Practice Innovation Program of. Jiangsu Province ...
Indian Academy of Sciences (India)
environmental as well as technical problems during fuel gas utilization. ... adsorption on some alloys of Pd, namely PdAu, PdAg ... ried out on small neutral and charged Au24,26,27, Cu,28 ... study of Zanti et al.29 on Pdn (n = 1–9) clusters.
Lutnaes, Ola B; Teale, Andrew M; Helgaker, Trygve; Tozer, David J; Ruud, Kenneth; Gauss, Jürgen
2009-10-14
An accurate set of benchmark rotational g tensors and magnetizabilities are calculated using coupled-cluster singles-doubles (CCSD) theory and coupled-cluster single-doubles-perturbative-triples [CCSD(T)] theory, in a variety of basis sets consisting of (rotational) London atomic orbitals. The accuracy of the results obtained is established for the rotational g tensors by careful comparison with experimental data, taking into account zero-point vibrational corrections. After an analysis of the basis sets employed, extrapolation techniques are used to provide estimates of the basis-set-limit quantities, thereby establishing an accurate benchmark data set. The utility of the data set is demonstrated by examining a wide variety of density functionals for the calculation of these properties. None of the density-functional methods are competitive with the CCSD or CCSD(T) methods. The need for a careful consideration of vibrational effects is clearly illustrated. Finally, the pure coupled-cluster results are compared with the results of density-functional calculations constrained to give the same electronic density. The importance of current dependence in exchange-correlation functionals is discussed in light of this comparison.
Energy Technology Data Exchange (ETDEWEB)
Degroote, M. [Rice Univ., Houston, TX (United States); Henderson, T. M. [Rice Univ., Houston, TX (United States); Zhao, J. [Rice Univ., Houston, TX (United States); Dukelsky, J. [Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Inst. de Estructura de la Materia; Scuseria, G. E. [Rice Univ., Houston, TX (United States)
2018-01-03
We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.
Sørensen, Lasse K; Olsen, Jeppe; Fleig, Timo
2011-06-07
A string-based coupled-cluster method of general excitation rank and with optimal scaling which accounts for special relativity within the four-component framework is presented. The method opens the way for the treatment of multi-reference problems through an active-space inspired single-reference based state-selective expansion of the model space. The evaluation of the coupled-cluster vector function is implemented by considering contractions of elementary second-quantized operators without setting up the amplitude equations explicitly. The capabilities of the new method are demonstrated in application to the electronic ground state of the bismuth monohydride molecule. In these calculations simulated multi-reference expansions with both doubles and triples excitations into the external space as well as the regular coupled-cluster hierarchy up to full quadruples excitations are compared. The importance of atomic outer core-correlation for obtaining accurate results is shown. Comparison to the non-relativistic framework is performed throughout to illustrate the additional work of the transition to the four-component relativistic framework both in implementation and application. Furthermore, an evaluation of the highest order scaling for general-order expansions is presented. © 2011 American Institute of Physics
Large N saddle formulation of quadratic building block theories
International Nuclear Information System (INIS)
Halpern, M.B.
1980-01-01
I develop a large N saddle point formulation for the broad class of 'theories of quadratic building blocks'. Such theories are those on which the sums over internal indices are contained in quadratic building blocks, e.g. PHI 2 = Σsup(N)sub(a-1)PHi sup(a)sup(a). The formulation applies as well to fermions, derivative coupling and non-polynomial interactions. In a related development, closed Schwinger-Dyson equations for Green functions of the building blocks are derived and solved for large N. (orig.)
Zhang, Yifan; Tang, Zhiqiang; Wu, Baoyuan; Ji, Qiang; Lu, Hanqing
2016-01-01
, we divide the problem into two tasks: face clustering which groups the faces depicting a certain person into a cluster, and name assignment which associates a name to each face. Each task is formulated as a structured prediction problem and modeled
Quadratic third-order tensor optimization problem with quadratic constraints
Directory of Open Access Journals (Sweden)
Lixing Yang
2014-05-01
Full Text Available Quadratically constrained quadratic programs (QQPs problems play an important modeling role for many diverse problems. These problems are in general NP hard and numerically intractable. Semidenite programming (SDP relaxations often provide good approximate solutions to these hard problems. For several special cases of QQP, e.g., convex programs and trust region subproblems, SDP relaxation provides the exact optimal value, i.e., there is a zero duality gap. However, this is not true for the general QQP, or even the QQP with two convex constraints, but a nonconvex objective.In this paper, we consider a certain QQP where the variable is neither vector nor matrix but a third-order tensor. This problem can be viewed as a generalization of the ordinary QQP with vector or matrix as it's variant. Under some mild conditions, we rst show that SDP relaxation provides exact optimal solutions for the original problem. Then we focus on two classes of homogeneous quadratic tensor programming problems which have no requirements on the constraints number. For one, we provide an easily implemental polynomial time algorithm to approximately solve the problem and discuss the approximation ratio. For the other, we show there is no gap between the SDP relaxation and itself.
Directory of Open Access Journals (Sweden)
Chenglin Wang
2017-11-01
Full Text Available Recognition and matching of litchi fruits are critical steps for litchi harvesting robots to successfully grasp litchi. However, due to the randomness of litchi growth, such as clustered growth with uncertain number of fruits and random occlusion by leaves, branches and other fruits, the recognition and matching of the fruit become a challenge. Therefore, this study firstly defined mature litchi fruit as three clustered categories. Then an approach for recognition and matching of clustered mature litchi fruit was developed based on litchi color images acquired by binocular charge-coupled device (CCD color cameras. The approach mainly included three steps: (1 calibration of binocular color cameras and litchi image acquisition; (2 segmentation of litchi fruits using four kinds of supervised classifiers, and recognition of the pre-defined categories of clustered litchi fruit using a pixel threshold method; and (3 matching the recognized clustered fruit using a geometric center-based matching method. The experimental results showed that the proposed recognition method could be robust against the influences of varying illumination and occlusion conditions, and precisely recognize clustered litchi fruit. In the tested 432 clustered litchi fruits, the highest and lowest average recognition rates were 94.17% and 92.00% under sunny back-lighting and partial occlusion, and sunny front-lighting and non-occlusion conditions, respectively. From 50 pairs of tested images, the highest and lowest matching success rates were 97.37% and 91.96% under sunny back-lighting and non-occlusion, and sunny front-lighting and partial occlusion conditions, respectively.
International Nuclear Information System (INIS)
Canola, Sofia; Pecoraro, Claudia; Negri, Fabrizia
2016-01-01
Hole transport properties are modeled for two polymorphs of pentacene: the single crystal polymorph and the thin film polymorph relevant for organic thin-film transistor applications. Electronic couplings are evaluated in the standard dimer approach but also considering a cluster approach in which the central molecule is surrounded by a large number of molecules quantum-chemically described. The effective electronic couplings suitable for the parametrization of a tight-binding model are derived either from the orthogonalization scheme limited to HOMO orbitals and from the orthogonalization of the full basis of molecular orbitals. The angular dependent mobilities estimated for the two polymorphs using the predicted pattern of couplings display different anisotropy characteristics as suggested from experimental investigations.
Energy Technology Data Exchange (ETDEWEB)
Canola, Sofia; Pecoraro, Claudia; Negri, Fabrizia
2016-10-20
Hole transport properties are modeled for two polymorphs of pentacene: the single crystal polymorph and the thin film polymorph relevant for organic thin-film transistor applications. Electronic couplings are evaluated in the standard dimer approach but also considering a cluster approach in which the central molecule is surrounded by a large number of molecules quantum-chemically described. The effective electronic couplings suitable for the parametrization of a tight-binding model are derived either from the orthogonalization scheme limited to HOMO orbitals and from the orthogonalization of the full basis of molecular orbitals. The angular dependent mobilities estimated for the two polymorphs using the predicted pattern of couplings display different anisotropy characteristics as suggested from experimental investigations.
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.95.084025
On Quadratic Variation of Martingales
Indian Academy of Sciences (India)
where D ( [ 0 , ∞ ) , R ) denotes the class of real valued r.c.l.l. functions on [ 0 , ∞ ) such that for a locally square integrable martingale ( M t ) with r.c.l.l. paths,. Ψ ( M . ( ) ) = A . ( ). gives the quadratic variation process (written usually as [ M , M ] t ) of ( M t ) . We also show that this process ( A t ) is the unique increasing ...
Exact solutions to quadratic gravity
Czech Academy of Sciences Publication Activity Database
Pravda, Vojtěch; Pravdová, Alena; Podolský, J.; Švarc, J.
2017-01-01
Roč. 95, č. 8 (2017), č. článku 084025. ISSN 2470-0010 R&D Projects: GA ČR GB14-37086G Institutional support: RVO:67985840 Keywords : quadratic gravity * exact solutions * Kundt spacetimes Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.568, year: 2016 https://journals. aps .org/prd/abstract/10.1103/PhysRevD.95.084025
Gain scheduled linear quadratic control for quadcopter
Okasha, M.; Shah, J.; Fauzi, W.; Hanouf, Z.
2017-12-01
This study exploits the dynamics and control of quadcopters using Linear Quadratic Regulator (LQR) control approach. The quadcopter’s mathematical model is derived using the Newton-Euler method. It is a highly manoeuvrable, nonlinear, coupled with six degrees of freedom (DOF) model, which includes aerodynamics and detailed gyroscopic moments that are often ignored in many literatures. The linearized model is obtained and characterized by the heading angle (i.e. yaw angle) of the quadcopter. The adopted control approach utilizes LQR method to track several reference trajectories including circle and helix curves with significant variation in the yaw angle. The controller is modified to overcome difficulties related to the continuous changes in the operating points and eliminate chattering and discontinuity that is observed in the control input signal. Numerical non-linear simulations are performed using MATLAB and Simulink to illustrate to accuracy and effectiveness of the proposed controller.
Quadratic gravity in first order formalism
Energy Technology Data Exchange (ETDEWEB)
Alvarez, Enrique; Anero, Jesus; Gonzalez-Martin, Sergio, E-mail: enrique.alvarez@uam.es, E-mail: jesusanero@gmail.com, E-mail: sergio.gonzalez.martin@uam.es [Departamento de Física Teórica and Instituto de Física Teórica (IFT-UAM/CSIC), Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid (Spain)
2017-10-01
We consider the most general action for gravity which is quadratic in curvature. In this case first order and second order formalisms are not equivalent. This framework is a good candidate for a unitary and renormalizable theory of the gravitational field; in particular, there are no propagators falling down faster than 1/ p {sup 2}. The drawback is of course that the parameter space of the theory is too big, so that in many cases will be far away from a theory of gravity alone. In order to analyze this issue, the interaction between external sources was examined in some detail. We find that this interaction is conveyed mainly by propagation of the three-index connection field. At any rate the theory as it stands is in the conformal invariant phase; only when Weyl invariance is broken through the coupling to matter can an Einstein-Hilbert term (and its corresponding Planck mass scale) be generated by quantum corrections.
A Coupled Hidden Markov Random Field Model for Simultaneous Face Clustering and Tracking in Videos
Wu, Baoyuan; Hu, Bao-Gang; Ji, Qiang
2016-01-01
Face clustering and face tracking are two areas of active research in automatic facial video processing. They, however, have long been studied separately, despite the inherent link between them. In this paper, we propose to perform simultaneous face
Orthogonality preserving infinite dimensional quadratic stochastic operators
International Nuclear Information System (INIS)
Akın, Hasan; Mukhamedov, Farrukh
2015-01-01
In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators
Extending the Scope of Robust Quadratic Optimization
Marandi, Ahmadreza; Ben-Tal, A.; den Hertog, Dick; Melenberg, Bertrand
In this paper, we derive tractable reformulations of the robust counterparts of convex quadratic and conic quadratic constraints with concave uncertainties for a broad range of uncertainty sets. For quadratic constraints with convex uncertainty, it is well-known that the robust counterpart is, in
Faraji, Shirin; Matsika, Spiridoula; Krylov, Anna I.
2018-01-01
We report an implementation of non-adiabatic coupling (NAC) forces within the equation-of-motion coupled-cluster with single and double excitations (EOM-CCSD) framework via the summed-state approach. Using illustrative examples, we compare NAC forces computed with EOM-CCSD and multi-reference (MR) wave functions (for selected cases, we also consider configuration interaction singles). In addition to the magnitude of the NAC vectors, we analyze their direction, which is important for the calculations of the rate of non-adiabatic transitions. Our benchmark set comprises three doublet radical-cations (hexatriene, cyclohexadiene, and uracil), neutral uracil, and sodium-doped ammonia clusters. When the characters of the states agree among different methods, we observe good agreement between the respective NAC vectors, both in the Franck-Condon region and away. In the cases of large discrepancies between the methods, the disagreement can be attributed to the difference in the states' character, which, in some cases, is very sensitive to electron correlation, both within single-reference and multi-reference frameworks. The numeric results confirm that the accuracy of NAC vectors depends critically on the quality of the underlying wave functions. Within their domain of applicability, EOM-CC methods provide a viable alternative to MR approaches.
Directory of Open Access Journals (Sweden)
Bo Jarneving
2007-01-01
Full Text Available In this study a novel method of science mapping is presented which combines bibliographic coupling, as a measure of document-document similarity, with an agglomerative hierarchical cluster method. The focus in this study is on the mapping of so called ‘core documents’, a concept presented first in 1995 by Glänzel and Czerwon. The term ‘core document’ denote documents that have a central position in the research front in terms of many and strong bibliographic coupling links. The identification and mapping of core documents usually requires a large multidisciplinary research setting and in this study the 2003 volume of the Science Citation Index was applied. From this database, a sub-set of core documents reporting on the outbreak of SARS in 2002 was chosen for the demonstration of the application of this mapping method. It was demonstrated that the method, in this case, successfully identified interpretable research themes and that iterative clustering on two subsequent levels of cluster agglomeration may provide with useful and current information.
Minenkov, Yury; Bistoni, Giovanni; Riplinger, Christoph; Auer, Alexander A.; Neese, Frank; Cavallo, Luigi
2017-01-01
In this work, we tested canonical and domain based pair natural orbital coupled cluster methods (CCSD(T) and DLPNO-CCSD(T), respectively) for a set of 32 ligand exchange and association/dissociation reaction enthalpies involving ionic complexes
Ku, Wai Lim; Girvan, Michelle; Ott, Edward
2015-12-01
In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.
Energy Technology Data Exchange (ETDEWEB)
Hu, Hanshi; Bhaskaran-Nair, Kiran; Apra, Edoardo; Govind, Niranjan; Kowalski, Karol
2014-10-02
In this paper we discuss the application of novel parallel implementation of the coupled cluster (CC) and equation-of-motion coupled cluster methods (EOMCC) in calculations of excitation energies of triplet states in beta-carotene. Calculated excitation energies are compared with experimental data, where available. We also provide a detailed description of the new parallel algorithms for iterative CC and EOMCC models involving single and doubles excitations.
Boogaard, N.M. van den; Kersten, F.A.M.; Goddijn, M.; Bossuyt, P.M.; Veen, F. van der; Hompes, P.G.; Hermens, R.P.M.G.; Braat, D.D.M.; Mol, B.W.; Nelen, W.L.D.M.; et al.,
2013-01-01
BACKGROUND: Prognostic models in reproductive medicine can help to identify subfertile couples who would benefit from fertility treatment. Expectant management in couples with a good chance of natural conception, i.e., tailored expectant management (TEM), prevents unnecessary treatment and is
van den Boogaard, Noortje M; Kersten, Fleur A M; Goddijn, Mariëtte; Bossuyt, Patrick M M; van der Veen, Fulco; Hompes, Peter G A; Hermens, Rosella P M G; Braat, Didi D M; Mol, Ben Willem J; Nelen, Willianne L D M; Hoek, Annemieke
2013-01-01
BACKGROUND: Prognostic models in reproductive medicine can help to identify subfertile couples who would benefit from fertility treatment. Expectant management in couples with a good chance of natural conception, i.e., tailored expectant management (TEM), prevents unnecessary treatment and is
Chimera and phase-cluster states in populations of coupled chemical oscillators
Tinsley, Mark R.; Nkomo, Simbarashe; Showalter, Kenneth
2012-09-01
Populations of coupled oscillators may exhibit two coexisting subpopulations, one with synchronized oscillations and the other with unsynchronized oscillations, even though all of the oscillators are coupled to each other in an equivalent manner. This phenomenon, discovered about ten years ago in theoretical studies, was then further characterized and named the chimera state after the Greek mythological creature made up of different animals. The highly counterintuitive coexistence of coherent and incoherent oscillations in populations of identical oscillators, each with an equivalent coupling structure, inspired great interest and a flurry of theoretical activity. Here we report on experimental studies of chimera states and their relation to other synchronization states in populations of coupled chemical oscillators. Our experiments with coupled Belousov-Zhabotinsky oscillators and corresponding simulations reveal chimera behaviour that differs significantly from the behaviour found in theoretical studies of phase-oscillator models.
Eriksen, Janus J; Matthews, Devin A; Jørgensen, Poul; Gauss, Jürgen
2016-05-21
The accuracy at which total energies of open-shell atoms and organic radicals may be calculated is assessed for selected coupled cluster perturbative triples expansions, all of which augment the coupled cluster singles and doubles (CCSD) energy by a non-iterative correction for the effect of triple excitations. Namely, the second- through sixth-order models of the recently proposed CCSD(T-n) triples series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)] are compared to the acclaimed CCSD(T) model for both unrestricted as well as restricted open-shell Hartree-Fock (UHF/ROHF) reference determinants. By comparing UHF- and ROHF-based statistical results for a test set of 18 modest-sized open-shell species with comparable RHF-based results, no behavioral differences are observed for the higher-order models of the CCSD(T-n) series in their correlated descriptions of closed- and open-shell species. In particular, we find that the convergence rate throughout the series towards the coupled cluster singles, doubles, and triples (CCSDT) solution is identical for the two cases. For the CCSD(T) model, on the other hand, not only its numerical consistency, but also its established, yet fortuitous cancellation of errors breaks down in the transition from closed- to open-shell systems. The higher-order CCSD(T-n) models (orders n > 3) thus offer a consistent and significant improvement in accuracy relative to CCSDT over the CCSD(T) model, equally for RHF, UHF, and ROHF reference determinants, albeit at an increased computational cost.
Energy Technology Data Exchange (ETDEWEB)
Eriksen, Janus J., E-mail: janusje@chem.au.dk; Jørgensen, Poul [qLEAP Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, DK-8000 Aarhus C (Denmark); Matthews, Devin A. [The Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712 (United States); Gauss, Jürgen [Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, D-55128 Mainz (Germany)
2016-05-21
The accuracy at which total energies of open-shell atoms and organic radicals may be calculated is assessed for selected coupled cluster perturbative triples expansions, all of which augment the coupled cluster singles and doubles (CCSD) energy by a non-iterative correction for the effect of triple excitations. Namely, the second- through sixth-order models of the recently proposed CCSD(T–n) triples series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)] are compared to the acclaimed CCSD(T) model for both unrestricted as well as restricted open-shell Hartree-Fock (UHF/ROHF) reference determinants. By comparing UHF- and ROHF-based statistical results for a test set of 18 modest-sized open-shell species with comparable RHF-based results, no behavioral differences are observed for the higher-order models of the CCSD(T–n) series in their correlated descriptions of closed- and open-shell species. In particular, we find that the convergence rate throughout the series towards the coupled cluster singles, doubles, and triples (CCSDT) solution is identical for the two cases. For the CCSD(T) model, on the other hand, not only its numerical consistency, but also its established, yet fortuitous cancellation of errors breaks down in the transition from closed- to open-shell systems. The higher-order CCSD(T–n) models (orders n > 3) thus offer a consistent and significant improvement in accuracy relative to CCSDT over the CCSD(T) model, equally for RHF, UHF, and ROHF reference determinants, albeit at an increased computational cost.
Pavošević, Fabijan; Neese, Frank; Valeev, Edward F.
2014-08-01
We present a production implementation of reduced-scaling explicitly correlated (F12) coupled-cluster singles and doubles (CCSD) method based on pair-natural orbitals (PNOs). A key feature is the reformulation of the explicitly correlated terms using geminal-spanning orbitals that greatly reduce the truncation errors of the F12 contribution. For the standard S66 benchmark of weak intermolecular interactions, the cc-pVDZ-F12 PNO CCSD F12 interaction energies reproduce the complete basis set CCSD limit with mean absolute error cost compared to the conventional CCSD F12.
International Nuclear Information System (INIS)
Hammer, C.; Paffrath, M.; Boeer, R.; Finnemann, H.; Jackson, C.J.
1996-01-01
The light water reactor core simulation code PANBOX has been coupled with the transient analysis code RELAP5 for the purpose of performing plant safety analyses with a three-dimensional (3-D) neutron kinetics model. The system has been parallelized to improve the computational efficiency. The paper describes the features of this system with emphasis on performance aspects. Performance results are given for different types of parallelization, i. e. for using an automatic parallelizing compiler, using the portable PVM platform on a workstation cluster, using PVM on a shared memory multiprocessor, and for using machine dependent interfaces. (author)
Krüger, S. E.; Darradi, R.; Richter, J.; Farnell, D. J. J
2006-01-01
We present a method for the direct calculation of the spin stiffness by means of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on the square, the triangular and the cubic lattices we calculate the stiffness in high orders of approximation. For the square and the cubic lattices our results are in very good agreement with the best results available in the literature. For the triangular lattice our result is more precise than any other result obtained so far by other a...
Guo, Yang; Becker, Ute; Neese, Frank
2018-03-01
Local correlation theories have been developed in two main flavors: (1) "direct" local correlation methods apply local approximation to the canonical equations and (2) fragment based methods reconstruct the correlation energy from a series of smaller calculations on subsystems. The present work serves two purposes. First, we investigate the relative efficiencies of the two approaches using the domain-based local pair natural orbital (DLPNO) approach as the "direct" method and the cluster in molecule (CIM) approach as the fragment based approach. Both approaches are applied in conjunction with second-order many-body perturbation theory (MP2) as well as coupled-cluster theory with single-, double- and perturbative triple excitations [CCSD(T)]. Second, we have investigated the possible merits of combining the two approaches by performing CIM calculations with DLPNO methods serving as the method of choice for performing the subsystem calculations. Our cluster-in-molecule approach is closely related to but slightly deviates from approaches in the literature since we have avoided real space cutoffs. Moreover, the neglected distant pair correlations in the previous CIM approach are considered approximately. Six very large molecules (503-2380 atoms) were studied. At both MP2 and CCSD(T) levels of theory, the CIM and DLPNO methods show similar efficiency. However, DLPNO methods are more accurate for 3-dimensional systems. While we have found only little incentive for the combination of CIM with DLPNO-MP2, the situation is different for CIM-DLPNO-CCSD(T). This combination is attractive because (1) the better parallelization opportunities offered by CIM; (2) the methodology is less memory intensive than the genuine DLPNO-CCSD(T) method and, hence, allows for large calculations on more modest hardware; and (3) the methodology is applicable and efficient in the frequently met cases, where the largest subsystem calculation is too large for the canonical CCSD(T) method.
Coherent states for quadratic Hamiltonians
International Nuclear Information System (INIS)
Contreras-Astorga, Alonso; Fernandez C, David J; Velazquez, Mercedes
2011-01-01
The coherent states for a set of quadratic Hamiltonians in the trap regime are constructed. A matrix technique which allows us to directly identify the creation and annihilation operators will be presented. Then, the coherent states as simultaneous eigenstates of the annihilation operators will be derived, and will be compared with those attained through the displacement operator method. The corresponding wavefunction will be found, and a general procedure for obtaining several mean values involving the canonical operators in these states will be described. The results will be illustrated through the asymmetric Penning trap.
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...
Factorization method of quadratic template
Kotyrba, Martin
2017-07-01
Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.
Optimal control linear quadratic methods
Anderson, Brian D O
2007-01-01
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the
Efficient coupling of high intensity short laser pulses into snow clusters
Palchan, T.; Pecker, S.; Henis, Z.; Eisenmann, S.; Zigler, A.
2007-01-01
Measurements of energy absorption of high intensity laser pulses in snow clusters are reported. Targets consisting of sapphire coated with snow nanoparticles were found to absorb more than 95% of the incident light compared to 50% absorption in flat sapphire targets.
Czech Academy of Sciences Publication Activity Database
Banik, Subrata; Ravichandran, Lalitha; Brabec, J.; Hubač, I.; Kowalski, K.; Pittner, Jiří
2015-01-01
Roč. 142, č. 11 (2015), s. 114106 ISSN 0021-9606 R&D Projects: GA MŠk LH13117; GA ČR GAP208/11/2222 Institutional support: RVO:61388955 Keywords : QUADRUPLY EXCITED CLUSTERS * QUASI-DEGENERATE STATES * DOUBLE-EXCITATION MODEL Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.894, year: 2015
Quadratic reactivity fuel cycle model
International Nuclear Information System (INIS)
Lewins, J.D.
1985-01-01
For educational purposes it is highly desirable to provide simple yet realistic models for fuel cycle and fuel economy. In particular, a lumped model without recourse to detailed spatial calculations would be very helpful in providing the student with a proper understanding of the purposes of fuel cycle calculations. A teaching model for fuel cycle studies based on a lumped model assuming the summability of partial reactivities with a linear dependence of reactivity usefully illustrates fuel utilization concepts. The linear burnup model does not satisfactorily represent natural enrichment reactors. A better model, showing the trend of initial plutonium production before subsequent fuel burnup and fission product generation, is a quadratic fit. The study of M-batch cycles, reloading 1/Mth of the core at end of cycle, is now complicated by nonlinear equations. A complete account of the asymptotic cycle for any order of M-batch refueling can be given and compared with the linear model. A complete account of the transient cycle can be obtained readily in the two-batch model and this exact solution would be useful in verifying numerical marching models. It is convenient to treat the parabolic fit rho = 1 - tau 2 as a special case of the general quadratic fit rho = 1 - C/sub tau/ - (1 - C)tau 2 in suitably normalized reactivity and cycle time units. The parabolic results are given in this paper
Energy Technology Data Exchange (ETDEWEB)
Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it [MR-Lab, Center for Mind/Brain Science, University of Trento, Italy and Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)
2014-12-01
In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties.
International Nuclear Information System (INIS)
Minati, Ludovico
2014-01-01
In this paper, experimental evidence of multiple synchronization phenomena in a large (n = 30) ring of chaotic oscillators is presented. Each node consists of an elementary circuit, generating spikes of irregular amplitude and comprising one bipolar junction transistor, one capacitor, two inductors, and one biasing resistor. The nodes are mutually coupled to their neighbours via additional variable resistors. As coupling resistance is decreased, phase synchronization followed by complete synchronization is observed, and onset of synchronization is associated with partial synchronization, i.e., emergence of communities (clusters). While component tolerances affect community structure, the general synchronization properties are maintained across three prototypes and in numerical simulations. The clusters are destroyed by adding long distance connections with distant notes, but are otherwise relatively stable with respect to structural connectivity changes. The study provides evidence that several fundamental synchronization phenomena can be reliably observed in a network of elementary single-transistor oscillators, demonstrating their generative potential and opening way to potential applications of this undemanding setup in experimental modelling of the relationship between network structure, synchronization, and dynamical properties
Sørensen, L. K.; Fleig, T.; Olsen, J.
2009-08-01
Aimed at obtaining complete and highly accurate potential energy surfaces for molecules containing heavy elements, we present a new general-order coupled cluster method which can be applied in the framework of the spin-free Dirac formalism. As an initial application we present a systematic study of electron correlation and relativistic effects on the spectroscopic and electric properties of the LiCs molecule in its electronic ground state. In particular, we closely investigate the importance of excitations higher than coupled cluster doubles, spin-free and spin-dependent relativistic effects and the correlation of outer-core electrons on the equilibrium bond length, the harmonic vibrational frequency, the dissociation energy, the dipole moment and the static electric dipole polarizability. We demonstrate that our new implementation allows for highly accurate calculations not only in the bonding region but also along the complete potential curve. The quality of our results is demonstrated by a vibrational analysis where an almost complete set of vibrational levels has been calculated accurately.
International Nuclear Information System (INIS)
Soerensen, L K; Fleig, T; Olsen, J
2009-01-01
Aimed at obtaining complete and highly accurate potential energy surfaces for molecules containing heavy elements, we present a new general-order coupled cluster method which can be applied in the framework of the spin-free Dirac formalism. As an initial application we present a systematic study of electron correlation and relativistic effects on the spectroscopic and electric properties of the LiCs molecule in its electronic ground state. In particular, we closely investigate the importance of excitations higher than coupled cluster doubles, spin-free and spin-dependent relativistic effects and the correlation of outer-core electrons on the equilibrium bond length, the harmonic vibrational frequency, the dissociation energy, the dipole moment and the static electric dipole polarizability. We demonstrate that our new implementation allows for highly accurate calculations not only in the bonding region but also along the complete potential curve. The quality of our results is demonstrated by a vibrational analysis where an almost complete set of vibrational levels has been calculated accurately.
