A real-space stochastic density matrix approach for density functional electronic structure.
Beck, Thomas L
2015-12-21
The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.
Density Functional Approach and Random Matrix Theory in Proteogenesis
NASA Astrophysics Data System (ADS)
Yamanaka, Masanori
2017-02-01
We study the energy-level statistics of amino acids by random matrix theory. The molecular orbital and the Kohn-Sham orbital energies are calculated using ab initio and density-functional formalisms for 20 different amino acids. To generate statistical data, we performed a multipoint calculation on 10000 molecular structures produced via a molecular dynamics simulation. For the valence orbitals, the energy-level statistics exhibit repulsion, but the universality in the random matrix cannot be determined. For the unoccupied orbitals, the energy-level statistics indicate an intermediate distribution between the Gaussian orthogonal ensemble and the semi-Poisson statistics for all 20 different amino acids. These amino acids are considered to be in a type of critical state.
Spectral density of the correlation matrix of factor models: a random matrix theory approach.
Lillo, F; Mantegna, R N
2005-07-01
We studied the eigenvalue spectral density of the correlation matrix of factor models of multivariate time series. By making use of the random matrix theory, we analytically quantified the effect of statistical uncertainty on the spectral density due to the finiteness of the sample. We considered a broad range of models, ranging from one-factor models to hierarchical multifactor models.
Sensitivity of the NMR density matrix to pulse sequence parameters: a simplified analytic approach.
Momot, Konstantin I; Takegoshi, K
2012-08-01
We present a formalism for the analysis of sensitivity of nuclear magnetic resonance pulse sequences to variations of pulse sequence parameters, such as radiofrequency pulses, gradient pulses or evolution delays. The formalism enables the calculation of compact, analytic expressions for the derivatives of the density matrix and the observed signal with respect to the parameters varied. The analysis is based on two constructs computed in the course of modified density-matrix simulations: the error interrogation operators and error commutators. The approach presented is consequently named the Error Commutator Formalism (ECF). It is used to evaluate the sensitivity of the density matrix to parameter variation based on the simulations carried out for the ideal parameters, obviating the need for finite-difference calculations of signal errors. The ECF analysis therefore carries a computational cost comparable to a single density-matrix or product-operator simulation. Its application is illustrated using a number of examples from basic NMR spectroscopy. We show that the strength of the ECF is its ability to provide analytic insights into the propagation of errors through pulse sequences and the behaviour of signal errors under phase cycling. Furthermore, the approach is algorithmic and easily amenable to implementation in the form of a programming code. It is envisaged that it could be incorporated into standard NMR product-operator simulation packages.
NASA Astrophysics Data System (ADS)
Nocera, A.; Alvarez, G.
2016-11-01
Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.
Eigenvalue density of linear stochastic dynamical systems: A random matrix approach
NASA Astrophysics Data System (ADS)
Adhikari, S.; Pastur, L.; Lytova, A.; Du Bois, J.
2012-02-01
Eigenvalue problems play an important role in the dynamic analysis of engineering systems modeled using the theory of linear structural mechanics. When uncertainties are considered, the eigenvalue problem becomes a random eigenvalue problem. In this paper the density of the eigenvalues of a discretized continuous system with uncertainty is discussed by considering the model where the system matrices are the Wishart random matrices. An analytical expression involving the Stieltjes transform is derived for the density of the eigenvalues when the dimension of the corresponding random matrix becomes asymptotically large. The mean matrices and the dispersion parameters associated with the mass and stiffness matrices are necessary to obtain the density of the eigenvalues in the frameworks of the proposed approach. The applicability of a simple eigenvalue density function, known as the Marenko-Pastur (MP) density, is investigated. The analytical results are demonstrated by numerical examples involving a plate and the tail boom of a helicopter with uncertain properties. The new results are validated using an experiment on a vibrating plate with randomly attached spring-mass oscillators where 100 nominally identical samples are physically created and individually tested within a laboratory framework.
Density matrix renormalization group approach to two-fluid open many-fermion systems
NASA Astrophysics Data System (ADS)
Rotureau, J.; Michel, N.; Nazarewicz, W.; Płoszajczak, M.; Dukelsky, J.
2009-01-01
We have extended the density matrix renormalization group (DMRG) approach to two-fluid open many-fermion systems governed by complex-symmetric Hamiltonians. The applications are carried out for three- and four-nucleon (proton-neutron) systems within the Gamow shell model (GSM) in the complex-energy plane. We study necessary and sufficient conditions for the GSM+DMRG method to yield the correct ground-state eigenvalue and discuss different truncation schemes within the DMRG. The proposed approach will enable configuration interaction studies of weakly bound and unbound strongly interacting complex systems, which, because of a prohibitively large size of Fock space, cannot be treated by means of the direct diagonalization.
Density matrix perturbation theory.
Niklasson, Anders M N; Challacombe, Matt
2004-05-14
An orbital-free quantum perturbation theory is proposed. It gives the response of the density matrix upon variation of the Hamiltonian by quadratically convergent recursions based on perturbed projections. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N(pert.)), and as O(1) with the total system size. The method allows efficient high order perturbation expansions, as demonstrated with an example involving a 10th order expansion. Density matrix analogs of Wigner's 2n+1 rule are also presented.
Shamloo, Amir; Mohammadaliha, Negar; Heilshorn, Sarah C; Bauer, Amy L
2016-04-01
A thorough understanding of determining factors in angiogenesis is a necessary step to control the development of new blood vessels. Extracellular matrix density is known to have a significant influence on cellular behaviors and consequently can regulate vessel formation. The utilization of experimental platforms in combination with numerical models can be a powerful method to explore the mechanisms of new capillary sprout formation. In this study, using an integrative method, the interplay between the matrix density and angiogenesis was investigated. Owing the fact that the extracellular matrix density is a global parameter that can affect other parameters such as pore size, stiffness, cell-matrix adhesion and cross-linking, deeper understanding of the most important biomechanical or biochemical properties of the ECM causing changes in sprout morphogenesis is crucial. Here, we implemented both computational and experimental methods to analyze the mechanisms responsible for the influence of ECM density on the sprout formation that is difficult to be investigated comprehensively using each of these single methods. For this purpose, we first utilized an innovative approach to quantify the correspondence of the simulated collagen fibril density to the collagen density in the experimental part. Comparing the results of the experimental study and computational model led to some considerable achievements. First, we verified the results of the computational model using the experimental results. Then, we reported parameters such as the ratio of proliferating cells to migrating cells that was difficult to obtain from experimental study. Finally, this integrative system led to gain an understanding of the possible mechanisms responsible for the effect of ECM density on angiogenesis. The results showed that stable and long sprouts were observed at an intermediate collagen matrix density of 1.2 and 1.9 mg/ml due to a balance between the number of migrating and proliferating
Pisani, Cesare; Erba, Alessandro; Ferrabone, Matteo; Dovesi, Roberto
2012-07-28
In the frame of the Born-Oppenheimer approximation, nuclear motions in crystals can be simulated rather accurately using a harmonic model. In turn, the electronic first-order density matrix (DM) can be expressed as the statistically weighted average over all its determinations each resulting from an instantaneous nuclear configuration. This model has been implemented in a computational scheme which adopts an ab initio one-electron (Hartree-Fock or Kohn-Sham) Hamiltonian in the CRYSTAL program. After selecting a supercell of reasonable size and solving the corresponding vibrational problem in the harmonic approximation, a Metropolis algorithm is adopted for generating a sample of nuclear configurations which reflects their probability distribution at a given temperature. For each configuration in the sample the "instantaneous" DM is calculated, and its contribution to the observables of interest is extracted. Translational and point symmetry of the crystal as reflected in its average DM are fully exploited. The influence of zero-point and thermal motion of nuclei on such important first-order observables as x-ray structure factors and Compton profiles can thus be estimated.
1983-12-15
T TAVIS UCASIFIED 15 DEC 83 TR-0 84(4925-03)-1 SD-TR-83-75 F/G 20/5 NENLS OE 0 ONE so hiE EhhhhhhhhhhhhE ImI INShIhIhhhhE . 1.8 11111 I2 fl...Amplification 00C in a Double Heterostructure GaAs Device Using the Density Matrix Approach M. T. TAVIS Electronics Research Laboratory Laboratory Operations... Tavis F04701-83-C-0084 9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASK The Aerospace Corporation AE OKUI UBR El Segundo
Biplab Dey, Michael E. McCracken, David G. Ireland, Curtis A. Meyer
2011-05-01
The complete expression for the intensity in pseudo-scalar meson photoproduction with a polarized beam, target, and recoil baryon is derived using a density matrix approach that offers great economy of notation. A Cartesian basis with spins for all particles quantized along a single direction, the longitudinal beam direction, is used for consistency and clarity in interpretation. A single spin-quantization axis for all particles enables the amplitudes to be written in a manifestly covariant fashion with simple relations to those of the well-known CGLN formalism. Possible sign discrepancies between theoretical amplitude-level expressions and experimentally measurable intensity profiles are dealt with carefully. Our motivation is to provide a coherent framework for coupled-channel partial-wave analysis of several meson photoproduction reactions, incorporating recently published and forthcoming polarization data from Jefferson Lab.
Dey, Biplab; Meyer, Curtis A.; McCracken, Michael E.; Ireland, David G.
2011-05-15
The complete expression for the intensity in pseudo-scalar meson photoproduction with a polarized beam, target, and recoil baryon is derived using a density matrix approach that offers great economy of notation. A Cartesian basis with spins for all particles quantized along a single direction, the longitudinal beam direction, is used for consistency and clarity in interpretation. A single spin-quantization axis for all particles enables the amplitudes to be written in a manifestly covariant fashion with simple relations to those of the well-known Chew-Goldberger-Low-Nambu formalism. Possible sign discrepancies between theoretical amplitude-level expressions and experimentally measurable intensity profiles are dealt with carefully. Our motivation is to provide a coherent framework for coupled-channel partial-wave analysis of several meson photoproduction reactions, incorporating recently published and forthcoming polarization data from Jefferson Lab.
Richter, Marten Knorr, Andreas
2010-04-15
Time convolution less density matrix theory (TCL) is a powerful and well established tool to investigate strong system-bath coupling for linear optical spectra. We show that TCL equations can be generalised to the nonlinear optical response up to a chosen order in the optical field. This goal is achieved via an time convolution less perturbation scheme for the reduced density matrices of the electronic system. In our approach, the most important results are the inclusion of a electron-phonon coupling non-diagonal in the electronic states and memory effects of the bath: First, the considered model system is introduced. Second, the time evolution of the statistical operator is expanded with respect to the external optical field. This expansion is the starting point to explain how a TCL theory can treat the response up to in a certain order in the external field. Third, new TCL equations, including bath memory effects, are derived and the problem of information loss in the reduced density matrix is analysed. For this purpose, new dimensions are added to the reduced statistical operator to compensate lack of information in comparison with the full statistical operator. The theory is benchmarked with a two level system and applied to a three level system including non-diagonal phonon coupling. In our analysis of pump-probe experiments, the bath memory is influenced by the system state occupied between pump and probe pulse. In particular, the memory of the bath influences the dephasing process of electronic coherences developing during the time interval between pump and probe pulses.
Hammond, Jeff R.; Mazziotti, David A.
2006-01-15
An alternative approach to open-shell molecular calculations using the variational two-electron reduced-density-matrix (2-RDM) theory [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] is presented. The energy and 2-RDM of the open-shell molecule (or radical) are computed from the limit of dissociating one or more hydrogen atoms from a molecule in a singlet state. Because the ground-state energy of an 'infinitely' separated hydrogen atom in a given finite basis is known, we can determine the energy of the radical by subtracting the energy of one or more hydrogen atoms from the energy of the total dissociated system. The 2-RDM is constrained to have singlet symmetry in all calculations. Two sets of N-representability conditions are employed: (i) two-positivity conditions, and (ii) two-positivity conditions plus the T{sub 2} condition, which is a subset of the three-positivity conditions. Optimization of the energy with respect to the 2-RDM is performed with a first-order algorithm for solving the semidefinite program within the variational 2-RDM method. We present calculations of several radicals near equilibrium as well as the dissociation curves of the diatomic radicals CH and OH.
Ness, H
2013-08-01
In this paper, we formally demonstrate that the nonequilibrium density matrix developed by Hershfield for the steady state has the form of a McLennan-Zubarev nonequilibrium ensemble. The correction term in this pseudoequilibrium Gibbs-like ensemble is directly related to the entropy production in the quantum open system. The fact that both methods state that a nonequilibrium steady state can be mapped onto a pseudoequilibrium, permits us to develop nonequilibrium quantities from formal expressions equivalent to the equilibrium case. We provide an example: the derivation of a nonequilibrium distribution function for the electron population in a scattering region in the context of quantum transport.
Khemani, Vedika; Pollmann, Frank; Sondhi, S L
2016-06-17
The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of MBL Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well-studied random field Heisenberg model in one dimension. At moderate to large disorder, the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.
NASA Astrophysics Data System (ADS)
Khemani, Vedika; Pollmann, Frank; Sondhi, S. L.
2016-06-01
The eigenstates of many-body localized (MBL) Hamiltonians exhibit low entanglement. We adapt the highly successful density-matrix renormalization group method, which is usually used to find modestly entangled ground states of local Hamiltonians, to find individual highly excited eigenstates of MBL Hamiltonians. The adaptation builds on the distinctive spatial structure of such eigenstates. We benchmark our method against the well-studied random field Heisenberg model in one dimension. At moderate to large disorder, the method successfully obtains excited eigenstates with high accuracy, thereby enabling a study of MBL systems at much larger system sizes than those accessible to exact-diagonalization methods.
NASA Astrophysics Data System (ADS)
Afzali, R.; Ebrahimian, N.; Eghbalifar, B.
2016-10-01
By approximating the energy gap, entering nano-size effect via gap fluctuation and calculating the Green's functions and the space-spin density matrix, the dependence of quantum correlation (entanglement, discord and tripartite entanglement) on the relative distance of two electron spins forming Cooper pairs, the energy gap and the length of bulk and nano interacting Fermi system (a nodal d-wave superconductor) is determined. In contrast to a s-wave superconductor, quantum correlation of the system is sensitive to the change of the gap magnitude and strongly depends on the length of the grain. Also, quantum discord oscillates. Furthermore, the entanglement length and the correlation length are investigated. Discord becomes zero at a characteristic length of the d-wave superconductor.
Yan, YiJing
2014-02-07
This work establishes a strongly correlated system-and-bath dynamics theory, the many-dissipaton density operators formalism. It puts forward a quasi-particle picture for environmental influences. This picture unifies the physical descriptions and algebraic treatments on three distinct classes of quantum environments, electron bath, phonon bath, and two-level spin or exciton bath, as their participating in quantum dissipation processes. Dynamical variables for theoretical description are no longer just the reduced density matrix for system, but remarkably also those for quasi-particles of bath. The present theoretical formalism offers efficient and accurate means for the study of steady-state (nonequilibrium and equilibrium) and real-time dynamical properties of both systems and hybridizing environments. It further provides universal evaluations, exact in principle, on various correlation functions, including even those of environmental degrees of freedom in coupling with systems. Induced environmental dynamics could be reflected directly in experimentally measurable quantities, such as Fano resonances and quantum transport current shot noise statistics.
Beau, Mathieu; Savoie, Baptiste
2014-05-15
In this paper, we rigorously investigate the reduced density matrix (RDM) associated to the ideal Bose gas in harmonic traps. We present a method based on a sum-decomposition of the RDM allowing to treat not only the isotropic trap, but also general anisotropic traps. When focusing on the isotropic trap, the method is analogous to the loop-gas approach developed by Mullin [“The loop-gas approach to Bose-Einstein condensation for trapped particles,” Am. J. Phys. 68(2), 120 (2000)]. Turning to the case of anisotropic traps, we examine the RDM for some anisotropic trap models corresponding to some quasi-1D and quasi-2D regimes. For such models, we bring out an additional contribution in the local density of particles which arises from the mesoscopic loops. The close connection with the occurrence of generalized-Bose-Einstein condensation is discussed. Our loop-gas-like approach provides relevant information which can help guide numerical investigations on highly anisotropic systems based on the Path Integral Monte Carlo method.
NASA Astrophysics Data System (ADS)
Jacobs, Verne
2015-05-01
The frequency-dependent transition rates for multi-photon processes in quantized many-electron systems are evaluated using a reduced-density-matrix approach. A fundamental foundation, based on quantum electrodynamics, is provided for systematic spectral simulations for electromagnetic interactions in quantized many-electron systems, including atomic, molecular, and solid-state systems. A perturbation expansion of the frequency-domain Liouville-space self-energy operator is employed in detailed evaluations of the spectral-line shapes. The self-energy contributions associated with environmental electron-photon and electron-phonon interactions are systematically taken into account. Detailed evaluations have been carried out for the spectral-line widths and shifts in the diagonal-resolvent, lowest order (Born), and short-memory-time (Markov) approximations. Work supported by the Office of Naval Research through the Basic Research Program at The Naval Research Laboratory.
Interaction picture density matrix quantum Monte Carlo
Malone, Fionn D. Lee, D. K. K.; Foulkes, W. M. C.; Blunt, N. S.; Shepherd, James J.; Spencer, J. S.
2015-07-28
The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.
Measuring Entanglement Spectrum via Density Matrix Exponentiation
NASA Astrophysics Data System (ADS)
Zhu, Guanyu; Seif, Alireza; Pichler, Hannes; Zoller, Peter; Hafezi, Mohammad
Entanglement spectrum (ES), the eigenvalues of the reduced density matrix of a subsystem, serves as a powerful theoretical tool to study many-body systems. For example, the gap and degeneracies of the entanglement spectrum have been used to identify various topological phases. However, the usefulness of such a concept in real experiments has been debated, since it is believed that obtaining the ES requires full state tomography, at a cost which exponentially grows with the systems size. Inspired by a recent density matrix exponentiation technique, we propose a scheme to measure ES by evolving the system with a Hamiltonian that is the subsystem's own reduced density matrix. Such a time evolution can be induced by an ancilla photon that is coupled to multiple qubits at the same time. The phase associated with the time evolution can be detected and converted into ES through either a digital or an analogue scheme. The digital scheme involves a modified quantum phase estimation algorithm based on random time evolution, while the analogue scheme is in the spirit of Ramsey interferometry. Both schemes are not limited by the size of the system, and are especially sensitive to the gap and degeneracies. We also discuss the implementation in cavity/circuit-QED and ion trap systems.
Density: A Discovery Approach.
ERIC Educational Resources Information Center
Rieck, William
1994-01-01
Describes an activity that allows students to discover the concept of density and that density is a determining physical property of a pure substance. Makes suggestions to further enhance students' understanding of density. (ZWH)
Transition matrices and orbitals from reduced density matrix theory
Etienne, Thibaud
2015-06-28
In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.
Localized density matrix minimization and linear-scaling algorithms
NASA Astrophysics Data System (ADS)
Lai, Rongjie; Lu, Jianfeng
2016-06-01
We propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise ℓ1 regularization to the free energy of the quantum system. Based on the fact that the density matrix decays exponentially away from the diagonal for insulating systems or systems at finite temperature, the proposed ℓ1 regularized variational method provides an effective way to approximate the original quantum system. We provide theoretical analysis of the approximation behavior and also design convergence guaranteed numerical algorithms based on Bregman iteration. More importantly, the ℓ1 regularized system naturally leads to localized density matrices with banded structure, which enables us to develop approximating algorithms to find the localized density matrices with computation cost linearly dependent on the problem size.
Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R
2016-07-07
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
NASA Astrophysics Data System (ADS)
Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.
2016-07-01
Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.
Matrix model approach to cosmology
NASA Astrophysics Data System (ADS)
Chaney, A.; Lu, Lei; Stern, A.
2016-03-01
We perform a systematic search for rotationally invariant cosmological solutions to toy matrix models. These models correspond to the bosonic sector of Lorentzian Ishibashi, Kawai, Kitazawa and Tsuchiya (IKKT)-type matrix models in dimensions d less than ten, specifically d =3 and d =5 . After taking a continuum (or commutative) limit they yield d -1 dimensional Poisson manifolds. The manifolds have a Lorentzian induced metric which can be associated with closed, open, or static space-times. For d =3 , we obtain recursion relations from which it is possible to generate rotationally invariant matrix solutions which yield open universes in the continuum limit. Specific examples of matrix solutions have also been found which are associated with closed and static two-dimensional space-times in the continuum limit. The solutions provide for a resolution of cosmological singularities, at least within the context of the toy matrix models. The commutative limit reveals other desirable features, such as a solution describing a smooth transition from an initial inflation to a noninflationary era. Many of the d =3 solutions have analogues in higher dimensions. The case of d =5 , in particular, has the potential for yielding realistic four-dimensional cosmologies in the continuum limit. We find four-dimensional de Sitter d S4 or anti-de Sitter AdS4 solutions when a totally antisymmetric term is included in the matrix action. A nontrivial Poisson structure is attached to these manifolds which represents the lowest order effect of noncommutativity. For the case of AdS4 , we find one particular limit where the lowest order noncommutativity vanishes at the boundary, but not in the interior.
Direct Measurement of the Density Matrix of a Quantum System
NASA Astrophysics Data System (ADS)
Thekkadath, G. S.; Giner, L.; Chalich, Y.; Horton, M. J.; Banker, J.; Lundeen, J. S.
2016-09-01
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.
Information Theory Density Matrix for a Simple Quantum System.
ERIC Educational Resources Information Center
Titus, William J.
1979-01-01
Derives the density matrix that best describes, according to information theory, a one-dimensional single particle quantum system when the only information available is the values for the linear and quadratic position-momentum moments. (Author/GA)
Deconstructing Wigner's density matrix concerning the mind-body question
NASA Astrophysics Data System (ADS)
Brandt, Howard E.
2002-06-01
In honor of the centennial of Eugene Wigner’s birth, a possible interpretation is given of the density matrix appearing in his classic paper, “Remarks on the mind-body question.” It is argued that nearinstantaneous vanishing of the quantum coherences of the reduced density matrix of the measured object would occur either in the case of Wigner’s friend, or in the case of any complex measuring automaton (conscious or not) making the measurement.
Stationary density matrix of a pumped polariton system.
Vera, Carlos Andrés; Cabo, Alejandro; González, Augusto
2009-03-27
The density matrix rho of a model polariton system is obtained numerically from a master equation which takes account of pumping and losses. In the stationary limit, the coherences between eigenstates of the Hamiltonian are 3 orders of magnitude smaller than the occupations, meaning that the stationary density matrix is approximately diagonal in the energy representation. A weakly distorted grand canonical Gibbs distribution fits well the occupations.
NASA Astrophysics Data System (ADS)
Miller, William H.; Cotton, Stephen J.
2016-08-01
It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory—e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states—and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.
Hedegård, Erik Donovan Knecht, Stefan; Reiher, Markus; Kielberg, Jesper Skau; Jensen, Hans Jørgen Aagaard
2015-06-14
We present a new hybrid multiconfigurational method based on the concept of range-separation that combines the density matrix renormalization group approach with density functional theory. This new method is designed for the simultaneous description of dynamical and static electron-correlation effects in multiconfigurational electronic structure problems.
The ab-initio density matrix renormalization group in practice
Olivares-Amaya, Roberto; Hu, Weifeng; Sharma, Sandeep; Yang, Jun; Chan, Garnet Kin-Lic; Nakatani, Naoki
2015-01-21
The ab-initio density matrix renormalization group (DMRG) is a tool that can be applied to a wide variety of interesting problems in quantum chemistry. Here, we examine the density matrix renormalization group from the vantage point of the quantum chemistry user. What kinds of problems is the DMRG well-suited to? What are the largest systems that can be treated at practical cost? What sort of accuracies can be obtained, and how do we reason about the computational difficulty in different molecules? By examining a diverse benchmark set of molecules: π-electron systems, benchmark main-group and transition metal dimers, and the Mn-oxo-salen and Fe-porphine organometallic compounds, we provide some answers to these questions, and show how the density matrix renormalization group is used in practice.
Revisting the Density Matrix Expansion with Regulated Chiral Interactions
NASA Astrophysics Data System (ADS)
Dyhdalo, Alexander; Furnstahl, Richard; Bogner, Scott; Schunck, Nicolas; Navarro Perez, Rodrigo
2016-09-01
The density matrix expansion provides a general way to map microscopic interactions to a local functional. Previous density matrix expansion formulations added unregulated chiral long-range potentials to a Skyrme-type functional, which accounted for the short-range contributions. We implement the expansion with new coordinate space regulators using the regulator cutoff as a tool to adiabatically turn on finite-range pion interactions. We discuss `smoking guns' for correct inclusion of 3-body forces, which are implemented in a normal-ordering prescription, and compare to ab initio calculations.
Auxiliary Density Matrix Methods for Hartree-Fock Exchange Calculations.
Guidon, Manuel; Hutter, Jürg; VandeVondele, Joost
2010-08-10
The calculation of Hartree-Fock exchange (HFX) is computationally demanding for large systems described with high-quality basis sets. In this work, we show that excellent performance and good accuracy can nevertheless be obtained if an auxiliary density matrix is employed for the HFX calculation. Several schemes to derive an auxiliary density matrix from a high-quality density matrix are discussed. Key to the accuracy of the auxiliary density matrix methods (ADMM) is the use of a correction based on standard generalized gradient approximations for HFX. ADMM integrates seamlessly in existing HFX codes and, in particular, can be employed in linear scaling implementations. Demonstrating the performance of the method, the effect of HFX on the structure of liquid water is investigated in detail using Born-Oppenheimer molecular dynamics simulations (300 ps) of a system of 64 molecules. Representative for large systems are calculations on a solvated protein (Rubredoxin), for which ADMM outperforms the corresponding standard HFX implementation by approximately a factor 20.
Communication: Four-component density matrix renormalization group
Knecht, Stefan Reiher, Markus; Legeza, Örs
2014-01-28
We present the first implementation of the relativistic quantum chemical two- and four-component density matrix renormalization group algorithm that includes a variational description of scalar-relativistic effects and spin–orbit coupling. Numerical results based on the four-component Dirac–Coulomb Hamiltonian are presented for the standard reference molecule for correlated relativistic benchmarks: thallium hydride.
Juxtaposing density matrix and classical path-based wave packet dynamics
Aghtar, Mortaza; Liebers, Jörg; Strümpfer, Johan; Schulten, Klaus; Kleinekathöfer, Ulrich
2012-01-01
In many physical, chemical, and biological systems energy and charge transfer processes are of utmost importance. To determine the influence of the environment on these transport processes, equilibrium molecular dynamics simulations become more and more popular. From these simulations, one usually determines the thermal fluctuations of certain energy gaps, which are then either used to perform ensemble-averaged wave packet simulations, also called Ehrenfest dynamics, or to employ a density matrix approach via spectral densities. These two approaches are analyzed through energy gap fluctuations that are generated to correspond to a predetermined spectral density. Subsequently, density matrix and wave packet simulations are compared through population dynamics and absorption spectra for different parameter regimes. Furthermore, a previously proposed approach to enforce the correct long-time behavior in the wave packet simulations is probed and an improvement is proposed. PMID:22697524
Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory.
Knizia, Gerald; Chan, Garnet Kin-Lic
2013-03-12
We extend our density matrix embedding theory (DMET) [Phys. Rev. Lett.2012, 109, 186404] from lattice models to the full chemical Hamiltonian. DMET allows the many-body embedding of arbitrary fragments of a quantum system, even when such fragments are open systems and strongly coupled to their environment (e.g., by covalent bonds). In DMET, empirical approaches to strong coupling, such as link atoms or boundary regions, are replaced by a small, rigorous quantum bath designed to reproduce the entanglement between a fragment and its environment. We describe the theory and demonstrate its feasibility in strongly correlated hydrogen ring and grid models; these are not only beyond the scope of traditional embeddings but even challenge conventional quantum chemistry methods themselves. We find that DMET correctly describes the notoriously difficult symmetric dissociation of a 4 × 3 hydrogen atom grid, even when the treated fragments are as small as single hydrogen atoms. We expect that DMET will open up new ways of treating complex strongly coupled, strongly correlated systems in terms of their individual fragments.
Improved density matrix expansion for spin-unsaturated nuclei
Gebremariam, B.; Bogner, S. K.; Duguet, T.
2010-07-15
A current objective of low-energy nuclear theory is to build nonempirical nuclear energy density functionals (EDFs) from underlying internucleon interactions and many-body perturbation theory (MBPT). The density matrix expansion (DME) of Negele and Vautherin is a convenient method to map highly nonlocal Hartree-Fock expressions into the form of a quasi-local Skyrme functional with density-dependent couplings. In this work, we assess the accuracy of the DME at reproducing the nonlocal exchange (Fock) contribution to the energy. In contrast to the scalar part of the density matrix for which the original formulation of Negele and Vautherin is reasonably accurate, we demonstrate the necessity to reformulate the DME for the vector part of the density matrix, which is needed for an accurate description of spin-unsaturated nuclei. Phase-space-averaging techniques are shown to yield a significant improvement for the vector part of the density matrix compared to the original formulation of Negele and Vautherin. The key to the improved accuracy is to take into account the anisotropy that characterizes the local momentum distribution in the surface region of finite Fermi systems. Optimizing separately the DME for the central, tensor, and spin-orbit contributions to the Fock energy, one reaches a few-percent accuracy over a representative set of semi-magic nuclei. With such an accuracy at hand, one can envision using the corresponding Skyrme-like energy functional as a microscopically constrained starting point around which future phenomenological parametrizations can be built and refined.
Magnesium Matrix Composite Foams-Density, Mechanical Properties, and Applications
2012-07-24
known that the effect of particle-matrix interfacial bonding is much less significant under compression compared to under tension [33,34]. One of the...parameter). Some syntactic foam composites are found to have less than 0.4 g/cc density in Figure 9. These data points belong to foams that contain...syntactic foams containing porosity only inside hollow particles. The yield strength values for various types of MMSFs, including aluminum, titanium , and
Jordan, Daniel K; Mazziotti, David A
2005-02-22
Two classes of linear-scaling methods to replace diagonalization of the one-particle Hamiltonian matrix in density functional theory are compared to each other. Purification takes a density matrix with the correct eigenfunctions and corrects the occupation numbers; density matrix minimization takes a density matrix with correct occupation numbers and corrects the eigenfunctions by rotating the orbitals. Computational comparisons are performed through modification of the MondoSCF program on water clusters and the protein endothelin. A purification scheme and a density matrix minimization scheme, based on the 1,2-contracted Schrodinger equation [D. A. Mazziotti, J. Chem. Phys. 115, 8305 (2001)] are implemented in large systems.
Random matrix approach to categorical data analysis
NASA Astrophysics Data System (ADS)
Patil, Aashay; Santhanam, M. S.
2015-09-01
Correlation and similarity measures are widely used in all the areas of sciences and social sciences. Often the variables are not numbers but are instead qualitative descriptors called categorical data. We define and study similarity matrix, as a measure of similarity, for the case of categorical data. This is of interest due to a deluge of categorical data, such as movie ratings, top-10 rankings, and data from social media, in the public domain that require analysis. We show that the statistical properties of the spectra of similarity matrices, constructed from categorical data, follow random matrix predictions with the dominant eigenvalue being an exception. We demonstrate this approach by applying it to the data for Indian general elections and sea level pressures in the North Atlantic ocean.
Two-body density matrix of a normal Fermi fluid
NASA Astrophysics Data System (ADS)
Ristig, M. L.; Clark, J. W.
1990-05-01
The microscopic study of the two-body density matrix ρ2(r1,r2,r'1,r'2) initiated for uniform Bose fluids in an earlier paper is continued for the Fermi case. We present formal results on the structure of the generalized momentum distribution n(p,q)=Σk⁁<Ψ\\|a†k⁁+qa†p⁁-qap⁁ak⁁\\|Ψ>, and its Fourier inverse ρ2(r1,r2,r'1,r2)≡ρ2(r1,r2,r'1), based on a variational ground-state wave function of Jastrow-Slater form. The structural relations are inferred from the cluster expansions of these objects, from the asymptotic condition relating ρ2(r1,r2,r'1) to the particle density and the one-body density matrix ρ1(r1,r'1), and from formal diagrammatic connections with the Bose problem. The two-body density-matrix elements ρ2(r1,r2,r'1) are thereby expressed in closed form in terms of certain sums of irreducible cluster diagrams. Some of these diagram sums are familiar from the analogous theory of the one-body density matrix; all can be evaluated quantitatively by solving a set of Fermi-hypernetted-chain (FHNC) equations. Upon invoking the sequential relation between ρ2(r1,r2,r'1) and ρ1(r1,r'1), the corresponding result for the generalized momentum distribution n(p,q) effects a resolution into contributions from various scattering processes occurring in the many-body medium, specified by form factors that are susceptible to FHNC evaluation. This decomposition is comparable to that derived earlier for the Bose-fluid ground state but is complicated by contributions from exchange scattering and by a dynamically dressed Pauli kinematic correction. Silver has proposed a simple expression for the generalized momentum distribution n(p,q), a function which plays an essential role in his theory of final-state effects in deep-inelastic neutron scattering from the helium liquids. Based on the present microscopic treatment, the quality of Silver's estimate is assessed for the case of normal liquid He3, by evaluating the necessary distribution
Shrinkage covariance matrix approach for microarray data
NASA Astrophysics Data System (ADS)
Karjanto, Suryaefiza; Aripin, Rasimah
2013-04-01
Microarray technology was developed for the purpose of monitoring the expression levels of thousands of genes. A microarray data set typically consists of tens of thousands of genes (variables) from just dozens of samples due to various constraints including the high cost of producing microarray chips. As a result, the widely used standard covariance estimator is not appropriate for this purpose. One such technique is the Hotelling's T2 statistic which is a multivariate test statistic for comparing means between two groups. It requires that the number of observations (n) exceeds the number of genes (p) in the set but in microarray studies it is common that n < p. This leads to a biased estimate of the covariance matrix. In this study, the Hotelling's T2 statistic with the shrinkage approach is proposed to estimate the covariance matrix for testing differential gene expression. The performance of this approach is then compared with other commonly used multivariate tests using a widely analysed diabetes data set as illustrations. The results across the methods are consistent, implying that this approach provides an alternative to existing techniques.