Granato, Gian Luigi; Ragone-Figueroa, Cinthia; Domínguez-Tenreiro, Rosa; Obreja, Aura; Borgani, Stefano; De Lucia, Gabriella; Murante, Giuseppe
2015-06-01
We compute and study the infrared and sub-mm properties of high-redshift (z ≳ 1) simulated clusters and protoclusters. The results of a large set of hydrodynamical zoom-in simulations including active galactic nuclei (AGN) feedback, have been treated with the recently developed radiative transfer code GRASIL-3D, which accounts for the effect of dust reprocessing in an arbitrary geometry. Here, we have slightly generalized the code to adapt it to the present purpose. Then we have post-processed boxes of physical size 2 Mpc encompassing each of the 24 most massive clusters identified at z = 0, at several redshifts between 0.5 and 3, producing IR and sub-mm mock images of these regions and spectral energy distributions (SEDs) of the radiation coming out from them. While this field is in its infancy from the observational point of view, rapid development is expected in the near future thanks to observations performed in the far-IR and sub-mm bands. Notably, we find that in this spectral regime our prediction are little affected by the assumption required by this post-processing, and the emission is mostly powered by star formation (SF) rather than accretion on to super massive black hole (SMBH). The comparison with the little observational information currently available, highlights that the simulated cluster regions never attain the impressive star formation rates suggested by these observations. This problem becomes more intriguing taking into account that the brightest cluster galaxies (BCGs) in the same simulations turn out to be too massive. It seems that the interplay between the feedback schemes and the star formation model should be revised, possibly incorporating a positive feedback mode.
Dynamical invariants for variable quadratic Hamiltonians
International Nuclear Information System (INIS)
Suslov, Sergei K
2010-01-01
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value problem for the time-dependent Schroedinger equation are emphasized. An eigenfunction expansion of the solution of the initial value problem is also found. A nonlinear superposition principle for generalized Ermakov systems is established as a result of decomposition of the general quadratic invariant in terms of the linear ones.
International Nuclear Information System (INIS)
Ehara, Masahiro; Piecuch, Piotr; Lutz, Jesse J.; Gour, Jeffrey R.
2012-01-01
Graphical abstract: Electronically excited states of CuCl 4 2- and CuBr 4 2- are determined using the scalar relativistic symmetry-adapted-cluster configuration-interaction and equation-of-motion coupled-cluster calculations. The results are compared with experimental spectra. Highlights: ► Electronic spectra of CuCl 4 2- and CuBr 4 2- are examined by SAC-CI and EOMCC methods. ► Relativistic SAC-CI and EOMCC results are compared with experimental spectra. ► An assignment of bands in the CuCl 4 2- and CuBr 4 2- absorption spectra is obtained. ► Relativistic effects affect excitation energies and ground-state geometries. ► The effect of relativity on the oscillator strengths is generally small. - Abstract: The valence excitation spectra of the copper tetrachloride and copper tetrabromide open-shell dianions, CuCl 4 2- and CuBr 4 2- , respectively, are investigated by a variety of symmetry-adapted-cluster configuration-interaction (SAC-CI) and equation-of-motion coupled-cluster (EOMCC) methods. The valence excited states of the CuCl 4 2- and CuBr 4 2- species that correspond to transitions from doubly occupied molecular orbitals (MOs) to a singly occupied MO (SOMO), for which experimental spectra are available, are examined with the ionized (IP) variants of the SAC-CI and EOMCC methods. The higher-energy excited states of CuCl 4 2- and CuBr 4 2- that correspond to transitions from SOMO to unoccupied MOs, which have not been characterized experimentally, are determined using the electron-attached (EA) SAC-CI and EOMCC approaches. An emphasis is placed on the scalar relativistic SAC-CI and EOMCC calculations based on the spin-free part of the second-order Douglass–Kroll–Hess Hamiltonian (DKH2) and on a comparison of the results of the IP and EA SAC-CI and EOMCC calculations with up to 2-hole-1-particle (2h-1p) and 2-particle-1-hole (2p-1h) excitations, referred to as the IP-SAC-CI SD-R and IP-EOMCCSD(2h-1p) methods in the IP case and EA-SAC-CI SD-R and EA
Geometrical and Graphical Solutions of Quadratic Equations.
Hornsby, E. John, Jr.
1990-01-01
Presented are several geometrical and graphical methods of solving quadratic equations. Discussed are Greek origins, Carlyle's method, von Staudt's method, fixed graph methods and imaginary solutions. (CW)
Multiobjective Optimization Involving Quadratic Functions
Directory of Open Access Journals (Sweden)
Oscar Brito Augusto
2014-01-01
Full Text Available Multiobjective optimization is nowadays a word of order in engineering projects. Although the idea involved is simple, the implementation of any procedure to solve a general problem is not an easy task. Evolutionary algorithms are widespread as a satisfactory technique to find a candidate set for the solution. Usually they supply a discrete picture of the Pareto front even if this front is continuous. In this paper we propose three methods for solving unconstrained multiobjective optimization problems involving quadratic functions. In the first, for biobjective optimization defined in the bidimensional space, a continuous Pareto set is found analytically. In the second, applicable to multiobjective optimization, a condition test is proposed to check if a point in the decision space is Pareto optimum or not and, in the third, with functions defined in n-dimensional space, a direct noniterative algorithm is proposed to find the Pareto set. Simple problems highlight the suitability of the proposed methods.
Quadratic Lagrangians and Legendre transformation
International Nuclear Information System (INIS)
Magnano, G.
1988-01-01
In recent years interest is grown about the so-called non-linear Lagrangians for gravitation. In particular, the quadratic lagrangians are currently believed to play a fundamental role both for quantum gravity and for the super-gravity approach. The higher order and high degree of non-linearity of these theories make very difficult to extract physical information out of them. The author discusses how the Legendre transformation can be applied to a wide class of non-linear theories: it corresponds to a conformal transformation whenever the Lagrangian depends only on the scalar curvature, while it has a more general form if the Lagrangian depends on the full Ricci tensor
Inter-cluster coupling effects in high-spin molecular magnets
International Nuclear Information System (INIS)
Affronte, M.; Lasjaunias, J.C.; Wernsdorfer, W.; Sessoli, R.; Gatteschi, D.; Heath, S.L.; Fort, A.; Rettori, A.
2004-01-01
We report evidences of antiferromagnetic (AF) transition in Fe 19 metheidi, a new molecular nanomagnet with a total spin S=((33)/(2)), among the highest known so far. The temperature (T) dependence of specific heat (C) shows a λ-anomaly at 1.19 K and at the same temperature an anomaly is also observed in the low field (B<0.12 T) magnetization M-vs.-T curves. Since the dipolar interaction between clusters is estimated to be ∼190 mK, the origin of the AF transition is probably due to superexchange
Inter-cluster coupling effects in high-spin molecular magnets
Energy Technology Data Exchange (ETDEWEB)
Affronte, M.; Lasjaunias, J.C.; Wernsdorfer, W.; Sessoli, R.; Gatteschi, D.; Heath, S.L.; Fort, A. E-mail: fort@fi.infn.it; Rettori, A
2004-05-01
We report evidences of antiferromagnetic (AF) transition in Fe{sub 19}metheidi, a new molecular nanomagnet with a total spin S=((33)/(2)), among the highest known so far. The temperature (T) dependence of specific heat (C) shows a {lambda}-anomaly at 1.19 K and at the same temperature an anomaly is also observed in the low field (B<0.12 T) magnetization M-vs.-T curves. Since the dipolar interaction between clusters is estimated to be {approx}190 mK, the origin of the AF transition is probably due to superexchange.
Energy Technology Data Exchange (ETDEWEB)
Verma, Prakash; Morales, Jorge A., E-mail: jorge.morales@ttu.edu [Department of Chemistry and Biochemistry, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061 (United States); Perera, Ajith [Department of Chemistry and Biochemistry, Texas Tech University, P.O. Box 41061, Lubbock, Texas 79409-1061 (United States); Department of Chemistry, Quantum Theory Project, University of Florida, Gainesville, Florida 32611 (United States)
2013-11-07
Coupled cluster (CC) methods provide highly accurate predictions of molecular properties, but their high computational cost has precluded their routine application to large systems. Fortunately, recent computational developments in the ACES III program by the Bartlett group [the OED/ERD atomic integral package, the super instruction processor, and the super instruction architecture language] permit overcoming that limitation by providing a framework for massively parallel CC implementations. In that scheme, we are further extending those parallel CC efforts to systematically predict the three main electron spin resonance (ESR) tensors (A-, g-, and D-tensors) to be reported in a series of papers. In this paper inaugurating that series, we report our new ACES III parallel capabilities that calculate isotropic hyperfine coupling constants in 38 neutral, cationic, and anionic radicals that include the {sup 11}B, {sup 17}O, {sup 9}Be, {sup 19}F, {sup 1}H, {sup 13}C, {sup 35}Cl, {sup 33}S,{sup 14}N, {sup 31}P, and {sup 67}Zn nuclei. Present parallel calculations are conducted at the Hartree-Fock (HF), second-order many-body perturbation theory [MBPT(2)], CC singles and doubles (CCSD), and CCSD with perturbative triples [CCSD(T)] levels using Roos augmented double- and triple-zeta atomic natural orbitals basis sets. HF results consistently overestimate isotropic hyperfine coupling constants. However, inclusion of electron correlation effects in the simplest way via MBPT(2) provides significant improvements in the predictions, but not without occasional failures. In contrast, CCSD results are consistently in very good agreement with experimental results. Inclusion of perturbative triples to CCSD via CCSD(T) leads to small improvements in the predictions, which might not compensate for the extra computational effort at a non-iterative N{sup 7}-scaling in CCSD(T). The importance of these accurate computations of isotropic hyperfine coupling constants to elucidate
Energy Technology Data Exchange (ETDEWEB)
Bhaskaran-Nair, Kiran; Brabec, Jiri; Apra, Edoardo; van Dam, Hubertus JJ; Pittner, Jiri; Kowalski, Karol
2012-09-07
In this paper we discuss the performance of the non-iterative State-Specific Mul- tireference Coupled Cluster (SS-MRCC) methods accounting for the effect of triply excited cluster amplitudes. The corrections to the Brillouin-Wigner and Mukherjee MRCC models based on the manifold of singly and doubly excited cluster amplitudes (BW-MRCCSD and Mk-MRCCSD, respectively) are tested and compared with the exact full configuration interaction results (FCI) for small systems (H2O, N2, and Be3). For larger systems (naphthyne isomers and -carotene), the non-iterative BW-MRCCSD(T) and Mk-MRCCSD(T) methods are compared against the results obtained with the single reference coupled cluster methods. We also report on the parallel performance of the non-iterative implementations based on the use of pro- cessor groups.
International Nuclear Information System (INIS)
Lerner, A.M.
1986-01-01
The first step towards evaluation of the neutron flux throughout a fuel cluster usually consists of obtaining the multigroup flux distribution in the average pin cell and in the circular outside system of shroud and bulk moderator. Here, an application of the so-called heterogeneous response method (HRM) is described to find this multigroup flux. The rather complex geometry is reduced to a microsystem, the average pin cell, and the outside or macrosystem of shroud and bulk moderator. In each of these systems, collision probabilities are used to obtain their response fluxes caused by sources and in-currents. The two systems are then coupled by cosine currents across that fraction of the average pin-cell boundary, called 'window', that represents the average common boundary between pin cells and the outside system. (author)
DEFF Research Database (Denmark)
Silva-Junior, Mario R.; Sauer, Stephan P. A.; Schreiber, Marko
2010-01-01
Vertical electronic excitation energies and one-electron properties of 28 medium-sized molecules from a previously proposed benchmark set are revisited using the augmented correlation-consistent triple-zeta aug-cc-pVTZ basis set in CC2, CCSDR(3), and CC3 calculations. The results are compared...... to those obtained previously with the smaller TZVP basis set. For each of the three coupled cluster methods, a correlation coefficient greater than 0.994 is found between the vertical excitation energies computed with the two basis sets. The deviations of the CC2 and CCSDR(3) results from the CC3 reference...... values are very similar for both basis sets, thus confirming previous conclusions on the intrinsic accuracy of CC2 and CCSDR(3). This similarity justifies the use of CC2- or CCSDR(3)-based corrections to account for basis set incompleteness in CC3 studies of vertical excitation energies. For oscillator...
Energy Technology Data Exchange (ETDEWEB)
Beaujean, Pierre; Champagne, Benoît, E-mail: benoit.champagne@unamur.be [Laboratoire de Chimie Théorique, Unité de Chimie Physique Théorique et Structurale, University of Namur, Rue de Bruxelles 61, B-5000 Namur (Belgium)
2016-07-28
The static and dynamic first (β{sub ‖}) and second (γ{sub ‖}) hyperpolarizabilities of water, methanol, and dimethyl ether have been evaluated within the response function approach using a hierarchy of coupled cluster levels of approximation and doubly augmented correlation consistent atomic basis sets. For the three compounds, the electronic β{sub ‖} and γ{sub ‖} values calculated at the CCSD and CC3 levels are in good agreement with gas phase electric field-induced second harmonic generation (EFISHG) measurements. In addition, for dimethyl ether, the frequency dispersion of both properties follows closely recent experimental values [V. W. Couling and D. P. Shelton, J. Chem. Phys. 143, 224307 (2015)] demonstrating the reliability of these methods and levels of approximation. This also suggests that the vibrational contributions to the EFISHG responses of these molecules are small.
Quadratic independence of coordinate functions of certain ...
Indian Academy of Sciences (India)
... are `quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C ( M ) such that the action leaves invariant the linear span of the above coordinate functions.
Sibling curves of quadratic polynomials | Wiggins | Quaestiones ...
African Journals Online (AJOL)
Sibling curves were demonstrated in [1, 2] as a novel way to visualize the zeroes of real valued functions. In [3] it was shown that a polynomial of degree n has n sibling curves. This paper focuses on the algebraic and geometric properites of the sibling curves of real and complex quadratic polynomials. Key words: Quadratic ...
An example in linear quadratic optimal control
Weiss, George; Zwart, Heiko J.
1998-01-01
We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme
Quadratic Boost A-Source Impedance Network
DEFF Research Database (Denmark)
Siwakoti, Yam Prasad; Blaabjerg, Frede; Chub, Andrii
2016-01-01
A novel quadratic boost A-source impedance network is proposed to realize converters that demand very high voltage gain. To satisfy the requirement, the network uses an autotransformer where the obtained gain is quadratically dependent on the duty ratio and is unmatched by any existing impedance...
A valence-universal coupled-cluster single- and double-excitations method for atoms: Pt. 3
International Nuclear Information System (INIS)
Jankowski, K.; Malinowski, P.
1994-01-01
To better understand the problems met when solving the equations of VU-CC approaches in the presence of intruder states, we are concerned with the following aspects of the solvability problem for sets of non-linear equations: the existence and properties of multiple solutions and the attainability of these solutions by means of various numerical methods. Our study is concentrated on the equations obtained for Be within the framework of the recently formulated atomically oriented form of the valence-universal coupled-cluster theory accounting for one- and two-electron excitations (VU-CCSD/R) and based on the complete model space (2s 2 , 2p 2 ). Six pairs of multiple solutions representing four 1 S states are found and discussed. Three of these solutions provide amplitudes describing the 2p 2 1 S state for which the intruder state problem has been considered as extremely serious. Several known numerical methods have been applied to solve the same set of non-linear equations for the two-valence cluster amplitudes. It is shown that these methods perform quite differently in the presence of intruder states, which seems to indicate that the intruder state problem for VU-CC methods is partly caused by the commonly used methods of solving the non-linear equations. (author)
van Dam, Hubertus J J; Vishnu, Abhinav; de Jong, Wibe A
2011-01-11
In the past couple of decades, the massive computational power provided by the most modern supercomputers has resulted in simulation of higher-order computational chemistry methods, previously considered intractable. As the system sizes continue to increase, the computational chemistry domain continues to escalate this trend using parallel computing with programming models such as Message Passing Interface (MPI) and Partitioned Global Address Space (PGAS) programming models such as Global Arrays. The ever increasing scale of these supercomputers comes at a cost of reduced Mean Time Between Failures (MTBF), currently on the order of days and projected to be on the order of hours for upcoming extreme scale systems. While traditional disk-based check pointing methods are ubiquitous for storing intermediate solutions, they suffer from high overhead of writing and recovering from checkpoints. In practice, checkpointing itself often brings the system down. Clearly, methods beyond checkpointing are imperative to handling the aggravating issue of reducing MTBF. In this paper, we address this challenge by designing and implementing an efficient fault tolerant version of the Coupled Cluster (CC) method with NWChem, using in-memory data redundancy. We present the challenges associated with our design, including an efficient data storage model, maintenance of at least one consistent data copy, and the recovery process. Our performance evaluation without faults shows that the current design exhibits a small overhead. In the presence of a simulated fault, the proposed design incurs negligible overhead in comparison to the state of the art implementation without faults.
International Nuclear Information System (INIS)
Malrieu, Jean-Paul
2012-01-01
Lattices of antiferromagnetically coupled spins, ruled by Heisenberg Hamiltonians, are intrinsically highly degenerate systems. The present work tries to estimate the ground state energy of regular bipartite spin lattices of S = 1 sites from a single reference Coupled Cluster expansion starting from a Néel function, taken as reference. The simultaneous changes of spin momentum on adjacent sites play the role of the double excitations in molecular electronic problems. Propagation of the spin changes plays the same role as the triple excitations. The treatment takes care of the deviation of multiple excitation energies from additivity. Specific difficulties appear for 1D chains, which are not due to a near degeneracy between the reference and the vectors which directly interact with it but to the complexity of the processes which lead to the low energy configurations where a consistent reversed-Néel domain is created inside the Néel starting spin wave. Despite these difficulties a reasonable value of the cohesive energy is obtained.
Malrieu, Jean-Paul
2012-06-01
Lattices of antiferromagnetically coupled spins, ruled by Heisenberg Hamiltonians, are intrinsically highly degenerate systems. The present work tries to estimate the ground state energy of regular bipartite spin lattices of S = 1 sites from a single reference Coupled Cluster expansion starting from a Néel function, taken as reference. The simultaneous changes of spin momentum on adjacent sites play the role of the double excitations in molecular electronic problems. Propagation of the spin changes plays the same role as the triple excitations. The treatment takes care of the deviation of multiple excitation energies from additivity. Specific difficulties appear for 1D chains, which are not due to a near degeneracy between the reference and the vectors which directly interact with it but to the complexity of the processes which lead to the low energy configurations where a consistent reversed-Néel domain is created inside the Néel starting spin wave. Despite these difficulties a reasonable value of the cohesive energy is obtained.
Quadratic Hedging of Basis Risk
Directory of Open Access Journals (Sweden)
Hardy Hulley
2015-02-01
Full Text Available This paper examines a simple basis risk model based on correlated geometric Brownian motions. We apply quadratic criteria to minimize basis risk and hedge in an optimal manner. Initially, we derive the Föllmer–Schweizer decomposition for a European claim. This allows pricing and hedging under the minimal martingale measure, corresponding to the local risk-minimizing strategy. Furthermore, since the mean-variance tradeoff process is deterministic in our setup, the minimal martingale- and variance-optimal martingale measures coincide. Consequently, the mean-variance optimal strategy is easily constructed. Simple pricing and hedging formulae for put and call options are derived in terms of the Black–Scholes formula. Due to market incompleteness, these formulae depend on the drift parameters of the processes. By making a further equilibrium assumption, we derive an approximate hedging formula, which does not require knowledge of these parameters. The hedging strategies are tested using Monte Carlo experiments, and are compared with results achieved using a utility maximization approach.
Faure, Guilhem; Callebaut, Isabelle
2013-07-15
Describing domain architecture is a critical step in the functional characterization of proteins. However, some orphan domains do not match any profile stored in dedicated domain databases and are thereby difficult to analyze. We present here an original novel approach, called TREMOLO-HCA, for the analysis of orphan domain sequences and inspired from our experience in the use of Hydrophobic Cluster Analysis (HCA). Hidden relationships between protein sequences can be more easily identified from the PSI-BLAST results, using information on domain architecture, HCA plots and the conservation degree of amino acids that may participate in the protein core. This can lead to reveal remote relationships with known families of domains, as illustrated here with the identification of a hidden Tudor tandem in the human BAHCC1 protein and a hidden ET domain in the Saccharomyces cerevisiae Taf14p and human AF9 proteins. The results obtained in such a way are consistent with those provided by HHPRED, based on pairwise comparisons of HHMs. Our approach can, however, be applied even in absence of domain profiles or known 3D structures for the identification of novel families of domains. It can also be used in a reverse way for refining domain profiles, by starting from known protein domain families and identifying highly divergent members, hitherto considered as orphan. We provide a possible integration of this approach in an open TREMOLO-HCA package, which is fully implemented in python v2.7 and is available on request. Instructions are available at http://www.impmc.upmc.fr/∼callebau/tremolohca.html. isabelle.callebaut@impmc.upmc.fr Supplementary Data are available at Bioinformatics online.
Fransson, Thomas; Coriani, Sonia; Christiansen, Ove; Norman, Patrick
2013-03-28
Near carbon K-edge X-ray absorption fine structure spectra of a series of fluorine-substituted ethenes and acetone have been studied using coupled cluster and density functional theory (DFT) polarization propagator methods, as well as the static-exchange (STEX) approach. With the complex polarization propagator (CPP) implemented in coupled cluster theory, relaxation effects following the excitation of core electrons are accounted for in terms of electron correlation, enabling a systematic convergence of these effects with respect to electron excitations in the cluster operator. Coupled cluster results have been used as benchmarks for the assessment of propagator methods in DFT as well as the state-specific static-exchange approach. Calculations on ethene and 1,1-difluoroethene illustrate the possibility of using nonrelativistic coupled cluster singles and doubles (CCSD) with additional effects of electron correlation and relativity added as scalar shifts in energetics. It has been demonstrated that CPP spectra obtained with coupled cluster singles and approximate doubles (CC2), CCSD, and DFT (with a Coulomb attenuated exchange-correlation functional) yield excellent predictions of chemical shifts for vinylfluoride, 1,1-difluoroethene, trifluoroethene, as well as good spectral features for acetone in the case of CCSD and DFT. Following this, CPP-DFT is considered to be a viable option for the calculation of X-ray absorption spectra of larger π-conjugated systems, and CC2 is deemed applicable for chemical shifts but not for studies of fine structure features. The CCSD method as well as the more approximate CC2 method are shown to yield spectral features relating to π∗-resonances in good agreement with experiment, not only for the aforementioned molecules but also for ethene, cis-1,2-difluoroethene, and tetrafluoroethene. The STEX approach is shown to underestimate π∗-peak separations due to spectral compressions, a characteristic which is inherent to this
International Nuclear Information System (INIS)
Dong Huanhe; Wang Xiangrong
2008-01-01
The trace identity is extended to the quadratic-form identity. The Hamiltonian structures of the NLS-MKdV hierarchy, and integrable coupling of multi-component Levi hierarchy are obtained by the quadratic-form identity. The method can be used to produce the Hamiltonian structures of the other integrable couplings or multi-component hierarchies
Directory of Open Access Journals (Sweden)
Tanwiwat Jaikuna
2017-02-01
Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.
Stošić, Dušan; Auroux, Aline
Basic principles of calorimetry coupled with other techniques are introduced. These methods are used in heterogeneous catalysis for characterization of acidic, basic and red-ox properties of solid catalysts. Estimation of these features is achieved by monitoring the interaction of various probe molecules with the surface of such materials. Overview of gas phase, as well as liquid phase techniques is given. Special attention is devoted to coupled calorimetry-volumetry method. Furthermore, the influence of different experimental parameters on the results of these techniques is discussed, since it is known that they can significantly influence the evaluation of catalytic properties of investigated materials.
Energy Technology Data Exchange (ETDEWEB)
Wykes, M., E-mail: mikewykes@gmail.com; Parambil, R.; Gierschner, J. [Madrid Institute for Advanced Studies, IMDEA Nanoscience, Calle Faraday 9, Campus Cantoblanco, 28049 Madrid (Spain); Beljonne, D. [Laboratory for Chemistry of Novel Materials, University of Mons, Place du Parc 20, 7000 Mons (Belgium)
2015-09-21
Here, we present a general approach to treating vibronic coupling in molecular crystals based on atomistic simulations of large clusters. Such clusters comprise model aggregates treated at the quantum chemical level embedded within a realistic environment treated at the molecular mechanics level. As we calculate ground and excited state equilibrium geometries and vibrational modes of model aggregates, our approach is able to capture effects arising from coupling to intermolecular degrees of freedom, absent from existing models relying on geometries and normal modes of single molecules. Using the geometries and vibrational modes of clusters, we are able to simulate the fluorescence spectra of aggregates for which the lowest excited state bears negligible oscillator strength (as is the case, e.g., ideal H-aggregates) by including both Franck-Condon (FC) and Herzberg-Teller (HT) vibronic transitions. The latter terms allow the adiabatic excited state of the cluster to couple with vibrations in a perturbative fashion via derivatives of the transition dipole moment along nuclear coordinates. While vibronic coupling simulations employing FC and HT terms are well established for single-molecules, to our knowledge this is the first time they are applied to molecular aggregates. Here, we apply this approach to the simulation of the low-temperature fluorescence spectrum of para-distyrylbenzene single-crystal H-aggregates and draw comparisons with coarse-grained Frenkel-Holstein approaches previously extensively applied to such systems.
Mukherjee, Debashis; Sahoo, B. K.; Nataraj, H. S.; Das, B. P.
2009-01-01
A relativistic many-body theory for the electric dipole moment (EDM) of paramagnetic atoms arising from the electric dipole moment of the electron is presented and implemented. The relativistic coupled-cluster method with single and double excitations (RCCSD) using the Dirac-Coulomb Hamiltonian and
Hubert, Mickaël; Olsen, Jeppe; Loras, Jessica; Fleig, Timo
2013-11-21
We present a new implementation of general excitation rank coupled cluster theory for electronically excited states based on the single-reference multi-reference formalism. The method may include active-space selected and/or general higher excitations by means of the general active space concept. It may employ molecular integrals over the four-component Lévy-Leblond Hamiltonian or the relativistic spin-orbit-free four-component Hamiltonian of Dyall. In an initial application to ground- and excited states of the scandium monohydride molecule we report spectroscopic constants using basis sets of up to quadruple-zeta quality and up to full iterative triple excitations in the cluster operators. Effects due to spin-orbit interaction are evaluated using two-component multi-reference configuration interaction for assessing the accuracy of the coupled cluster results.
International Nuclear Information System (INIS)
Borschevsky, A.; Eliav, E.; Kaldor, U.; Vilkas, M.J.; Ishikawa, Y.
2007-01-01
Complete text of publication follows: Measurements of the spectroscopic properties of the superheavy elements present a serious challenge to the experimentalist. Their short lifetimes and the low quantities of their production necessitate reliable prediction of transition energies to avoid the need for broad wavelength scans and to assist in identifying the lines. Thus, reliable high-accuracy calculations are necessary prior and parallel to experimental research. Nobelium and Lawrencium are at present the two most likely candidates for spectroscopic measurements, with the first experiments planned at GSI, Darmstadt. The intermediate Hamiltonian (IH) coupled cluster method is applied to the ionization potentials, electron affinities, and excitation energies of atomic nobelium and lawrencium. Large basis sets are used (37s31p26d21f16g11h6i). All levels of a particular atom are obtained simultaneously by diagonalizing the IH matrix. The matrix elements correspond to all excitations from correlated occupied orbitals to virtual orbitals in a large P space, and are 'dressed' by folding in excitations to higher virtual orbitals (Q space) at the coupled cluster singles-and-doubles level. Lamb-shift corrections are included. The same approach was applied to the lighter homologues of Lr and No, lutetium and ytterbium, for which many transition energies are experimentally known, in order to assess the accuracy of the calculation. The average absolute error of 20 excitation energies of Lu is 423 cm -1 , and the error limits for Lr are therefore put at 700 cm -1 . Predicted Lr excitations with large transition moments in the prime range for the planned experiment, 20,000-30,000 cm -1 , are 7p → 8s at 20,100 cm -1 and 7p →p 7d at 28,100 cm -1 . In case of Yb, the calculated ionization potential was within 20 cm -1 of the experiment, and the average error of the 20 lowest calculated excitations was about 300 cm -1 . Hence, the error limits of nobelium are set to 800 cm -1
Quadratic time dependent Hamiltonians and separation of variables
International Nuclear Information System (INIS)
Anzaldo-Meneses, A.