New pole placement algorithm - Polynomial matrix approach
NASA Technical Reports Server (NTRS)
Shafai, B.; Keel, L. H.
1990-01-01
A simple and direct pole-placement algorithm is introduced for dynamical systems having a block companion matrix A. The algorithm utilizes well-established properties of matrix polynomials. Pole placement is achieved by appropriately assigning coefficient matrices of the corresponding matrix polynomial. This involves only matrix additions and multiplications without requiring matrix inversion. A numerical example is given for the purpose of illustration.
The problem of the universal density functional and the density matrix functional theory
Bobrov, V. B. Trigger, S. A.
2013-04-15
The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.
Development and application of a density dependent matrix ...
Ranging along the Atlantic coast from US Florida to the Maritime Provinces of Canada, the Atlantic killifish (Fundulus heteroclitus) is an important and well-studied model organism for understanding the effects of pollutants and other stressors in estuarine and marine ecosystems. Matrix population models are useful tools for ecological risk assessment because they integrate effects across the life cycle, provide a linkage between endpoints observed in the individual and ecological risk to the population as a whole, and project outcomes for many generations in the future. We developed a density dependent matrix population model for Atlantic killifish by modifying a model developed for fathead minnow (Pimephales promelas) that has proved to be extremely useful, e.g. to incorporate data from laboratory studies and project effects of endocrine disrupting chemicals. We developed a size-structured model (as opposed to one that is based upon developmental stages or age class structure) so that we could readily incorporate output from a Dynamic Energy Budget (DEB) model, currently under development. Due to a lack of sufficient data to accurately define killifish responses to density dependence, we tested a number of scenarios realistic for other fish species in order to demonstrate the outcome of including this ecologically important factor. We applied the model using published data for killifish exposed to dioxin-like compounds, and compared our results to those using
Generalized Pauli constraints in reduced density matrix functional theory
Theophilou, Iris; Helbig, Nicole; Lathiotakis, Nektarios N.; Marques, Miguel A. L.
2015-04-21
Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman’s ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.
Watching excitons move: the time-dependent transition density matrix
NASA Astrophysics Data System (ADS)
Ullrich, Carsten
2012-02-01
Time-dependent density-functional theory allows one to calculate excitation energies and the associated transition densities in principle exactly. The transition density matrix (TDM) provides additional information on electron-hole localization and coherence of specific excitations of the many-body system. We have extended the TDM concept into the real-time domain in order to visualize the excited-state dynamics in conjugated molecules. The time-dependent TDM is defined as an implicit density functional, and can be approximately obtained from the time-dependent Kohn-Sham orbitals. The quality of this approximation is assessed in simple model systems. A computational scheme for real molecular systems is presented: the time-dependent Kohn-Sham equations are solved with the OCTOPUS code and the time-dependent Kohn-Sham TDM is calculated using a spatial partitioning scheme. The method is applied to show in real time how locally created electron-hole pairs spread out over neighboring conjugated molecular chains. The coupling mechanism, electron-hole coherence, and the possibility of charge separation are discussed.
Hermitian one-particle density matrix through a semiclassical gradient expansion
NASA Astrophysics Data System (ADS)
Bencheikh, K.; Räsänen, E.
2016-01-01
We carry out the semiclassical expansion of the one-particle density matrix up to the second order in {{\\hslash }}. We use the method of Grammaticos and Voros based on the Wigner transform of operators. We show that the resulting density matrix is Hermitian and idempotent in contrast with the well-known result of the semiclassical Kirzhnits expansion. Our density matrix leads to the same particle density and kinetic energy density as in the literature, and it satisfies the consistency criterion of the Euler equation. The derived Hermitian density matrix clarifies the ambiguity in the usefulness of gradient expansion approximations and might reignite the development of density functionals with semiclassical methods.
Matrix product density operators: Renormalization fixed points and boundary theories
NASA Astrophysics Data System (ADS)
Cirac, J. I.; Pérez-García, D.; Schuch, N.; Verstraete, F.
2017-03-01
We consider the tensors generating matrix product states and density operators in a spin chain. For pure states, we revise the renormalization procedure introduced in (Verstraete et al., 2005) and characterize the tensors corresponding to the fixed points. We relate them to the states possessing zero correlation length, saturation of the area law, as well as to those which generate ground states of local and commuting Hamiltonians. For mixed states, we introduce the concept of renormalization fixed points and characterize the corresponding tensors. We also relate them to concepts like finite correlation length, saturation of the area law, as well as to those which generate Gibbs states of local and commuting Hamiltonians. One of the main result of this work is that the resulting fixed points can be associated to the boundary theories of two-dimensional topological states, through the bulk-boundary correspondence introduced in (Cirac et al., 2011).
Reduced density matrix and order parameters of a topological insulator
NASA Astrophysics Data System (ADS)
Yu, Wing Chi; Li, Yan Chao; Sacramento, P. D.; Lin, Hai-Qing
2016-12-01
It has been recently proposed that the reduced density matrix may be used to derive the order parameter of a condensed matter system. Here we propose order parameters for the phases of a topological insulator, specifically a spinless Su-Schrieffer-Heeger (SSH) model, and consider the effect of short-range interactions. All the derived order parameters and their possible corresponding quantum phases are verified by the entanglement entropy and electronic configuration analysis results. The order parameter appropriate to the topological regions is further proved by calculating the Berry phase under twisted boundary conditions. It is found that the topological nontrivial phase is robust to the introduction of repulsive intersite interactions and can appear in the topological trivial parameter region when appropriate interactions are added.
NASA Astrophysics Data System (ADS)
Micha, David A.
This contribution deals with two approaches for localized phenomena in excited many-atom systems. The first approach develops a quantum quasi-classical treatment for the density operator, including all atoms. It is based on a partial Wigner representation and is illustrated with applications to photodissociation of NaI, and to light emission of excited Li interacting with a He cluster. This second application describes the direct dynamics with a time-dependent electronic density matrix, expanded in a basis set of atomic functions. It shows that such an approach can deal with electronically excited many-atom systems involving tens of quantum states and hundreds of classical variables. The second approach makes use of the reduced density operator description for a system in a medium. This allows for dissipative dynamics, which can be instantaneous or delayed. An application is presented for femtosecond photodesorption using a Markovian dissipation and construction of the density operator from density amplitudes, for CO/Cu(001). A second application of a reduced density operator has been made to vibrational relaxation of adsorbates, solving integrodifferential equations to compare delayed, instantaneous, and Markovian dissipation. It is concluded that delayed dissipation is needed at short times and that a Markovian treatment is suitable for the interpretation of cross-sectional measurements that involve long-term dynamics.
The "JK-only" approximation in density matrix functional and wave function theory.
Kollmar, Christian
2004-12-15
Various energy functionals applying the "JK-only" approximation which leads to two-index two-electron integrals instead of four-index two-electron integrals in the electron-electron interaction term of the electronic energy are presented. Numerical results of multiconfiguration self-consistent field calculations for the best possible "JK-only" wave function are compared to those obtained from the pair excitation multiconfiguration self-consistent (PEMCSCF) method and two versions of density matrix functional theory. One of these is derived making explicit use of some necessary conditions for N representability of the second-order density matrix. It is shown that this method models the energy functional based on the best possible "JK-only" wave function with good accuracy. The calculations also indicate that only a minor fraction of the total correlation energy is incorporated by "JK-only" approaches for larger molecules.
Huo, Pengfei; Coker, David F
2012-12-14
Powerful approximate methods for propagating the density matrix of complex systems that are conveniently described in terms of electronic subsystem states and nuclear degrees of freedom have recently been developed that involve linearizing the density matrix propagator in the difference between the forward and backward paths of the nuclear degrees of freedom while keeping the interference effects between the different forward and backward paths of the electronic subsystem described in terms of the mapping Hamiltonian formalism and semi-classical mechanics. Here we demonstrate that different approaches to developing the linearized approximation to the density matrix propagator can yield a mean-field like approximate propagator in which the nuclear variables evolve classically subject to Ehrenfest-like forces that involve an average over quantum subsystem states, and by adopting an alternative approach to linearizing we obtain an algorithm that involves classical like nuclear dynamics influenced by a quantum subsystem state dependent force reminiscent of trajectory surface hopping methods. We show how these different short time approximations can be implemented iteratively to achieve accurate, stable long time propagation and explore their implementation in different representations. The merits of the different approximate quantum dynamics methods that are thus consistently derived from the density matrix propagator starting point and different partial linearization approximations are explored in various model system studies of multi-state scattering problems and dissipative non-adiabatic relaxation in condensed phase environments that demonstrate the capabilities of these different types of approximations for treating non-adiabatic electronic relaxation, bifurcation of nuclear distributions, and the passage from nonequilibrium coherent dynamics at short times to long time thermal equilibration in the presence of a model dissipative environment.
Efficient perturbation theory to improve the density matrix renormalization group
NASA Astrophysics Data System (ADS)
Tirrito, Emanuele; Ran, Shi-Ju; Ferris, Andrew J.; McCulloch, Ian P.; Lewenstein, Maciej
2017-02-01
The density matrix renormalization group (DMRG) is one of the most powerful numerical methods available for many-body systems. It has been applied to solve many physical problems, including the calculation of ground states and dynamical properties. In this work, we develop a perturbation theory of the DMRG (PT-DMRG) to greatly increase its accuracy in an extremely simple and efficient way. Using the canonical matrix product state (MPS) representation for the ground state of the considered system, a set of orthogonal basis functions {| ψi> } is introduced to describe the perturbations to the ground state obtained by the conventional DMRG. The Schmidt numbers of the MPS that are beyond the bond dimension cutoff are used to define these perturbation terms. The perturbed Hamiltonian is then defined as H˜i j=< ψi| H ̂|ψj> ; its ground state permits us to calculate physical observables with a considerably improved accuracy compared to the original DMRG results. We benchmark the second-order perturbation theory with the help of a one-dimensional Ising chain in a transverse field and the Heisenberg chain, where the precision of the DMRG is shown to be improved O (10 ) times. Furthermore, for moderate L the errors of the DMRG and PT-DMRG both scale linearly with L-1 (with L being the length of the chain). The linear relation between the dimension cutoff of the DMRG and that of the PT-DMRG at the same precision shows a considerable improvement in efficiency, especially for large dimension cutoffs. In the thermodynamic limit we show that the errors of the PT-DMRG scale with √{L-1}. Our work suggests an effective way to define the tangent space of the ground-state MPS, which may shed light on the properties beyond the ground state. This second-order PT-DMRG can be readily generalized to higher orders, as well as applied to models in higher dimensions.
NASA Astrophysics Data System (ADS)
Baker, Thomas E.; Wagner, Lucas O.; Stoudenmire, E. Miles; White, Steven R.; Burke, Kieron
2014-03-01
Kohn-Sham Density Functional Theory (DFT) is a mathematically exact method that requires approximation to the exchange correlation energy which may exclude features seen in experiment or provide inadequate estimates. Meanwhile, we may use Density Matrix Renormalization Group (DMRG), a numerical method which can accurately treat strongly correlated electrons in one dimension, to find exact DFT quantities such as the Kohn-Sham potential. We use DMRG in one dimension as a benchmark to test new functionals. Further, recommendations for calculations in two and three dimensional systems are discussed as well as computational proof of principles. We graciously acknowledge the support of the Department of Energy (DE-SC0008696). L.O.W. also thanks the Korean Global Research Network Grant (No. NRF-2010-220-C00017).
Density matrix reconstruction of a large angular momentum
NASA Astrophysics Data System (ADS)
Klose, Gerd
2001-10-01
A complete description of the quantum state of a physical system is the fundamental knowledge necessary to statistically predict the outcome of measurements. In turning this statement around, Wolfgang Pauli raised already in 1933 the question, whether an unknown quantum state could be uniquely determined by appropriate measurements-a problem that has gained new relevance in recent years. In order to harness the prospects of quantum computing, secure communication, teleportation, and the like, the development of techniques to accurately control and measure quantum states has now become a matter of practical as well as fundamental interest. However, there is no general answer to Pauli's very basic question, and quantum state reconstruction algorithms have been developed and experimentally demonstrated only for a few systems so far. This thesis presents a novel experimental method to measure the unknown and generally mixed quantum state for an angular momentum of arbitrary magnitude. The (2F + 1) x (2F + 1) density matrix describing the quantum state is hereby completely determined from a set of Stern-Gerlach measurements with (4F + 1) different orientations of the quantization axis. This protocol is implemented for laser cooled Cesium atoms in the 6S1/2(F = 4) hyperfine ground state manifold, and is applied to a number of test states prepared by optical pumping and Larmor precession. A comparison of the input and the measured states shows successful reconstructions with fidelities of about 0.95.
NASA Astrophysics Data System (ADS)
Wouters, Sebastian; Nakatani, Naoki; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2013-08-01
The similarities between Hartree-Fock (HF) theory and the density matrix renormalization group (DMRG) are explored. Both methods can be formulated as the variational optimization of a wave-function Ansatz. Linearization of the time-dependent variational principle near a variational minimum allows to derive the random phase approximation (RPA). We show that the nonredundant parameterization of the matrix product state (MPS) tangent space [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.070601 107, 070601 (2011)] leads to the Thouless theorem for MPS, i.e., an explicit nonredundant parameterization of the entire MPS manifold, starting from a specific MPS reference. Excitation operators are identified, which extends the analogy between HF and DMRG to the Tamm-Dancoff approximation (TDA), the configuration interaction (CI) expansion, and coupled cluster theory. For a small one-dimensional Hubbard chain, we use a CI-MPS Ansatz with single and double excitations to improve on the ground state and to calculate low-lying excitation energies. For a symmetry-broken ground state of this model, we show that RPA-MPS allows to retrieve the Goldstone mode. We also discuss calculations of the RPA-MPS correlation energy. With the long-range quantum chemical Pariser-Parr-Pople Hamiltonian, low-lying TDA-MPS and RPA-MPS excitation energies for polyenes are obtained.
NASA Astrophysics Data System (ADS)
Saini, Anshul; Stojkovic, Dejan
2016-09-01
We study time-dependent Hawking-like radiation as seen by an infalling observer during gravitational collapse of a thin shell. We calculate the occupation number of particles of which the frequencies are measured in the proper time of an infalling observer in Eddington-Finkelstein coordinates. We solve the equations for the whole process from the beginning of the collapse till the moment when the collapsing shell reaches zero radius. The radiation distribution is not thermal in the whole frequency regime, but it is approximately thermal for the wavelengths of the order of the Schwarzschild radius of the collapsing shell. After the Schwarzschild radius is crossed, the temperature increases without limits as the singularity is approached. We also calculate the density matrix associated with this radiation. It turns out that the off-diagonal correlation terms to the diagonal Hawking leading-order terms are very important. While the trace of the diagonal (Hawking) density matrix squared decreases during the evolution, the trace of the total density matrix squared remains unity at all times and all frequencies.
Shrinkage approach for EEG covariance matrix estimation.
Beltrachini, Leandro; von Ellenrieder, Nicolas; Muravchik, Carlos H
2010-01-01
We present a shrinkage estimator for the EEG spatial covariance matrix of the background activity. We show that such an estimator has some advantages over the maximum likelihood and sample covariance estimators when the number of available data to carry out the estimation is low. We find sufficient conditions for the consistency of the shrinkage estimators and results concerning their numerical stability. We compare several shrinkage schemes and show how to improve the estimator by incorporating known structure of the covariance matrix.
The origin of linear scaling Fock matrix calculation with density prescreening
Mitin, Alexander V.