2017-01-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green’s function is obtained and a comparison with the classical Hamilton–Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei–Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü–Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems. - Highlights: • Exact unitary transformation reducing time dependent quadratic quantum Hamiltonian to zero. • New separation of variables method and simultaneous uncoupling of modes. • Explicit examples of transformations for one to four dimensional problems. • New general evolution equation for quadratic form in the action, respectively Green’s function.
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard; Wonka, Peter; Cao, Yuanhao
2015-01-01
be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution
Schur Stability Regions for Complex Quadratic Polynomials
Cheng, Sui Sun; Huang, Shao Yuan
2010-01-01
Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)
Bokhan, Denis; Trubnikov, Dmitrii N.; Perera, Ajith; Bartlett, Rodney J.
2018-04-01
An explicitly-correlated method of calculation of excited states with spin-orbit couplings, has been formulated and implemented. Developed approach utilizes left and right eigenvectors of equation-of-motion coupled-cluster model, which is based on the linearly approximated explicitly correlated coupled-cluster singles and doubles [CCSD(F12)] method. The spin-orbit interactions are introduced by using the spin-orbit mean field (SOMF) approximation of the Breit-Pauli Hamiltonian. Numerical tests for several atoms and molecules show good agreement between explicitly-correlated results and the corresponding values, calculated in complete basis set limit (CBS); the highly-accurate excitation energies can be obtained already at triple- ζ level.
Linear quadratic optimization for positive LTI system
Muhafzan, Yenti, Syafrida Wirma; Zulakmal
2017-05-01
Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.
Radiotherapy treatment planning linear-quadratic radiobiology
Chapman, J Donald
2015-01-01
Understand Quantitative Radiobiology from a Radiation Biophysics PerspectiveIn the field of radiobiology, the linear-quadratic (LQ) equation has become the standard for defining radiation-induced cell killing. Radiotherapy Treatment Planning: Linear-Quadratic Radiobiology describes tumor cell inactivation from a radiation physics perspective and offers appropriate LQ parameters for modeling tumor and normal tissue responses.Explore the Latest Cell Killing Numbers for Defining Iso-Effective Cancer TreatmentsThe book compil
Solitons in quadratic nonlinear photonic crystals
DEFF Research Database (Denmark)
Corney, Joel Frederick; Bang, Ole
2001-01-01
We study solitons in one-dimensional quadratic nonlinear photonic crystals with modulation of both the linear and nonlinear susceptibilities. We derive averaged equations that include induced cubic nonlinearities, which can be defocusing, and we numerically find previously unknown soliton families....... Because of these induced cubic terms, solitons still exist even when the effective quadratic nonlinearity vanishes and conventional theory predicts that there can be no soliton. We demonstrate that both bright and dark forms of these solitons can propagate stably....
Energy Technology Data Exchange (ETDEWEB)
Varghese, Jithin J.; Mushrif, Samir H., E-mail: shmushrif@ntu.edu.sg [School of Chemical and Biomedical Engineering, Nanyang Technological University, 62 Nanyang Drive, 637459 (Singapore)
2015-05-14
Small metal clusters exhibit unique size and morphology dependent catalytic activity. The search for alternate minimum energy pathways and catalysts to transform methane to more useful chemicals and carbon nanomaterials led us to investigate collision induced dissociation of methane on small Cu clusters. We report here for the first time, the free energy barriers for the collision induced activation, dissociation, and coupling of methane on small Cu clusters (Cu{sub n} where n = 2–12) using ab initio molecular dynamics and metadynamics simulations. The collision induced activation of the stretching and bending vibrations of methane significantly reduces the free energy barrier for its dissociation. Increase in the cluster size reduces the barrier for dissociation of methane due to the corresponding increase in delocalisation of electron density within the cluster, as demonstrated using the electron localisation function topology analysis. This enables higher probability of favourable alignment of the C–H stretching vibration of methane towards regions of high electron density within the cluster and makes higher number of sites available for the chemisorption of CH{sub 3} and H upon dissociation. These characteristics contribute in lowering the barrier for dissociation of methane. Distortion and reorganisation of cluster geometry due to high temperature collision dynamics disturb electron delocalisation within them and increase the barrier for dissociation. Coupling reactions of CH{sub x} (x = 1–3) species and recombination of H with CH{sub x} have free energy barriers significantly lower than complete dehydrogenation of methane to carbon. Thus, competition favours the former reactions at high hydrogen saturation on the clusters.
International Nuclear Information System (INIS)
Varghese, Jithin J.; Mushrif, Samir H.
2015-01-01
Small metal clusters exhibit unique size and morphology dependent catalytic activity. The search for alternate minimum energy pathways and catalysts to transform methane to more useful chemicals and carbon nanomaterials led us to investigate collision induced dissociation of methane on small Cu clusters. We report here for the first time, the free energy barriers for the collision induced activation, dissociation, and coupling of methane on small Cu clusters (Cu n where n = 2–12) using ab initio molecular dynamics and metadynamics simulations. The collision induced activation of the stretching and bending vibrations of methane significantly reduces the free energy barrier for its dissociation. Increase in the cluster size reduces the barrier for dissociation of methane due to the corresponding increase in delocalisation of electron density within the cluster, as demonstrated using the electron localisation function topology analysis. This enables higher probability of favourable alignment of the C–H stretching vibration of methane towards regions of high electron density within the cluster and makes higher number of sites available for the chemisorption of CH 3 and H upon dissociation. These characteristics contribute in lowering the barrier for dissociation of methane. Distortion and reorganisation of cluster geometry due to high temperature collision dynamics disturb electron delocalisation within them and increase the barrier for dissociation. Coupling reactions of CH x (x = 1–3) species and recombination of H with CH x have free energy barriers significantly lower than complete dehydrogenation of methane to carbon. Thus, competition favours the former reactions at high hydrogen saturation on the clusters
Energy Technology Data Exchange (ETDEWEB)
Kowalski, Karol; Krishnamoorthy, Sriram; Olson, Ryan M.; Tipparaju, Vinod; Apra, Edoardo
2011-11-30
The development of reliable tools for excited-state simulations is emerging as an extremely powerful computational chemistry tool for understanding complex processes in the broad class of light harvesting systems and optoelectronic devices. Over the last years we have been developing equation of motion coupled cluster (EOMCC) methods capable of tackling these problems. In this paper we discuss the parallel performance of EOMCC codes which provide accurate description of the excited-state correlation effects. Two aspects are discuss in details: (1) a new algorithm for the iterative EOMCC methods based on the novel task scheduling algorithms, and (2) parallel algorithms for the non-iterative methods describing the effect of triply excited configurations. We demonstrate that the most computationally intensive non-iterative part can take advantage of 210,000 cores of the Cray XT5 system at OLCF. In particular, we demonstrate the importance of non-iterative many-body methods for achieving experimental level of accuracy for several porphyrin-based system.
Sharma, Lalita; Sahoo, Bijaya Kumar; Malkar, Pooja; Srivastava, Rajesh
2018-01-01
A relativistic coupled-cluster theory is implemented to study electron impact excitations of atomic species. As a test case, the electron impact excitations of the 3 s 2 S 1/2-3 p 2 P 1/2;3/2 resonance transitions are investigated in the singly charged magnesium (Mg+) ion using this theory. Accuracies of wave functions of Mg+ are justified by evaluating its attachment energies of the relevant states and compared with the experimental values. The continuum wave function of the projectile electron are obtained by solving Dirac equations assuming distortion potential as static potential of the ground state of Mg+. Comparison of the calculated electron impact excitation differential and total cross-sections with the available measurements are found to be in very good agreements at various incident electron energies. Further, calculations are carried out in the plasma environment in the Debye-Hückel model framework, which could be useful in the astrophysics. Influence of plasma strength on the cross-sections as well as linear polarization of the photon emission in the 3 p 2 P 3/2-3 s 2 S 1/2 transition is investigated for different incident electron energies.
Li, Cheng-Bin; Yu, Yan-Mei; Sahoo, B. K.
2018-02-01
Roles of electron correlation effects in the determination of attachment energies, magnetic-dipole hyperfine-structure constants, and electric-dipole (E 1 ) matrix elements of the low-lying states in the singly charged cadmium ion (Cd+) have been analyzed. We employ the singles and doubles approximated relativistic coupled-cluster (RCC) method to calculate these properties. Intermediate results from the Dirac-Hartree-Fock approximation,the second-order many-body perturbation theory, and considering only the linear terms of the RCC method are given to demonstrate propagation of electron correlation effects in this ion. Contributions from important RCC terms are also given to highlight the importance of various correlation effects in the evaluation of these properties. At the end, we also determine E 1 polarizabilities (αE 1) of the ground and 5 p 2P1 /2 ;3 /2 states of Cd+ in the ab initio approach. We estimate them again by replacing some of the E 1 matrix elements and energies from the measurements to reduce their uncertainties so that they can be used in the high-precision experiments of this ion.
International Nuclear Information System (INIS)
Das, Madhulita; Chaudhuri, Rajat K; Chattopadhyay, Sudip; Sinha Mahapatra, Uttam
2011-01-01
In view of its importance in high precision spectroscopy, the valence universal multireference coupled cluster (VU-MRCC) method with four-component relativistic spinors has been applied to compute ionization potential (IP) and excitation energies (EEs) of the indium atom (In I). The effect of electron correlations on the ground and excited state properties is investigated using different levels of CC approximations and basis sets. This study reveals that for a given basis, the linearized VU-MRCC method tends to underestimate the IP, EEs and other one-electron properties such as magnetic hyperfine constant (A) compared to the full blown VU-MRCC method. Our computed results have been compared with available theoretical and experimental data. The IP, EEs, A and oscillator strengths (f) determined at the VU-MRCC level are in excellent agreement with the experimental results. The properties reported here further demonstrate that a basis set with at least h-type of orbitals is ubiquitous to achieve converged results.
An accurate potential energy surface for the F + H2 → HF + H reaction by the coupled-cluster method
International Nuclear Information System (INIS)
Chen, Jun; Sun, Zhigang; Zhang, Dong H.
2015-01-01
A three dimensional potential energy surface for the F + H 2 → HF + H reaction has been computed by the spin unrestricted coupled cluster method with singles, doubles, triples, and perturbative quadruples [UCCSDT(2) Q ] using the augmented correlation-consistent polarised valence quadruple zeta basis set for the fluorine atom and the correlation-consistent polarised valence quadruple zeta basis set for the hydrogen atom. All the calculations are based on the restricted open-shell Hartree-Fock orbitals, together with the frozen core approximations, and the UCCSD(T)/complete basis set (CBS) correction term was included. The global potential energy surface was calculated by fitting the sampled ab initio points without any scaling factor for the correlation energy part using a neutral network function method. Extensive dynamics calculations have been carried out on the potential energy surface. The reaction rate constants, integral cross sections, product rotational states distribution, and forward and backward scattering as a function of collision energy of the F + HD → HF + D, F + HD → DF + H, and F + H 2 reaction, were calculated by the time-independent quantum dynamics scattering theory using the new surface. The satisfactory agreement with the reported experimental observations previously demonstrates the accuracy of the new potential energy surface
Caricato, Marco
2018-04-01
We report the theory and the implementation of the linear response function of the coupled cluster (CC) with the single and double excitations method combined with the polarizable continuum model of solvation, where the correlation solvent response is approximated with the perturbation theory with energy and singles density (PTES) scheme. The singles name is derived from retaining only the contribution of the CC single excitation amplitudes to the correlation density. We compare the PTES working equations with those of the full-density (PTED) method. We then test the PTES scheme on the evaluation of excitation energies and transition dipoles of solvated molecules, as well as of the isotropic polarizability and specific rotation. Our results show a negligible difference between the PTED and PTES schemes, while the latter affords a significantly reduced computational cost. This scheme is general and can be applied to any solvation model that includes mutual solute-solvent polarization, including explicit models. Therefore, the PTES scheme is a competitive approach to compute response properties of solvated systems using CC methods.
International Nuclear Information System (INIS)
Bozkaya, Uğur; Sherrill, C. David
2016-01-01
An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the “gradient terms”: computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C 10 H 22 ), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies.
Madsen, Niels Kristian; Godtliebsen, Ian H.; Losilla, Sergio A.; Christiansen, Ove
2018-01-01
A new implementation of vibrational coupled-cluster (VCC) theory is presented, where all amplitude tensors are represented in the canonical polyadic (CP) format. The CP-VCC algorithm solves the non-linear VCC equations without ever constructing the amplitudes or error vectors in full dimension but still formally includes the full parameter space of the VCC[n] model in question resulting in the same vibrational energies as the conventional method. In a previous publication, we have described the non-linear-equation solver for CP-VCC calculations. In this work, we discuss the general algorithm for evaluating VCC error vectors in CP format including the rank-reduction methods used during the summation of the many terms in the VCC amplitude equations. Benchmark calculations for studying the computational scaling and memory usage of the CP-VCC algorithm are performed on a set of molecules including thiadiazole and an array of polycyclic aromatic hydrocarbons. The results show that the reduced scaling and memory requirements of the CP-VCC algorithm allows for performing high-order VCC calculations on systems with up to 66 vibrational modes (anthracene), which indeed are not possible using the conventional VCC method. This paves the way for obtaining highly accurate vibrational spectra and properties of larger molecules.
International Nuclear Information System (INIS)
Barnes, J.; Dekel, A.; Efstathiou, G.; Frenk, C.S.; Yale Univ., New Haven, CT; California Univ., Santa Barbara; Cambridge Univ., England; Sussex Univ., Brighton, England)
1985-01-01
The cluster correlation function xi sub c(r) is compared with the particle correlation function, xi(r) in cosmological N-body simulations with a wide range of initial conditions. The experiments include scale-free initial conditions, pancake models with a coherence length in the initial density field, and hybrid models. Three N-body techniques and two cluster-finding algorithms are used. In scale-free models with white noise initial conditions, xi sub c and xi are essentially identical. In scale-free models with more power on large scales, it is found that the amplitude of xi sub c increases with cluster richness; in this case the clusters give a biased estimate of the particle correlations. In the pancake and hybrid models (with n = 0 or 1), xi sub c is steeper than xi, but the cluster correlation length exceeds that of the points by less than a factor of 2, independent of cluster richness. Thus the high amplitude of xi sub c found in studies of rich clusters of galaxies is inconsistent with white noise and pancake models and may indicate a primordial fluctuation spectrum with substantial power on large scales. 30 references
Linear-quadratic control and quadratic differential forms for multidimensional behaviors
Napp, D.; Trentelman, H.L.
2011-01-01
This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear-quadratic control problem where the performance functional is the integral of a quadratic differential form. We look
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2006-01-01
This paper considers the cardinality constrained quadratic knapsack problem (QKP) and the quadratic selective travelling salesman problem (QSTSP). The QKP is a generalization of the knapsack problem and the QSTSP is a generalization of the travelling salesman problem. Thus, both problems are NP...
Energy Technology Data Exchange (ETDEWEB)
Peng, Bo [William R. Wiley Environmental; Kowalski, Karol [William R. Wiley Environmental
2017-08-11
The representation and storage of two-electron integral tensors are vital in large- scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this paper, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of atomic basis set N_b ranging from ~ 100 up to ~ 2, 000, the observed numerical scaling of our implementation shows O(N_b^{2.5~3}) versus O(N_b^{3~4}) of single CD in most of other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic-orbital (AO) two-electron integral tensor from O(N_b^4) to O(N_b^2 log_{10}(N_b)) with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled- cluster formalism employing single and double excitations (CCSD) on several bench- mark systems including the C_{60} molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10^{-4} to 10^{-3} to give acceptable compromise between efficiency and accuracy.
Eriksen, Janus J; Matthews, Devin A; Jørgensen, Poul; Gauss, Jürgen
2016-05-21
We extend our assessment of the potential of perturbative coupled cluster (CC) expansions for a test set of open-shell atoms and organic radicals to the description of quadruple excitations. Namely, the second- through sixth-order models of the recently proposed CCSDT(Q-n) quadruples series [J. J. Eriksen et al., J. Chem. Phys. 140, 064108 (2014)] are compared to the prominent CCSDT(Q) and ΛCCSDT(Q) models. From a comparison of the models in terms of their recovery of total CC singles, doubles, triples, and quadruples (CCSDTQ) energies, we find that the performance of the CCSDT(Q-n) models is independent of the reference used (unrestricted or restricted (open-shell) Hartree-Fock), in contrast to the CCSDT(Q) and ΛCCSDT(Q) models, for which the accuracy is strongly dependent on the spin of the molecular ground state. By further comparing the ability of the models to recover relative CCSDTQ total atomization energies, the discrepancy between them is found to be even more pronounced, stressing how a balanced description of both closed- and open-shell species-as found in the CCSDT(Q-n) models-is indeed of paramount importance if any perturbative CC model is to be of chemical relevance for high-accuracy applications. In particular, the third-order CCSDT(Q-3) model is found to offer an encouraging alternative to the existing choices of quadruples models used in modern computational thermochemistry, since the model is still only of moderate cost, albeit markedly more costly than, e.g., the CCSDT(Q) and ΛCCSDT(Q) models.
International Nuclear Information System (INIS)
Farnell, D J J; Zinke, R; Richter, J; Schulenburg, J
2009-01-01
We apply the coupled cluster method (CCM) in order to study the ground-state properties of the (unfrustrated) square-lattice and (frustrated) triangular-lattice spin-half Heisenberg antiferromagnets in the presence of external magnetic fields. Approximate methods are difficult to apply to the triangular-lattice antiferromagnet because of frustration, and so, for example, the quantum Monte Carlo (QMC) method suffers from the 'sign problem'. Results for this model in the presence of magnetic field are rarer than those for the square-lattice system. Here we determine and solve the basic CCM equations by using the localized approximation scheme commonly referred to as the 'LSUBm' approximation scheme and we carry out high-order calculations by using intensive computational methods. We calculate the ground-state energy, the uniform susceptibility, the total (lattice) magnetization and the local (sublattice) magnetizations as a function of the magnetic field strength. Our results for the lattice magnetization of the square-lattice case compare well to the results from QMC approaches for all values of the applied external magnetic field. We find a value for the magnetic susceptibility of χ = 0.070 for the square-lattice antiferromagnet, which is also in agreement with the results from other approximate methods (e.g., χ = 0.0669 obtained via the QMC approach). Our estimate for the range of the extent of the (M/M s =) 1/3 magnetization plateau for the triangular-lattice antiferromagnet is 1.37 SWT = 0.0794. Higher-order calculations are thus suggested for both SWT and CCM LSUBm calculations in order to determine the value of χ for the triangular lattice conclusively.
We propose to investigate, with MINIBALL coupled to T-REX, the one-valence-proton $^{133}$Sb nucleus by the cluster transfer reaction of $^{132}$Sn on $^{7}$Li. The excited $^{133}$Sb will be populated by transfer of a triton into $^{132}$Sn, followed by the emission of an $\\alpha$-particle (detected in T-REX) and 2 neutrons. The aim of the experiment is to locate states arising from the coupling of the valence proton of $^{133}$Sb to the collective low-lying phonon excitations of $^{132}$Sn (in particular the 3$^−$). According to calculations in the weak-coupling approach, these states lie in the 4$\\, - \\,$5 MeV excitation energy region and in the spin interval 1/2$\\, - \\,$ 19/2, i.e., in the region populated by the cluster transfer reaction. The results will be used to perform advanced tests of different types of nuclear interactions, usually employed in the description of particle-phonon coupled excitations. States arising from couplings of the proton with simpler core excitations, involving few nucleons...
Huntington, Lee M J; Krupička, Martin; Neese, Frank; Izsák, Róbert
2017-11-07
The similarity transformed equation of motion coupled-cluster approach is extended for applications to high-spin open-shell systems, within the unrestricted Hartree-Fock (UHF) formalism. An automatic active space selection scheme has also been implemented such that calculations can be performed in a black-box fashion. It is observed that both the canonical and automatic active space selecting similarity transformed equation of motion (STEOM) approaches perform about as well as the more expensive equation of motion coupled-cluster singles doubles (EOM-CCSD) method for the calculation of the excitation energies of doublet radicals. The automatic active space selecting UHF STEOM approach can therefore be employed as a viable, lower scaling alternative to UHF EOM-CCSD for the calculation of excited states in high-spin open-shell systems.
Huntington, Lee M. J.; Krupička, Martin; Neese, Frank; Izsák, Róbert
2017-11-01
The similarity transformed equation of motion coupled-cluster approach is extended for applications to high-spin open-shell systems, within the unrestricted Hartree-Fock (UHF) formalism. An automatic active space selection scheme has also been implemented such that calculations can be performed in a black-box fashion. It is observed that both the canonical and automatic active space selecting similarity transformed equation of motion (STEOM) approaches perform about as well as the more expensive equation of motion coupled-cluster singles doubles (EOM-CCSD) method for the calculation of the excitation energies of doublet radicals. The automatic active space selecting UHF STEOM approach can therefore be employed as a viable, lower scaling alternative to UHF EOM-CCSD for the calculation of excited states in high-spin open-shell systems.
Czech Academy of Sciences Publication Activity Database
Pittner, Jiří; Šmydke, Jan; Čársky, Petr; Hubač, I.
2001-01-01
Roč. 547, - (2001), s. 239-244 ISSN 0166-1280 R&D Projects: GA MŠk OC D9.10; GA ČR GA203/99/D009 Institutional research plan: CEZ:AV0Z4040901 Keywords : potential curve * spectroscopic constants of F2 * multireference coupled clusters Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 0.919, year: 2001
Guises and disguises of quadratic divergences
Energy Technology Data Exchange (ETDEWEB)
Cherchiglia, A.L., E-mail: adriano@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Vieira, A.R., E-mail: arvieira@fisica.ufmg.br [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Hiller, Brigitte, E-mail: brigitte@teor.fis.uc.pt [Departamento de Física, Faculdade de Ciências e Tecnologia, Universidade de Coimbra, 3004-516 Coimbra (Portugal); Baêta Scarpelli, A.P., E-mail: scarpelli.apbs@dpf.gov.br [Setor Técnico-Científico, Departamento de Polícia Federal, Rua Hugo D’Antola, 95 - Lapa, São Paulo (Brazil); Sampaio, Marcos, E-mail: marcos.sampaio@durham.ac.uk [Departamento de Física, ICEx, Universidade Federal de Minas Gerais, P.O. BOX 702, 30.161-970, Belo Horizonte, MG (Brazil); Centre for Particle Theory, Department of Mathematical Sciences, Durham University, South Road Durham DH1 3LE (United Kingdom)
2014-12-15
In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.
Nonlinear dynamics of quadratically cubic systems
International Nuclear Information System (INIS)
Rudenko, O V
2013-01-01
We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)
PSQP: Puzzle Solving by Quadratic Programming.
Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome
2017-02-01
In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.
Cascaded Quadratic Soliton Compression in Waveguide Structures
DEFF Research Database (Denmark)
Guo, Hairun
between the Kerr nonlinear effects and the dispersive effects in the medium. A Kerr-like nonlinearity is produced through the cascaded phase mismatched quadratic process, e.g. the second harmonic generation process, which can be flexibly tuned in both the sign and the amplitude, making possible a strong......-phase-matching technology is not necessarily needed. In large-RI-changed waveguides, CQSC is extended to the mid-infrared range to generate single-cycle pulses with purely nonlinear interactions, since an all-normal dispersion profile could be achieved within the guidance band. We believe that CQSC in quadratic waveguides...
On orthogonality preserving quadratic stochastic operators
Energy Technology Data Exchange (ETDEWEB)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd [Department of Computational and Theoretical Sciences, Faculty of Science International Islamic University Malaysia, P.O. Box 141, 25710 Kuantan, Pahang Malaysia (Malaysia)
2015-05-15
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.
Bound constrained quadratic programming via piecewise
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, M. C.
1999-01-01
of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of lambda/sub 1/ , how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive......We consider the strictly convex quadratic programming problem with bounded variables. A dual problem is derived using Lagrange duality. The dual problem is the minimization of an unconstrained, piecewise quadratic function. It involves a lower bound of lambda/sub 1/ , the smallest eigenvalue...
On orthogonality preserving quadratic stochastic operators
International Nuclear Information System (INIS)
Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd
2015-01-01
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too
Eigenfunctions of quadratic hamiltonians in Wigner representation
International Nuclear Information System (INIS)
Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.
1984-01-01
Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail
Sahoo, B K; Das, B P
2018-05-18
Recent relativistic coupled-cluster (RCC) calculations of electric dipole moments (EDMs) of diamagnetic atoms due to parity and time-reversal violating (P,T-odd) interactions, which are essential ingredients for probing new physics beyond the standard model of particle interactions, differ substantially from the previous theoretical results. It is therefore necessary to perform an independent test of the validity of these results. In view of this, the normal coupled-cluster method has been extended to the relativistic regime [relativistic normal coupled-cluster (RNCC) method] to calculate the EDMs of atoms by simultaneously incorporating the electrostatic and P,T-odd interactions in order to overcome the shortcomings of the ordinary RCC method. This new relativistic method has been applied to ^{199}Hg, which currently has a lower EDM limit than that of any other system. The results of our RNCC and self-consistent RCC calculations of the EDM of this atom are found to be close. The discrepancies between these two results on the one hand and those of previous calculations on the other are elucidated. Furthermore, the electric dipole polarizability of this atom, which has computational similarities with the EDM, is evaluated and it is in very good agreement with its measured value.
Sahoo, B. K.; Das, B. P.
2018-05-01
Recent relativistic coupled-cluster (RCC) calculations of electric dipole moments (EDMs) of diamagnetic atoms due to parity and time-reversal violating (P ,T -odd) interactions, which are essential ingredients for probing new physics beyond the standard model of particle interactions, differ substantially from the previous theoretical results. It is therefore necessary to perform an independent test of the validity of these results. In view of this, the normal coupled-cluster method has been extended to the relativistic regime [relativistic normal coupled-cluster (RNCC) method] to calculate the EDMs of atoms by simultaneously incorporating the electrostatic and P ,T -odd interactions in order to overcome the shortcomings of the ordinary RCC method. This new relativistic method has been applied to 199Hg, which currently has a lower EDM limit than that of any other system. The results of our RNCC and self-consistent RCC calculations of the EDM of this atom are found to be close. The discrepancies between these two results on the one hand and those of previous calculations on the other are elucidated. Furthermore, the electric dipole polarizability of this atom, which has computational similarities with the EDM, is evaluated and it is in very good agreement with its measured value.
Engwerda, Jacob
2015-01-01
This note deals with solving scalar coupled algebraic Riccati equations. These equations arise in finding linear feedback Nash equilibria of the scalar N-player affine quadratic differential game. A numerical procedure is provided to compute all the stabilizing solutions. The main idea is to
Quadratic mass relations in topological bootstrap theory
International Nuclear Information System (INIS)
Jones, C.E.; Uschersohn, J.
1980-01-01
From the requirement of reality of discontinuities of scattering amplitudes at the spherical level of the topological bootstrap theory, a large number of mass relations for hadrons is derived. Quadratic mass formulas for the symmetry-breaking pattern of both mesons and baryon is obtained and their relation to conventional models of symmetry breaking is briefly discussed
STABILIZED SEQUENTIAL QUADRATIC PROGRAMMING: A SURVEY
Directory of Open Access Journals (Sweden)
Damián Fernández
2014-12-01
Full Text Available We review the motivation for, the current state-of-the-art in convergence results, and some open questions concerning the stabilized version of the sequential quadratic programming algorithm for constrained optimization. We also discuss the tools required for its local convergence analysis, globalization challenges, and extentions of the method to the more general variational problems.
The Quadratic Selective Travelling Salesman Problem
DEFF Research Database (Denmark)
Thomadsen, Tommy; Stidsen, Thomas K.
2003-01-01
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective TSP (STSP): Each node has an associated profit and instead of visiting all nodes, the most profitable set of nodes, taking into account the tour cost, is visited. The Quadratic STSP (QSTSP) adds the additional...
orthogonal and scaling transformations of quadratic functions
African Journals Online (AJOL)
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functions of sub-problems of various nonlinear programming problems that employ methods such as sequential quadratic programming and trust-region methods (Sorensen, 1982; Eldersveld,. 1991; Nocedal and Wright, 1999). Various problems in Algebra, Functional Analysis,. Analytic Geometry and Computational Mathe-.
Fundamental quadratic variational principle underlying general relativity
International Nuclear Information System (INIS)
Atkins, W.K.
1983-01-01
The fundamental result of Lanczos is used in a new type of quadratic variational principle whose field equations are the Einstein field equations together with the Yang-Mills type equations for the Riemann curvature. Additionally, a spin-2 theory of gravity for the special case of the Einstein vacuum is discussed
Investigating Students' Mathematical Difficulties with Quadratic Equations
O'Connor, Bronwyn Reid; Norton, Stephen
2016-01-01
This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…
Commuting quantum traces for quadratic algebras
International Nuclear Information System (INIS)
Nagy, Zoltan; Avan, Jean; Doikou, Anastasia; Rollet, Genevieve
2005-01-01
Consistent tensor products on auxiliary spaces, hereafter denoted 'fusion procedures', and commuting transfer matrices are defined for general quadratic algebras, nondynamical and dynamical, inspired by results on reflection algebras. Applications of these procedures then yield integer-indexed families of commuting Hamiltonians
Fisher, Jane; Rowe, Heather; Wynter, Karen; Tran, Thach; Lorgelly, Paula; Amir, Lisa H; Proimos, Jenny; Ranasinha, Sanjeeva; Hiscock, Harriet; Bayer, Jordana; Cann, Warren
2016-03-07
Interventions to prevent postpartum common mental disorders (PCMD) among unselected populations of women have had limited success. The aim was to determine whether What Were We Thinking (WWWT) a gender-informed, psychoeducational programme for couples and babies can prevent PCMD among primiparous women 6 months postpartum. Cluster-randomised controlled trial. 48 Maternal and Child Health Centres (MCHCs) from 6 Local Government Areas in Melbourne, Australia were allocated randomly to usual care (24) or usual care plus WWWT (24). English-speaking primiparous women receiving primary care at trial MCHCs were recruited to the intervention (204) and control (196) conditions. Of these, 187 (91.7%) and 177 (90.3%) provided complete data. WWWT is a manualised programme comprising primary care from a trained nurse, print materials and a face-to-face seminar. Data sources were standardised and study-specific measures collected in blinded computer-assisted telephone interviews at 6 and 26 weeks postpartum. The primary outcome was PCMD assessed by Composite International Diagnostic Interviews and Patient Health Questionnaire (PHQ) Depression and Generalised Anxiety Disorder modules. In intention-to-treat analyses the adjusted OR (AOR) of PCMD in the intervention compared to the usual care group was 0.78 (95% CI 0.38 to 1.63, ns), but mild to moderate anxiety symptoms (AOR 0.58, 95% CI 0.35 to 0.97) and poor self-rated health (AOR 0.46, 95% CI 0.22 to 0.97) were significantly lower. In a per protocol analysis, comparing the full (three component) intervention and usual care groups, the AOR of PCMD was 0.36, (95% CI 0.14 to 0.95). The WWWT seminar was appraised as salient, comprehensible and useful by >85% participants. No harms were detected. WWWT is readily integrated into primary care, enables inclusion of fathers and addresses modifiable risks for PCMD directly. The full intervention appears a promising programme for preventing PCMD, optimising family functioning, and as the
Directory of Open Access Journals (Sweden)
Hilary Graham
2016-12-01
Full Text Available Research on multiple health behaviours is increasing but little is known about parental behaviours and how they covary. Our study investigates cigarette smoking, alcohol intake, fruit and vegetable (F&V consumption and physical activity among mothers and co-resident partners in England. Using the UK Household Longitudinal Study, we examined (i clustering of health behaviours using observed-expected ratios and latent class analysis (ii socio-demographic correlates of the derived latent classes and (iii intra-couple concordance of individual health behaviours and their latent classes. We identified five latent classes for mothers and partners: Never smoked drinkers (28% of mothers; 29% of partners, Abstainers (25%; 17%, Drinkers and ex-smokers (19%; 26%, Unhealthy low frequency drinkers (18%; 16% and Unhealthiest behaviour group (11%; 12%. These had distinctive social profiles. Never smoked drinkers were more likely than those in other groups to be white and socially advantaged: married, older, and with higher educational qualifications and incomes. Abstainers were non-smokers who never or occasionally drank, and were disproportionately drawn from ethnic minority groups and middle/lower income families. Drinkers and ex-smokers were the most physically active group and were more likely to be socially advantaged. Unhealthy low frequency drinkers were more likely to be disadvantaged and have a limiting long-standing illness. The Unhealthiest behaviour group had the highest proportion of smokers, heavy smokers and binge drinkers and the lowest F&V intake and physical activity levels. They were largely white and socially disadvantaged: younger, non-married and with lower educational levels. Mothers and their partners typically shared the same risk behaviours, and 44 per cent of partners and mothers belonged to the same latent class. Our findings point to the potential for a broadening of research and policy perspectives, from separate behaviours to
Tetsassi Feugmo, Conrard Giresse; Liégeois, Vincent; Champagne, Benoît
2017-11-15
The first vibrational sum frequency generation (SFG) spectra based on molecular properties calculated at the coupled cluster singles and doubles (CCSD) level of approximation have been simulated for interfacial model alkyl chains, providing benchmark data for comparisons with approximate methods, including density functional theory (DFT). The approach proceeds in three steps. In the first two steps, the molecular spectral properties are determined: the vibrational normal modes and frequencies and then the derivatives of the dipole moment and of the polarizability with respect to the normal coordinates. These derivatives are evaluated with a numerical differentiation approach, of which the accuracy was monitored using Romberg's procedure. Then, in the last step, a three-layer model is employed to evaluate the macroscopic second-order nonlinear optical responses and thereby the simulated SFG spectra of the alkyl interface. Results emphasize the following facts: (i) the dipole and polarizability derivatives calculated at the DFT level with the B3LYP exchange-correlation functional can differ, with respect to CCSD, by as much as ±10 to 20% and ±20 to 50% for the CH 3 and CH 2 vibrations, respectively; (ii) these differences are enhanced when considering the SFG intensities as well as their variations as a function of the experimental configuration (ppp versus ssp) and as a function of the tilt and rotation angles, defining the orientation of the alkyl chain at the interface; (iii) these differences originate from both the vibrational normal coordinates and the Cartesian derivatives of the dipole moment and polarizability; (iv) freezing the successive fragments of the alkyl chain strongly modifies the SFG spectrum and enables highlighting the delocalization effects between the terminal CH 3 group and its neighboring CH 2 units; and finally (v) going from the free chain to the free methyl model, and further to C 3v constraints on leads to large variations of two ratios
Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients
Directory of Open Access Journals (Sweden)
Xue-Gang Zhou
2014-01-01
Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.
Robust Weak Chimeras in Oscillator Networks with Delayed Linear and Quadratic Interactions
Bick, Christian; Sebek, Michael; Kiss, István Z.
2017-10-01
We present an approach to generate chimera dynamics (localized frequency synchrony) in oscillator networks with two populations of (at least) two elements using a general method based on a delayed interaction with linear and quadratic terms. The coupling design yields robust chimeras through a phase-model-based design of the delay and the ratio of linear and quadratic components of the interactions. We demonstrate the method in the Brusselator model and experiments with electrochemical oscillators. The technique opens the way to directly bridge chimera dynamics in phase models and real-world oscillator networks.
International Nuclear Information System (INIS)
Hong-Bin, Zhang; Jian-Wei, Xia; Yong-Bin, Yu; Chuang-Yin, Dang
2010-01-01
This paper investigates the chaos synchronisation between two coupled chaotic Chua's circuits. The sufficient condition presented by linear matrix inequalities (LMIs) of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions (pwLDIs) model of synchronisation error dynamics, then we design a switching (piecewise-linear) feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results
Cyclic subgroups in class groups of real quadratic fields
International Nuclear Information System (INIS)
Washington, L.C.; Zhang Xianke.
1994-01-01
While examining the class numbers of the real quadratic field Q(√n 2 + 3n + 9), we observed that the class number is often a multiple of 3. There is a simple explanation for this, namely -27 = (2n + 3) 2 - 4(n 2 + 3n + 9), so the cubes of the prime ideals above 3 are principal. If the prime ideals themselves are non-principal then 3 must divide the class number. In the present paper, we study this idea from a couple different directions. In the first section we present a criterion that allows us to show that the ideal class group of a real quadratic field has a cyclic subgroup of a given order n. We then give several families of fields to which this criterion applies, hence in which the ideal class groups contain elements of order n. In the second section, we discuss the situation where there is only a potential element of order p (=an odd prime) in the class group, such as the situation described above. We present a modification of the Cohen-Lenstra heuristics for the probability that in this situation the class number is actually a multiple of p. We also extend this idea to predict how often the potential element of order p is actually non-trivial. Both of these predictions agree fairly well with the numerical data. (author). 14 refs, 2 tabs
Consensus of satellite cluster flight using an energy-matching optimal control method
Luo, Jianjun; Zhou, Liang; Zhang, Bo
2017-11-01
This paper presents an optimal control method for consensus of satellite cluster flight under a kind of energy matching condition. Firstly, the relation between energy matching and satellite periodically bounded relative motion is analyzed, and the satellite energy matching principle is applied to configure the initial conditions. Then, period-delayed errors are adopted as state variables to establish the period-delayed errors dynamics models of a single satellite and the cluster. Next a novel satellite cluster feedback control protocol with coupling gain is designed, so that the satellite cluster periodically bounded relative motion consensus problem (period-delayed errors state consensus problem) is transformed to the stability of a set of matrices with the same low dimension. Based on the consensus region theory in the research of multi-agent system consensus issues, the coupling gain can be obtained to satisfy the requirement of consensus region and decouple the satellite cluster information topology and the feedback control gain matrix, which can be determined by Linear quadratic regulator (LQR) optimal method. This method can realize the consensus of satellite cluster period-delayed errors, leading to the consistency of semi-major axes (SMA) and the energy-matching of satellite cluster. Then satellites can emerge the global coordinative cluster behavior. Finally the feasibility and effectiveness of the present energy-matching optimal consensus for satellite cluster flight is verified through numerical simulations.
Directory of Open Access Journals (Sweden)
Anita Raj
Full Text Available Despite ongoing recommendations to increase male engagement and gender-equity (GE counseling in family planning (FP services, few such programs have been implemented and rigorously evaluated. This study evaluates the impact of CHARM, a three-session GE+FP counseling intervention delivered by male health care providers to married men, alone (sessions 1&2 and with their wives (session 3 in India.A two-armed cluster randomized controlled trial was conducted with young married couples (N = 1081 couples recruited from 50 geographic clusters (25 clusters randomized to CHARM and a control condition, respectively in rural Maharashtra, India. Couples were surveyed on demographics, contraceptive behaviors, and intimate partner violence (IPV attitudes and behaviors at baseline and 9 &18-month follow-ups, with pregnancy testing at baseline and 18-month follow-up. Outcome effects on contraceptive use and incident pregnancy, and secondarily, on contraceptive communication and men's IPV attitudes and behaviors, were assessed using logistic generalized linear mixed models. Most men recruited from CHARM communities (91.3% received at least one CHARM intervention session; 52.5% received the couple's session with their wife. Findings document that women from the CHARM condition, relative to controls, were more likely to report contraceptive communication at 9-month follow-up (AOR = 1.77, p = 0.04 and modern contraceptive use at 9 and 18-month follow-ups (AORs = 1.57-1.58, p = 0.05, and they were less likely to report sexual IPV at 18-month follow-up (AOR = 0.48, p = 0.01. Men in the CHARM condition were less likely than those in the control clusters to report attitudes accepting of sexual IPV at 9-month (AOR = 0.64, p = 0.03 and 18-month (AOR = 0.51, p = 0.004 follow-up, and attitudes accepting of physical IPV at 18-month follow-up (AOR = 0.64, p = 0.02. No significant effect on pregnancy was seen.Findings demonstrate that men can be engaged in FP programming in
Geometric Approaches to Quadratic Equations from Other Times and Places.
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Coherent states of systems with quadratic Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Bagrov, V.G., E-mail: bagrov@phys.tsu.ru [Department of Physics, Tomsk State University, Tomsk (Russian Federation); Gitman, D.M., E-mail: gitman@if.usp.br [Tomsk State University, Tomsk (Russian Federation); Pereira, A.S., E-mail: albertoufcg@hotmail.com [Universidade de Sao Paulo (USP), Sao Paulo, SP (Brazil). Instituto de Fisica
2015-06-15
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
Coherent states of systems with quadratic Hamiltonians
International Nuclear Information System (INIS)
Bagrov, V.G.; Gitman, D.M.; Pereira, A.S.
2015-01-01
Different families of generalized coherent states (CS) for one-dimensional systems with general time-dependent quadratic Hamiltonian are constructed. In principle, all known CS of systems with quadratic Hamiltonian are members of these families. Some of the constructed generalized CS are close enough to the well-known due to Schroedinger and Glauber CS of a harmonic oscillator; we call them simply CS. However, even among these CS, there exist different families of complete sets of CS. These families differ by values of standard deviations at the initial time instant. According to the values of these initial standard deviations, one can identify some of the families with semiclassical CS. We discuss properties of the constructed CS, in particular, completeness relations, minimization of uncertainty relations and so on. As a unknown application of the general construction, we consider different CS of an oscillator with a time dependent frequency. (author)
On quadratic residue codes and hyperelliptic curves
Directory of Open Access Journals (Sweden)
David Joyner
2008-01-01
Full Text Available For an odd prime p and each non-empty subset S⊂GF(p, consider the hyperelliptic curve X S defined by y 2 =f S (x, where f S (x = ∏ a∈S (x-a. Using a connection between binary quadratic residue codes and hyperelliptic curves over GF(p, this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S⊂GF(p for which the bound |X S (GF(p| > 1.39p holds. We also use the quasi-quadratic residue codes defined below to construct an example of a formally self-dual optimal code whose zeta function does not satisfy the ``Riemann hypothesis.''
Quaternion orders, quadratic forms, and Shimura curves
Alsina, Montserrat
2004-01-01
Shimura curves are a far-reaching generalization of the classical modular curves. They lie at the crossroads of many areas, including complex analysis, hyperbolic geometry, algebraic geometry, algebra, and arithmetic. The text provides an introduction to the subject from a theoretic and algorithmic perspective. The main topics covered in it are Shimura curves defined over the rational number field, the construction of their fundamental domains, and the determination of their complex multiplication points. The study of complex multiplication points in Shimura curves leads to the study of families of binary quadratic forms with algebraic coefficients and to their classification by arithmetic Fuchsian groups. In this regard, the authors develop a theory full of new possibilities which parallels Gauss' theory on the classification of binary quadratic forms with integral coefficients by the action of the modular group. Each topic covered in the book begins with a theoretical discussion followed by carefully worked...
Quadratic hamiltonians and relativistic quantum mechanics
International Nuclear Information System (INIS)
Razumov, A.V.; Solov'ev, V.O.; Taranov, A.Yu.
1981-01-01
For the case of a charged scalar field described by a quadratic hamiltonian the equivalent relativistic quantum mechanics is constructed in one-particle sector. Complete investigation of a charged relativistic particle motion in the Coulomb field is carried out. Subcritical as well as supercritical cases are considered. In the course of investigation of the charged scalar particle in the Coulomb field the diagonalization of the quadratic hamiltonian describing the charged scalar quantized field interaction with the external Coulomb field has taken place. Mathematically this problem is bound to the construction of self-conjugated expansions of the symmetric operator. The construction of such expansion is necessary at any small external field magnitude [ru
Lambda-lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, O.; Schultz, U.P.
2004-01-01
-lifting transforms a block-structured program into a set of recursive equations, one for each local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters......Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...
Quadratic Interpolation and Linear Lifting Design
Directory of Open Access Journals (Sweden)
Joel Solé
2007-03-01
Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2003-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2004-01-01
Lambda-lifting is a program transformation that is used in compilers, partial evaluators, and program transformers. In this article, we show how to reduce its complexity from cubic time to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting...... that yields the cubic factor in the traditional formulation of lambda-lifting, which is due to Johnsson. This search is carried out by computing a transitive closure. To reduce the complexity of lambda-lifting, we partition the call graph of the source program into strongly connected components, based...... of lambda-lifting from O(n^3) to O(n^2) . where n is the size of the program. Since a lambda-lifter can output programs of size O(n^2), our algorithm is asympotically optimal....
Temporal quadratic expansion nodal Green's function method
International Nuclear Information System (INIS)
Liu Cong; Jing Xingqing; Xu Xiaolin
2000-01-01
A new approach is presented to efficiently solve the three-dimensional space-time reactor dynamics equation which overcomes the disadvantages of current methods. In the Temporal Quadratic Expansion Nodal Green's Function Method (TQE/NGFM), the Quadratic Expansion Method (QEM) is used for the temporal solution with the Nodal Green's Function Method (NGFM) employed for the spatial solution. Test calculational results using TQE/NGFM show that its time step size can be 5-20 times larger than that of the Fully Implicit Method (FIM) for similar precision. Additionally, the spatial mesh size with NGFM can be nearly 20 times larger than that using the finite difference method. So, TQE/NGFM is proved to be an efficient reactor dynamics analysis method
Collective excitations with chiral NN+3N interactions from coupled-cluster and in-medium SRG
International Nuclear Information System (INIS)
Trippel, Richard
2016-01-01
that end, we extend the RPA formalism to include ground-state correlations from two different many-body methods, the in-medium similarity renormalization group (IM-SRG) and coupled-cluster theory with singles and doubles excitations (CCSD). Both methods have been applied with great success for the calculation of ground-state energies. We develop a formalism based on density matrices for CC-RPA that enables RPA based on an CCSD ground state. The use of IM-SRG transformed matrix elements gives us the possibility to include ground-state correlations even at the level of SRPA. For both methods we observe a strong upward shift in the strength distributions, and, unexpectedly, we find a good agreement between IM-RPA and CC-RPA results. The structure of the transitions remains largely unchanged. We conclude that correlations have significant impact on the energetic positions, but not on the structure of the strength distributions. Employing IM-SRPA we find a strong downward shift in energy similar to the case of SRPA. The agreement of both methods with experiment is comparable.
Collective excitations with chiral NN+3N interactions from coupled-cluster and in-medium SRG
Energy Technology Data Exchange (ETDEWEB)
Trippel, Richard
2016-12-19
that end, we extend the RPA formalism to include ground-state correlations from two different many-body methods, the in-medium similarity renormalization group (IM-SRG) and coupled-cluster theory with singles and doubles excitations (CCSD). Both methods have been applied with great success for the calculation of ground-state energies. We develop a formalism based on density matrices for CC-RPA that enables RPA based on an CCSD ground state. The use of IM-SRG transformed matrix elements gives us the possibility to include ground-state correlations even at the level of SRPA. For both methods we observe a strong upward shift in the strength distributions, and, unexpectedly, we find a good agreement between IM-RPA and CC-RPA results. The structure of the transitions remains largely unchanged. We conclude that correlations have significant impact on the energetic positions, but not on the structure of the strength distributions. Employing IM-SRPA we find a strong downward shift in energy similar to the case of SRPA. The agreement of both methods with experiment is comparable.
Walking solitons in quadratic nonlinear media
Torner Sabata, Lluís; Mazilu, D; Mihalache, Dumitru
1996-01-01
We study self-action of light in parametric wave interactions in nonlinear quadratic media. We show the existence of stationary solitons in the presence of Poynting vector beam walk-off or different group velocities between the waves. We discover that the new solitons constitute a two-parameter family, and they exist for different wave intensities and transverse velocities. We discuss the properties of the walking solitons and their experimental implications. Peer Reviewed
Quadratic Term Structure Models in Discrete Time
Marco Realdon
2006-01-01
This paper extends the results on quadratic term structure models in continuos time to the discrete time setting. The continuos time setting can be seen as a special case of the discrete time one. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors. Pricing bond options requires simple integration. Model parameters may well be time dependent without scuppering such tractability. Model estimation does not require a r...
Least Squares Problems with Absolute Quadratic Constraints
Directory of Open Access Journals (Sweden)
R. Schöne
2012-01-01
Full Text Available This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein's conic-fitting and Fitzgibbon's direct ellipse-specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens' rotations. Finally, four applications of this approach are presented.
Stochastic Linear Quadratic Optimal Control Problems
International Nuclear Information System (INIS)
Chen, S.; Yong, J.
2001-01-01
This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well
Quadratic time dependent Hamiltonians and separation of variables
Anzaldo-Meneses, A.
2017-06-01
Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.
Quadratic tracer dynamical models tobacco growth
International Nuclear Information System (INIS)
Qiang Jiyi; Hua Cuncai; Wang Shaohua
2011-01-01
In order to study the non-uniformly transferring process of some tracer dosages, we assume that the absorption of some tracer by tobacco is a quadratic function of the tracer quantity of the tracer in the case of fast absorption, whereas the exclusion of the tracer from tobacco is a linear function of the tracer quantity in the case of slow exclusion, after the tracer is introduced into tobacco once at zero time. A single-compartment quadratic dynamical model of Logistic type is established for the leaves of tobacco. Then, a two-compartment quadratic dynamical model is established for leaves and calms of the tobacco. Qualitative analysis of the models shows that the tracer applied to the leaves of the tobacco is excluded finally; however, the tracer stays at the tobacco for finite time. Two methods are also given for computing the parameters in the models. Finally, the results of the models are verified by the 32 P experiment for the absorption of tobacco. (authors)
International Nuclear Information System (INIS)
Riplinger, Christoph; Pinski, Peter; Becker, Ute; Neese, Frank; Valeev, Edward F.
2016-01-01
Domain based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)) is a highly efficient local correlation method. It is known to be accurate and robust and can be used in a black box fashion in order to obtain coupled cluster quality total energies for large molecules with several hundred atoms. While previous implementations showed near linear scaling up to a few hundred atoms, several nonlinear scaling steps limited the applicability of the method for very large systems. In this work, these limitations are overcome and a linear scaling DLPNO-CCSD(T) method for closed shell systems is reported. The new implementation is based on the concept of sparse maps that was introduced in Part I of this series [P. Pinski, C. Riplinger, E. F. Valeev, and F. Neese, J. Chem. Phys. 143, 034108 (2015)]. Using the sparse map infrastructure, all essential computational steps (integral transformation and storage, initial guess, pair natural orbital construction, amplitude iterations, triples correction) are achieved in a linear scaling fashion. In addition, a number of additional algorithmic improvements are reported that lead to significant speedups of the method. The new, linear-scaling DLPNO-CCSD(T) implementation typically is 7 times faster than the previous implementation and consumes 4 times less disk space for large three-dimensional systems. For linear systems, the performance gains and memory savings are substantially larger. Calculations with more than 20 000 basis functions and 1000 atoms are reported in this work. In all cases, the time required for the coupled cluster step is comparable to or lower than for the preceding Hartree-Fock calculation, even if this is carried out with the efficient resolution-of-the-identity and chain-of-spheres approximations. The new implementation even reduces the error in absolute correlation energies by about a factor of two, compared to the already accurate
A Finite Continuation Algorithm for Bound Constrained Quadratic Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa C.
1999-01-01
The dual of the strictly convex quadratic programming problem with unit bounds is posed as a linear $\\ell_1$ minimization problem with quadratic terms. A smooth approximation to the linear $\\ell_1$ function is used to obtain a parametric family of piecewise-quadratic approximation problems...
Graphical Solution of the Monic Quadratic Equation with Complex Coefficients
Laine, A. D.
2015-01-01
There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…
International Nuclear Information System (INIS)
Wloch, Marta; Gour, Jeffrey R; Piecuch, Piotr; Dean, David J; Hjorth-Jensen, Morten; Papenbrock, Thomas
2005-01-01
We discuss large-scale ab initio calculations of ground and excited states of 16 O and preliminary calculations for 15 O and 17 O using coupled-cluster methods and algorithms developed in quantum chemistry. By using realistic two-body interactions and the renormalized form of the Hamiltonian obtained with a no-core G-matrix approach, we are able to obtain the virtually converged results for 16 O and promising results for 15 O and 17 O at the level of two-body interactions. The calculated properties other than binding and excitation energies include charge radius and charge form factor. The relatively low costs of coupled-cluster calculations, which are characterized by the low-order polynomial scaling with the system size, enable us to probe large model spaces with up to seven or eight major oscillator shells, for which nontruncated shell-model calculations for nuclei with A = 15-17 active particles are presently not possible
Abe, M.; Prasannaa, V. S.; Das, B. P.
2018-03-01
Heavy polar diatomic molecules are currently among the most promising probes of fundamental physics. Constraining the electric dipole moment of the electron (e EDM ), in order to explore physics beyond the standard model, requires a synergy of molecular experiment and theory. Recent advances in experiment in this field have motivated us to implement a finite-field coupled-cluster (FFCC) approach. This work has distinct advantages over the theoretical methods that we had used earlier in the analysis of e EDM searches. We used relativistic FFCC to calculate molecular properties of interest to e EDM experiments, that is, the effective electric field (Eeff) and the permanent electric dipole moment (PDM). We theoretically determine these quantities for the alkaline-earth monofluorides (AEMs), the mercury monohalides (Hg X ), and PbF. The latter two systems, as well as BaF from the AEMs, are of interest to e EDM searches. We also report the calculation of the properties using a relativistic finite-field coupled-cluster approach with single, double, and partial triples' excitations, which is considered to be the gold standard of electronic structure calculations. We also present a detailed error estimate, including errors that stem from our choice of basis sets, and higher-order correlation effects.
Quadratic stochastic operators: Results and open problems
International Nuclear Information System (INIS)
Ganikhodzhaev, R.N.; Rozikov, U.A.
2009-03-01
The history of the quadratic stochastic operators can be traced back to the work of S. Bernshtein (1924). For more than 80 years this theory has been developed and many papers were published. In recent years it has again become of interest in connection with numerous applications in many branches of mathematics, biology and physics. But most results of the theory were published in non English journals, full text of which are not accessible. In this paper we give a brief description of the results and discuss several open problems. (author)
Sequential Quadratic Programming Algorithms for Optimization
1989-08-01
quadratic program- ma ng (SQ(2l ) aIiatain.seenis to be relgarded aIs tie( buest choice for the solution of smiall. dlense problema (see S tour L)toS...For the step along d, note that a < nOing + 3 szH + i3.ninA A a K f~Iz,;nd and from Id1 _< ,,, we must have that for some /3 , np , 11P11 < dn"p. 5.2...Nevertheless, many of these problems are considered hard to solve. Moreover, for some of these problems the assumptions made in Chapter 2 to establish the
On a quadratic inverse eigenvalue problem
International Nuclear Information System (INIS)
Cai, Yunfeng; Xu, Shufang
2009-01-01
This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable
Phase space eigenfunctions of multidimensional quadratic Hamiltonians
International Nuclear Information System (INIS)
Dodonov, V.V.; Man'ko, V.I.
1986-01-01
We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)
Quadratic forms for Feynman-Kac semigroups
International Nuclear Information System (INIS)
Hibey, Joseph L.; Charalambous, Charalambos D.
2006-01-01
Some problems in a stochastic setting often involve the need to evaluate the Feynman-Kac formula that follows from models described in terms of stochastic differential equations. Equivalent representations in terms of partial differential equations are also of interest, and these establish the well-known connection between probabilistic and deterministic formulations of these problems. In this Letter, this connection is studied in terms of the quadratic form associated with the Feynman-Kac semigroup. The probability measures that naturally arise in this approach, and thus define how Brownian motion is killed at a specified rate while exiting a set, are interpreted as a random time change of the original stochastic differential equation. Furthermore, since random time changes alter the diffusion coefficients in stochastic differential equations while Girsanov-type measure transformations alter their drift coefficients, their simultaneous use should lead to more tractable solutions for some classes of problems. For example, the minimization of some quadratic forms leads to solutions that satisfy certain partial differential equations and, therefore, the techniques discussed provide a variational approach for finding these solutions
DEFF Research Database (Denmark)
Mak, Vicky; Thomadsen, Tommy
2004-01-01
A well-known extension of the Travelling Salesman Problem (TSP) is the Selective (or Prize-collecting) TSP: In addition to the edge-costs, each node has an associated reward (denoted the node-reward) and instead of visiting all nodes, only profitable nodes are visited. The Quadratic Selective TSP...
International Nuclear Information System (INIS)
Juárez-Reyes, L; Pastor, G M; Stepanyuk, V S
2014-01-01
The effects of external electric fields (EFs) on the magnetic state and substrate-mediated magnetic coupling between Mn dimers on Cu(1 1 1) have been studied using a first-principles theoretical method. The calculations show that a change in the ground-state magnetic order, from antiferromagnetic (AF) to ferromagnetic (FM), can be induced within an isolated Mn 2 on Cu(1 1 1) by applying a moderately strong EF of about 1 V Å −1 . The magnetic exchange coupling between pairs of dimers displays Ruderman–Kittel–Kasuya–Yosida-like oscillations as a function of the interdimer distance, which depend significantly on the magnetic order within the dimers (FM or AF) and on their relative orientation on the surface. Moreover, it is observed that applying EFs allows modulation of the exchange coupling within and between the clusters as a function of the intercluster distance. At short distances, AF order within the dimers is favoured even in the presence of EFs, while for large distances the EF can induce a FM order. EFs pointing outwards and inwards with respect to the surface favour parallel and antiparallel magnetic alignment between the dimers, resspectively. The dependence of the substrate-mediated interaction on the magnetic state of Mn 2 is qualitatively interpreted in terms of the differences in the scattering of spin-polarized surface electrons. (paper)
A garden of orchids: a generalized Harper equation at quadratic irrational frequencies
International Nuclear Information System (INIS)
Mestel, B D; Osbaldestin, A H
2004-01-01
We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case
A garden of orchids: a generalized Harper equation at quadratic irrational frequencies
Energy Technology Data Exchange (ETDEWEB)
Mestel, B D [Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA (United Kingdom); Osbaldestin, A H [Department of Mathematics, University of Portsmouth, Portsmouth PO1 3HE (United Kingdom)
2004-10-01
We consider a generalized Harper equation at quadratic irrational flux, showing, in the strong coupling limit, the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set. This work generalizes previous analyses which have considered only the golden mean case. Projections of the renormalization strange sets are illustrated analogous to the 'orchid' present in the golden mean case.