2015-12-31
A theorem was proven, which reads that the number of nonzero two-electron integrals scales linearly with respect to the number of basis functions for large molecular systems. This permits to show that linear scaling property of the Fock matrix calculation with using density prescreening arises due to linear scaling properties of the number of nonzero two-electron integrals and the number of leading matrix elements of density matrix. This property is reinforced by employing the density prescreening technique. The use of the density difference prescreening further improves the linear scaling property of the Fock matrix calculation method. As a result, the linear scaling regime of the Fock matrix calculation can begin from the number of basis functions of 2000–3000 in dependence on the basis function type in molecular calculations. It was also shown that the conventional algorithm of Fock matrix calculation from stored nonzero two-electron integrals with density prescreening possesses linear scaling property.
Reduced density-matrix functional theory: Correlation and spectroscopy
Di Sabatino, S.; Romaniello, P.; Berger, J. A.; Reining, L.
2015-07-14
In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.
Nuclear level density: Shell-model approach
NASA Astrophysics Data System (ADS)
Sen'kov, Roman; Zelevinsky, Vladimir
2016-06-01
Knowledge of the nuclear level density is necessary for understanding various reactions, including those in the stellar environment. Usually the combinatorics of a Fermi gas plus pairing is used for finding the level density. Recently a practical algorithm avoiding diagonalization of huge matrices was developed for calculating the density of many-body nuclear energy levels with certain quantum numbers for a full shell-model Hamiltonian. The underlying physics is that of quantum chaos and intrinsic thermalization in a closed system of interacting particles. We briefly explain this algorithm and, when possible, demonstrate the agreement of the results with those derived from exact diagonalization. The resulting level density is much smoother than that coming from conventional mean-field combinatorics. We study the role of various components of residual interactions in the process of thermalization, stressing the influence of incoherent collision-like processes. The shell-model results for the traditionally used parameters are also compared with standard phenomenological approaches.
Performance of the density matrix functional theory in the quantum theory of atoms in molecules.
García-Revilla, Marco; Francisco, E; Costales, A; Martín Pendás, A
2012-02-02
The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.
NASA Astrophysics Data System (ADS)
Mendoza-Arenas, J. J.; Franco, R.; Silva-Valencia, J.
2010-01-01
We analyze the one-dimensional Kondo necklace model, at zero temperature, with an anisotropy parameter η in the interaction of the conduction chain, by means of the density matrix renormalization group. We calculate the energy gap and estimate the quantum critical points that separate a Kondo singlet state from an antiferromagnetic state, assuming a Kosterlitz-Thouless tendency. We also observe the correlation functions and the structure factors that support our critical points. The resulting phase diagram is presented and compared to that reported previously using Lanczos calculations. It is shown that the quantum critical points vary very slowly with η , but when η approaches zero, they drop abruptly.
NASA Astrophysics Data System (ADS)
Huo, Pengfei; Coker, David F.
2011-11-01
An approach for treating dissipative, non-adiabatic quantum dynamics in general model systems at finite temperature based on linearizing the density matrix evolution in the forward-backward path difference for the environment degrees of freedom is presented. We demonstrate that the approach can capture both short time coherent quantum dynamics and long time thermal equilibration in an application to excitation energy transfer in a model photosynthetic light harvesting complex. Results are also presented for some nonadiabatic scattering models which indicate that, even though the method is based on a "mean trajectory" like scheme, it can accurately capture electronic population branching through multiple avoided crossing regions and that the approach offers a robust and reliable way to treat quantum dynamical phenomena in a wide range of condensed phase applications.
Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study
Krogel, Jaron T; Kim, Jeongnim; Reboredo, Fernando A
2014-01-01
We develop an energy density matrix that parallels the one-body reduced density matrix (1RDM) for many-body quantum systems. Just as the density matrix gives access to the number density and occupation numbers, the energy density matrix yields the energy density and orbital occupation energies. The eigenvectors of the matrix provide a natural orbital partitioning of the energy density while the eigenvalues comprise a single particle energy spectrum obeying a total energy sum rule. For mean-field systems the energy density matrix recovers the exact spectrum. When correlation becomes important, the occupation energies resemble quasiparticle energies in some respects. We explore the occupation energy spectrum for the finite 3D homogeneous electron gas in the metallic regime and an isolated oxygen atom with ground state quantum Monte Carlo techniques imple- mented in the QMCPACK simulation code. The occupation energy spectrum for the homogeneous electron gas can be described by an effective mass below the Fermi level. Above the Fermi level evanescent behavior in the occupation energies is observed in similar fashion to the occupation numbers of the 1RDM. A direct comparison with total energy differences demonstrates a quantita- tive connection between the occupation energies and electron addition and removal energies for the electron gas. For the oxygen atom, the association between the ground state occupation energies and particle addition and removal energies becomes only qualitative. The energy density matrix provides a new avenue for describing energetics with quantum Monte Carlo methods which have traditionally been limited to total energies.
Studying genetic code by a matrix approach.
Crowder, Tanner; Li, Chi-Kwong
2010-05-01
Following Petoukhov and his collaborators, we use two length n zero-one sequences, alpha and beta, to represent a length n genetic sequence (alpha/beta) so that the columns of (alpha/beta) have the following correspondence with the nucleotides: C ~ (0/0), U ~ (1/0), G ~ (1/1), A ~ (0/1). Using the Gray code ordering to arrange alpha and beta, we build a 2(n) x 2(n) matrix C(n) including all the 4(n) length n genetic sequences. Furthermore, we use the Hamming distance of alpha and beta to construct a 2(n) x 2(n) matrix D(n). We explore structures of these matrices, refine the results in earlier papers, and propose new directions for further research.
Skyrmion Approach to Finite Density and Temperature
NASA Astrophysics Data System (ADS)
Park, Byung-Yoon; Riska, D. O.
We review an approach, developed over the past few years, to describe hadronic matter at finite density and temperature, whose underlying theoretical framework is the Skyrme model, an effective low energy theory rooted in large Nc QCD. In this approach matter is described by various crystal structures of skyrmions, classical topological solitons carrying baryon number, from which conventional baryons appear by quantization. Chiral and scale symmetries play a crucial role in the dynamics as described by pion, dilaton and vector meson degrees of freedom. When compressed or heated skyrmion matter describes a rich phase diagram which has strong connections with the confinement/deconfinement phase transition.
Requist, Ryan; Pankratov, Oleg
2011-05-15
We prove that if the two-body terms in the equation of motion for the one-body reduced density matrix are approximated by ground-state functionals, the eigenvalues of the one-body reduced density matrix (occupation numbers) remain constant in time. This deficiency is related to the inability of such an approximation to account for relative phases in the two-body reduced density matrix. We derive an exact differential equation giving the functional dependence of these phases in an interacting Landau-Zener model and study their behavior in short- and long-time regimes. The phases undergo resonances whenever the occupation numbers approach the boundaries of the interval [0,1]. In the long-time regime, the occupation numbers display correlation-induced oscillations and the memory dependence of the functionals assumes a simple form.
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions.
Changlani, Hitesh J; Zheng, Huihuo; Wagner, Lucas K
2015-09-14
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U(∗)/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.
A random matrix approach to credit risk.
Münnix, Michael C; Schäfer, Rudi; Guhr, Thomas
2014-01-01
We estimate generic statistical properties of a structural credit risk model by considering an ensemble of correlation matrices. This ensemble is set up by Random Matrix Theory. We demonstrate analytically that the presence of correlations severely limits the effect of diversification in a credit portfolio if the correlations are not identically zero. The existence of correlations alters the tails of the loss distribution considerably, even if their average is zero. Under the assumption of randomly fluctuating correlations, a lower bound for the estimation of the loss distribution is provided.
High-harmonic spectra from time-dependent two-particle reduced-density-matrix theory
NASA Astrophysics Data System (ADS)
Lackner, Fabian; Březinová, Iva; Sato, Takeshi; Ishikawa, Kenichi L.; Burgdörfer, Joachim
2017-03-01
The ab initio description of the nonlinear response of many-electron systems to strong-laser fields remains a major challenge. In order to address larger systems, alternative methods need to be developed that bypass the exponential scaling with particle number inherent to conventional wave-function-based approaches. In this paper we present a fully three-dimensional implementation of the time-dependent two-particle reduced-density-matrix (TD-2RDM) method for many-electron atoms. We benchmark this approach by a comparison with multiconfigurational time-dependent Hartree-Fock results for the harmonic spectra of beryllium and neon. We show that the TD-2RDM is very well suited to describe the nonlinear atomic response and to reveal the influence of electron-correlation effects.
Multivariate and matrix-variate analogues of Maxwell-Boltzmann and Raleigh densities
NASA Astrophysics Data System (ADS)
Mathai, A. M.; Princy, T.
2017-02-01
The Maxwell-Boltzmann and Raleigh densities are basic densities in many problems in Physics. A multivariate analogue and a rectangular matrix-variate analogue of these densities are explored in this article. The results may become useful in extending the usual theories, where these densities for the real scalar variable case occur, to multivariate and matrix variable situations. Various properties are studied and connection to the volumes of parallelotopes determined by p linearly independent random points in Euclidean n-space, n ≥ p, is also established. Structural decompositions of these random determinants and pathway extensions of Maxwell-Boltzmann and Raleigh densities are also considered.
Edgar, Lowell T.; Hoying, James B.; Weiss, Jeffrey A.
2015-01-01
Mechanical interactions during angiogenesis, i.e., traction applied by neovessels to the extracellular matrix and the corresponding deformation, are important regulators of growth and neovascularization. We have previously designed, implemented, and validated a coupled model of angiogenesis in which a discrete microvessel growth model interacts with a continuous finite element mesh through the application of local remodeling sprout stresses (Edgar et al. in Biomech Model Mechanobiol, 2014). However, the initial implementation of this framework does not take matrix density into account when determined these remodeling stresses and is therefore insufficient for the study of angiogenesis within heterogeneous matrix environments such as those found in vivo. The objective of this study was to implement sensitivity to matrix density in the active stress generation within AngioFE in order to allow the study of angiogenic growth within a heterogeneous density environment. We accomplished this by scaling active sprout stresses relative to local matrix density using a scaling factor previously determined from experimental data. We then exercised the new functionality of the model by simulating angiogenesis within four different scenarios: homogeneous density, a narrow gap model, and matrix density gradient, and a construct subjected to repeated loading/unloading and preconditioning. These numerical experiments predicted heterogeneous matrix density in the initially homogeneous case, the closure and alignment of microvessels along a low-density gap, the formation of a unique cap-like structure during angiogenesis within a density gradient, and the alignment of microvessels in the absence of applied load due to preconditioning. The result of these in silico investigations demonstrate how matrix heterogeneity affects neovascularization and matrix deformation and provides a platform for studying angiogenesis in complicated and multi-faceted mechanical environments that
Metal-insulator transition in disordered systems from the one-body density matrix
NASA Astrophysics Data System (ADS)
Olsen, Thomas; Resta, Raffaele; Souza, Ivo
2017-01-01
The insulating state of matter can be probed by means of a ground state geometrical marker, which is closely related to the modern theory of polarization (based on a Berry phase). In the present work we show that this marker can be applied to determine the metal-insulator transition in disordered systems. In particular, for noninteracting systems the geometrical marker can be obtained from the configurational average of the norm-squared one-body density matrix, which can be calculated within open as well as periodic boundary conditions. This is in sharp contrast to a classification based on the static conductivity, which is only sensible within periodic boundary conditions. We exemplify the method by considering a simple lattice model, known to have a metal-insulator transition as a function of the disorder strength, and demonstrate that the transition point can be obtained accurately from the one-body density matrix. The approach has a general ab initio formulation and could in principle be applied to realistic disordered materials by standard electronic structure methods.
The reduced density matrix method and the role of three-index representability conditions
NASA Astrophysics Data System (ADS)
Braams, Bastiaan J.; Zhao, Zhengji; Fukuda, Mituhiro; Overton, Michael L.; Percus, Jerome K.
2004-03-01
The variational approach for electronic structure based on the two-body reduced density matrix is studied, incorporating two representability conditions beyond the previously used P, Q and G conditions. The additional conditions (called T1 and T2 here) are implicit in work of R. M. Erdahl and extend the well-known three-index diagonal conditions also known as the Weinhold-Wilson inequalities. Calculations of the ground state energy and the dipole moment are reported for 47 different systems, in each case using an STO-6G basis set and comparing with Hartree-Fock, SDCI, BD(T), CCSD(T) and full CI calculations [2]. It is found that the use of the T1 and T2 conditions gives a significant improvement over just the P, Q and G conditions, and provides in all cases that we have studied more accurate results than the other mentioned approximations. [1] R. M. Erdahl, Int. J. Quantum Chem. 13, 697--718 (1978). [2] Zhengji Zhao, Bastiaan J. Braams, Mituhiro Fukuda, Michael L. Overton and Jerome K. Percus: "The reduced density matrix method and the role of three-index representability conditions". Accepted for publication in Journal of Chemical Physics.
Quantum Monte Carlo with density matrix: potential energy curve derived properties.
Bonfim, Víctor S; Borges, Nádia M; Martins, João B L; Gargano, Ricardo; Politi, José Roberto Dos S
2017-04-01
In this work, we used diffusion quantum Monte Carlo with density matrix (d-DMC) and variational quantum Monte Carlo (d-VMC) to determine the potential energy curve (PEC) and obtain the spectroscopic constants of H2 molecule in the ground state, in order to evaluate the capability of these methods to provide an accurate PEC description. These quantum Monte Carlo methods build with density matrix are new approaches to conventional quantum Monte Carlo methods based on wave function formed by product of α and β determinants. To investigate the robustness of d-DMC, we performed calculations with two different basis sets and analyzed the influence of the size of these sets on results. To the best of our knowledge, this is the first study that shows the dissociation energy and rotational constant obtained from d-QMC. We found that the quality of PEC described by the d-DMC is essentially coincident with the most accurate results available in the literature, regardless of the complexity of basis set employed.
Density matrix perturbation theory for magneto-optical response of periodic insulators
NASA Astrophysics Data System (ADS)
Lebedeva, Irina; Tokatly, Ilya; Rubio, Angel
2015-03-01
Density matrix perturbation theory offers an ideal theoretical framework for the description of response of solids to arbitrary electromagnetic fields. In particular, it allows to consider perturbations introduced by uniform electric and magnetic fields under periodic boundary conditions, though the corresponding potentials break the translational invariance of the Hamiltonian. We have implemented the density matrix perturbation theory in the open-source Octopus code on the basis of the efficient Sternheimer approach. The procedures for responses of different order to electromagnetic fields, including electric polarizability, orbital magnetic susceptibility and magneto-optical response, have been developed and tested by comparison with the results for finite systems and for wavefunction-based perturbation theory, which is already available in the code. Additional analysis of the orbital magneto-optical response is performed on the basis of analytical models. Symmetry limitations to observation of the magneto-optical response are discussed. The financial support from the Marie Curie Fellowship PIIF-GA-2012-326435 (RespSpatDisp) is gratefully acknowledged.
The single-particle density matrix of a quantum bright soliton from the coordinate Bethe ansatz
NASA Astrophysics Data System (ADS)
Ayet, Alex; Brand, Joachim
2017-02-01
We present a novel approach for computing reduced density matrices for superpositions of eigenstates of a Bethe-ansatz solvable model by direct integration of the wave function in coordinate representation. A diagrammatic approach is developed to keep track of relevant terms and identify symmetries, which helps to reduce the number of terms that have to be evaluated numerically. As a first application we compute with modest numerical resources the single-particle density matrix and its eigenvalues including the condensate fraction for a quantum bright soliton with up to N = 10 bosons. The latter are constructed as superpositions of string-type Bethe-ansatz eigenstates of nonrelativistic bosons in one spatial dimension with attractive contact interaction. Upon delocalising the superposition in momentum space we find that the condensate fraction reaches maximum values larger than 97% with weak particle-number dependence in the range of particles studied. The presented approach is suitable for studying time-dependent problems and generalises to higher-order correlation functions.
NASA Astrophysics Data System (ADS)
Longbiao, Li
2015-12-01
The matrix multicracking evolution of cross-ply ceramic-matrix composites (CMCs) has been investigated using energy balance approach. The multicracking of cross-ply CMCs was classified into five modes, i.e., (1) mode 1: transverse multicracking; (2) mode 2: transverse multicracking and matrix multicracking with perfect fiber/matrix interface bonding; (3) mode 3: transverse multicracking and matrix multicracking with fiber/matrix interface debonding; (4) mode 4: matrix multicracking with perfect fiber/matrix interface bonding; and (5) mode 5: matrix multicracking with fiber/matrix interface debonding. The stress distributions of four cracking modes, i.e., mode 1, mode 2, mode 3 and mode 5, are analysed using shear-lag model. The matrix multicracking evolution of mode 1, mode 2, mode 3 and mode 5, has been determined using energy balance approach. The effects of ply thickness and fiber volume fraction on matrix multicracking evolution of cross-ply CMCs have been investigated.
Density matrix of radiation of a black hole with a fluctuating horizon
NASA Astrophysics Data System (ADS)
Iofa, Mikhail Z.