Sibanda, Euphemia L; Tumushime, Mary; Mufuka, Juliet; Mavedzenge, Sue Napierala; Gudukeya, Stephano; Bautista-Arredondo, Sergio; Hatzold, Karin; Thirumurthy, Harsha; McCoy, Sandra I; Padian, Nancy; Copas, Andrew; Cowan, Frances M
2017-09-01
Couples' HIV testing and counselling (CHTC) is associated with greater engagement with HIV prevention and care than individual testing and is cost-effective, but uptake remains suboptimal. Initiating discussion of CHTC might result in distrust between partners. Offering incentives for CHTC could change the focus of the pre-test discussion. We aimed to determine the impact of incentives for CHTC on uptake of couples testing and HIV case diagnosis in rural Zimbabwe. In this cluster-randomised trial, 68 rural communities (the clusters) in four districts receiving mobile HIV testing services were randomly assigned (1:1) to incentives for CHTC or not. Allocation was not masked to participants and researchers. Randomisation was stratified by district and proximity to a health facility. Within each stratum random permutation was done to allocate clusters to the study groups. In intervention communities, residents were informed that couples who tested together could select one of three grocery items worth US$1·50. Standard mobilisation for testing was done in comparison communities. The primary outcome was the proportion of individuals testing with a partner. Analysis was by intention to treat. 3 months after CHTC, couple-testers from four communities per group individually completed a telephone survey to evaluate any social harms resulting from incentives or CHTC. The effect of incentives on CHTC was estimated using logistic regression with random effects adjusting for clustering. The trial was registered with the Pan African Clinical Trial Registry, number PACTR201606001630356. From May 26, 2015, to Jan 29, 2016, of 24 679 participants counselled with data recorded, 14 099 (57·1%) were in the intervention group and 10 580 (42·9%) in the comparison group. 7852 (55·7%) testers in the intervention group versus 1062 (10·0%) in the comparison group tested with a partner (adjusted odds ratio 13·5 [95% CI 10·5-17·4]). Among 427 (83·7%) of 510 eligible
Quadratic residues and non-residues selected topics
Wright, Steve
2016-01-01
This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapters present some basic facts and the history of quadratic residues and non-residues and discuss various proofs of the Law of Quadratic Reciprosity in depth, with an emphasis on the six proofs that Gauss published. The remaining seven chapters explore some interesting applications of the Law of Quadratic Reciprocity, prove some results concerning the distribution and arithmetic structure of quadratic residues and non-residues, provide a detailed proof of Dirichlet’s Class-Number Formula, and discuss the question of whether quadratic residues are randomly distributed. The text is a valuable resource for graduate and advanced undergraduate students as well as for mathematicians interested in number theory.
Exact cancellation of quadratic divergences in top condensation models
International Nuclear Information System (INIS)
Blumhofer, A.
1995-01-01
We discuss the hierarchy problem and the corresponding quadratic divergences in the top mode Standard Model. Quadratic divergences appear at each order 1/N c since fermionic and bosonic contributions are of different order 1/N c . It is shown that the full dynamical system to all orders in 1/N c admits a solution, where the sum of all quadratic divergent contributions disappears. ((orig.))
Bourasseau, Emeric; Maillet, Jean-Bernard
2011-04-21
This paper presents a new method to obtain chemical equilibrium properties of detonation products mixtures including a solid carbon phase. In this work, the solid phase is modelled through a mesoparticle immersed in the fluid, such that the heterogeneous character of the mixture is explicitly taken into account. Inner properties of the clusters are taken from an equation of state obtained in a previous work, and interaction potential between the nanocluster and the fluid particles is derived from all-atoms simulations using the LCBOPII potential (Long range Carbon Bond Order Potential II). It appears that differences in chemical equilibrium results obtained with this method and the "composite ensemble method" (A. Hervouet et al., J. Phys. Chem. B, 2008, 112.), where fluid and solid phases are considered as non-interacting, are not significant, underlining the fact that considering the inhomogeneity of such system is crucial.
Jin, S.; Tamura, M.; Susaki, J.
2014-09-01
Leaf area index (LAI) is one of the most important structural parameters of forestry studies which manifests the ability of the green vegetation interacted with the solar illumination. Classic understanding about LAI is to consider the green canopy as integration of horizontal leaf layers. Since multi-angle remote sensing technique developed, LAI obliged to be deliberated according to the observation geometry. Effective LAI could formulate the leaf-light interaction virtually and precisely. To retrieve the LAI/effective LAI from remotely sensed data therefore becomes a challenge during the past decades. Laser scanning technique can provide accurate surface echoed coordinates with densely scanned intervals. To utilize the density based statistical algorithm for analyzing the voluminous amount of the 3-D points data is one of the subjects of the laser scanning applications. Computational geometry also provides some mature applications for point cloud data (PCD) processing and analysing. In this paper, authors investigated the feasibility of a new application for retrieving the effective LAI of an isolated broad leaf tree. Simplified curvature was calculated for each point in order to remove those non-photosynthetic tissues. Then PCD were discretized into voxel, and clustered by using Gaussian mixture model. Subsequently the area of each cluster was calculated by employing the computational geometry applications. In order to validate our application, we chose an indoor plant to estimate the leaf area, the correlation coefficient between calculation and measurement was 98.28 %. We finally calculated the effective LAI of the tree with 6 × 6 assumed observation directions.
Energy Technology Data Exchange (ETDEWEB)
Bhaskaran-Nair, Kiran [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70802 (United States); Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Cain Department of Chemical Engineering, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Kowalski, Karol, E-mail: karol.kowalski@pnnl.gov [William R. Wiley Environmental Molecular Sciences Laboratory, Battelle, Pacific Northwest National Laboratory, K8-91, P.O.Box 999, Richland, Washington 99352 (United States); Moreno, Juana; Jarrell, Mark [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70802 (United States); Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Shelton, William A. [Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803 (United States); Cain Department of Chemical Engineering, Louisiana State University, Baton Rouge, Louisiana 70803 (United States)
2014-08-21
In both molecular and periodic solid-state systems there is a need for the accurate determination of the ionization potential and the electron affinity for systems ranging from light harvesting polymers and photocatalytic compounds to semiconductors. The development of a Green's function approach based on the coupled cluster (CC) formalism would be a valuable tool for addressing many properties involving many-body interactions along with their associated correlation functions. As a first step in this direction, we have developed an accurate and parallel efficient approach based on the equation of motion-CC technique. To demonstrate the high degree of accuracy and numerical efficiency of our approach we calculate the ionization potential and electron affinity for C{sub 60} and C{sub 70}. Accurate predictions for these molecules are well beyond traditional molecular scale studies. We compare our results with experiments and both quantum Monte Carlo and GW calculations.
International Nuclear Information System (INIS)
Shepherd, James J.; Henderson, Thomas M.; Scuseria, Gustavo E.
2016-01-01
Over the past few years, pair coupled cluster doubles (pCCD) has shown promise for the description of strong correlation. This promise is related to its apparent ability to match results from doubly occupied configuration interaction (DOCI), even though the latter method has exponential computational cost. Here, by modifying the full configuration interaction quantum Monte Carlo algorithm to sample only the seniority zero sector of Hilbert space, we show that the DOCI and pCCD energies are in agreement for a variety of 2D Hubbard models, including for systems well out of reach for conventional configuration interaction algorithms. Our calculations are aided by the sign problem being much reduced in the seniority zero space compared with the full space. We present evidence for this and then discuss the sign problem in terms of the wave function of the system which appears to have a simplified sign structure.
DEFF Research Database (Denmark)
Sauer, Stephan P. A.; Ul Haq, Inam; Sabin, John R.
2014-01-01
by about 1%. For the two-electron systems He and H2, our CCSD results (for a Lanczos chain length equal to the full excitation space), I0 = 42:28 eV (Helium) and I0 = 19:62 eV (H2), correspond to full conguration interaction results and are therefore the exact, non-relativistic theoretical values......Using an asymmetric-Lanczos-chain algorithm for the calculation of the coupled cluster linear response functions at the CCSD and CC2 levels of approximation, we have calculated the mean excitation energies of the noble gases He, Ne and Ar, and of the hydrogen molecule H2. Convergence with respect...... for the mean excitation energy of these two systems within the Bethe theory for the chosen basis set and, in the case of H2, at the experimental equilibrium geometry....
Small, David W; Head-Gordon, Martin
2017-07-14
The Coupled Cluster Valence Bond (CCVB) method, previously presented for closed-shell (CS) systems, is extended to open-shell (OS) systems. The theoretical development is based on embedding the basic OS CCVB wavefunction in a fictitious singlet super-system. This approach reveals that the OS CCVB amplitude equations are quite similar to those of CS CCVB, and thus that OS CCVB requires the same level of computational effort as CS CCVB, which is an inexpensive method. We present qualitatively correct CCVB potential energy curves for all low-lying spin states of P 2 and Mn 2 + . CCVB is successfully applied to the low-lying spin states of some model linear polycarbenes, systems that appear to be a hindrance to standard density functionals. We examine an octa-carbene dimer in a side-by-side orientation, which, in the monomer dissociation limit, exhibits maximal strong correlation over the length of the polycarbene.
Energy Technology Data Exchange (ETDEWEB)
Piecuch, Piotr; Li, Wei; Lutz, Jesse J. [Department of Chemistry, Michigan State University, East Lansing, MI 48824 (United States); Włoch, Marta [Department of Chemistry, Michigan Technological University, Houghton, Michigan 49931 (United States); Gour, Jeffrey R. [Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA and Department of Chemistry, Stanford University, Stanford, California 94305 (United States)
2015-01-22
Coupled-cluster (CC) theory has become the de facto standard for high-accuracy molecular calculations, but the widely used CC and equation-of-motion (EOM) CC approaches, such as CCSD(T) and EOMCCSD, have difficulties with capturing stronger electron correlations that characterize multi-reference molecular problems. This presentation demonstrates that many of these difficulties can be addressed by exploiting the completely renormalized (CR) CC and EOMCC approaches, such as CR-CC(2,3), CR-EOMCCSD(T), and CR-EOMCC(2,3), and their local correlation counterparts applicable to systems with hundreds of atoms, and the active-space CC/EOMCC approaches, such as CCSDt and EOMCCSDt, and their extensions to valence systems via the electron-attached and ionized formalisms.
Rendell, Alistair P.; Lee, Timothy J.
1991-01-01
The analytic energy gradient for the single and double excitation coupled-cluster (CCSD) wave function has been reformulated and implemented in a new set of programs. The reformulated set of gradient equations have a smaller computational cost than any previously published. The iterative solution of the linear equations and the construction of the effective density matrices are fully vectorized, being based on matrix multiplications. The new method has been used to investigate the Cl2O2 molecule, which has recently been postulated as an important intermediate in the destruction of ozone in the stratosphere. In addition to reporting computational timings, the CCSD equilibrium geometries, harmonic vibrational frequencies, infrared intensities, and relative energetics of three isomers of Cl2O2 are presented.
Kowalski, Karol
2009-05-21
In this article we discuss the problem of proper balancing of the noniterative corrections to the ground- and excited-state energies obtained with approximate coupled cluster (CC) and equation-of-motion CC (EOMCC) approaches. It is demonstrated that for a class of excited states dominated by single excitations and for states with medium doubly excited component, the newly introduced nested variant of the method of moments of CC equations provides mathematically rigorous way of balancing the ground- and excited-state correlation effects. The resulting noniterative methodology accounting for the effect of triples is tested using its parallel implementation on the systems, for which iterative CC/EOMCC calculations with full inclusion of triply excited configurations or their most important subset are numerically feasible.
DEFF Research Database (Denmark)
Prihandoko, Rudi; Alvarez-Curto, Elisa; Hudson, Brian D
2016-01-01
of these phosphoacceptor sites to alanine completely prevented phosphorylation of mFFA4 but did not limit receptor coupling to extracellular signal regulated protein kinase 1 and 2 (ERK1/2) activation. Rather, an inhibitor of Gq/11proteins completely prevented receptor signaling to ERK1/2. By contrast, the recruitment...... activation. These unique observations define differential effects on signaling mediated by phosphorylation at distinct locations. This hallmark feature supports the possibility that the signaling outcome of mFFA4 activation can be determined by the pattern of phosphorylation (phosphorylation barcode...
Distance matrices and quadratic embedding of graphs
Directory of Open Access Journals (Sweden)
Nobuaki Obata
2018-04-01
Full Text Available A connected graph is said to be of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently, if the distance matrix is conditionally negative definite. Several criteria for a graph to be of QE class are derived from the point of view of graph operations. For a quantitative criterion the QE constant is introduced and concrete examples are shown with explicit calculation. If the distance matrix admits a constant row sum, the QE constant coincides with the second largest eigenvalue of the distance matrix. The QE constants are determined for all graphs on $n$ vertices with $n\\le5$, among which two are not of QE class.
Low-rank quadratic semidefinite programming
Yuan, Ganzhao
2013-04-01
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers
International Nuclear Information System (INIS)
Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.
2005-01-01
The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules
Charged black holes in quadratic gravity
International Nuclear Information System (INIS)
Matyjasek, Jerzy; Tryniecki, Dariusz
2004-01-01
Iterative solutions to fourth-order gravity describing static and electrically charged black holes are constructed. The obtained solutions are parametrized by two integration constants which are related to the electric charge and the exact location of the event horizon. Special emphasis is put on the extremal black holes. It is explicitly demonstrated that in the extremal limit the exact location of the (degenerate) event horizon is given by r + =|e|. Similarly to the classical Reissner-Nordstroem solution, the near-horizon geometry of the charged black holes in quadratic gravity, when expanded into the whole manifold, is simply that of Bertotti and Robinson. Similar considerations have been carried out for boundary conditions of the second type which employ the electric charge and the mass of the system as seen by a distant observer. The relations between results obtained within the framework of each method are briefly discussed
Lambda-Lifting in Quadratic Time
DEFF Research Database (Denmark)
Danvy, Olivier; Schultz, Ulrik Pagh
2002-01-01
Lambda-lifting is a program transformation used in compilers and in partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one for each...... local function in the source program. Each equation carries extra parameters to account for the free variables of the corresponding local function and of all its callees. It is the search for these extra parameters that yields the cubic factor in the traditional formulation of lambda-lifting, which...... is not needed. We therefore simplify the search for extra parameters by treating each strongly connected component instead of each function as a unit, thereby reducing the time complexity of lambda-lifting from O(n 3 log n)toO(n2 log n), where n is the size of the program. Since a lambda-lifter can output...
Low-rank quadratic semidefinite programming
Yuan, Ganzhao; Zhang, Zhenjie; Ghanem, Bernard; Hao, Zhifeng
2013-01-01
Low rank matrix approximation is an attractive model in large scale machine learning problems, because it can not only reduce the memory and runtime complexity, but also provide a natural way to regularize parameters while preserving learning accuracy. In this paper, we address a special class of nonconvex quadratic matrix optimization problems, which require a low rank positive semidefinite solution. Despite their non-convexity, we exploit the structure of these problems to derive an efficient solver that converges to their local optima. Furthermore, we show that the proposed solution is capable of dramatically enhancing the efficiency and scalability of a variety of concrete problems, which are of significant interest to the machine learning community. These problems include the Top-k Eigenvalue problem, Distance learning and Kernel learning. Extensive experiments on UCI benchmarks have shown the effectiveness and efficiency of our proposed method. © 2012.
A ''quadratized'' augmented plane wave method
International Nuclear Information System (INIS)
Smrcka, L.
1982-02-01
The exact radial solution inside the muffin-tin sphere is replaced by its Taylor expansion with respect to the energy, truncated after the quadratic term. Making use of it the energy independent augmented plane waves are formed which lead to the secular equations linear in energy. The method resembles the currently used linearized APW method but yields higher accuracy. The analysis of solution inside one muffin-tin sphere shows that the eigenvalue error is proportional to (E-E 0 ) 6 as compared with (E-E 0 ) 4 for LAPW. The error of eigenfunctions is (E-E 0 ) 3 ((E-E 0 ) 2 for LAPW). These conclusions are confirmed by direct numerical calculation of band structure of Cu and Al. (author)
Bistoni, Giovanni; Riplinger, Christoph; Minenkov, Yury; Cavallo, Luigi; Auer, Alexander A.; Neese, Frank
2017-01-01
The validity of the main approximations used in canonical and domain based pair natural orbital coupled cluster methods (CCSD(T) and DLPNO-CCSD(T), respectively) in standard chemical applications is discussed. In particular, we investigate the dependence of the results on the number of electrons included in the correlation treatment in frozen-core (FC) calculations and on the main threshold governing the accuracy of DLPNO all-electron (AE) calculations. Initially, scalar relativistic orbital energies for the ground state of the atoms from Li to Rn in the periodic table are calculated. An energy criterion is applied for determining the orbitals that can be excluded from the correlation treatment in FC coupled cluster calculations without significant loss of accuracy. The heterolytic dissociation energy (HDE) of a series of metal compounds (LiF, NaF, AlF3, CaF2, CuF, GaF3, YF3, AgF, InF3, HfF4 and AuF) is calculated at the canonical CCSD(T) level, and the dependence of the results on the number of correlated electrons is investigated. Although for many of the studied reactions sub-valence correlation effects contribute significantly to the HDE, the use of an energy criterion permits a conservative definition of the size of the core, allowing FC calculations to be performed in a black-box fashion while retaining chemical accuracy. A comparison of the CCSD and the DLPNO-CCSD methods in describing the core-core, core-valence and valence-valence components of the correlation energy is given. It is found that more conservative thresholds must be used for electron pairs containing at least one core electron in order to achieve high accuracy in AE DLPNO-CCSD calculations relative to FC calculations. With the new settings, the DLPNO-CCSD method reproduces canonical CCSD results in both AE and FC calculations with the same accuracy.
Bistoni, Giovanni
2017-06-12
The validity of the main approximations used in canonical and domain based pair natural orbital coupled cluster methods (CCSD(T) and DLPNO-CCSD(T), respectively) in standard chemical applications is discussed. In particular, we investigate the dependence of the results on the number of electrons included in the correlation treatment in frozen-core (FC) calculations and on the main threshold governing the accuracy of DLPNO all-electron (AE) calculations. Initially, scalar relativistic orbital energies for the ground state of the atoms from Li to Rn in the periodic table are calculated. An energy criterion is applied for determining the orbitals that can be excluded from the correlation treatment in FC coupled cluster calculations without significant loss of accuracy. The heterolytic dissociation energy (HDE) of a series of metal compounds (LiF, NaF, AlF3, CaF2, CuF, GaF3, YF3, AgF, InF3, HfF4 and AuF) is calculated at the canonical CCSD(T) level, and the dependence of the results on the number of correlated electrons is investigated. Although for many of the studied reactions sub-valence correlation effects contribute significantly to the HDE, the use of an energy criterion permits a conservative definition of the size of the core, allowing FC calculations to be performed in a black-box fashion while retaining chemical accuracy. A comparison of the CCSD and the DLPNO-CCSD methods in describing the core-core, core-valence and valence-valence components of the correlation energy is given. It is found that more conservative thresholds must be used for electron pairs containing at least one core electron in order to achieve high accuracy in AE DLPNO-CCSD calculations relative to FC calculations. With the new settings, the DLPNO-CCSD method reproduces canonical CCSD results in both AE and FC calculations with the same accuracy.
Large-scale sequential quadratic programming algorithms
Energy Technology Data Exchange (ETDEWEB)
Eldersveld, S.K.
1992-09-01
The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.
Yore, Jennifer; Dasgupta, Anindita; Ghule, Mohan; Battala, Madhusadana; Nair, Saritha; Silverman, Jay; Saggurti, Niranjan; Balaiah, Donta; Raj, Anita
2016-02-20
Globally, 41% of all pregnancies are unintended, increasing risk for unsafe abortion, miscarriage and maternal and child morbidities and mortality. One in four pregnancies in India (3.3 million pregnancies, annually) are unintended; 2/3 of these occur in the context of no modern contraceptive use. In addition, no contraceptive use until desired number and sex composition of children is achieved remains a norm in India. Research shows that globally and in India, the youngest and most newly married wives are least likely to use contraception and most likely to report husband's exclusive family planning decision-making control, suggesting that male engagement and family planning support is important for this group. Thus, the Counseling Husbands to Achieve Reproductive Health and Marital Equity (CHARM) intervention was developed in recognition of the need for more male engagement family planning models that include gender equity counseling and focus on spacing contraception use in rural India. For this study, a multi-session intervention delivered to men but inclusive of their wives was developed and evaluated as a two-armed cluster randomized controlled design study conducted across 50 mapped clusters in rural Maharashtra, India. Eligible rural young husbands and their wives (N = 1081) participated in a three session gender-equity focused family planning program delivered to the men (Sessions 1 and 2) and their wives (Session 3) by village health providers in rural India. Survey assessments were conducted at baseline and 9&18 month follow-ups with eligible men and their wives, and pregnancy tests were obtained from wives at baseline and 18-month follow-up. Additional in-depth understanding of how intervention impact occurred was assessed via in-depth interviews at 18 month follow-up with VHPs and a subsample of couples (n = 50, 2 couples per intervention cluster). Process evaluation was conducted to collect feedback from husbands, wives, and VHPs on program
Energy Technology Data Exchange (ETDEWEB)
Datta, Dipayan, E-mail: datta@uni-mainz.de; Gauss, Jürgen, E-mail: gauss@uni-mainz.de [Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Duesbergweg 10-14, D-55128 Mainz (Germany)
2014-09-14
An analytic scheme is presented for the evaluation of first derivatives of the energy for a unitary group based spin-adapted coupled cluster (CC) theory, namely, the combinatoric open-shell CC (COSCC) approach within the singles and doubles approximation. The widely used Lagrange multiplier approach is employed for the derivation of an analytical expression for the first derivative of the energy, which in combination with the well-established density-matrix formulation, is used for the computation of first-order electrical properties. Derivations of the spin-adapted lambda equations for determining the Lagrange multipliers and the expressions for the spin-free effective density matrices for the COSCC approach are presented. Orbital-relaxation effects due to the electric-field perturbation are treated via the Z-vector technique. We present calculations of the dipole moments for a number of doublet radicals in their ground states using restricted open-shell Hartree-Fock (ROHF) and quasi-restricted HF (QRHF) orbitals in order to demonstrate the applicability of our analytic scheme for computing energy derivatives. We also report calculations of the chlorine electric-field gradients and nuclear quadrupole-coupling constants for the CCl, CH{sub 2}Cl, ClO{sub 2}, and SiCl radicals.
Bartlett, Rodney J; Musiał, Monika
2006-11-28
The nCC hierarchy of coupled-cluster approximations, where n guarantees exactness for n electrons and all products of n electrons are derived and applied to several illustrative problems. The condition of exactness for n=2 defines nCCSD=2CC, with nCCSDT=3CC and nCCSDTQ=4CC being exact for three and four electrons. To achieve this, the minimum number of diagrams is evaluated, which is less than in the corresponding CC model. For all practical purposes, nCC is also the proper definition of a size-extensive CI. 2CC is also an orbitally invariant coupled electron pair approximation. The numerical results of nCC are close to those for the full CC variant, and in some cases are closer to the full CI reference result. As 2CC is exact for separated electron pairs, it is the natural zeroth-order approximation for the correlation problem in molecules with other effects introduced as these units start to interact. The nCC hierarchy of approximations has all the attractive features of CC including its size extensivity, orbital invariance, and orbital insensitivity, but in a conceptually appealing form suited to bond breaking, while being computationally less demanding. Excited states from the equation of motion (EOM-2CC) are also reported, which show results frequently approaching those of EOM-CCSDT.
Orthogonal and Scaling Transformations of Quadratic Functions with ...
African Journals Online (AJOL)
In this paper we present a non-singular transformation that can reduce a given quadratic function defined on Rn to another simpler quadratic function and study the impact of the transformation in relation to the problem of minimization of the function. In particular, we construct a non-singular transformation that can reduce a ...
Quadratic Twists of Rigid Calabi–Yau Threefolds Over
DEFF Research Database (Denmark)
Gouvêa, Fernando Q.; Kiming, Ian; Yui, Noriko
2013-01-01
of weight 4 on some Γ 0(N). We show that quadratic twisting of a threefold corresponds to twisting the attached newform by quadratic characters and illustrate with a number of obvious and not so obvious examples. The question is motivated by the deeper question of which newforms of weight 4 on some Γ 0(N...
Approximate *-derivations and approximate quadratic *-derivations on C*-algebras
Directory of Open Access Journals (Sweden)
Park Choonkil
2011-01-01
Full Text Available Abstract In this paper, we prove the stability of *-derivations and of quadratic *-derivations on Banach *-algebras. We moreover prove the superstability of *-derivations and of quadratic *-derivations on C*-algebras. 2000 Mathematics Subject Classification: 39B52; 47B47; 46L05; 39B72.
A Linear Programming Reformulation of the Standard Quadratic Optimization Problem
de Klerk, E.; Pasechnik, D.V.
2005-01-01
The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an (exponentially
Effects of Classroom Instruction on Students' Understanding of Quadratic Equations
Vaiyavutjamai, Pongchawee; Clements, M. A.
2006-01-01
Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…
Analysis of Students' Error in Learning of Quadratic Equations
Zakaria, Effandi; Ibrahim; Maat, Siti Mistima
2010-01-01
The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…
Sketching the General Quadratic Equation Using Dynamic Geometry Software
Stols, G. H.
2005-01-01
This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…
Tangent Lines without Derivatives for Quadratic and Cubic Equations
Carroll, William J.
2009-01-01
In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)
Visualising the Roots of Quadratic Equations with Complex Coefficients
Bardell, Nicholas S.
2014-01-01
This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…
Directory of Open Access Journals (Sweden)
von Baum Heike
2006-07-01
Full Text Available Abstract Background Spread of antibiotic resistance in hospitals is a well-known problem, but studies investigating the importance of factors potentially related to the spread of resistant bacteria in outpatients are sparse. Methods Stool samples were obtained from 206 healthy couples in a community setting in Southern Germany in 2002–2003. E. coli was cultured and minimal inhibition concentrations were tested. Prevalences of E. coli resistance to commonly prescribed antibiotics according to potential risk factors were ascertained. Results Prevalences of ampicillin resistance were 15.7% and 19.4% for women and men, respectively. About ten percent and 15% of all isolates were resistant to cotrimoxazole and doxycycline, respectively. A partner carrying resistance was the main risk factor for being colonized with resistant E. coli. Odds ratios (95% CI for ampicillin and cotrimoxazole resistance given carriage of resistant isolates by the partner were 6.9 (3.1–15.5 and 3.3 (1.5–18.0, respectively. Conclusion Our data suggest that conjugal transmission may be more important for the spread of antibiotic resistance in the community setting than commonly suspected risk factors such as previous antibiotic intake or hospital contacts.
International Nuclear Information System (INIS)
2005-01-01
Nature of physical problem solved: AUTOJOM is a computer program that will generate the coefficients of any quadratic equation used to define conic volumes and also the coefficients of the planes needed to define parallelepipeds, wedges, and pyramids. JOMREAD is a computer code to check any 3D geometry composed of and constructed with quadratic surfaces
Are ghost surfaces quadratic-flux-minimizing?
International Nuclear Information System (INIS)
Hudson, S.R.; Dewar, R.L.
2009-01-01
Two candidates for 'almost-invariant' toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbits are obtained by displacing closed field lines in the direction of steepest descent of magnetic action, ∫A.dl. A generalized Hamiltonian definition of ghost surfaces is given and specialized to the usual Lagrangian definition. A modified Hamilton's Principle is introduced that allows the use of Lagrangian integration for calculation of the QFMin pseudo-orbits. Numerical calculations show QFMin and Lagrangian ghost surfaces give very similar results for a chaotic magnetic field perturbed from an integrable case, and this is explained using a perturbative construction of an auxiliary poloidal angle for which QFMin and Lagrangian ghost surfaces are the same up to second order. While presented in the context of 3-dimensional magnetic field line systems, the concepts are applicable to defining almost-invariant tori in other 11/2 degree-of-freedom nonintegrable Lagrangian/Hamiltonian systems.
Securing Digital Audio using Complex Quadratic Map
Suryadi, MT; Satria Gunawan, Tjandra; Satria, Yudi
2018-03-01
In This digital era, exchanging data are common and easy to do, therefore it is vulnerable to be attacked and manipulated from unauthorized parties. One data type that is vulnerable to attack is digital audio. So, we need data securing method that is not vulnerable and fast. One of the methods that match all of those criteria is securing the data using chaos function. Chaos function that is used in this research is complex quadratic map (CQM). There are some parameter value that causing the key stream that is generated by CQM function to pass all 15 NIST test, this means that the key stream that is generated using this CQM is proven to be random. In addition, samples of encrypted digital sound when tested using goodness of fit test are proven to be uniform, so securing digital audio using this method is not vulnerable to frequency analysis attack. The key space is very huge about 8.1×l031 possible keys and the key sensitivity is very small about 10-10, therefore this method is also not vulnerable against brute-force attack. And finally, the processing speed for both encryption and decryption process on average about 450 times faster that its digital audio duration.
Designing Camera Networks by Convex Quadratic Programming
Ghanem, Bernard
2015-05-04
In this paper, we study the problem of automatic camera placement for computer graphics and computer vision applications. We extend the problem formulations of previous work by proposing a novel way to incorporate visibility constraints and camera-to-camera relationships. For example, the placement solution can be encouraged to have cameras that image the same important locations from different viewing directions, which can enable reconstruction and surveillance tasks to perform better. We show that the general camera placement problem can be formulated mathematically as a convex binary quadratic program (BQP) under linear constraints. Moreover, we propose an optimization strategy with a favorable trade-off between speed and solution quality. Our solution is almost as fast as a greedy treatment of the problem, but the quality is significantly higher, so much so that it is comparable to exact solutions that take orders of magnitude more computation time. Because it is computationally attractive, our method also allows users to explore the space of solutions for variations in input parameters. To evaluate its effectiveness, we show a range of 3D results on real-world floorplans (garage, hotel, mall, and airport).
Directory of Open Access Journals (Sweden)
Minnis AM
2015-05-01
Full Text Available Alexandra M Minnis,1,2 Irene A Doherty,1,3 Tracy L Kline,1 William A Zule,1 Bronwyn Myers,4,5 Tara Carney,4 Wendee M Wechsberg1,3,6,7 1RTI International, Research Triangle Park, NC, 2School of Public Health, University of California, Berkeley, CA, 3University of North Carolina, Chapel Hill, NC, USA; 4Alcohol, Tobacco and Other Drug Research Unit, South African Medical Research Council, 5Department of Psychiatry and Mental Health, University of Cape Town, Cape Town, South Africa; 6North Carolina State University, Raleigh, 7Duke University School of Medicine, Durham, NC, USA Background: Inequitable gender-based power in relationships and intimate partner violence contribute to persistently high rates of HIV infection among South African women. We examined the effects of two group-based HIV prevention interventions that engaged men and their female partners together in a couples intervention (Couples Health CoOp [CHC] and a gender-separate intervention (Men’s Health CoOp/Women’s Health CoOp [MHC/WHC] on women’s reports of power, communication, and conflict in relationships. Methods: The cluster-randomized field experiment included heterosexual couples from a high-density South African township in which neighborhoods were randomized to one of the intervention arms or a control arm that received the WHC only. Participants completed in-person study visits at baseline and 6-month follow-up. We examined group differences using one-way analysis of variance and multivariable regression models.Results: Of the 290 couples enrolled, 255 women remained in the same partnership over 6 months. Following the intervention, women in the CHC arm compared with those in the WHC arm were more likely to report an increase in relationship control (ß=0.92, 95% confidence interval [CI]: 0.02, 1.83, P=0.045 and gender norms supporting female autonomy in relationships (ß=0.99, 95% CI: 0.07, 1.91, P=0.035. Women in the MHC/WHC arm were more likely to report increases
Datta, Dipayan; Kossmann, Simone; Neese, Frank
2016-09-01
The domain-based local pair-natural orbital coupled-cluster (DLPNO-CC) theory has recently emerged as an efficient and powerful quantum-chemical method for the calculation of energies of molecules comprised of several hundred atoms. It has been demonstrated that the DLPNO-CC approach attains the accuracy of a standard canonical coupled-cluster calculation to about 99.9% of the basis set correlation energy while realizing linear scaling of the computational cost with respect to system size. This is achieved by combining (a) localized occupied orbitals, (b) large virtual orbital correlation domains spanned by the projected atomic orbitals (PAOs), and (c) compaction of the virtual space through a truncated pair natural orbital (PNO) basis. In this paper, we report on the implementation of an analytic scheme for the calculation of the first derivatives of the DLPNO-CC energy for basis set independent perturbations within the singles and doubles approximation (DLPNO-CCSD) for closed-shell molecules. Perturbation-independent one-particle density matrices have been implemented in order to account for the response of the CC wave function to the external perturbation. Orbital-relaxation effects due to external perturbation are not taken into account in the current implementation. We investigate in detail the dependence of the computed first-order electrical properties (e.g., dipole moment) on the three major truncation parameters used in a DLPNO-CC calculation, namely, the natural orbital occupation number cutoff used for the construction of the PNOs, the weak electron-pair cutoff, and the domain size cutoff. No additional truncation parameter has been introduced for property calculation. We present benchmark calculations on dipole moments for a set of 10 molecules consisting of 20-40 atoms. We demonstrate that 98%-99% accuracy relative to the canonical CCSD results can be consistently achieved in these calculations. However, this comes with the price of tightening the
Chen, Zhenhua; Hoffmann, Mark R
2012-07-07
A unitary wave operator, exp (G), G(+) = -G, is considered to transform a multiconfigurational reference wave function Φ to the potentially exact, within basis set limit, wave function Ψ = exp (G)Φ. To obtain a useful approximation, the Hausdorff expansion of the similarity transformed effective Hamiltonian, exp (-G)Hexp (G), is truncated at second order and the excitation manifold is limited; an additional separate perturbation approximation can also be made. In the perturbation approximation, which we refer to as multireference unitary second-order perturbation theory (MRUPT2), the Hamiltonian operator in the highest order commutator is approximated by a Mo̸ller-Plesset-type one-body zero-order Hamiltonian. If a complete active space self-consistent field wave function is used as reference, then the energy is invariant under orbital rotations within the inactive, active, and virtual orbital subspaces for both the second-order unitary coupled cluster method and its perturbative approximation. Furthermore, the redundancies of the excitation operators are addressed in a novel way, which is potentially more efficient compared to the usual full diagonalization of the metric of the excited configurations. Despite the loss of rigorous size-extensivity possibly due to the use of a variational approach rather than a projective one in the solution of the amplitudes, test calculations show that the size-extensivity errors are very small. Compared to other internally contracted multireference perturbation theories, MRUPT2 only needs reduced density matrices up to three-body even with a non-complete active space reference wave function when two-body excitations within the active orbital subspace are involved in the wave operator, exp (G). Both the coupled cluster and perturbation theory variants are amenable to large, incomplete model spaces. Applications to some widely studied model systems that can be problematic because of geometry dependent quasidegeneracy, H4, P4
A revisit to quadratic programming with fuzzy parameters
International Nuclear Information System (INIS)
Liu, S.-T.
2009-01-01
Quadratic programming has been widely applied to solving real-world problems. Recently, Liu describes a solution method for solving a class of fuzzy quadratic programming problems, where the cost coefficients of the linear terms in objective function, constraint coefficients, and right-hand sides are fuzzy numbers [Liu ST. Quadratic programming with fuzzy parameters: a membership function approach. Chaos, Solitons and Fractals 2009;40:237-45]. In this paper, we generalize Liu's method to a more general fuzzy quadratic programming problem, where the cost coefficients in objective function, constraint coefficients, and right-hand sides are all fuzzy numbers. A pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. With the ability of calculating the fuzzy objective value developed in this paper, it might help initiate wider applications.
Algorithms for sparse, symmetric, definite quadratic lambda-matrix eigenproblems
International Nuclear Information System (INIS)
Scott, D.S.; Ward, R.C.
1981-01-01
Methods are presented for computing eigenpairs of the quadratic lambda-matrix, M lambda 2 + C lambda + K, where M, C, and K are large and sparse, and have special symmetry-type properties. These properties are sufficient to insure that all the eigenvalues are real and that theory analogous to the standard symmetric eigenproblem exists. The methods employ some standard techniques such as partial tri-diagonalization via the Lanczos Method and subsequent eigenpair calculation, shift-and- invert strategy and subspace iteration. The methods also employ some new techniques such as Rayleigh-Ritz quadratic roots and the inertia of symmetric, definite, quadratic lambda-matrices
International Nuclear Information System (INIS)
Hirata, So
2003-01-01
We develop a symbolic manipulation program and program generator (Tensor Contraction Engine or TCE) that automatically derives the working equations of a well-defined model of second-quantized many-electron theories and synthesizes efficient parallel computer programs on the basis of these equations. Provided an ansatz of a many-electron theory model, TCE performs valid contractions of creation and annihilation operators according to Wick's theorem, consolidates identical terms, and reduces the expressions into the form of multiple tensor contractions acted by permutation operators. Subsequently, it determines the binary contraction order for each multiple tensor contraction with the minimal operation and memory cost, factorizes common binary contractions (defines intermediate tensors), and identifies reusable intermediates. The resulting ordered list of binary tensor contractions, additions, and index permutations is translated into an optimized program that is combined with the NWChem and UTChem computational chemistry software packages. The programs synthesized by TCE take advantage of spin symmetry, Abelian point-group symmetry, and index permutation symmetry at every stage of calculations to minimize the number of arithmetic operations and storage requirement, adjust the peak local memory usage by index range tiling, and support parallel I/O interfaces and dynamic load balancing for parallel executions. We demonstrate the utility of TCE through automatic derivation and implementation of parallel programs for various models of configuration-interaction theory (CISD, CISDT, CISDTQ), many-body perturbation theory[MBPT(2), MBPT(3), MBPT(4)], and coupled-cluster theory (LCCD, CCD, LCCSD, CCSD, QCISD, CCSDT, and CCSDTQ)
Minenkov, Yury; Bistoni, Giovanni; Riplinger, Christoph; Auer, Alexander A; Neese, Frank; Cavallo, Luigi
2017-04-05
In this work, we tested canonical and domain based pair natural orbital coupled cluster methods (CCSD(T) and DLPNO-CCSD(T), respectively) for a set of 32 ligand exchange and association/dissociation reaction enthalpies involving ionic complexes of Li, Be, Na, Mg, Ca, Sr, Ba and Pb(ii). Two strategies were investigated: in the former, only valence electrons were included in the correlation treatment, giving rise to the computationally very efficient FC (frozen core) approach; in the latter, all non-ECP electrons were included in the correlation treatment, giving rise to the AE (all electron) approach. Apart from reactions involving Li and Be, the FC approach resulted in non-homogeneous performance. The FC approach leads to very small errors (correlation effects. These large errors are reduced to a few kcal mol -1 if the AE approach is used or the sub-valence orbitals of metals are included in the correlation treatment. On the technical side, the CCSD(T) and DLPNO-CCSD(T) results differ by a fraction of kcal mol -1 , indicating the latter method as the perfect choice when the CPU efficiency is essential. For completely black-box applications, as requested in catalysis or thermochemical calculations, we recommend the DLPNO-CCSD(T) method with all electrons that are not covered by effective core potentials included in the correlation treatment and correlation-consistent polarized core valence basis sets of cc-pwCVQZ(-PP) quality.
International Nuclear Information System (INIS)
Bishop, Raymond F; Krueger, Sven E
2003-01-01
The coupled cluster method (CCM) of microscopic quantum many-body theory has become an ab initio method of first choice in quantum chemistry and many fields of nuclear, subnuclear and condensed matter physics, when results of high accuracy are required. In recent years it has begun to be applied with equal success to strongly correlated systems of electrons or quantum spins defined on a regular spatial lattice. One regularly finds that the CCM is able to describe accurately the various zero-temperature phases and the quantum phase transitions between them, even when frustration is present and other methods such as quantum Monte Carlo often fail. We illustrate the use and powerfulness of the method here by applying it to a square-lattice spin-half Heisenberg model where frustration is introduced by competing nearest neighbour bonds. The model exhibits the physically interesting phenomenon of competition between magnetic order and dimerization. Results obtained for the model with the CCM are compared with those found from spin-wave theory and from extrapolating the results of exact diagonalizations of small lattices. We show that the CCM is essentially unique among available methods in being able both to describe accurately all phases of this complex model and to provide accurate predictions of the various phase boundaries and the order of the corresponding transitions
Garza, Alejandro J.; Bulik, Ireneusz W.; Alencar, Ana G. Sousa; Sun, Jianwei; Perdew, John P.; Scuseria, Gustavo E.
2016-04-01
Contrary to standard coupled cluster doubles (CCD) and Brueckner doubles (BD), singlet-paired analogues of CCD and BD (denoted here as CCD0 and BD0) do not break down when static correlation is present, but neglect substantial amounts of dynamic correlation. In fact, CCD0 and BD0 do not account for any contributions from multielectron excitations involving only same-spin electrons at all. We exploit this feature to add - without introducing double counting, self-interaction, or increase in cost - the missing correlation to these methods via meta-GGA (generalised gradient approximation) density functionals (Tao-Perdew-Staroverov-Scuseria and strongly constrained and appropriately normed). Furthermore, we improve upon these CCD0+DFT blends by invoking range separation: the short- and long-range correlations absent in CCD0/BD0 are evaluated with density functional theory and the direct random phase approximation, respectively. This corrects the description of long-range van der Waals forces. Comprehensive benchmarking shows that the combinations presented here are very accurate for weakly correlated systems, while also providing a reasonable description of strongly correlated problems without resorting to symmetry breaking.
Jagau, Thomas-C.
2018-01-01
The impact of residual electron correlation beyond the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) approximation on positions and widths of electronic resonances is investigated. To establish a method that accomplishes this task in an economical manner, several approaches proposed for the approximate treatment of triple excitations are reviewed with respect to their performance in the electron attachment (EA) variant of EOM-CC theory. The recently introduced EOM-CCSD(T)(a)* method [D. A. Matthews and J. F. Stanton, J. Chem. Phys. 145, 124102 (2016)], which includes non-iterative corrections to the reference and the target states, reliably reproduces vertical attachment energies from EOM-EA-CC calculations with single, double, and full triple excitations in contrast to schemes in which non-iterative corrections are applied only to the target states. Applications of EOM-EA-CCSD(T)(a)* augmented by a complex absorbing potential (CAP) to several temporary anions illustrate that shape resonances are well described by EOM-EA-CCSD, but that residual electron correlation often makes a non-negligible impact on their positions and widths. The positions of Feshbach resonances, on the other hand, are significantly improved when going from CAP-EOM-EA-CCSD to CAP-EOM-EA-CCSD(T)(a)*, but the correct energetic order of the relevant electronic states is still not achieved.
Lutz, Jesse J.; Duan, Xiaofeng F.; Burggraf, Larry W.
2018-03-01
Valence excitation spectra are computed for deep-center silicon-vacancy defects in 3C, 4H, and 6H silicon carbide (SiC), and comparisons are made with literature photoluminescence measurements. Optimizations of nuclear geometries surrounding the defect centers are performed within a Gaussian basis-set framework using many-body perturbation theory or density functional theory (DFT) methods, with computational expenses minimized by a QM/MM technique called SIMOMM. Vertical excitation energies are subsequently obtained by applying excitation-energy, electron-attached, and ionized equation-of-motion coupled-cluster (EOMCC) methods, where appropriate, as well as time-dependent (TD) DFT, to small models including only a few atoms adjacent to the defect center. We consider the relative quality of various EOMCC and TD-DFT methods for (i) energy-ordering potential ground states differing incrementally in charge and multiplicity, (ii) accurately reproducing experimentally measured photoluminescence peaks, and (iii) energy-ordering defects of different types occurring within a given polytype. The extensibility of this approach to transition-metal defects is also tested by applying it to silicon-substituted chromium defects in SiC and comparing with measurements. It is demonstrated that, when used in conjunction with SIMOMM-optimized geometries, EOMCC-based methods can provide a reliable prediction of the ground-state charge and multiplicity, while also giving a quantitative description of the photoluminescence spectra, accurate to within 0.1 eV of measurement for all cases considered.
Wang, Ying; Qian, Hu-Jun; Morokuma, Keiji; Irle, Stephan
2012-07-05
Ab initio coupled cluster and density functional theory studies of atomic hydrogen addition to the central region of pyrene and coronene as molecular models for graphene hydrogenation were performed. Fully relaxed potential energy curves (PECs) were computed at the spin-unrestricted B3LYP/cc-pVDZ level of theory for the atomic hydrogen attack of a center carbon atom (site A), the midpoint of a neighboring carbon bond (site B), and the center of a central hexagon (site C). Using the B3LYP/cc-pVDZ PEC geometries, we evaluated energies at the PBE density functional, as well as ab initio restricted open-shell ROMP2, ROCCSD, and ROCCSD(T) levels of theory, employing cc-pVDZ and cc-pVTZ basis sets, and performed a G2MS extrapolation to the ROCCSD(T)/cc-pVTZ level of theory. In agreement with earlier studies, we find that only site A attack leads to chemisorption. The G2MS entrance channel barrier heights, binding energies, and PEC profiles are found to agree well with a recent ab initio multireference wave function theory study (Bonfanti et al. J. Chem. Phys.2011, 135, 164701), indicating that single-reference open-shell methods including B3LYP are sufficient for the theoretical treatment of the interaction of graphene with a single hydrogen atom.
Energy Technology Data Exchange (ETDEWEB)
Chen, Jun; Sun, Zhigang, E-mail: zsun@dicp.ac.cn, E-mail: zhangdh@dicp.ac.cn; Zhang, Dong H., E-mail: zsun@dicp.ac.cn, E-mail: zhangdh@dicp.ac.cn [State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023 (China)
2015-01-14
A three dimensional potential energy surface for the F + H{sub 2} → HF + H reaction has been computed by the spin unrestricted coupled cluster method with singles, doubles, triples, and perturbative quadruples [UCCSDT(2){sub Q}] using the augmented correlation-consistent polarised valence quadruple zeta basis set for the fluorine atom and the correlation-consistent polarised valence quadruple zeta basis set for the hydrogen atom. All the calculations are based on the restricted open-shell Hartree-Fock orbitals, together with the frozen core approximations, and the UCCSD(T)/complete basis set (CBS) correction term was included. The global potential energy surface was calculated by fitting the sampled ab initio points without any scaling factor for the correlation energy part using a neutral network function method. Extensive dynamics calculations have been carried out on the potential energy surface. The reaction rate constants, integral cross sections, product rotational states distribution, and forward and backward scattering as a function of collision energy of the F + HD → HF + D, F + HD → DF + H, and F + H{sub 2} reaction, were calculated by the time-independent quantum dynamics scattering theory using the new surface. The satisfactory agreement with the reported experimental observations previously demonstrates the accuracy of the new potential energy surface.
Nascimento, Daniel R; DePrince, A Eugene
2017-07-06
An explicitly time-dependent (TD) approach to equation-of-motion (EOM) coupled-cluster theory with single and double excitations (CCSD) is implemented for simulating near-edge X-ray absorption fine structure in molecular systems. The TD-EOM-CCSD absorption line shape function is given by the Fourier transform of the CCSD dipole autocorrelation function. We represent this transform by its Padé approximant, which provides converged spectra in much shorter simulation times than are required by the Fourier form. The result is a powerful framework for the blackbox simulation of broadband absorption spectra. K-edge X-ray absorption spectra for carbon, nitrogen, and oxygen in several small molecules are obtained from the real part of the absorption line shape function and are compared with experiment. The computed and experimentally obtained spectra are in good agreement; the mean unsigned error in the predicted peak positions is only 1.2 eV. We also explore the spectral signatures of protonation in these molecules.
Clustering of near clusters versus cluster compactness
International Nuclear Information System (INIS)
Yu Gao; Yipeng Jing
1989-01-01
The clustering properties of near Zwicky clusters are studied by using the two-point angular correlation function. The angular correlation functions for compact and medium compact clusters, for open clusters, and for all near Zwicky clusters are estimated. The results show much stronger clustering for compact and medium compact clusters than for open clusters, and that open clusters have nearly the same clustering strength as galaxies. A detailed study of the compactness-dependence of correlation function strength is worth investigating. (author)
Integrable Hamiltonian systems and interactions through quadratic constraints
International Nuclear Information System (INIS)
Pohlmeyer, K.
1975-08-01
Osub(n)-invariant classical relativistic field theories in one time and one space dimension with interactions that are entirely due to quadratic constraints are shown to be closely related to integrable Hamiltonian systems. (orig.) [de
A perturbative solution for gravitational waves in quadratic gravity
International Nuclear Information System (INIS)
Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de
2003-01-01
We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin
Accurate nonlocal theory for cascaded quadratic soliton compression
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Moses, Jeffrey
2007-01-01
We study soliton compression in bulk quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....
Resolving Actuator Redundancy - Control Allocation vs. Linear Quadratic Control
Härkegård, Ola
2004-01-01
When designing control laws for systems with more inputs than controlled variables, one issue to consider is how to deal with actuator redundancy. Two tools for distributing the control effort among a redundant set of actuators are control allocation and linear quadratic control design. In this paper, we investigate the relationship between these two design tools when a quadratic performance index is used for control allocation. We show that for a particular class of linear systems, they give...
Quadratic measurement and conditional state preparation in an optomechanical system
DEFF Research Database (Denmark)
A. Brawley, George; Vanner, Michael A.; Bowen, Warwick P.
2014-01-01
We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator.......We experimentally demonstrate, for the first time, quadratic measurement of mechanical motion in an optomechanical system. We use this nonlinear easurement to conditionally prepare classical non-Gaussian states of motion of a micro-mechanical oscillator....
Scale-Invariant Rotating Black Holes in Quadratic Gravity
Directory of Open Access Journals (Sweden)
Guido Cognola
2015-07-01
Full Text Available Black hole solutions in pure quadratic theories of gravity are interesting since they allow the formulation of a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.
A Trust-region-based Sequential Quadratic Programming Algorithm
DEFF Research Database (Denmark)
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints.......This technical note documents the trust-region-based sequential quadratic programming algorithm used in other works by the authors. The algorithm seeks to minimize a convex nonlinear cost function subject to linear inequalty constraints and nonlinear equality constraints....
Staff turnover in hotels : exploring the quadratic and linear relationships.
Mohsin, A.; Lengler, J.F.B.; Aguzzoli, R.L.
2015-01-01
The aim of this study is to assess whether the relationship between intention to leave the job and its antecedents is quadratic or linear. To explore those relationships a theoretical model (see Fig. 1) and eight hypotheses are proposed. Each linear hypothesis is followed by an alternative quadratic hypothesis. The alternative hypotheses propose that the relationship between the four antecedent constructs and intention to leave the job might not be linear, as the existing literature suggests....
On wave-packet dynamics in a decaying quadratic potential
DEFF Research Database (Denmark)
Møller, Klaus Braagaard; Henriksen, Niels Engholm
1997-01-01
We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics.......We consider the time-dependent Schrodinger equation for a quadratic potential with an exponentially decaying force constant. General analytical solutions are presented and we highlight in particular, the signatures of classical mechanics in the wave packet dynamics....
The stability of quadratic-reciprocal functional equation
Song, Aimin; Song, Minwei
2018-04-01
A new quadratic-reciprocal functional equation f ((k +1 )x +k y )+f ((k +1 )x -k y )=2/f (x )f (y )[(k+1 ) 2f (y )+k2f (x )] [(k+1)2f (y )-k2f (x )] 2 is introduced. The Hyers-Ulam stability for the quadratic-reciprocal functional equations is proved in Banach spaces using the direct method and the fixed point method, respectively.
Burgers' turbulence problem with linear or quadratic external potential
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole Eiler; Leonenko, N.N.
2005-01-01
We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions.......We consider solutions of Burgers' equation with linear or quadratic external potential and stationary random initial conditions of Ornstein-Uhlenbeck type. We study a class of limit laws that correspond to a scale renormalization of the solutions....
Sen, Sangita; Shee, Avijit; Mukherjee, Debashis
2018-02-01
The orbital relaxation attendant on ionization is particularly important for the core electron ionization potential (core IP) of molecules. The Unitary Group Adapted State Universal Coupled Cluster (UGA-SUMRCC) theory, recently formulated and implemented by Sen et al. [J. Chem. Phys. 137, 074104 (2012)], is very effective in capturing orbital relaxation accompanying ionization or excitation of both the core and the valence electrons [S. Sen et al., Mol. Phys. 111, 2625 (2013); A. Shee et al., J. Chem. Theory Comput. 9, 2573 (2013)] while preserving the spin-symmetry of the target states and using the neutral closed-shell spatial orbitals of the ground state. Our Ansatz invokes a normal-ordered exponential representation of spin-free cluster-operators. The orbital relaxation induced by a specific set of cluster operators in our Ansatz is good enough to eliminate the need for different sets of orbitals for the ground and the core-ionized states. We call the single configuration state function (CSF) limit of this theory the Unitary Group Adapted Open-Shell Coupled Cluster (UGA-OSCC) theory. The aim of this paper is to comprehensively explore the efficacy of our Ansatz to describe orbital relaxation, using both theoretical analysis and numerical performance. Whenever warranted, we also make appropriate comparisons with other coupled-cluster theories. A physically motivated truncation of the chains of spin-free T-operators is also made possible by the normal-ordering, and the operational resemblance to single reference coupled-cluster theory allows easy implementation. Our test case is the prediction of the 1s core IP of molecules containing a single light- to medium-heavy nucleus and thus, in addition to demonstrating the orbital relaxation, we have addressed the scalar relativistic effects on the accuracy of the IPs by using a hierarchy of spin-free Hamiltonians in conjunction with our theory. Additionally, the contribution of the spin-free component of the two
Sen, Sangita; Shee, Avijit; Mukherjee, Debashis
2018-02-07
The orbital relaxation attendant on ionization is particularly important for the core electron ionization potential (core IP) of molecules. The Unitary Group Adapted State Universal Coupled Cluster (UGA-SUMRCC) theory, recently formulated and implemented by Sen et al. [J. Chem. Phys. 137, 074104 (2012)], is very effective in capturing orbital relaxation accompanying ionization or excitation of both the core and the valence electrons [S. Sen et al., Mol. Phys. 111, 2625 (2013); A. Shee et al., J. Chem. Theory Comput. 9, 2573 (2013)] while preserving the spin-symmetry of the target states and using the neutral closed-shell spatial orbitals of the ground state. Our Ansatz invokes a normal-ordered exponential representation of spin-free cluster-operators. The orbital relaxation induced by a specific set of cluster operators in our Ansatz is good enough to eliminate the need for different sets of orbitals for the ground and the core-ionized states. We call the single configuration state function (CSF) limit of this theory the Unitary Group Adapted Open-Shell Coupled Cluster (UGA-OSCC) theory. The aim of this paper is to comprehensively explore the efficacy of our Ansatz to describe orbital relaxation, using both theoretical analysis and numerical performance. Whenever warranted, we also make appropriate comparisons with other coupled-cluster theories. A physically motivated truncation of the chains of spin-free T-operators is also made possible by the normal-ordering, and the operational resemblance to single reference coupled-cluster theory allows easy implementation. Our test case is the prediction of the 1s core IP of molecules containing a single light- to medium-heavy nucleus and thus, in addition to demonstrating the orbital relaxation, we have addressed the scalar relativistic effects on the accuracy of the IPs by using a hierarchy of spin-free Hamiltonians in conjunction with our theory. Additionally, the contribution of the spin-free component of the two
Quadratic programming with fuzzy parameters: A membership function approach
International Nuclear Information System (INIS)
Liu, S.-T.
2009-01-01
Quadratic programming has been widely applied to solving real world problems. The conventional quadratic programming model requires the parameters to be known constants. In the real world, however, the parameters are seldom known exactly and have to be estimated. This paper discusses the fuzzy quadratic programming problems where the cost coefficients, constraint coefficients, and right-hand sides are represented by convex fuzzy numbers. Since the parameters in the program are fuzzy numbers, the derived objective value is a fuzzy number as well. Using Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the upper bound and lower bound of the objective values of the fuzzy quadratic program. Based on the duality theorem and by applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a family of conventional one-level quadratic programs. Solving the pair of quadratic programs produces the fuzzy objective values of the problem. An example illustrates method proposed in this paper.
Two healing lengths in a two-band GL-model with quadratic terms: Numerical results
Macias-Medri, A. E.; Rodríguez-Núñez, J. J.