2016-09-01
The density matrix of Hawking radiation is calculated in the model of a black hole with a fluctuating horizon. Quantum fluctuations smear the classical horizon of a black hole and modify the density matrix of radiation producing the off-diagonal elements. The off-diagonal elements may store information on correlations between the radiation and the black hole. The smeared density matrix was constructed by convolution of the density matrix calculated with the instantaneous horizon with the Gaussian distribution over the instantaneous horizons. The distribution has the extremum at the classical radius of the black hole and the width of order of the Planck length. Calculations were performed in the model of a black hole formed by the thin collapsing shell which follows a trajectory that is a solution of the matching equations connecting the interior and exterior geometries.
A Problem-Centered Approach to Canonical Matrix Forms
ERIC Educational Resources Information Center
Sylvestre, Jeremy
2014-01-01
This article outlines a problem-centered approach to the topic of canonical matrix forms in a second linear algebra course. In this approach, abstract theory, including such topics as eigenvalues, generalized eigenspaces, invariant subspaces, independent subspaces, nilpotency, and cyclic spaces, is developed in response to the patterns discovered…
The transfer matrix approach to circular graphene quantum dots
NASA Astrophysics Data System (ADS)
Chau Nguyen, H.; Nguyen, Nhung T. T.; Nguyen, V. Lien
2016-07-01
We adapt the transfer matrix (T-matrix) method originally designed for one-dimensional quantum mechanical problems to solve the circularly symmetric two-dimensional problem of graphene quantum dots. Similar to one-dimensional problems, we show that the generalized T-matrix contains rich information about the physical properties of these quantum dots. In particular, it is shown that the spectral equations for bound states as well as quasi-bound states of a circular graphene quantum dot and related quantities such as the local density of states and the scattering coefficients are all expressed exactly in terms of the T-matrix for the radial confinement potential. As an example, we use the developed formalism to analyse physical aspects of a graphene quantum dot induced by a trapezoidal radial potential. Among the obtained results, it is in particular suggested that the thermal fluctuations and electrostatic disorders may appear as an obstacle to controlling the valley polarization of Dirac electrons.
Technology Transfer Automated Retrieval System (TEKTRAN)
Ecological edge effects are sensitive to landscape context. In particular, edge effects can be altered by matrix type and by the presence of other nearby edges. We experimentally altered patch configurations in an African savanna to determine how edge density and matrix type influence edge effect de...
Transforming DOD Capabilities. A Matrix Approach
2003-01-01
transformation of DoD. 3 WHY TRANSFORM PPBS? According to one student of the process, Lieutenant Colonel William H. Maglin , II, USA, “The PPBS is DoD’s...of the Systems Approach,” Principia Cybernetica Web, 19 October 1998, <http://pespmc1.vub.ac.be/SYSAPPR.html> (15 Apr 2003). 4 LTC William H. Maglin ...II, USA, “Reforming PPBS: Its Time Has Come,” USAWC Strategy Research Project, (U. S. Army War College, Carlisle Barracks, PA, 1998), 2. 5 Maglin
Shell Model Approach to Nuclear Level Density
NASA Astrophysics Data System (ADS)
Horoi, Mihai
2000-04-01
Nuclear level densities (NLD) are traditionally estimated using variations of Fermi Gas Formula (FGF) or combinatoric techniques. Recent investigations using Monte Carlo Shell Model (MCSM) techniques indicate that a shell model description of NLD may be an accurate and stable approach. Full shell model calculations of NLD are very difficult. We calculated the NLD for all nuclei in the sd shell and show that the results can be described by a single particle combinatoric model, which depends on two parameters similar to FGF. We further investigated other models and find that a sum of gaussians with means and variances given by French and Ratcliff averages (Phys. Rev. C 3, 94(1971)) is able to accurately describe shell model NLD, even when shell effects are present. The contribution of the spurious center-of-mass motion to the shell model NLD is also discussed.
2017-01-01
We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex. PMID:28094988
Freitag, Leon; Knecht, Stefan; Angeli, Celestino; Reiher, Markus
2017-02-14
We present a second-order N-electron valence state perturbation theory (NEVPT2) based on a density matrix renormalization group (DMRG) reference wave function that exploits a Cholesky decomposition of the two-electron repulsion integrals (CD-DMRG-NEVPT2). With a parameter-free multireference perturbation theory approach at hand, the latter allows us to efficiently describe static and dynamic correlation in large molecular systems. We demonstrate the applicability of CD-DMRG-NEVPT2 for spin-state energetics of spin-crossover complexes involving calculations with more than 1000 atomic basis functions. We first assess, in a study of a heme model, the accuracy of the strongly and partially contracted variant of CD-DMRG-NEVPT2 before embarking on resolving a controversy about the spin ground state of a cobalt tropocoronand complex.
Symmetry-conserving purification of quantum states within the density matrix renormalization group
Nocera, Alberto; Alvarez, Gonzalo
2016-01-28
The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces andmore » using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.« less
Symmetry-conserving purification of quantum states within the density matrix renormalization group
Nocera, Alberto; Alvarez, Gonzalo
2016-01-28
The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero-temperature or ground-state properties of one-dimensional strongly correlated quantum systems. The development of the algorithm at finite temperature has been a topic of much interest, because of the usefulness of thermodynamics quantities in understanding the physics of condensed matter systems, and because of the increased complexity associated with efficiently computing temperature-dependent properties. The ancilla method is a DMRG technique that enables the computation of these thermodynamic quantities. In this paper, we review the ancilla method, and improve its performance by working on reduced Hilbert spaces and using canonical approaches. Furthermore we explore its applicability beyond spins systems to t-J and Hubbard models.
NASA Astrophysics Data System (ADS)
Ito, Fumiyuki
2010-12-01
The supermolecule approach has been used to model molecules embedded in solid argon matrix, wherein interaction between the guest and the host atoms in the first solvation shell is evaluated with the use of density functional calculations. Structural stability and simulated spectra have been obtained for formic acid dimer (FAD)-Arn (n = 21-26) clusters. The calculations at the B971/6-31++G(3df,3pd) level have shown that the tetrasubstitutional site on Ar(111) plane is likely to incorporate FAD most stably, in view of consistency with the matrix shifts available experimentally.
Distinguishing chaotic time series from noise: A random matrix approach
NASA Astrophysics Data System (ADS)
Ye, Bin; Chen, Jianxing; Ju, Chen; Li, Huijun; Wang, Xuesong
2017-03-01
Deterministically chaotic systems can often give rise to random and unpredictable behaviors which make the time series obtained from them to be almost indistinguishable from noise. Motivated by the fact that data points in a chaotic time series will have intrinsic correlations between them, we propose a random matrix theory (RMT) approach to identify the deterministic or stochastic dynamics of the system. We show that the spectral distributions of the correlation matrices, constructed from the chaotic time series, deviate significantly from the predictions of random matrix ensembles. On the contrary, the eigenvalue statistics for a noisy signal follow closely those of random matrix ensembles. Numerical results also indicate that the approach is to some extent robust to additive observational noise which pollutes the data in many practical situations. Our approach is efficient in recognizing the continuous chaotic dynamics underlying the evolution of the time series.
NASA Astrophysics Data System (ADS)
Todoroki, Akira; Omagari, Kazuomi
Carbon Fiber Reinforced Plastic (CFRP) laminates are adopted for fuel tank structures of next generation space rockets or automobiles. Matrix cracks may cause fuel leak or trigger fatigue damage. A monitoring system of the matrix crack density is required. The authors have developed an electrical resistance change method for the monitoring of delamination cracks in CFRP laminates. Reinforcement fibers are used as a self-sensing system. In the present study, the electric potential method is adopted for matrix crack density monitoring. Finite element analysis (FEA) was performed to investigate the possibility of monitoring matrix crack density using multiple electrodes mounted on a single surface of a specimen. The FEA reveals the matrix crack density increases electrical resistance for a target segment between electrodes. Experimental confirmation was also performed using cross-ply laminates. Eight electrodes were mounted on a single surface of a specimen using silver paste after polishing of the specimen surface with sandpaper. The two outermost electrodes applied electrical current, and the inner electrodes measured electric voltage changes. The slope of electrical resistance during reloading is revealed to be an appropriate index for the detection of matrix crack density.
Construct order parameters from the reduced density matrix spectra
Gu, Shi-Jian; Yu, Wing Chi; Lin, Hai-Qing
2013-09-15
In this paper, we try to establish a connection between a quantum information concept, i.e., the mutual information, and the conventional order parameter in condensed matter physics. We show that non-vanishing mutual information between two subsystems separated by a long distance means the existence of long-range orders in the system. By analyzing the spectra of the reduced density matrices that are used to calculate the mutual information, we show how to derive the local order operators that identify various ordered phases in condensed matter physics. -- Highlights: •Discussed the relation between long-range order and the mutual information (MI). •Pointed out how to check the existence of long-range order from MI. •Proposed a scheme to derive the diagonal and off-diagonal order parameter. •Gave three examples to show the effectiveness of the scheme.
NASA Technical Reports Server (NTRS)
Bhatt, Ramakrishna T.; Kiser, Lames D.
1990-01-01
The room temperature mechanical properties were measured for SiC fiber reinforced reaction-bonded silicon nitride composites (SiC/RBSN) of different densities. The composites consisted of approx. 30 vol percent uniaxially aligned 142 micron diameter SiC fibers (Textron SCS-6) in a reaction-bonded Si3N4 matrix. The composite density was varied by changing the consolidation pressure during RBSN processing and by hot isostatically pressing the SiC/RBSN composites. Results indicate that as the consolidation pressure was increased from 27 to 138 MPa, the average pore size of the nitrided composites decreased from 0.04 to 0.02 microns and the composite density increased from 2.07 to 2.45 gm/cc. Nonetheless, these improvements resulted in only small increases in the first matrix cracking stress, primary elastic modulus, and ultimate tensile strength values of the composites. In contrast, HIP consolidation of SiC/RBSN resulted in a fully dense material whose first matrix cracking stress and elastic modulus were approx. 15 and 50 percent higher, respectively, and ultimate tensile strength values were approx. 40 percent lower than those for unHIPed SiC/RBSN composites. The modulus behavior for all specimens can be explained by simple rule-of-mixture theory. Also, the loss in ultimate strength for the HIPed composites appears to be related to a degradation in fiber strength at the HIP temperature. However, the density effect on matrix fracture strength was much less than would be expected based on typical monolithic Si3N4 behavior, suggesting that composite theory is indeed operating. Possible practical implications of these observations are discussed.
A Contemporary Matrix Approach to Defining Shared Governance.
ERIC Educational Resources Information Center
Davenport, Richard; Daniels, Elaine; Jones, James; Kesseler, Roger; Mowrey, Merlyn
This paper outlines a matrix approach to shared governance developed at Central Michigan University (CMU), designed to help faculty and administrators focus on specific decision areas and to define existing roles more clearly. The process began at CMU in spring 1998 with the formation of an ad hoc committee on governance which surveyed faculty and…
A Surrogate Measure of Cortical Bone Matrix Density by Long T2-Suppressed MRI
Seifert, Alan C.; Li, Cheng; Wehrli, Suzanne L.; Wehrli, Felix W.
2015-01-01
Magnetic resonance has the potential to image and quantify two pools of water within bone: free water within the Haversian pore system (transverse relaxation time, T2 > 1 ms), and water hydrogen-bonded to matrix collagen (T2 ~ 300–400 µs). While total bone water concentration quantified by MRI has been shown to scale with porosity, greater insight into bone matrix density and porosity may be gained by relaxation-based separation of bound and pore water fractions. The objective of this study was to evaluate a recently developed surrogate measurement for matrix density, single adiabatic inversion recovery (SIR) zero echo-time (ZTE) MRI, in human bone. Specimens of tibial cortical bone from 15 donors (27–97 y/o, eight female and seven male) were examined at 9.4T field strength using two methods: (1) 1H ZTE MRI, to capture total 1H signal, and (2) 1H SIR-ZTE MRI, to selectively image matrix-associated 1H signal. Total water, bone matrix, and bone mineral densities were also quantified gravimetrically, and porosity was measured by micro-CT. ZTE apparent total water 1H concentration was 32.7±3.2 M (range: 28.5–40.3 M), and was correlated positively with porosity (R2 = 0.80) and negatively with matrix and mineral densities (R2 = 0.90 and 0.82, respectively). SIR-ZTE apparent bound water 1H concentration was 32.9±3.9 M (range: 24.4–39.8 M), and its correlations were opposite to those of apparent total water: negative with porosity (R2 = 0.73) and positive with matrix density (R2 = 0.74) and mineral density (R2 = 0.72). Porosity was strongly correlated with gravimetric matrix density (R2 = 0.91, negative) and total water density (R2 = 0.92, positive). The strong correlations of SIR-ZTE-derived apparent bound water 1H concentration with ground-truth measurements suggest that this quantitative solid-state MRI method provides a nondestructive surrogate measure of bone matrix density. PMID:26085307
Smallwood, D.O.
1995-08-07
It is shown that the usual method for computing the coherence functions (ordinary, partial, and multiple) for a general multiple-input/multiple-output problem can be expressed as a modified form of Cholesky decomposition of the cross spectral density matrix of the inputs and outputs. The modified form of Cholesky decomposition used is G{sub zz} = LCL{prime}, where G is the cross spectral density matrix of inputs and outputs, L is a lower; triangular matrix with ones on the diagonal, and C is a diagonal matrix, and the symbol {prime} denotes the conjugate transpose. If a diagonal element of C is zero, the off diagonal elements in the corresponding column of L are set to zero. It is shown that the results can be equivalently obtained using singular value decomposition (SVD) of G{sub zz}. The formulation as a SVD problem suggests a way to order the inputs when a natural physical order of the inputs is absent.
Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions
Changlani, Hitesh J.; Zheng, Huihuo; Wagner, Lucas K.
2015-09-14
We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U{sup ∗}/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.
Nonequilibrium density-matrix description of steady-state quantum transport.
Dhar, Abhishek; Saito, Keiji; Hänggi, Peter
2012-01-01
With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the explicit result for the reduced density matrix of quantum transport when the system, the connecting reservoirs, and the system-reservoir interactions are described by quadratic Hamiltonians. Our procedure is detailed for both electronic transport described by the tight-binding Hamiltonian and for phonon transport described by harmonic Hamiltonians. For the special case of weak system-reservoir couplings, a more detailed description of the steady-state density matrix is obtained. Several paradigm transport setups for interelectrode electron transport and low-dimensional phonon heat flux are elucidated.
Alternative Approaches to High Energy Density Fusion
NASA Astrophysics Data System (ADS)
Hammer, J.
2016-10-01
This paper explores selected approaches to High Energy Density (HED) fusion, beginning with discussion of ignition requirements at the National Ignition Facility (NIF). The needed improvements to achieve ignition are closely tied to the ability to concentrate energy in the implosion, manifested in the stagnation pressure, Pstag. The energy that must be assembled in the imploded state to ignite varies roughly as Pstag-2, so among other requirements, there is a premium on reaching higher Pstag to achieve ignition with the available laser energy. The U.S. inertial confinement fusion program (ICF) is pursuing higher Pstag on NIF through improvements to capsule stability and symmetry. One can argue that recent experiments place an approximate upper bound on the ultimate ignition energy requirement. Scaling the implosions consistently in spatial, temporal and energy scales shows that implosions of the demonstrated quality ignite robustly at 9-15 times the current energy of NIF. While lasers are unlikely to reach that bounding energy, it appears that pulsed-power sources could plausibly do so, giving a range of paths forward for ICF depending on success in improving energy concentration. In this paper, I show the scaling arguments then discuss topics from my own involvement in HED fusion. The recent Viewfactor experiments at NIF have shed light on both the observed capsule drive deficit and errors in the detailed modelling of hohlraums. The latter could be important factors in the inability to achieve the needed symmetry and energy concentration. The paper then recounts earlier work in Fast Ignition and the uses of pulsed-power for HED and fusion applications. It concludes with a description of a method for improving pulsed-power driven hohlraums that could potentially provide a factor of 10 in energy at NTF-like drive conditions and reach the energy bound for indirect drive ICF.
Progressive delamination in polymer matrix composite laminates: A new approach
NASA Technical Reports Server (NTRS)
Chamis, C. C.; Murthy, P. L. N.; Minnetyan, L.
1992-01-01
A new approach independent of stress intensity factors and fracture toughness parameters has been developed and is described for the computational simulation of progressive delamination in polymer matrix composite laminates. The damage stages are quantified based on physics via composite mechanics while the degradation of the laminate behavior is quantified via the finite element method. The approach accounts for all types of composite behavior, laminate configuration, load conditions, and delamination processes starting from damage initiation, to unstable propagation, and to laminate fracture. Results of laminate fracture in composite beams, panels, plates, and shells are presented to demonstrate the effectiveness and versatility of this new approach.
Approach of high density coal preparation method
Yang, Y.; Chen, Q.
1996-12-31
Density difference of aged anthracite coal of high density and discard is less than that of general coal and discard; conventional separation methods are difficult to be used. For the special coal, coal dry beneficiation technology with air-dense medium fluidized bed has obvious superiority over other separation methods.
Matrix sublimation method for the formation of high-density amorphous ice
NASA Astrophysics Data System (ADS)
Kouchi, A.; Hama, T.; Kimura, Y.; Hidaka, H.; Escribano, R.; Watanabe, N.
2016-08-01
A novel method for the formation of amorphous ice involving matrix sublimation has been developed. A CO-rich CO:H2O mixed ice was deposited at 8-10 K under ultra-high vacuum condition, which was then allowed to warm. After the sublimation of matrix CO at 35 K, amorphous ice remained. The amorphous ice formed exhibits a highly porous microscale texture; however, it also rather exhibits a density similar to that of high-density amorphous ice formed under high pressure. Furthermore, unlike conventional vapor-deposited amorphous ice, the amorphous ice is stable up to 140 K, where it transforms directly to cubic ice Ic.
Edgar, Lowell T.; Underwood, Clayton J.; Guilkey, James E.; Hoying, James B.; Weiss, Jeffrey A.
2014-01-01
Angiogenesis is regulated by the local microenvironment, including the mechanical interactions between neovessel sprouts and the extracellular matrix (ECM). However, the mechanisms controlling the relationship of mechanical and biophysical properties of the ECM to neovessel growth during sprouting angiogenesis are just beginning to be understood. In this research, we characterized the relationship between matrix density and microvascular topology in an in vitro 3D organ culture model of sprouting angiogenesis. We used these results to design and calibrate a computational growth model to demonstrate how changes in individual neovessel behavior produce the changes in vascular topology that were observed experimentally. Vascularized gels with higher collagen densities produced neovasculatures with shorter vessel lengths, less branch points, and reduced network interconnectivity. The computational model was able to predict these experimental results by scaling the rates of neovessel growth and branching according to local matrix density. As a final demonstration of utility of the modeling framework, we used our growth model to predict several scenarios of practical interest that could not be investigated experimentally using the organ culture model. Increasing the density of the ECM significantly reduced angiogenesis and network formation within a 3D organ culture model of angiogenesis. Increasing the density of the matrix increases the stiffness of the ECM, changing how neovessels are able to deform and remodel their surroundings. The computational framework outlined in this study was capable of predicting this observed experimental behavior by adjusting neovessel growth rate and branching probability according to local ECM density, demonstrating that altering the stiffness of the ECM via increasing matrix density affects neovessel behavior, thereby regulated vascular topology during angiogenesis. PMID:24465500
Prevention of accidental exposure in radiotherapy: the risk matrix approach.
Vilaragut, J J; Duménigo, C; Delgado, J M; Morales, J; McDonnell, J D; Ferro, R; Ortiz López, P; Ramírez, M L; Pérez Mulas, A; Papadopulos, S; Gonçalves, M; López Morones, R; Sánchez Cayuela, C; Cascajo Castresana, A; Somoano, F; Álvarez, C; Guillén, A; Rodríguez, M; Pereira, P P; Nader, A
2013-02-01
Knowledge and lessons from past accidental exposures in radiotherapy are very helpful in finding safety provisions to prevent recurrence. Disseminating lessons is necessary but not sufficient. There may be additional latent risks for other accidental exposures, which have not been reported or have not occurred, but are possible and may occur in the future if not identified, analyzed, and prevented by safety provisions. Proactive methods are available for anticipating and quantifying risk from potential event sequences. In this work, proactive methods, successfully used in industry, have been adapted and used in radiotherapy. Risk matrix is a tool that can be used in individual hospitals to classify event sequences in levels of risk. As with any anticipative method, the risk matrix involves a systematic search for potential risks; that is, any situation that can cause an accidental exposure. The method contributes new insights: The application of the risk matrix approach has identified that another group of less catastrophic but still severe single-patient events may have a higher probability, resulting in higher risk. The use of the risk matrix approach for safety assessment in individual hospitals would provide an opportunity for self-evaluation and managing the safety measures that are most suitable to the hospital's own conditions.
Computing the Density Matrix in Electronic Structure Theory on Graphics Processing Units.
Cawkwell, M J; Sanville, E J; Mniszewski, S M; Niklasson, Anders M N
2012-11-13
The self-consistent solution of a Schrödinger-like equation for the density matrix is a critical and computationally demanding step in quantum-based models of interatomic bonding. This step was tackled historically via the diagonalization of the Hamiltonian. We have investigated the performance and accuracy of the second-order spectral projection (SP2) algorithm for the computation of the density matrix via a recursive expansion of the Fermi operator in a series of generalized matrix-matrix multiplications. We demonstrate that owing to its simplicity, the SP2 algorithm [Niklasson, A. M. N. Phys. Rev. B2002, 66, 155115] is exceptionally well suited to implementation on graphics processing units (GPUs). The performance in double and single precision arithmetic of a hybrid GPU/central processing unit (CPU) and full GPU implementation of the SP2 algorithm exceed those of a CPU-only implementation of the SP2 algorithm and traditional matrix diagonalization when the dimensions of the matrices exceed about 2000 × 2000. Padding schemes for arrays allocated in the GPU memory that optimize the performance of the CUBLAS implementations of the level 3 BLAS DGEMM and SGEMM subroutines for generalized matrix-matrix multiplications are described in detail. The analysis of the relative performance of the hybrid CPU/GPU and full GPU implementations indicate that the transfer of arrays between the GPU and CPU constitutes only a small fraction of the total computation time. The errors measured in the self-consistent density matrices computed using the SP2 algorithm are generally smaller than those measured in matrices computed via diagonalization. Furthermore, the errors in the density matrices computed using the SP2 algorithm do not exhibit any dependence of system size, whereas the errors increase linearly with the number of orbitals when diagonalization is employed.
Kinetic equations for a density matrix describing nonlinear effects in spectral line wings
Parkhomenko, A. I. Shalagin, A. M.
2011-11-15
Kinetic quantum equations are derived for a density matrix with collision integrals describing nonlinear effects in spectra line wings. These equations take into account the earlier established inequality of the spectral densities of Einstein coefficients for absorption and stimulated radiation emission by a two-level quantum system in the far wing of a spectral line in the case of frequent collisions. The relationship of the absorption and stimulated emission probabilities with the characteristics of radiation and an elementary scattering event is found.
Wen, Xiaotong; Rangarajan, Govindan; Ding, Mingzhou
2013-08-28
Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix.
Collagen Matrix Density Drives the Metabolic Shift in Breast Cancer Cells.
Morris, Brett A; Burkel, Brian; Ponik, Suzanne M; Fan, Jing; Condeelis, John S; Aguirre-Ghiso, Julio A; Castracane, James; Denu, John M; Keely, Patricia J
2016-11-01
Increased breast density attributed to collagen I deposition is associated with a 4-6 fold increased risk of developing breast cancer. Here, we assessed cellular metabolic reprogramming of mammary carcinoma cells in response to increased collagen matrix density using an in vitro 3D model. Our initial observations demonstrated changes in functional metabolism in both normal mammary epithelial cells and mammary carcinoma cells in response to changes in matrix density. Further, mammary carcinoma cells grown in high density collagen matrices displayed decreased oxygen consumption and glucose metabolism via the tricarboxylic acid (TCA) cycle compared to cells cultured in low density matrices. Despite decreased glucose entry into the TCA cycle, levels of glucose uptake, cell viability, and ROS were not different between high and low density matrices. Interestingly, under high density conditions the contribution of glutamine as a fuel source to drive the TCA cycle was significantly enhanced. These alterations in functional metabolism mirrored significant changes in the expression of metabolic genes involved in glycolysis, oxidative phosphorylation, and the serine synthesis pathway. This study highlights the broad importance of the collagen microenvironment to cellular expression profiles, and shows that changes in density of the collagen microenvironment can modulate metabolic shifts of cancer cells.
Progressive fracture of polymer matrix composite structures: A new approach
NASA Technical Reports Server (NTRS)
Chamis, C. C.; Murthy, P. L. N.; Minnetyan, L.
1992-01-01
A new approach independent of stress intensity factors and fracture toughness parameters has been developed and is described for the computational simulation of progressive fracture of polymer matrix composite structures. The damage stages are quantified based on physics via composite mechanics while the degradation of the structural behavior is quantified via the finite element method. The approach account for all types of composite behavior, structures, load conditions, and fracture processes starting from damage initiation, to unstable propagation and to global structural collapse. Results of structural fracture in composite beams, panels, plates, and shells are presented to demonstrate the effectiveness and versatility of this new approach. Parameters and guidelines are identified which can be used as criteria for structural fracture, inspection intervals, and retirement for cause. Generalization to structures made of monolithic metallic materials are outlined and lessons learned in undertaking the development of new approaches, in general, are summarized.
Exact and approximate many-body dynamics with stochastic one-body density matrix evolution
Lacroix, Denis
2005-06-01
We show that the dynamics of interacting fermions can be exactly replaced by a quantum jump theory in the many-body density matrix space. In this theory, jumps occur between densities formed of pairs of Slater determinants, D{sub ab}= vertical bar {phi}{sub a}><{phi}{sub b} vertical bar, where each state evolves according to the stochastic Schroedinger equation given by O. Juillet and Ph. Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. A stochastic Liouville-von Neumann equation is derived as well as the associated. Bogolyubov-Born-Green-Kirwood-Yvon hierarchy. Due to the specific form of the many-body density along the path, the presented theory is equivalent to a stochastic theory in one-body density matrix space, in which each density matrix evolves according to its own mean-field augmented by a one-body noise. Guided by the exact reformulation, a stochastic mean-field dynamics valid in the weak coupling approximation is proposed. This theory leads to an approximate treatment of two-body effects similar to the extended time-dependent Hartree-Fock scheme. In this stochastic mean-field dynamics, statistical mixing can be directly considered and jumps occur on a coarse-grained time scale. Accordingly, numerical effort is expected to be significantly reduced for applications.
Reduced-density-matrix spectrum and block entropy of permutationally invariant many-body systems.
Salerno, Mario; Popkov, Vladislav
2010-07-01
Spectral properties of the reduced density matrix (RDM) of permutational invariant quantum many-body systems are investigated. The RDM block diagonalization which accounts for all symmetries of the Hamiltonian is achieved. The analytical expression of the RDM spectrum is provided for arbitrary parameters and rigorously proved in the thermodynamical limit. The existence of several sum rules and recurrence relations among RDM eigenvalues is also demonstrated and the distribution function of RDM eigenvalues (including degeneracies) characterized. In particular, we prove that the distribution function approaches a two-dimensional Gaussian in the limit of large subsystem sizes n>1. As a physical application we discuss the von Neumann entropy (VNE) of a block of size n for a system of hard-core bosons on a complete graph, as a function of n and of the temperature T. The occurrence of a crossover of VNE from purely logarithmic behavior at T=0 to a purely linear behavior in n for T≥Tc, is demonstrated.
Analysis of gene set using shrinkage covariance matrix approach
NASA Astrophysics Data System (ADS)
Karjanto, Suryaefiza; Aripin, Rasimah
2013-09-01
Microarray methodology has been exploited for different applications such as gene discovery and disease diagnosis. This technology is also used for quantitative and highly parallel measurements of gene expression. Recently, microarrays have been one of main interests of statisticians because they provide a perfect example of the paradigms of modern statistics. In this study, the alternative approach to estimate the covariance matrix has been proposed to solve the high dimensionality problem in microarrays. The extension of traditional Hotelling's T2 statistic is constructed for determining the significant gene sets across experimental conditions using shrinkage approach. Real data sets were used as illustrations to compare the performance of the proposed methods with other methods. The results across the methods are consistent, implying that this approach provides an alternative to existing techniques.
On the ``Matrix Approach'' to Interacting Particle Systems
NASA Astrophysics Data System (ADS)
de Sanctis, L.; Isopi, M.
2004-04-01
Derrida et al. and Schütz and Stinchcombe gave algebraic formulas for the correlation functions of the partially asymmetric simple exclusion process. Here we give a fairly general recipe of how to get these formulas and extend them to the whole time evolution (starting from the generator of the process), for a certain class of interacting systems. We then analyze the algebraic relations obtained to show that the matrix approach does not work with some models such as the voter and the contact processes.
Infections on Temporal Networks—A Matrix-Based Approach
Koher, Andreas; Lentz, Hartmut H. K.; Hövel, Philipp; Sokolov, Igor M.
2016-01-01
We extend the concept of accessibility in temporal networks to model infections with a finite infectious period such as the susceptible-infected-recovered (SIR) model. This approach is entirely based on elementary matrix operations and unifies the disease and network dynamics within one algebraic framework. We demonstrate the potential of this formalism for three examples of networks with high temporal resolution: networks of social contacts, sexual contacts, and livestock-trade. Our investigations provide a new methodological framework that can be used, for instance, to estimate the epidemic threshold, a quantity that determines disease parameters, for which a large-scale outbreak can be expected. PMID:27035128
T-Matrix Approach to Strongly Coupled QGP
NASA Astrophysics Data System (ADS)
Liu, Shuai Y. F.; Rapp, Ralf
2017-01-01
Based on a thermodynamic T-matrix approach we extract the potential V between two static charges in the quark-gluon plasma (QGP) from ts to the pertinent lattice-QCD free energy. With suitable relativistic corrections we utilize this new potential to compute heavy-quark transport coefficients and compare the results to previous calculations using either F or U as potential. We then discuss a generalization of the T-matrix re-summation to a “matrix log” re-summation of t-channel diagrams for the grand partition function of the QGP in the Luttinger-Ward skeleton diagram formalism. With V as a non-perturbative driving kernel in the light-parton sector, we obtain the QGP equation of state from ts to lattice-QCD data. The resulting light-parton spectral functions are characterized by large thermal widths at small momenta, indicating the dissolution of quasi-particles in a strongly coupled QGP.
Partitioned density functional approach for a Lennard-Jones fluid.
Zhou, Shiqi
2003-12-01
The existing classical density functional approach for nonuniform Lennard-Jones fluid, which is based on dividing the Lennard-Jones interaction potential into a short-range, repulsive part, and a smoothly varying, long-range, attractive tail, was improved by dividing the bulk second-order direct correlation function into strongly density-depending short-range part and weakly density-depending long-range part. The latter is treated by functional perturbation expansion truncated at the lowest order whose accuracy depends on how weakly the long-range part depends on the bulk density. The former is treated by the truncated functional perturbation expansion which is rewritten in the form of the simple weighted density approximation and incorporates the omitted higher-order terms by applying Lagrangian theorem of differential calculus to the reformulated form. The two approximations are put into the density profile equation of the density functional theory formalism to predict the density distribution for Lennard-Jones fluid in contact with a hard wall or between two hard walls within the whole density range for reduced temperature T(*)=1.35 and a density point for reduced temperature T(*)=1. The present partitioned density functional theory performs much better than several previous density functional perturbation theory approaches and a recently proposed bridge density functional approximation.
Saitow, Masaaki; Kurashige, Yuki; Yanai, Takeshi
2013-07-28
We report development of the multireference configuration interaction (MRCI) method that can use active space scalable to much larger size references than has previously been possible. The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry offers the ability to describe static correlation in a large active space. The present MRCI method provides a critical correction to the DMRG reference by including high-level dynamic correlation through the CI treatment. When the DMRG and MRCI theories are combined (DMRG-MRCI), the full internal contraction of the reference in the MRCI ansatz, including contraction of semi-internal states, plays a central role. However, it is thought to involve formidable complexity because of the presence of the five-particle rank reduced-density matrix (RDM) in the Hamiltonian matrix elements. To address this complexity, we express the Hamiltonian matrix using commutators, which allows the five-particle rank RDM to be canceled out without any approximation. Then we introduce an approximation to the four-particle rank RDM by using a cumulant reconstruction from lower-particle rank RDMs. A computer-aided approach is employed to derive the exceedingly complex equations of the MRCI in tensor-contracted form and to implement them into an efficient parallel computer code. This approach extends to the size-consistency-corrected variants of MRCI, such as the MRCI+Q, MR-ACPF, and MR-AQCC methods. We demonstrate the capability of the DMRG-MRCI method in several benchmark applications, including the evaluation of single-triplet gap of free-base porphyrin using 24 active orbitals.