2018-05-01
A two-band and quartic interaction order Ginzburg-Landau model in the presence of a single vortex is studied in this work. Interactions of second (quadratic, with coupling parameter γ) and fourth (quartic, with coupling parameter γ˜) order between the two superconducting order parameters (fi with i = 1,2) are incorporated in a functional. Terms beyond quadratic gradient contributions are neglected in the corresponding minimized free energy. The solution of the system of coupled equations is solved by numerical methods to obtain the fi-profiles, where our starting point was the calculation of the superconducting critical temperature Tc. With this at hand, we evaluate fi and the magnetic field along the z-axis, B0, as function of γ, γ˜, the radial distance r/λ1(0) and the temperature T, for T ≈ Tc. The self-consistent equations allow us to compute λ (penetration depth) and the healing lengths of fi (Lhi with i = 1,2) as functions of T, γ and γ˜. At the end, relevant discussions about type-1.5 superconductivity in the compounds we have studied are presented.
Directory of Open Access Journals (Sweden)
Cari Jo Clark
2017-01-01
Full Text Available Abstract Background Intimate partner violence (IPV is a significant public health issue that affects 1 in 3 women globally and a similarly large number of women in Nepal. Over the past decade, important policy and programmatic steps have been taken to address violence against women in Nepal. There remains a dearth of evidence on the effectiveness of primary violence prevention strategies. The Change Starts at Home study begins to fill this gap by utilizing a multi-component social behaviour change communication (SBCC strategy involving a radio drama and community mobilization to shift attitudes, norms and behaviours that underpin IPV perpetration in Nepal. Methods/Design The study uses a concurrent mixed-methods design. The quantitative aspect of the evaluation is a pair-matched, repeated cross-sectional 2-armed, single-blinded cluster trial (RCT: N = 36 clusters, 1440 individuals, comparing a social behaviour change communication (SBCC strategy to radio programming alone for its impact on physical and / or sexual IPV at the end of programming (12 months’ post-baseline and 6-months post the cessation of project activities (18-months post baseline. The qualitative aspects of the design include several longitudinal approaches to understand the impact of the intervention and to examine mechanisms of change including in-depth interviews with participants (N = 18 couples, and focus group discussions with community leaders (N = 3 groups, and family members of participants (N = 12 groups. Treatment effects will be estimated with generalized logistic mixed models specified to compare differences in primary outcome from baseline to 12-month follow-up, and baseline to 18-months follow-up in accordance with intention-to-treat principles. Discussion The study rigorously evaluates the effectiveness of a promising strategy to prevent IPV. The results of the trial will be immediately useful for governmental, nongovernmental, and donor funded
Stationary solutions and self-trapping in discrete quadratic nonlinear systems
DEFF Research Database (Denmark)
Bang, Ole; Christiansen, Peter Leth; Clausen, Carl A. Balslev
1998-01-01
We consider the simplest equations describing coupled quadratic nonlinear (chi((2))) systems, which each consists of a fundamental mode resonantly interacting with its second harmonic. Such discrete equations apply, e.g., to optics, where they can describe arrays of chi((2)) waveguides...... the nonintegrable dimer reduce to the discrete nonlinear Schrodinger (DNLS) equation with two degrees of freedom, which is integrable. We show how the stationary solutions to the two systems correspond to each other and how the self-trapped DNLS solutions gradually develop chaotic dynamics in the chi((2)) system...
Minenkov, Yury
2017-03-07
In this work, we tested canonical and domain based pair natural orbital coupled cluster methods (CCSD(T) and DLPNO-CCSD(T), respectively) for a set of 32 ligand exchange and association/dissociation reaction enthalpies involving ionic complexes of Li, Be, Na, Mg, Ca, Sr, Ba and Pb(ii). Two strategies were investigated: in the former, only valence electrons were included in the correlation treatment, giving rise to the computationally very efficient FC (frozen core) approach; in the latter, all non-ECP electrons were included in the correlation treatment, giving rise to the AE (all electron) approach. Apart from reactions involving Li and Be, the FC approach resulted in non-homogeneous performance. The FC approach leads to very small errors (<2 kcal mol-1) for some reactions of Na, Mg, Ca, Sr, Ba and Pb, while for a few reactions of Ca and Ba deviations up to 40 kcal mol-1 have been obtained. Large errors are both due to artificial mixing of the core (sub-valence) orbitals of metals and the valence orbitals of oxygen and halogens in the molecular orbitals treated as core, and due to neglecting core-core and core-valence correlation effects. These large errors are reduced to a few kcal mol-1 if the AE approach is used or the sub-valence orbitals of metals are included in the correlation treatment. On the technical side, the CCSD(T) and DLPNO-CCSD(T) results differ by a fraction of kcal mol-1, indicating the latter method as the perfect choice when the CPU efficiency is essential. For completely black-box applications, as requested in catalysis or thermochemical calculations, we recommend the DLPNO-CCSD(T) method with all electrons that are not covered by effective core potentials included in the correlation treatment and correlation-consistent polarized core valence basis sets of cc-pwCVQZ(-PP) quality.
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.
Guo, Yang
2018-01-04
In this communication, an improved perturbative triples correction (T) algorithm for domain based local pair-natural orbital singles and doubles coupled cluster (DLPNO-CCSD) theory is reported. In our previous implementation, the semi-canonical approximation was used and linear scaling was achieved for both the DLPNO-CCSD and (T) parts of the calculation. In this work, we refer to this previous method as DLPNO-CCSD(T0) to emphasize the semi-canonical approximation. It is well-established that the DLPNO-CCSD method can predict very accurate absolute and relative energies with respect to the parent canonical CCSD method. However, the (T0) approximation may introduce significant errors in absolute energies as the triples correction grows up in magnitude. In the majority of cases, the relative energies from (T0) are as accurate as the canonical (T) results of themselves. Unfortunately, in rare cases and in particular for small gap systems, the (T0) approximation breaks down and relative energies show large deviations from the parent canonical CCSD(T) results. To address this problem, an iterative (T) algorithm based on the previous DLPNO-CCSD(T0) algorithm has been implemented [abbreviated here as DLPNO-CCSD(T)]. Using triples natural orbitals to represent the virtual spaces for triples amplitudes, storage bottlenecks are avoided. Various carefully designed approximations ease the computational burden such that overall, the increase in the DLPNO-(T) calculation time over DLPNO-(T0) only amounts to a factor of about two (depending on the basis set). Benchmark calculations for the GMTKN30 database show that compared to DLPNO-CCSD(T0), the errors in absolute energies are greatly reduced and relative energies are moderately improved. The particularly problematic case of cumulene chains of increasing lengths is also successfully addressed by DLPNO-CCSD(T).
Guo, Yang; Riplinger, Christoph; Becker, Ute; Liakos, Dimitrios G.; Minenkov, Yury; Cavallo, Luigi; Neese, Frank
2018-01-01
In this communication, an improved perturbative triples correction (T) algorithm for domain based local pair-natural orbital singles and doubles coupled cluster (DLPNO-CCSD) theory is reported. In our previous implementation, the semi-canonical approximation was used and linear scaling was achieved for both the DLPNO-CCSD and (T) parts of the calculation. In this work, we refer to this previous method as DLPNO-CCSD(T0) to emphasize the semi-canonical approximation. It is well-established that the DLPNO-CCSD method can predict very accurate absolute and relative energies with respect to the parent canonical CCSD method. However, the (T0) approximation may introduce significant errors in absolute energies as the triples correction grows up in magnitude. In the majority of cases, the relative energies from (T0) are as accurate as the canonical (T) results of themselves. Unfortunately, in rare cases and in particular for small gap systems, the (T0) approximation breaks down and relative energies show large deviations from the parent canonical CCSD(T) results. To address this problem, an iterative (T) algorithm based on the previous DLPNO-CCSD(T0) algorithm has been implemented [abbreviated here as DLPNO-CCSD(T)]. Using triples natural orbitals to represent the virtual spaces for triples amplitudes, storage bottlenecks are avoided. Various carefully designed approximations ease the computational burden such that overall, the increase in the DLPNO-(T) calculation time over DLPNO-(T0) only amounts to a factor of about two (depending on the basis set). Benchmark calculations for the GMTKN30 database show that compared to DLPNO-CCSD(T0), the errors in absolute energies are greatly reduced and relative energies are moderately improved. The particularly problematic case of cumulene chains of increasing lengths is also successfully addressed by DLPNO-CCSD(T).
Mondal, Bhaskar; Neese, Frank; Ye, Shengfa
2015-08-03
The development of efficient catalysts with base metals for CO2 hydrogenation has always been a major thrust of interest. A series of experimental and theoretical work has revealed that the catalytic cycle typically involves two key steps, namely, base-promoted heterolytic H2 splitting and hydride transfer to CO2, either of which can be the rate-determining step (RDS) of the entire reaction. To explore the determining factor for the nature of RDS, we present herein a comparative mechanistic investigation on CO2 hydrogenation mediated by [M(H)(η(2)-H2)(PP3(Ph))](n+) (M = Fe(II), Ru(II), and Co(III); PP3(Ph) = tris(2-(diphenylphosphino)phenyl)phosphine) type complexes. In order to construct reliable free energy profiles, we used highly correlated wave function based ab initio methods of the coupled cluster type alongside the standard density functional theory. Our calculations demonstrate that the hydricity of the metal-hydride intermediate generated by H2 splitting dictates the nature of the RDS for the Fe(II) and Co(III) systems, while the RDS for the Ru(II) catalyst appears to be ambiguous. CO2 hydrogenation catalyzed by the Fe(II) complex that possesses moderate hydricity traverses an H2-splitting RDS, whereas the RDS for the high-hydricity Co(III) species is found to be the hydride transfer. Thus, our findings suggest that hydricity can be used as a practical guide in future catalyst design. Enhancing the electron-accepting ability of low-hydricity catalysts is likely to improve their catalytic performance, while increasing the electron-donating ability of high-hydricity complexes may speed up CO2 conversion. Moreover, we also established the active roles of base NEt3 in directing the heterolytic H2 splitting and assisting product release through the formation of an acid-base complex.
International Nuclear Information System (INIS)
Bahar, M.K.; Yasuk, F.
2013-01-01
Approximate solutions of the Dirac equation with positron-dependent mass are presented for the inversely quadratic Yukawa potential and Coulomb-like tensor interaction by using the asymptotic iteration method. The energy eigenvalues and the corresponding normalized eigenfunctions are obtained in the case of positron-dependent mass and arbitrary spin-orbit quantum number k state and approximation on the spin-orbit coupling term. (author)
Comparison between linear quadratic and early time dose models
International Nuclear Information System (INIS)
Chougule, A.A.; Supe, S.J.
1993-01-01
During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs
Matter scattering in quadratic gravity and unitarity
Abe, Yugo; Inami, Takeo; Izumi, Keisuke; Kitamura, Tomotaka
2018-03-01
We investigate the ultraviolet (UV) behavior of two-scalar elastic scattering with graviton exchanges in higher-curvature gravity theory. In Einstein gravity, matter scattering is shown not to satisfy the unitarity bound at tree level at high energy. Among some of the possible directions for the UV completion of Einstein gravity, such as string theory, modified gravity, and inclusion of high-mass/high-spin states, we take R_{μν}^2 gravity coupled to matter. We show that matter scattering with graviton interactions satisfies the unitarity bound at high energy, even with negative norm states due to the higher-order derivatives of metric components. The difference in the unitarity property of these two gravity theories is probably connected to that in another UV property, namely, the renormalizability property of the two.
The quadratic reciprocity law a collection of classical proofs
Baumgart, Oswald
2015-01-01
This book is the English translation of Baumgart’s thesis on the early proofs of the quadratic reciprocity law (“Über das quadratische Reciprocitätsgesetz. Eine vergleichende Darstellung der Beweise”), first published in 1885. It is divided into two parts. The first part presents a very brief history of the development of number theory up to Legendre, as well as detailed descriptions of several early proofs of the quadratic reciprocity law. The second part highlights Baumgart’s comparisons of the principles behind these proofs. A current list of all known proofs of the quadratic reciprocity law, with complete references, is provided in the appendix. This book will appeal to all readers interested in elementary number theory and the history of number theory.
Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems
International Nuclear Information System (INIS)
Marquette, Ian
2011-01-01
There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.
The bounds of feasible space on constrained nonconvex quadratic programming
Zhu, Jinghao
2008-03-01
This paper presents a method to estimate the bounds of the radius of the feasible space for a class of constrained nonconvex quadratic programmingsE Results show that one may compute a bound of the radius of the feasible space by a linear programming which is known to be a P-problem [N. Karmarkar, A new polynomial-time algorithm for linear programming, Combinatorica 4 (1984) 373-395]. It is proposed that one applies this method for using the canonical dual transformation [D.Y. Gao, Canonical duality theory and solutions to constrained nonconvex quadratic programming, J. Global Optimization 29 (2004) 377-399] for solving a standard quadratic programming problem.
Symmetry breaking in two interacting populations of quadratic integrate-and-fire neurons
Ratas, Irmantas; Pyragas, Kestutis
2017-10-01
We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both inherently spiking and excitable neurons. The coupling within and between the populations is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neuron's firing rates and the mean membrane potentials in both populations. The reduced equations are exact in the infinite-size limit. The bifurcation analysis of the equations reveals a rich variety of nonsymmetric patterns, including a splay state, antiphase periodic oscillations, chimera-like states, and chaotic oscillations as well as bistabilities between various states. The validity of the reduced equations is confirmed by direct numerical simulations of the finite-size networks.
Cieluch, Ewelina; Pietryga, Krzysztof; Sarewicz, Marcin; Osyczka, Artur
2010-02-01
Cytochrome c(1) of Rhodobacter (Rba.) species provides a series of mutants which change barriers for electron transfer through the cofactor chains of cytochrome bc(1) by modifying heme c(1) redox midpoint potential. Analysis of post-flash electron distribution in such systems can provide useful information about the contribution of individual reactions to the overall electron flow. In Rba. capsulatus, the non-functional low-potential forms of cytochrome c(1) which are devoid of the disulfide bond naturally present in this protein revert spontaneously by introducing a second-site suppression (mutation A181T) that brings the potential of heme c(1) back to the functionally high levels, yet maintains it some 100 mV lower from the native value. Here we report that the disulfide and the mutation A181T can coexist in one protein but the mutation exerts a dominant effect on the redox properties of heme c(1) and the potential remains at the same lower value as in the disulfide-free form. This establishes effective means to modify a barrier for electron transfer between the FeS cluster and heme c(1) without breaking disulfide. A comparison of the flash-induced electron transfers in native and mutated cytochrome bc(1) revealed significant differences in the post-flash equilibrium distribution of electrons only when the connection of the chains with the quinone pool was interrupted at the level of either of the catalytic sites by the use of specific inhibitors, antimycin or myxothiazol. In the non-inhibited system no such differences were observed. We explain the results using a kinetic model in which a shift in the equilibrium of one reaction influences the equilibrium of all remaining reactions in the cofactor chains. It follows a rather simple description in which the direction of electron flow through the coupled chains of cytochrome bc(1) exclusively depends on the rates of all reversible partial reactions, including the Q/QH2 exchange rate to/from the catalytic sites
Vogt, Natalja; Marochkin, Ilya I; Rykov, Anatolii N
2018-04-18
The accurate molecular structure of picolinic acid has been determined from experimental data and computed at the coupled cluster level of theory. Only one conformer with the O[double bond, length as m-dash]C-C-N and H-O-C[double bond, length as m-dash]O fragments in antiperiplanar (ap) positions, ap-ap, has been detected under conditions of the gas-phase electron diffraction (GED) experiment (Tnozzle = 375(3) K). The semiexperimental equilibrium structure, rsee, of this conformer has been derived from the GED data taking into account the anharmonic vibrational effects estimated from the ab initio force field. The equilibrium structures of the two lowest-energy conformers, ap-ap and ap-sp (with the synperiplanar H-O-C[double bond, length as m-dash]O fragment), have been fully optimized at the CCSD(T)_ae level of theory in conjunction with the triple-ζ basis set (cc-pwCVTZ). The quality of the optimized structures has been improved due to extrapolation to the quadruple-ζ basis set. The high accuracy of both GED determination and CCSD(T) computations has been disclosed by a correct comparison of structures having the same physical meaning. The ap-ap conformer has been found to be stabilized by the relatively strong NH-O hydrogen bond of 1.973(27) Å (GED) and predicted to be lower in energy by 16 kJ mol-1 with respect to the ap-sp conformer without a hydrogen bond. The influence of this bond on the structure of picolinic acid has been analyzed within the Natural Bond Orbital model. The possibility of the decarboxylation of picolinic acid has been considered in the GED analysis, but no significant amounts of pyridine and carbon dioxide could be detected. To reveal the structural changes reflecting the mesomeric and inductive effects due to the carboxylic substituent, the accurate structure of pyridine has been also computed at the CCSD(T)_ae level with basis sets from triple- to 5-ζ quality. The comprehensive structure computations for pyridine as well as for
International Nuclear Information System (INIS)
Curtiss, L.A.; Raghavachari, K.; Pople, J.A.
1995-01-01
The performance of Gaussian-2 theory is investigated when higher level theoretical methods are included for correlation effects, geometries, and zero-point energies. A higher level of correlation treatment is examined using Brueckner doubles [BD(T)] and coupled cluster [CCSD(T)] methods rather than quadratic configuration interaction [QCISD(T)]. The use of geometries optimized at the QCISD level rather than the second-order Moller--Plesset level (MP2) and the use of scaled MP2 zero-point energies rather than scaled Hartree--Fock (HF) zero-point energies have also been examined. The set of 125 energies used for validation of G2 theory [J. Chem. Phys. 94, 7221 (1991)] is used to test out these variations of G2 theory. Inclusion of higher levels of correlation treatment has little effect except in the cases of multiply-bonded systems. In these cases better agreement is obtained in some cases and poorer agreement in others so that there is no improvement in overall performance. The use of QCISD geometries yields significantly better agreement with experiment for several cases including the ionization potentials of CS and O 2 , electron affinity of CN, and dissociation energies of N 2 , O 2 , CN, and SO 2 . This leads to a slightly better agreement with experiment overall. The MP2 zero-point energies gives no overall improvement. These methods may be useful for specific systems
Semi-Supervised Half-Quadratic Nonnegative Matrix Factorization for Face Recognition
Alghamdi, Masheal M.
2014-05-01
Face recognition is a challenging problem in computer vision. Difficulties such as slight differences between similar faces of different people, changes in facial expressions, light and illumination condition, and pose variations add extra complications to the face recognition research. Many algorithms are devoted to solving the face recognition problem, among which the family of nonnegative matrix factorization (NMF) algorithms has been widely used as a compact data representation method. Different versions of NMF have been proposed. Wang et al. proposed the graph-based semi-supervised nonnegative learning (S2N2L) algorithm that uses labeled data in constructing intrinsic and penalty graph to enforce separability of labeled data, which leads to a greater discriminating power. Moreover the geometrical structure of labeled and unlabeled data is preserved through using the smoothness assumption by creating a similarity graph that conserves the neighboring information for all labeled and unlabeled data. However, S2N2L is sensitive to light changes, illumination, and partial occlusion. In this thesis, we propose a Semi-Supervised Half-Quadratic NMF (SSHQNMF) algorithm that combines the benefits of S2N2L and the robust NMF by the half- quadratic minimization (HQNMF) algorithm.Our algorithm improves upon the S2N2L algorithm by replacing the Frobenius norm with a robust M-Estimator loss function. A multiplicative update solution for our SSHQNMF algorithmis driven using the half- 4 quadratic (HQ) theory. Extensive experiments on ORL, Yale-A and a subset of the PIE data sets for nine M-estimator loss functions for both SSHQNMF and HQNMF algorithms are investigated, and compared with several state-of-the-art supervised and unsupervised algorithms, along with the original S2N2L algorithm in the context of classification, clustering, and robustness against partial occlusion. The proposed algorithm outperformed the other algorithms. Furthermore, SSHQNMF with Maximum Correntropy
Remarks on second-order quadratic systems in algebras
Directory of Open Access Journals (Sweden)
Art Sagle
2017-10-01
Full Text Available This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.
Dhage Iteration Method for Generalized Quadratic Functional Integral Equations
Directory of Open Access Journals (Sweden)
Bapurao C. Dhage
2015-01-01
Full Text Available In this paper we prove the existence as well as approximations of the solutions for a certain nonlinear generalized quadratic functional integral equation. An algorithm for the solutions is developed and it is shown that the sequence of successive approximations starting at a lower or upper solution converges monotonically to the solutions of related quadratic functional integral equation under some suitable mixed hybrid conditions. We rely our main result on Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014 in partially ordered normed linear spaces. An example is also provided to illustrate the abstract theory developed in the paper.
Quantum tomography and classical propagator for quadratic quantum systems
International Nuclear Information System (INIS)
Man'ko, O.V.
1999-03-01
The classical propagator for tomographic probability (which describes the quantum state instead of wave function or density matrix) is presented for quadratic quantum systems and its relation to the quantum propagator is considered. The new formalism of quantum mechanics, based on the probability representation of the state, is applied to particular quadratic systems - the harmonic oscillator, particle's free motion, problems of an ion in a Paul trap and in asymmetric Penning trap, and to the process of stimulated Raman scattering. The classical propagator for these systems is written in an explicit form. (author)
New robust chaotic system with exponential quadratic term
International Nuclear Information System (INIS)
Bao Bocheng; Li Chunbiao; Liu Zhong; Xu Jianping
2008-01-01
This paper proposes a new robust chaotic system of three-dimensional quadratic autonomous ordinary differential equations by introducing an exponential quadratic term. This system can display a double-scroll chaotic attractor with only two equilibria, and can be found to be robust chaotic in a very wide parameter domain with positive maximum Lyapunov exponent. Some basic dynamical properties and chaotic behaviour of novel attractor are studied. By numerical simulation, this paper verifies that the three-dimensional system can also evolve into periodic and chaotic behaviours by a constant controller. (general)
Subgroups of class groups of algebraic quadratic function fields
International Nuclear Information System (INIS)
Wang Kunpeng; Zhang Xianke
2001-09-01
Ideal class groups H(K) of algebraic quadratic function fields K are studied, by using mainly the theory of continued fractions of algebraic functions. Properties of such continued fractions are discussed first. Then a necessary and sufficient condition is given for the class group H(K) to contain a cyclic subgroup of any order n, this criterion condition holds true for both real and imaginary fields K. Furthermore, several series of function fields K, including real, inertia imaginary, as well as ramified imaginary quadratic function fields, are given, and their class groups H(K) are proved to contain cyclic subgroups of order n. (author)
Smoothing optimization of supporting quadratic surfaces with Zernike polynomials
Zhang, Hang; Lu, Jiandong; Liu, Rui; Ma, Peifu
2018-03-01
A new optimization method to get a smooth freeform optical surface from an initial surface generated by the supporting quadratic method (SQM) is proposed. To smooth the initial surface, a 9-vertex system from the neighbor quadratic surface and the Zernike polynomials are employed to establish a linear equation system. A local optimized surface to the 9-vertex system can be build by solving the equations. Finally, a continuous smooth optimization surface is constructed by stitching the above algorithm on the whole initial surface. The spot corresponding to the optimized surface is no longer discrete pixels but a continuous distribution.
Decentralized linear quadratic power system stabilizers for multi ...
Indian Academy of Sciences (India)
Linear quadratic stabilizers are well-known for their superior control capabilities when compared to the conventional lead–lag power system stabilizers. However, they have not seen much of practical importance as the state variables are generally not measurable; especially the generator rotor angle measurement is not ...
Diagonalization of bosonic quadratic Hamiltonians by Bogoliubov transformations
DEFF Research Database (Denmark)
Nam, Phan Thanh; Napiorkowski, Marcin; Solovej, Jan Philip
2016-01-01
We provide general conditions for which bosonic quadratic Hamiltonians on Fock spaces can be diagonalized by Bogoliubov transformations. Our results cover the case when quantum systems have infinite degrees of freedom and the associated one-body kinetic and paring operators are unbounded. Our...
ON WEIGHTED GENERALIZED FUNCTIONS ASSOCIATED WITH QUADRATIC FORMS
Directory of Open Access Journals (Sweden)
E. L. Shishkina
2016-12-01
Full Text Available In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic equations with the Bessel operator and for constructing negative real powers of ultra-hyperbolic operators with the Bessel operator.
Feedback nash equilibria for linear quadratic descriptor differential games
Engwerda, J.C.; Salmah, S.
2012-01-01
In this paper, we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a
Initial post dynamic buckling of a quadratic-cubic column ...
African Journals Online (AJOL)
In this investigation, we determine the dynamic buckling load of an imperfect finite column resting on a mixed quadratic-cubic nonlinear elastic foundation trapped by an explicitly time dependent sinusoidally slowly varying dynamic load .The resultant coefficients are dynamically slowly varying and the formulation contains ...
Quadratic algebras in the noncommutative integration method of wave equation
International Nuclear Information System (INIS)
Varaksin, O.L.
1995-01-01
The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras
Propagator of a time-dependent unbound quadratic Hamiltonian system
International Nuclear Information System (INIS)
Yeon, K.H.; Kim, H.J.; Um, C.I.; George, T.F.; Pandey, L.N.
1996-01-01
The propagator for a time-dependent unbound quadratic Hamiltonian system is explicitly evaluated using the path integral method. Two time-invariant quantities of the system are found where these invariants determine whether or not the system is bound. Several examples are considered to illustrate that the propagator obtained for the unbound systems is correct
On Fredholm-Stieltjes quadratic integral equation with supremum
International Nuclear Information System (INIS)
Darwish, M.A.
2007-08-01
We prove an existence theorem of monotonic solutions for a quadratic integral equation of Fredholm-Stieltjes type in C[0,1]. The concept of measure of non-compactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof. (author)
Quadratic theory and feedback controllers for linear time delay systems
International Nuclear Information System (INIS)
Lee, E.B.
1976-01-01
Recent research on the design of controllers for systems having time delays is discussed. Results for the ''open loop'' and ''closed loop'' designs will be presented. In both cases results for minimizing a quadratic cost functional are given. The usefulness of these results is not known, but similar results for the non-delay case are being routinely applied. (author)
Pareto optimality in infinite horizon linear quadratic differential games
Reddy, P.V.; Engwerda, J.C.
2013-01-01
In this article we derive conditions for the existence of Pareto optimal solutions for linear quadratic infinite horizon cooperative differential games. First, we present a necessary and sufficient characterization for Pareto optimality which translates to solving a set of constrained optimal
Special cases of the quadratic shortest path problem
Sotirov, Renata; Hu, Hao
2017-01-01
The quadratic shortest path problem (QSPP) is the problem of finding a path with prespecified start vertex s and end vertex t in a digraph such that the sum of weights of arcs and the sum of interaction costs over all pairs of arcs on the path is minimized. We first consider a variant of the QSPP
Quadratic Poisson brackets compatible with an algebra structure
Balinsky, A. A.; Burman, Yu.
1994-01-01
Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among compatible brackets, a subclass of coboundary brackets is described, and such brackets are enumerated in a number of examples.
On misclassication probabilities of linear and quadratic classiers ...
African Journals Online (AJOL)
We study the theoretical misclassication probability of linear and quadratic classiers and examine the performance of these classiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift. Keywords: ...
Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games
Engwerda, J.C.; Salmah, Y.
2010-01-01
In this note we consider the non-cooperative linear feedback Nash quadratic differential game with an infinite planning horizon for descriptor systems of index one. The performance function is assumed to be indefinite. We derive both necessary and sufficient conditions under which this game has a
A Unified Approach to Teaching Quadratic and Cubic Equations.
Ward, A. J. B.
2003-01-01
Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)
Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions
Leyendekkers, J. V.; Shannon, A. G.
2004-01-01
An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.
Visualising the Complex Roots of Quadratic Equations with Real Coefficients
Bardell, Nicholas S.
2012-01-01
The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
Linear and quadratic in temperature resistivity from holography
Energy Technology Data Exchange (ETDEWEB)
Ge, Xian-Hui [Department of Physics, Shanghai University, Shanghai 200444 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Shanghai Key Lab for Astrophysics,100 Guilin Road, 200234 Shanghai (China); Tian, Yu [School of Physics, University of Chinese Academy of Sciences,Beijing, 100049 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Wu, Shang-Yu [Department of Electrophysics, National Chiao Tung University,Hsinchu 300 (China); Wu, Shao-Feng [Department of Physics, Shanghai University, Shanghai 200444 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai 200444 (China); Shanghai Key Lab for Astrophysics,100 Guilin Road, 200234 Shanghai (China)
2016-11-22
We present a new black hole solution in the asymptotic Lifshitz spacetime with a hyperscaling violating factor. A novel computational method is introduced to compute the DC thermoelectric conductivities analytically. We find that both the linear-T and quadratic-T contributions to the resistivity can be realized, indicating that a more detailed comparison with experimental phenomenology can be performed in this scenario.