Biggs, Jason D.; Voll, Judith A.; Mukamel, Shaul
2012-01-01
Two types of diagrammatic approaches for the design and simulation of nonlinear optical experiments (closed-time path loops based on the wave function and double-sided Feynman diagrams for the density matrix) are presented and compared. We give guidelines for the assignment of relevant pathways and provide rules for the interpretation of existing nonlinear experiments in carotenoids. PMID:22753822
NASA Astrophysics Data System (ADS)
Liang, Wenkel; Isborn, Christine M.; Li, Xiaosong
2009-11-01
The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the α and β electrons to achieve the two-electron excited states of minimal basis H2 and HeH+ [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H2, HeH+, lithium hydride, ethylene, and butadiene.
NASA Astrophysics Data System (ADS)
Nemes, Csaba; Barcza, Gergely; Nagy, Zoltán; Legeza, Örs; Szolgay, Péter
2014-06-01
In the numerical analysis of strongly correlated quantum lattice models one of the leading algorithms developed to balance the size of the effective Hilbert space and the accuracy of the simulation is the density matrix renormalization group (DMRG) algorithm, in which the run-time is dominated by the iterative diagonalization of the Hamilton operator. As the most time-dominant step of the diagonalization can be expressed as a list of dense matrix operations, the DMRG is an appealing candidate to fully utilize the computing power residing in novel kilo-processor architectures. In the paper a smart hybrid CPU-GPU implementation is presented, which exploits the power of both CPU and GPU and tolerates problems exceeding the GPU memory size. Furthermore, a new CUDA kernel has been designed for asymmetric matrix-vector multiplication to accelerate the rest of the diagonalization. Besides the evaluation of the GPU implementation, the practical limits of an FPGA implementation are also discussed.
NASA Astrophysics Data System (ADS)
Yanai, Takeshi; Kurashige, Yuki; Neuscamman, Eric; Chan, Garnet Kin-Lic
2010-01-01
We describe the joint application of the density matrix renormalization group and canonical transformation theory to multireference quantum chemistry. The density matrix renormalization group provides the ability to describe static correlation in large active spaces, while the canonical transformation theory provides a high-order description of the dynamic correlation effects. We demonstrate the joint theory in two benchmark systems designed to test the dynamic and static correlation capabilities of the methods, namely, (i) total correlation energies in long polyenes and (ii) the isomerization curve of the [Cu2O2]2+ core. The largest complete active spaces and atomic orbital basis sets treated by the joint DMRG-CT theory in these systems correspond to a (24e,24o) active space and 268 atomic orbitals in the polyenes and a (28e,32o) active space and 278 atomic orbitals in [Cu2O2]2+.
Distance matrix-based approach to protein structure prediction.
Kloczkowski, Andrzej; Jernigan, Robert L; Wu, Zhijun; Song, Guang; Yang, Lei; Kolinski, Andrzej; Pokarowski, Piotr
2009-03-01
Much structural information is encoded in the internal distances; a distance matrix-based approach can be used to predict protein structure and dynamics, and for structural refinement. Our approach is based on the square distance matrix D = [r(ij)(2)] containing all square distances between residues in proteins. This distance matrix contains more information than the contact matrix C, that has elements of either 0 or 1 depending on whether the distance r (ij) is greater or less than a cutoff value r (cutoff). We have performed spectral decomposition of the distance matrices D = sigma lambda(k)V(k)V(kT), in terms of eigenvalues lambda kappa and the corresponding eigenvectors v kappa and found that it contains at most five nonzero terms. A dominant eigenvector is proportional to r (2)--the square distance of points from the center of mass, with the next three being the principal components of the system of points. By predicting r (2) from the sequence we can approximate a distance matrix of a protein with an expected RMSD value of about 7.3 A, and by combining it with the prediction of the first principal component we can improve this approximation to 4.0 A. We can also explain the role of hydrophobic interactions for the protein structure, because r is highly correlated with the hydrophobic profile of the sequence. Moreover, r is highly correlated with several sequence profiles which are useful in protein structure prediction, such as contact number, the residue-wise contact order (RWCO) or mean square fluctuations (i.e. crystallographic temperature factors). We have also shown that the next three components are related to spatial directionality of the secondary structure elements, and they may be also predicted from the sequence, improving overall structure prediction. We have also shown that the large number of available HIV-1 protease structures provides a remarkable sampling of conformations, which can be viewed as direct structural information about the
Testing the density matrix expansion against ab initio calculations of trapped neutron drops
Bogner, S. K.; Hergert, H.; Furnstahl, R. J.; Kortelainen, Erno M; Stoitsov, M. V.; Maris, Pieter; Vary, J. P.
2011-01-01
Microscopic input to a universal nuclear energy density functional can be provided through the density matrix expansion (DME), which has recently been revived and improved. Several DME implementation strategies are tested for neutron drop systems in harmonic traps by comparing to Hartree-Fock (HF) and ab initio no-core full configuration (NCFC) calculations with a model interaction (Minnesota potential). The new DME with exact treatment of Hartree contributions is found to best reproduce HF results and supplementing the functional with fit Skyrme-like contact terms shows systematic improvement toward the full NCFC results.
Matrix density effects on the mechanical properties of SiC/RBSN composites
NASA Technical Reports Server (NTRS)
Bhatt, Ramakrishna T.; Kiser, James D.
1990-01-01
The room temperature mechanical properties were measured for SiC fiber reinforced reaction-bonded silicon nitride composites (SiC/RBSN) of different densities. The composites consisted of approx. 30 vol percent uniaxially aligned 142 micron diameter SiC fibers (Textron SCS-6) in a reaction-bonded Si3N4 matrix. The composite density was varied by changing the consolidation pressure during RBSN processing and by hot isostatically pressing the SiC/RBSN composites. Results indicate that as the consolidation pressure was increased from 27 to 138 MPa, the average pore size of the nitrided composites decreased from 0.04 to 0.02 microns and the composite density increased from 2.07 to 2.45 gm/cc. Nonetheless, these improvements resulted in only small increases in the first matrix cracking stress, primary elastic modulus, and ultimate tensile strength values of the composites. In contrast, HIP consolidation of SiC/RBSN resulted in a fully dense material whose first matrix cracking stress and elastic modulus were approx. 15 and 50 percent higher, respectively, and ultimate tensile strength values were approx. 40 percent lower than those for unHIPed SiC/RBSN composites. The modulus behavior for all specimens can be explained by simple rule-of-mixture theory. Also, the loss in ultimate strength for the HIPed composites appears to be related to a degradation in fiber strength at the HIP temperature. However, the density effect on matrix fracture strength was much less than would be expected based on typical monolithic Si3N4 behavior, suggesting that composite theory is indeed operating. Possible practical implications of these observations are discussed.
Derivation of the density matrix of a single photon produced in parametric down-conversion
Kolenderski, Piotr; Wasilewski, Wojciech
2009-07-15
We discuss an effective numerical method of density matrix determination of fiber coupled single photon generated in process of spontaneous parametric down conversion in type I noncollinear configuration. The presented theory has been successfully applied in case of source utilized to demonstrate the experimental characterization of spectral state of single photon, what was reported in Wasilewski, Kolenderski, and Frankowski [Phys. Rev. Lett. 99, 123601 (2007)].
Density-matrix formalism for the photoion-electron entanglement in atomic photoionization
Radtke, T.; Fritzsche, S.; Surzhykov, A.
2006-09-15
The density-matrix theory, based on Dirac's relativistic equation, is applied for studying the entanglement between the photoelectron and residual ion in the course of the photoionization of atoms and ions. In particular, emphasis is placed on deriving the final-state density matrix of the overall system 'photoion+electron', including interelectronic effects and the higher multipoles of the radiation field. This final-state density matrix enables one immediately to analyze the change of entanglement as a function of the energy, angle and the polarization of the incoming light. Detailed computations have been carried out for the 5s photoionization of neutral strontium, leading to a photoion in a 5s {sup 2}S J{sub f}=1/2 level. It is found that the photoion-electron entanglement decreases significantly near the ionization threshold and that, in general, it depends on both the photon energy and angle. The possibility to extract photoion-electron pairs with a well-defined degree of entanglement may have far-reaching consequences for quantum information and elsewhere.
Stoitsov, M. V.; Kortelainen, Erno M; Bogner, S. K.; Duguet, T.; Furnstahl, R. J.; Gebremariam, B.; Schunck, N.
2010-01-01
In a recent series of papers, Gebremariam, Bogner, and Duguet derived a microscopically-based nuclear energy density functional by applying the Density Matrix Expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory (EFT) two- and three-nucleon interactions. Due to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Since the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present paper is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition (SVD) optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction in {chi}^{2} compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.
Stoitsov, M.; Kortelainen, M.; Schunck, N.; Bogner, S. K.; Gebremariam, B.; Duguet, T.
2010-11-15
In a recent series of articles, Gebremariam, Bogner, and Duguet derived a microscopically based nuclear energy density functional by applying the density matrix expansion (DME) to the Hartree-Fock energy obtained from chiral effective field theory two- and three-nucleon interactions. Owing to the structure of the chiral interactions, each coupling in the DME functional is given as the sum of a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the finite-range pion exchanges. Because the contact contributions have essentially the same structure as those entering empirical Skyrme functionals, a microscopically guided Skyrme phenomenology has been suggested in which the contact terms in the DME functional are released for optimization to finite-density observables to capture short-range correlation energy contributions from beyond Hartree-Fock. The present article is the first attempt to assess the ability of the newly suggested DME functional, which has a much richer set of density dependencies than traditional Skyrme functionals, to generate sensible and stable results for nuclear applications. The results of the first proof-of-principle calculations are given, and numerous practical issues related to the implementation of the new functional in existing Skyrme codes are discussed. Using a restricted singular value decomposition optimization procedure, it is found that the new DME functional gives numerically stable results and exhibits a small but systematic reduction of our test {chi}{sup 2} function compared to standard Skyrme functionals, thus justifying its suitability for future global optimizations and large-scale calculations.
Two functions of the density matrix and their relation to the chemical bond
NASA Astrophysics Data System (ADS)
Schmider, Hartmut L.; Becke, Axel D.
2002-02-01
We examine and compare two previously introduced functions of the one-particle density matrix that are suitable to represent its off-diagonal structure in a condensed form and that have illustrative connections to the nature of the chemical bond. One of them, the Localized-Orbital Locator (LOL) [J. Molec. Struct. (THEOCHEM) 527, 51 (2000)], is based only on the noninteracting kinetic-energy density τ and the charge density ρ at a point, and gives an intuitive measure of the relative speed of electrons in its vicinity. Alternatively, LOL focuses on regions that are dominated by single localized orbitals. The other one, the Parity Function P [J. Chem. Phys. 105, 11134 (1996)], is a section through the Wigner phase-space function at zero momentum, and contains information about the phase of the interference of atomiclike orbital contributions from bound centers. In this paper, we discuss the way in which these functions condense information in the density matrix, and illustrate on a variety of examples of unusual chemical bonds how they can help to understand the nature of "covalence."
Density hysteresis of heavy water confined in a nanoporous silica matrix
Zhang, Yang; Faraone, Antonio; Kamitakahara, William; Liu, Kao-Hsiang; Mou, Chung-Yuan; Leao, Juscelino B; Chang, Sung C; Chen, Sow-hsin H
2011-01-01
A neutron scattering technique was developed to measure the density of heavy water confined in a nanoporous silica matrix in a temperature-pressure range, from 300 to 130 K and from 1 to 2,900 bars, where bulk water will crystalize. We observed a prominent hysteresis phenomenon in the measured density profiles between warming and cooling scans above 1,000 bars. We inter- pret this hysteresis phenomenon as support (although not a proof) of the hypothetical existence of a first-order liquid liquid phase transition of water that would exist in the macroscopic system if crystallization could be avoided in the relevant phase region. Moreover, the density data we obtained for the confined heavy water under these conditions are valuable to large communities in biology and earth and planetary sciences interested in phenomena in which nanometer-sized water layers are involved.
Density hysteresis of heavy water confined in a nanoporous silica matrix
Zhang, Yang; Faraone, Antonio; Kamitakahara, William A.; Liu, Kao-Hsiang; Mou, Chung-Yuan; Leão, Juscelino B.; Chang, Sung; Chen, Sow-Hsin
2011-01-01
A neutron scattering technique was developed to measure the density of heavy water confined in a nanoporous silica matrix in a temperature-pressure range, from 300 to 130 K and from 1 to 2,900 bars, where bulk water will crystalize. We observed a prominent hysteresis phenomenon in the measured density profiles between warming and cooling scans above 1,000 bars. We interpret this hysteresis phenomenon as support (although not a proof) of the hypothetical existence of a first-order liquid–liquid phase transition of water that would exist in the macroscopic system if crystallization could be avoided in the relevant phase region. Moreover, the density data we obtained for the confined heavy water under these conditions are valuable to large communities in biology and earth and planetary sciences interested in phenomena in which nanometer-sized water layers are involved. PMID:21746898
Roemelt, Michael
2015-07-28
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
NASA Astrophysics Data System (ADS)
Roemelt, Michael
2015-07-01
Spin Orbit Coupling (SOC) is introduced to molecular ab initio density matrix renormalization group (DMRG) calculations. In the presented scheme, one first approximates the electronic ground state and a number of excited states of the Born-Oppenheimer (BO) Hamiltonian with the aid of the DMRG algorithm. Owing to the spin-adaptation of the algorithm, the total spin S is a good quantum number for these states. After the non-relativistic DMRG calculation is finished, all magnetic sublevels of the calculated states are constructed explicitly, and the SOC operator is expanded in the resulting basis. To this end, spin orbit coupled energies and wavefunctions are obtained as eigenvalues and eigenfunctions of the full Hamiltonian matrix which is composed of the SOC operator matrix and the BO Hamiltonian matrix. This treatment corresponds to a quasi-degenerate perturbation theory approach and can be regarded as the molecular equivalent to atomic Russell-Saunders coupling. For the evaluation of SOC matrix elements, the full Breit-Pauli SOC Hamiltonian is approximated by the widely used spin-orbit mean field operator. This operator allows for an efficient use of the second quantized triplet replacement operators that are readily generated during the non-relativistic DMRG algorithm, together with the Wigner-Eckart theorem. With a set of spin-orbit coupled wavefunctions at hand, the molecular g-tensors are calculated following the scheme proposed by Gerloch and McMeeking. It interprets the effective molecular g-values as the slope of the energy difference between the lowest Kramers pair with respect to the strength of the applied magnetic field. Test calculations on a chemically relevant Mo complex demonstrate the capabilities of the presented method.
Non-Hermitian random matrix models: Free random variable approach
Janik, R.A.,; Nowak, M.A., ||; Papp, G.,; Wambach, J.,; Zahed, I., |
1997-04-01
Using the standard concepts of free random variables, we show that for a large class of non-Hermitian random matrix models, the support of the eigenvalue distribution follows from their Hermitian analogs using a conformal transformation. We also extend the concepts of free random variables to the class of non-Hermitian matrices, and apply them to the models discussed by Ginibre-Girko (elliptic ensemble) [J. Ginibre, J. Math. Phys. {bold 6}, 1440 (1965); V. L. Girko, {ital Spectral Theory of Random Matrices} (in Russian) (Nauka, Moscow, 1988)] and Mahaux-Weidenm{umlt u}ller (chaotic resonance scattering) [C. Mahaux and H. A. Weidenm{umlt u}ller, {ital Shell-model Approach to Nuclear Reactions} (North-Holland, Amsterdam, 1969)]. {copyright} {ital 1997} {ital The American Physical Society}
Extending the range of real time density matrix renormalization group simulations
NASA Astrophysics Data System (ADS)
Kennes, D. M.; Karrasch, C.
2016-03-01
We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement these modifications within any standard matrix product state (MPS) based formulation of the method. Most importantly, we show how to 'combine' the Schrödinger and Heisenberg time evolutions of arbitrary pure states | ψ > and operators A in the evaluation of ψ(t) = < ψ | A(t) | ψ > . This includes quantum quenches. The generalization to (non-)thermal mixed state dynamics ρ(t) =Tr [ ρA(t) ] induced by an initial density matrix ρ is straightforward. In the context of linear response (ground state or finite temperature T > 0) correlation functions, one can extend the simulation time by a factor of two by 'exploiting time translation invariance', which is efficiently implementable within MPS DMRG. We present a simple analytic argument for why a recently-introduced disentangler succeeds in reducing the effort of time-dependent simulations at T > 0. Finally, we advocate the python programming language as an elegant option for beginners to set up a DMRG code.