International Nuclear Information System (INIS)
Das, Sonjoy; Goswami, Kundan; Datta, Biswa N.
2014-01-01
Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology
Energy Technology Data Exchange (ETDEWEB)
Das, Sonjoy; Goswami, Kundan [University at Buffalo, NY (United States); Datta, Biswa N. [Northern Illinois University, IL (United States)
2014-12-10
Failure of structural systems under dynamic loading can be prevented via active vibration control which shifts the damped natural frequencies of the systems away from the dominant range of loading spectrum. The damped natural frequencies and the dynamic load typically show significant variations in practice. A computationally efficient methodology based on quadratic partial eigenvalue assignment technique and optimization under uncertainty has been formulated in the present work that will rigorously account for these variations and result in an economic and resilient design of structures. A novel scheme based on hierarchical clustering and importance sampling is also developed in this work for accurate and efficient estimation of probability of failure to guarantee the desired resilience level of the designed system. Numerical examples are presented to illustrate the proposed methodology.
Czech Academy of Sciences Publication Activity Database
Agrawal, Divya; Schröder, Detlef; Frech, C. M.
2011-01-01
Roč. 30, č. 13 (2011), s. 3579-3587 ISSN 0276-7333 Institutional research plan: CEZ:AV0Z40550506 Keywords : catalysis * C-C coupling * electrospray ionization * palladium * Suzuki-Miyaura coupling Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.963, year: 2011
International Nuclear Information System (INIS)
Sallah, M.; Margeanu, C. A.
2016-01-01
The space-fractional neutron transport equation is used to describe the neutrons transport in finite disturbed reactors. It is approximated using the Pomraning-Eddington technique to yield two space-fractional differential equations, in terms of neutron density and net neutron flux. These resultant equations are coupled into a fractional diffusion-like equation for the neutron density whose solution is obtained by using Laplace transformation method. The solution is represented in terms of the Mittag-Leffler function and its different orders. The scattering is considered as quadratic scattering to offer a more realistic, compact representation of the system, and to increase the accuracy of the estimated neutronic parameters. The results are presented graphically to illustrate the fractional parameter effect in addition to the effect of radiative-transfer properties on the physical parameters of interest (reflection coefficient, transmission coefficient, neutron energy, and net neutron flux). The neutron transport problem in finite disturbed reactor with quadratic scattering is considered in investigating the shielding effectiveness, by using MAVRIC shielding module from SCALE6 programs package. The fractional parameter can be used to adjust the analysed data on neutron energy and flux, both for the theoretical model and the neutron transport application. (authors)
The cyclicity of period annulus of a quadratic reversible Lotka–Volterra system
International Nuclear Information System (INIS)
Li, Chengzhi; Llibre, Jaume
2009-01-01
We prove that by perturbing the periodic annulus of the quadratic polynomial reversible Lotka–Volterra differential system, inside the class of all quadratic polynomial differential systems we can obtain at most two limit cycles
Induced motion of domain walls in multiferroics with quadratic interaction
Energy Technology Data Exchange (ETDEWEB)
Gerasimchuk, Victor S., E-mail: viktor.gera@gmail.com [National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremohy Avenue 37, 03056 Kiev (Ukraine); Shitov, Anatoliy A., E-mail: shitov@mail.ru [Donbass National Academy of Civil Engineering, Derzhavina Street 2, 86123 Makeevka, Donetsk Region (Ukraine)
2013-10-15
We theoretically study the dynamics of 180-degree domain wall of the ab-type in magnetic materials with quadratic magnetoelectric interaction in external alternating magnetic and electric fields. The features of the oscillatory and translational motions of the domain walls and stripe structures depending on the parameters of external fields and characteristics of the multiferroics are discussed. The possibility of the domain walls drift in a purely electric field is established. - Highlights: • We study DW and stripe DS in multiferroics with quadratic magnetoelectric interaction. • We build up the theory of oscillatory and translational (drift) DW and DS motion. • DW motion can be caused by crossed alternating electric and magnetic fields. • DW motion can be caused by alternating “pure” electric field. • DW drift velocity is formed by the AFM and Dzyaloshinskii interaction terms.
Quadratic grating apodized photon sieves for simultaneous multiplane microscopy
Cheng, Yiguang; Zhu, Jiangping; He, Yu; Tang, Yan; Hu, Song; Zhao, Lixin
2017-10-01
We present a new type of imaging device, named quadratic grating apodized photon sieve (QGPS), used as the objective for simultaneous multiplane imaging in X-rays. The proposed QGPS is structured based on the combination of two concepts: photon sieves and quadratic gratings. Its design principles are also expounded in detail. Analysis of imaging properties of QGPS in terms of point-spread function shows that QGPS can image multiple layers within an object field onto a single image plane. Simulated and experimental results in visible light both demonstrate the feasibility of QGPS for simultaneous multiplane imaging, which is extremely promising to detect dynamic specimens by X-ray microscopy in the physical and life sciences.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2014-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.
Linear Quadratic Controller with Fault Detection in Compact Disk Players
DEFF Research Database (Denmark)
Vidal, Enrique Sanchez; Hansen, K.G.; Andersen, R.S.
2001-01-01
The design of the positioning controllers in Optical Disk Drives are today subjected to a trade off between an acceptable suppression of external disturbances and an acceptable immunity against surfaces defects. In this paper an algorithm is suggested to detect defects of the disk surface combined...... with an observer and a Linear Quadratic Regulator. As a result, the mentioned trade off is minimized and the playability of the tested compact disk player is considerably enhanced....
Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality
Acikmese, Ahmet Behcet; Corless, Martin
2004-01-01
We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.
Information sets as permutation cycles for quadratic residue codes
Directory of Open Access Journals (Sweden)
Richard A. Jenson
1982-01-01
Full Text Available The two cases p=7 and p=23 are the only known cases where the automorphism group of the [p+1, (p+1/2] extended binary quadratic residue code, O(p, properly contains PSL(2,p. These codes have some of their information sets represented as permutation cycles from Aut(Q(p. Analysis proves that all information sets of Q(7 are so represented but those of Q(23 are not.
On a linear-quadratic problem with Caputo derivative
Directory of Open Access Journals (Sweden)
Dariusz Idczak
2016-01-01
Full Text Available In this paper, we study a linear-quadratic optimal control problem with a fractional control system containing a Caputo derivative of unknown function. First, we derive the formulas for the differential and gradient of the cost functional under given constraints. Next, we prove an existence result and derive a maximum principle. Finally, we describe the gradient and projection of the gradient methods for the problem under consideration.
Stationary walking solitons in bulk quadratic nonlinear media
Mihalache, Dumitru; Mazilu, D; Crasonavn, L C; Torner Sabata, Lluís
1997-01-01
We study the mutual trapping of fundamental and second-harmonic light beams propagating in bulk quadratic nonlinear media in the presence of Poynting vector beam walk-off. We show numerically the existence of a two-parameter family of (2 + 1)-dimensional stationary, spatial walking solitons. We have found that the solitons exist at various values of material parameters with different wave intensities and soliton velocities. We discuss the differences between (2 + 1) and (1 + 1)-dimensional wa...
Bifurcation in Z2-symmetry quadratic polynomial systems with delay
International Nuclear Information System (INIS)
Zhang Chunrui; Zheng Baodong
2009-01-01
Z 2 -symmetry systems are considered. Firstly the general forms of Z 2 -symmetry quadratic polynomial system are given, and then a three-dimensional Z 2 equivariant system is considered, which describes the relations of two predator species for a single prey species. Finally, the explicit formulas for determining the Fold and Hopf bifurcations are obtained by using the normal form theory and center manifold argument.
Design of Linear-Quadratic-Regulator for a CSTR process
Meghna, P. R.; Saranya, V.; Jaganatha Pandian, B.
2017-11-01
This paper aims at creating a Linear Quadratic Regulator (LQR) for a Continuous Stirred Tank Reactor (CSTR). A CSTR is a common process used in chemical industries. It is a highly non-linear system. Therefore, in order to create the gain feedback controller, the model is linearized. The controller is designed for the linearized model and the concentration and volume of the liquid in the reactor are kept at a constant value as required.
A Note on 5-bit Quadratic Permutations’ Classification
Božilov, Dušan; Bilgin, Begül; Sahin, Hacı Ali
2017-01-01
Classification of vectorial Boolean functions up to affine equivalence is used widely to analyze various cryptographic and implementation properties of symmetric-key algorithms. We show that there exist 75 affine equivalence classes of 5-bit quadratic permutations. Furthermore, we explore important cryptographic properties of these classes, such as linear and differential properties and degrees of their inverses, together with multiplicative complexity and existence of uniform threshold reali...
Integrable systems with quadratic nonlinearity in Fourier space
International Nuclear Information System (INIS)
Marikhin, V.G.
2003-01-01
The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The known systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and Degasperis-Procesi systems are represented in this list. Some new systems are obtained as well. Two-dimensional and discrete generalizations are discussed
Complex eigenvalues for neutron transport equation with quadratically anisotropic scattering
International Nuclear Information System (INIS)
Sjoestrand, N.G.
1981-01-01
Complex eigenvalues for the monoenergetic neutron transport equation in the buckling approximation have been calculated for various combinations of linearly and quadratically anisotropic scattering. The results are discussed in terms of the time-dependent case. Tables are given of complex bucklings for real decay constants and of complex decay constants for real bucklings. The results fit nicely into the pattern of real and purely imaginary eigenvalues obtained earlier. (author)
Quantum annealing for combinatorial clustering
Kumar, Vaibhaw; Bass, Gideon; Tomlin, Casey; Dulny, Joseph
2018-02-01
Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of within-the-cluster distances between points. The straightforward approach involves examining all the possible assignments of points to each of the clusters. This approach guarantees the solution will be a global minimum; however, the number of possible assignments scales quickly with the number of data points and becomes computationally intractable even for very small datasets. In order to circumvent this issue, cost function minima are found using popular local search-based heuristic approaches such as k-means and hierarchical clustering. Due to their greedy nature, such techniques do not guarantee that a global minimum will be found and can lead to sub-optimal clustering assignments. Other classes of global search-based techniques, such as simulated annealing, tabu search, and genetic algorithms, may offer better quality results but can be too time-consuming to implement. In this work, we describe how quantum annealing can be used to carry out clustering. We map the clustering objective to a quadratic binary optimization problem and discuss two clustering algorithms which are then implemented on commercially available quantum annealing hardware, as well as on a purely classical solver "qbsolv." The first algorithm assigns N data points to K clusters, and the second one can be used to perform binary clustering in a hierarchical manner. We present our results in the form of benchmarks against well-known k-means clustering and discuss the advantages and disadvantages of the proposed techniques.
A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces
Energy Technology Data Exchange (ETDEWEB)
Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at [University of Innsbruck, Department of Mathematics (Austria); Tuffaha, Amjad, E-mail: atufaha@aus.edu [American University of Sharjah, Department of Mathematics (United Arab Emirates)
2017-06-15
We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solution of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.
Pfeil, W. H.; De Los Reyes, G.; Bobula, G. A.
1985-01-01
A power turbine governor was designed for a recent-technology turboshaft engine coupled to a modern, articulated rotor system using Linear Quadratic Regulator (LQR) and Kalman Filter (KF) techniques. A linear, state-space model of the engine and rotor system was derived for six engine power settings from flight idle to maximum continuous. An integrator was appended to the fuel flow input to reduce the steady-state governor error to zero. Feedback gains were calculated for the system states at each power setting using the LQR technique. The main rotor tip speed state is not measurable, so a Kalman Filter of the rotor was used to estimate this state. The crossover of the system was increased to 10 rad/s compared to 2 rad/sec for a current governor. Initial computer simulations with a nonlinear engine model indicate a significant decrease in power turbine speed variation with the LQR governor compared to a conventional governor.
General quadratic gauge theory: constraint structure, symmetries and physical functions
Energy Technology Data Exchange (ETDEWEB)
Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V [Lebedev Physics Institute, Moscow (Russian Federation)
2005-06-17
How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation to specific features of the theory in the Lagrangian formulation, especially relate the constraint structure to the gauge transformation structure of the Lagrangian action? How can we construct the general expression for the gauge charge if the constraint structure in the Hamiltonian formulation is known? Whether we can identify the physical functions defined as commuting with first-class constraints in the Hamiltonian formulation and the physical functions defined as gauge invariant functions in the Lagrangian formulation? The aim of the present paper is to consider the general quadratic gauge theory and to answer the above questions for such a theory in terms of strict assertions. To fulfil such a programme, we demonstrate the existence of the so-called superspecial phase-space variables in terms of which the quadratic Hamiltonian action takes a simple canonical form. On the basis of such a representation, we analyse a functional arbitrariness in the solutions of the equations of motion of the quadratic gauge theory and derive the general structure of symmetries by analysing a symmetry equation. We then use these results to identify the two definitions of physical functions and thus prove the Dirac conjecture.
Design of reinforced areas of concrete column using quadratic polynomials
Arif Gunadi, Tjiang; Parung, Herman; Rachman Djamaluddin, Abd; Arwin Amiruddin, A.
2017-11-01
Designing of reinforced concrete columns mostly carried out by a simple planning method which uses column interaction diagram. However, the application of this method is limited because it valids only for certain compressive strenght of the concrete and yield strength of the reinforcement. Thus, a more applicable method is still in need. Another method is the use of quadratic polynomials as a basis for the approach in designing reinforced concrete columns, where the ratio of neutral lines to the effective height of a cross section (ξ) if associated with ξ in the same cross-section with different reinforcement ratios is assumed to form a quadratic polynomial. This is identical to the basic principle used in the Simpson rule for numerical integral using quadratic polynomials and had a sufficiently accurate level of accuracy. The basis of this approach to be used both the normal force equilibrium and the moment equilibrium. The abscissa of the intersection of the two curves is the ratio that had been mentioned, since it fulfill both of the equilibrium. The application of this method is relatively more complicated than the existing method but provided with tables and graphs (N vs ξN ) and (M vs ξM ) so that its used could be simplified. The uniqueness of these tables are only distinguished based on the compresssive strength of the concrete, so in application it could be combined with various yield strenght of the reinforcement available in the market. This method could be solved by using programming languages such as Fortran.
Fast, multiple optimizations of quadratic dose objective functions in IMRT
International Nuclear Information System (INIS)
Breedveld, Sebastiaan; Storchi, Pascal R M; Keijzer, Marleen; Heijmen, Ben J M
2006-01-01
Inverse treatment planning for intensity-modulated radiotherapy may include time consuming, multiple minimizations of an objective function. In this paper, methods are presented to speed up the process of (repeated) minimization of the well-known quadratic dose objective function, extended with a smoothing term that ensures generation of clinically acceptable beam profiles. In between two subsequent optimizations, the voxel-dependent importance factors of the quadratic terms will generally be adjusted, based on an intermediate plan evaluation. The objective function has been written in matrix-vector format, facilitating the use of a recently published, fast quadratic minimization algorithm, instead of commonly applied gradient-based methods. This format also reduces the calculation time in between subsequent minimizations, related to adjustment of the voxel-dependent importance factors. Sparse matrices are used to limit the required amount of computer memory. For three patients, comparisons have been made with a gradient method. Mean speed improvements of up to a factor of 37 have been achieved
Measurement of quadratic electrogyration effect in castor oil
Izdebski, Marek; Ledzion, Rafał; Górski, Piotr
2015-07-01
This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.
Orms, Natalie; Krylov, Anna I
2018-04-12
The experimental photoelectron spectra of di- and triatomic copper oxide anions have been reported previously. We present an analysis of the experimental spectra of the CuO - , Cu 2 O - , and CuO 2 - anions using equation-of-motion coupled-cluster (EOM-CC) methods. The open-shell electronic structure of each molecule demands a unique combination of EOM-CC methods to achieve an accurate and balanced representation of the multiconfigurational anionic- and neutral-state manifolds. Analysis of the Dyson orbitals associated with photodetachment from CuO - reveals the strong non-Koopmans character of the CuO states. For the lowest detachment energy, a good agreement between theoretical and experimental values is obtained with CCSD(T) (coupled-cluster with single and double excitations and perturbative account of triple excitations). The (T) correction is particularly important for Cu 2 O - . Use of a relativistic pseudopotential and matching basis set improves the quality of results in most cases. EOM-DIP-CCSD analysis of the low-lying states of CuO 2 - reveals multiple singlet and triplet anionic states near the triplet ground state, adding an extra layer of complexity to the interpretation of the experimental CuO 2 - photoelectron spectrum.
International Nuclear Information System (INIS)
Kowalski, Karol; Valiev, Marat
2009-01-01
The recently introduced energy expansion based on the use of generating functional (GF) [K. Kowalski and P. D. Fan, J. Chem. Phys. 130, 084112 (2009)] provides a way of constructing size-consistent noniterative coupled cluster (CC) corrections in terms of moments of the CC equations. To take advantage of this expansion in a strongly interacting regime, the regularization of the cluster amplitudes is required in order to counteract the effect of excessive growth of the norm of the CC wave function. Although proven to be efficient, the previously discussed form of the regularization does not lead to rigorously size-consistent corrections. In this paper we address the issue of size-consistent regularization of the GF expansion by redefining the equations for the cluster amplitudes. The performance and basic features of proposed methodology are illustrated on several gas-phase benchmark systems. Moreover, the regularized GF approaches are combined with quantum mechanical molecular mechanics module and applied to describe the S N 2 reaction of CHCl 3 and OH - in aqueous solution.
Lesmana, E.; Chaerani, D.; Khansa, H. N.
2018-03-01
Energy-Saving Generation Dispatch (ESGD) is a scheme made by Chinese Government in attempt to minimize CO2 emission produced by power plant. This scheme is made related to global warming which is primarily caused by too much CO2 in earth’s atmosphere, and while the need of electricity is something absolute, the power plants producing it are mostly thermal-power plant which produced many CO2. Many approach to fulfill this scheme has been made, one of them came through Minimum Cost Flow in which resulted in a Quadratically Constrained Quadratic Programming (QCQP) form. In this paper, ESGD problem with Minimum Cost Flow in QCQP form will be solved using Lagrange’s Multiplier Method
Histamine headache; Headache - histamine; Migrainous neuralgia; Headache - cluster; Horton's headache; Vascular headache - cluster ... Doctors do not know exactly what causes cluster headaches. They ... (chemical in the body released during an allergic response) or ...
On the analysis of clonogenic survival data: Statistical alternatives to the linear-quadratic model
International Nuclear Information System (INIS)
Unkel, Steffen; Belka, Claus; Lauber, Kirsten
2016-01-01
The most frequently used method to quantitatively describe the response to ionizing irradiation in terms of clonogenic survival is the linear-quadratic (LQ) model. In the LQ model, the logarithm of the surviving fraction is regressed linearly on the radiation dose by means of a second-degree polynomial. The ratio of the estimated parameters for the linear and quadratic term, respectively, represents the dose at which both terms have the same weight in the abrogation of clonogenic survival. This ratio is known as the α/β ratio. However, there are plausible scenarios in which the α/β ratio fails to sufficiently reflect differences between dose-response curves, for example when curves with similar α/β ratio but different overall steepness are being compared. In such situations, the interpretation of the LQ model is severely limited. Colony formation assays were performed in order to measure the clonogenic survival of nine human pancreatic cancer cell lines and immortalized human pancreatic ductal epithelial cells upon irradiation at 0-10 Gy. The resulting dataset was subjected to LQ regression and non-linear log-logistic regression. Dimensionality reduction of the data was performed by cluster analysis and principal component analysis. Both the LQ model and the non-linear log-logistic regression model resulted in accurate approximations of the observed dose-response relationships in the dataset of clonogenic survival. However, in contrast to the LQ model the non-linear regression model allowed the discrimination of curves with different overall steepness but similar α/β ratio and revealed an improved goodness-of-fit. Additionally, the estimated parameters in the non-linear model exhibit a more direct interpretation than the α/β ratio. Dimensionality reduction of clonogenic survival data by means of cluster analysis was shown to be a useful tool for classifying radioresistant and sensitive cell lines. More quantitatively, principal component analysis allowed
International Nuclear Information System (INIS)
Lopez de la Cruz, J.; Gutierrez, M.A.
2008-01-01
This paper presents a stochastic analysis of spatial point patterns as effect of localized pitting corrosion. The Quadrat Counts method is studied with two empirical pit patterns. The results are dependent on the quadrat size and bias is introduced when empty quadrats are accounted for the analysis. The spatially inhomogeneous Poisson process is used to improve the performance of the Quadrat Counts method. The latter combines Quadrat Counts with distance-based statistics in the analysis of pit patterns. The Inter-Event and the Nearest-Neighbour statistics are here implemented in order to compare their results. Further, the treatment of patterns in irregular domains is discussed
Czech Academy of Sciences Publication Activity Database
Vilhanová, B.; Václavík, Jiří; Artiglia, L.; Ranocchiari, M.; Togni, A.; van Bokhoven, J. A.
2017-01-01
Roč. 7, č. 5 (2017), s. 3414-3418 ISSN 2155-5435 Institutional support: RVO:61388963 Keywords : alkyne coupling * gold * heterogeneous catalysis * hypervalent iodine * subnanometer Subject RIV: CC - Organic Chemistry OBOR OECD: Organic chemistry Impact factor: 10.614, year: 2016
Vacuum solutions of Bianchi cosmologies in quadratic gravity
International Nuclear Information System (INIS)
Deus, Juliano Alves de; Muller, Daniel
2011-01-01
Full text: In this work we solve numerically the vacuum solutions of field equations of Bianchi homogeneous universes in the context of Semiclassical theory. Our interest is to study the quadratic theory of gravity with regard in the cosmological description of our universe in periods of intense fields. Bianchi cosmologies are anisotropic homogeneous cosmological models, but can include the isotropic models as particular cases (Bianchi I, VII and IX include homogeneous and isotropic Friedmann models plane, hyperbolic and spherical, respectively). Homogeneous models are good cosmological representations of our universe. With focus in solutions for intense fields, like the early universe, where isotropy is not necessarily required, the adopted scenario is the vacuum solutions, where the geometry is dominant in determining the gravitation. Still following in this way, the Semiclassical theory, which considers quantum matter fields propagating in classical geometrical background, is addressed to give the field equations. This formalism leads to fourth-order ordinary differential equations, in contrast to second-order equations from General Relativity. The Lagrangian of the theory is quadratic in the Ricci scalar and in the Ricci tensor. The equations system is highly non-linear and can be only numerically solved, except perhaps for few particular cases. We obtained numerical solutions for Bianchi V II A evolving to Minkowski and to de Sitter solutions, and also to singularities. The both first and second solutions were obtained choosing initial conditions near from respective exact vacuum solutions from Einstein theory, which are also exact solutions of the quadratic theory. Other Bianchi types are still under study. (author)
Shan, Mingqiu; Li, Sam Fong Yau; Yu, Sheng; Qian, Yan; Guo, Shuchen; Zhang, Li; Ding, Anwei
2018-01-01
Platycladi cacumen (dried twigs and leaves of Platycladus orientalis (L.) Franco) is a frequently utilized Chinese medicinal herb. To evaluate the quality of the phytomedcine, an ultra-performance liquid chromatographic method with diode array detection was established for chemical fingerprinting and quantitative analysis. In this study, 27 batches of P. cacumen from different regions were collected for analysis. A chemical fingerprint with 20 common peaks was obtained using Similarity Evaluation System for Chromatographic Fingerprint of Traditional Chinese Medicine (Version 2004A). Among these 20 components, seven flavonoids (myricitrin, isoquercitrin, quercitrin, afzelin, cupressuflavone, amentoflavone and hinokiflavone) were identified and determined simultaneously. In the method validation, the seven analytes showed good regressions (R ≥ 0.9995) within linear ranges and good recoveries from 96.4% to 103.3%. Furthermore, with the contents of these seven flavonoids, hierarchical clustering analysis was applied to distinguish the 27 batches into five groups. The chemometric results showed that these groups were almost consistent with geographical positions and climatic conditions of the production regions. Integrating fingerprint analysis, simultaneous determination and hierarchical clustering analysis, the established method is rapid, sensitive, accurate and readily applicable, and also provides a significant foundation for quality control of P. cacumen efficiently. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Lipschitz stability of the K-quadratic functional equation | Chahbi ...
African Journals Online (AJOL)
Let N be the set of all positive integers, G an Abelian group with a metric d and E a normed space. For any f : G → E we define the k-quadratic difference of the function f by the formula Qk ƒ(x; y) := 2ƒ(x) + 2k2ƒ(y) - f(x + ky) - f(x - ky) for x; y ∈ G and k ∈ N. Under some assumptions about f and Qkƒ we prove that if Qkƒ is ...
Uniform sparse bounds for discrete quadratic phase Hilbert transforms
Kesler, Robert; Arias, Darío Mena
2017-09-01
For each α \\in T consider the discrete quadratic phase Hilbert transform acting on finitely supported functions f : Z → C according to H^{α }f(n):= \\sum _{m ≠ 0} e^{iα m^2} f(n - m)/m. We prove that, uniformly in α \\in T , there is a sparse bound for the bilinear form for every pair of finitely supported functions f,g : Z→ C . The sparse bound implies several mapping properties such as weighted inequalities in an intersection of Muckenhoupt and reverse Hölder classes.
BRST operator for superconformal algebras with quadratic nonlinearity
International Nuclear Information System (INIS)
Khviengia, Z.; Sezgin, E.
1993-07-01
We construct the quantum BRST operators for a large class of superconformal and quasi-superconformal algebras with quadratic nonlinearity. The only free parameter in these algebras is the level of the (super) Kac-Moody sector. The nilpotency of the quantum BRST operator imposes a condition on the level. We find this condition for (quasi) superconformal algebras with a Kac-Moody sector based on a simple Lie algebra and for the Z 2 x Z 2 -graded superconformal algebras with a Kac-Moody sector based on the superalgebra osp(N modul 2M) or sl (N + 2 modul N). (author). 22 refs, 3 tabs
Quadratic integrand double-hybrid made spin-component-scaled
Energy Technology Data Exchange (ETDEWEB)
Brémond, Éric, E-mail: eric.bremond@iit.it; Savarese, Marika [CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa (Italy); Sancho-García, Juan C.; Pérez-Jiménez, Ángel J. [Departamento de Química Física, Universidad de Alicante, E-03080 Alicante (Spain); Adamo, Carlo [CompuNet, Istituto Italiano di Tecnologia, via Morego 30, I-16163 Genoa (Italy); Chimie ParisTech, PSL Research University, CNRS, Institut de Recherche de Chimie Paris IRCP, F-75005 Paris (France); Institut Universitaire de France, 103 Boulevard Saint Michel, F-75005 Paris (France)
2016-03-28
We propose two analytical expressions aiming to rationalize the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) schemes for double-hybrid exchange-correlation density-functionals. Their performances are extensively tested within the framework of the nonempirical quadratic integrand double-hybrid (QIDH) model on energetic properties included into the very large GMTKN30 benchmark database, and on structural properties of semirigid medium-sized organic compounds. The SOS variant is revealed as a less computationally demanding alternative to reach the accuracy of the original QIDH model without losing any theoretical background.
SPEECH EMOTION RECOGNITION USING MODIFIED QUADRATIC DISCRIMINATION FUNCTION
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Quadratic Discrimination Function(QDF)is commonly used in speech emotion recognition,which proceeds on the premise that the input data is normal distribution.In this Paper,we propose a transformation to normalize the emotional features,then derivate a Modified QDF(MQDF) to speech emotion recognition.Features based on prosody and voice quality are extracted and Principal Component Analysis Neural Network (PCANN) is used to reduce dimension of the feature vectors.The results show that voice quality features are effective supplement for recognition.and the method in this paper could improve the recognition ratio effectively.
On Exponential Hedging and Related Quadratic Backward Stochastic Differential Equations
International Nuclear Information System (INIS)
Sekine, Jun
2006-01-01
The dual optimization problem for the exponential hedging problem is addressed with a cone constraint. Without boundedness conditions on the terminal payoff and the drift of the Ito-type controlled process, the backward stochastic differential equation, which has a quadratic growth term in the drift, is derived as a necessary and sufficient condition for optimality via a variational method and dynamic programming. Further, solvable situations are given, in which the value and the optimizer are expressed in closed forms with the help of the Clark-Haussmann-Ocone formula
Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori
T. Sardari, Naser
2018-03-01
Let Q( X) be any integral primitive positive definite quadratic form in k variables, where {k≥4}, and discriminant D. For any integer n, we give an upper bound on the number of integral solutions of Q( X) = n in terms of n, k, and D. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus {T^d} for {d≥ 5}. This conjecture is motivated by the work of Berry [2,3] on the semiclassical eigenfunction hypothesis.