Controlled-surface-wettability-based fabrication of hydrogel substrates with matrix tethering density variations
NASA Astrophysics Data System (ADS)
Rahman, Md. Mahmudur; Lee, Donghee; Bhagirath, Divya; Zhao, Xiangshan; Band, Vimla; Ryu, Sangjin
2014-03-01
It is widely accepted that cells behave differently responding to the stiffness of extracellular matrix (ECM). Such observations were made by culturing cells on hydrogel substrates of tunable stiffness. However, it was recently proposed that cells actually sense how strongly they are tethered to ECM, not the local stiffness of ECM. To investigate the hypothesis, we develop constant-stiffness hydrogel substrates with varying matrix tethering density (the number of anchoring sites between the gel and the ECM protein molecules). We fabricate polyacrylamide gel of static stiffness and conjugate ECM proteins to the gel using a cross-linker. When treating the gel with the cross-linker, we control positioning of cross-linker solutions with different concentrations using superhydrophobic barriers on glass, functionalize the gel by pressing it to the aligned cross-linker solutions, and conjugate an ECM protein of constant concentration to the gel. We expect that the gel will be functionalized to different degrees depending on the concentration distribution of the cross-linker and thus the gel will have variations of matrix tethering density even with constant ECM protein concentration. We acknowledge support from Bioengineering for Human Health grant of UNL-UNMC.
Mniszewski, S M; Cawkwell, M J; Wall, M E; Mohd-Yusof, J; Bock, N; Germann, T C; Niklasson, A M N
2015-10-13
We present an algorithm for the calculation of the density matrix that for insulators scales linearly with system size and parallelizes efficiently on multicore, shared memory platforms with small and controllable numerical errors. The algorithm is based on an implementation of the second-order spectral projection (SP2) algorithm [ Niklasson, A. M. N. Phys. Rev. B 2002 , 66 , 155115 ] in sparse matrix algebra with the ELLPACK-R data format. We illustrate the performance of the algorithm within self-consistent tight binding theory by total energy calculations of gas phase poly(ethylene) molecules and periodic liquid water systems containing up to 15,000 atoms on up to 16 CPU cores. We consider algorithm-specific performance aspects, such as local vs nonlocal memory access and the degree of matrix sparsity. Comparisons to sparse matrix algebra implementations using off-the-shelf libraries on multicore CPUs, graphics processing units (GPUs), and the Intel many integrated core (MIC) architecture are also presented. The accuracy and stability of the algorithm are illustrated with long duration Born-Oppenheimer molecular dynamics simulations of 1000 water molecules and a 303 atom Trp cage protein solvated by 2682 water molecules.
Adiabatic approximation in time-dependent reduced-density-matrix functional theory
Requist, Ryan; Pankratov, Oleg
2010-04-15
With the aim of describing real-time electron dynamics, we introduce an adiabatic approximation for the equation of motion of the one-body reduced density matrix (one-matrix). The eigenvalues of the one-matrix, which represent the occupation numbers of single-particle orbitals, are obtained from the constrained minimization of the instantaneous ground-state energy functional rather than from their dynamical equations. The performance of the approximation vis-a-vis nonadiabatic effects is assessed in real-time simulations of a two-site Hubbard model. Due to Landau-Zener-type transitions, the system evolves into a nonstationary state with persistent oscillations in the observables. The amplitude of the oscillations displays a strongly nonmonotonic dependence on the strength of the electron-electron interaction and the rate of variation of the external potential. We interpret an associated resonance behavior in the phase of the oscillations in terms of 'scattering' with spectator energy levels. To clarify the motivation for the minimization condition, we derive a sequence of energy functionals E{sub v}{sup (n)}, for which the corresponding sequence of minimizing one-matrices is asymptotic to the exact one-matrix in the adiabatic limit.
Capillary condensation in pores with rough walls: a density functional approach.
Bryk, P; Rzysko, W; Malijevsky, Al; Sokołowski, S
2007-09-01
The effect of surface roughness of slit-like pore walls on the capillary condensation of a spherical particles and short chains is studied. The gas molecules interact with the substrate by a Lennard-Jones (9,3) potential. The rough layer at each pore wall has a variable thickness and density and consists of a disordered quenched matrix of spherical particles. The system is described in the framework of a density functional approach and using computer simulations. The contribution due to attractive van der Waals interactions between adsorbate molecules is described by using first-order mean spherical approximation and mean-field approximation.
Iterative solutions to the steady-state density matrix for optomechanical systems
NASA Astrophysics Data System (ADS)
Nation, P. D.; Johansson, J. R.; Blencowe, M. P.; Rimberg, A. J.
2015-01-01
We present a sparse matrix permutation from graph theory that gives stable incomplete lower-upper preconditioners necessary for iterative solutions to the steady-state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance. This reordering optimizes the condition number of the approximate inverse and is the only method found to be stable at large Hilbert space dimensions. This allows for steady-state solutions to otherwise intractable quantum optomechanical systems.
NASA Astrophysics Data System (ADS)
Chen, Xin
2014-04-01
Understanding the roles of the temporary and spatial structures of quantum functional noise in open multilevel quantum molecular systems attracts a lot of theoretical interests. I want to establish a rigorous and general framework for functional quantum noises from the constructive and computational perspectives, i.e., how to generate the random trajectories to reproduce the kernel and path ordering of the influence functional with effective Monte Carlo methods for arbitrary spectral densities. This construction approach aims to unify the existing stochastic models to rigorously describe the temporary and spatial structure of Gaussian quantum noises. In this paper, I review the Euclidean imaginary time influence functional and propose the stochastic matrix multiplication scheme to calculate reduced equilibrium density matrices (REDM). In addition, I review and discuss the Feynman-Vernon influence functional according to the Gaussian quadratic integral, particularly its imaginary part which is critical to the rigorous description of the quantum detailed balance. As a result, I establish the conditions under which the influence functional can be interpreted as the average of exponential functional operator over real-valued Gaussian processes for open multilevel quantum systems. I also show the difference between the local and nonlocal phonons within this framework. With the stochastic matrix multiplication scheme, I compare the normalized REDM with the Boltzmann equilibrium distribution for open multilevel quantum systems.
Chen, Xin
2014-04-21
Understanding the roles of the temporary and spatial structures of quantum functional noise in open multilevel quantum molecular systems attracts a lot of theoretical interests. I want to establish a rigorous and general framework for functional quantum noises from the constructive and computational perspectives, i.e., how to generate the random trajectories to reproduce the kernel and path ordering of the influence functional with effective Monte Carlo methods for arbitrary spectral densities. This construction approach aims to unify the existing stochastic models to rigorously describe the temporary and spatial structure of Gaussian quantum noises. In this paper, I review the Euclidean imaginary time influence functional and propose the stochastic matrix multiplication scheme to calculate reduced equilibrium density matrices (REDM). In addition, I review and discuss the Feynman-Vernon influence functional according to the Gaussian quadratic integral, particularly its imaginary part which is critical to the rigorous description of the quantum detailed balance. As a result, I establish the conditions under which the influence functional can be interpreted as the average of exponential functional operator over real-valued Gaussian processes for open multilevel quantum systems. I also show the difference between the local and nonlocal phonons within this framework. With the stochastic matrix multiplication scheme, I compare the normalized REDM with the Boltzmann equilibrium distribution for open multilevel quantum systems.
Control-matrix approach to stellarator design and control
Mynick, H.E.; Pomphrey, N.
2000-02-09
The full space Z always equal to {l{underscore}brace}Zj=1,..Nz{r{underscore}brace} of independent variables defining a stellarator configuration is large. To find attractive design points in this space, or to understand operational flexibility about a given design point, one needs insight into the topography in Z-space of the physics figures of merit Pi which characterize the machine performance, and means of determining those directions in Z-space which give one independent control over the Pi, as well as those which affect none of them, and so are available for design flexibility. The control matrix (CM) approach described here provides a mathematical means of obtaining these. In this work, the authors describe the CM approach and use it in studying some candidate Quasi-Axisymmetric (QA) stellarator configurations the NCSX design group has been considering. In the process of the analysis, a first exploration of the topography of the configuration space in the vicinity of these candidate systems has been performed, whose character is discussed.
Parker, Shane M.; Shiozaki, Toru
2014-12-07
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE{sub h} or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
Analysis of NMR self-diffusion measurements by a density matrix calculation
NASA Astrophysics Data System (ADS)
Stepišnik, J.
1981-04-01
The density matrix formalism with the Magnus expansion of the time evolution operator is used to study the nmr response in a pulsed magnetic field gradient (mfg) spin-echo experiment. The results show that the spin-echo cannot only measure the self-diffusion coefficient but can determine the spectrum of the single-particle velocity autocorrelation function as well. The proper combination of rf and mfg pulse sequences are proposed for measuring self-diffusion in spin systems with strong dipolar coupling where the classical method fails.
Highly linear high-density vector quantiser and vector-matrix multiplier
NASA Astrophysics Data System (ADS)
Pedroni, V. A.
1994-06-01
Simplicity is a key factor in the development of high-density systems. The authors discuss a balanced, four-quadrant, fully-analogue vector-matrix multiplier (VMM) and a vector quantiser (VQ) which require very small silicon area for their implementations, while presenting high linearity, a totally flexible input dynamic range, a symmetric power consumption behaviour, and are inherently suitable for parallel operation. The circuits require only four transistors per synapse in the VMM and two in the VQ, plus two (small) refresh transistors.
NASA Astrophysics Data System (ADS)
Silvi, Pietro; Calarco, Tommaso; Morigi, Giovanna; Montangero, Simone
2014-03-01
Ions of the same charge inside confining potentials can form crystalline structures which can be controlled by means of the ion density and of the external trap parameters. In particular, a linear chain of trapped ions exhibits a transition to a zigzag equilibrium configuration, which is controlled by the strength of the transverse confinement. Studying this phase transition in the quantum regime is a challenging problem, even when employing numerical methods to simulate microscopically quantum many-body systems. Here we present a compact analytical treatment to map the original long-range problem into a short-range quantum field theory on a lattice. We provide a complete numerical architecture, based on the density matrix renormalization group, to address the effective quantum ϕ4 model. This technique is instrumental in giving a complete characterization of the phase diagram, as well as pinpointing the universality class of the criticality.
Low excitations of 16O using generalized density matrix random phase approximation GDRPA
NASA Astrophysics Data System (ADS)
Taqi, Ali H.; Radhi, R. A.; Hussein, Adil M.
2014-07-01
The random phase approximation (RPA) equations based on the generalized density matrix (GDM), the so-called GDRPA are reformulated in a more compact matrix form, which renders the method especially suitable for realistic nuclear structure calculations. The GDRPA Hamiltonian is expressed in terms of the one-body particle-particle (pp) and hole-hole (hh) density matrices, and the nuclear force contributes not only in the particle-hole (ph) channel, as in normal ph-RPA, but also in the pp and hh channels. The Hamiltonian is diagonalized iteratively starting from initial guess values and the iterating process is carried out until self-consistency is achieved. The calculation in the model space 1p, 1d and 2s using Warburton and Brown interaction WBP is performed for 16O. The GDRPA in the ph shell model calculations is tested, by comparing the energy eigenvalues and the electron scattering form factors with the results of the normal RPA and with the available experimental data.
Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations
Blanchet, Steve; Bari, Pasquale Di; Jones, David A.; Marzola, Luca E-mail: pdb1d08@soton.ac.uk E-mail: daj1g08@soton.ac.uk
2013-01-01
Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N{sub 1}-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.
Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations
NASA Astrophysics Data System (ADS)
Blanchet, Steve; Di Bari, Pasquale; Jones, David A.; Marzola, Luca
2013-01-01
Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N1-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.
NASA Astrophysics Data System (ADS)
Ridder, Barbara; Foertsch, Tobias C.; Welle, Alexander; Mattes, Daniela S.; von Bojnicic-Kninski, Clemens M.; Loeffler, Felix F.; Nesterov-Mueller, Alexander; Meier, Michael A. R.; Breitling, Frank
2016-12-01
Poly(dimethylacrylamide) (PDMA) based matrix materials were developed for laser-based in situ solid phase peptide synthesis to produce high density arrays. In this specific array synthesis approach, amino acid derivatives are embedded into a matrix material, serving as a "solid" solvent material at room temperature. Then, a laser pulse transfers this mixture to the target position on a synthesis slide, where the peptide array is synthesized. Upon heating above the glass transition temperature of the matrix material, it softens, allowing diffusion of the amino acid derivatives to the synthesis surface and serving as a solvent for peptide bond formation. Here, we synthesized PDMA six-arm star polymers, offering the desired matrix material properties, using atom transfer radical polymerization. With the synthesized polymers as matrix material, we structured and synthesized arrays with combinatorial laser transfer. With densities of up to 20,000 peptide spots per cm2, the resolution could be increased compared to the commercially available standard matrix material. Time-of-Flight Secondary Ion Mass Spectrometry experiments revealed the penetration behavior of an amino acid derivative into the prepared acceptor synthesis surface and the effectiveness of the washing protocols.
A discrete approach for modeling cell-matrix adhesions
NASA Astrophysics Data System (ADS)
Escribano, J.; Sánchez, M. T.; García-Aznar, J. M.
2014-06-01
During recent years the interaction between the extracellular matrix and the cytoskeleton of the cell has been object of numerous studies due to its importance in cell migration processes. These interactions are performed through protein clutches, known as focal adhesions. For migratory cells these focal adhesions along with force generating processes in the cytoskeleton are responsible for the formation of protrusion structures like lamellipodia or filopodia. Much is known about these structures: the different proteins that conform them, the players involved in their formation or their role in cell migration. Concretely, growth-cone filopodia structures have attracted significant attention because of their role as cell sensors of their surrounding environment and its complex behavior. On this matter, a vast myriad of mathematical models has been presented to explain its mechanical behavior. In this work, we aim to study the mechanical behavior of these structures through a discrete approach. This numerical model provides an individual analysis of the proteins involved including spatial distribution, interaction between them, and study of different phenomena, such as clutches unbinding or protein unfolding.
A cantilever-free approach to dot-matrix nanoprinting
Brown, Keith A.; Eichelsdoerfer, Daniel J.; Shim, Wooyoung; Rasin, Boris; Radha, Boya; Liao, Xing; Schmucker, Abrin L.; Liu, Guoliang; Mirkin, Chad A.
2013-01-01
Scanning probe lithography (SPL) is a promising candidate approach for desktop nanofabrication, but trade-offs in throughput, cost, and resolution have limited its application. The recent development of cantilever-free scanning probe arrays has allowed researchers to define nanoscale patterns in a low-cost and high-resolution format, but with the limitation that these are duplication tools where each probe in the array creates a copy of a single pattern. Here, we report a cantilever-free SPL architecture that can generate 100 nanometer-scale molecular features using a 2D array of independently actuated probes. To physically actuate a probe, local heating is used to thermally expand the elastomeric film beneath a single probe, bringing it into contact with the patterning surface. Not only is this architecture simple and scalable, but it addresses fundamental limitations of 2D SPL by allowing one to compensate for unavoidable imperfections in the system. This cantilever-free dot-matrix nanoprinting will enable the construction of surfaces with chemical functionality that is tuned across the nano- and macroscales. PMID:23861495
Chebyshev matrix product state approach for time evolution
NASA Astrophysics Data System (ADS)
Halimeh, Jad C.; Kolley, Fabian; McCulloch, Ian P.
2015-09-01
We present and test a new algorithm for time-evolving quantum many-body systems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011), 10.1103/PhysRevB.83.195115]. The approach is based on merging the matrix product state (MPS) formalism with the method of expanding the time-evolution operator in Chebyshev polynomials. We calculate time-dependent observables of a system of hardcore bosons quenched under the Bose-Hubbard Hamiltonian on a one-dimensional lattice. We compare the new algorithm to more standard methods using the MPS architecture. We find that the Chebyshev method gives numerically exact results for small times. However, the reachable times are smaller than the ones obtained with the other state-of-the-art methods. We further extend the new method using a spectral-decomposition-based projective scheme that utilizes an effective bandwidth significantly smaller than the full bandwidth, leading to longer evolution times than the nonprojective method and more efficient information storage, data compression, and less computational effort.
SivaRanjan, Uppala; Ramachandran, Ramesh
2014-02-07
A quantum-mechanical model integrating the concepts of reduced density matrix and effective Hamiltonians is proposed to explain the multi-spin effects observed in rotational resonance (R{sup 2}) nuclear magnetic resonance (NMR) experiments. Employing this approach, the spin system of interest is described in a reduced subspace inclusive of its coupling to the surroundings. Through suitable model systems, the utility of our theory is demonstrated and verified with simulations emerging from both analytic and numerical methods. The analytic results presented in this article provide an accurate description/interpretation of R{sup 2} experimental results and could serve as a test-bed for distinguishing coherent/incoherent effects in solid-state NMR.
Perturbative approach to covariance matrix of the matter power spectrum
Mohammed, Irshad; Seljak, Uros; Vlah, Zvonimir
2016-06-30
We evaluate the covariance matrix of the matter power spectrum using perturbation theory up to dominant terms at 1-loop order and compare it to numerical simulations. We decompose the covariance matrix into the disconnected (Gaussian) part, trispectrum from the modes outside the survey (beat coupling or super-sample variance), and trispectrum from the modes inside the survey, and show how the different components contribute to the overall covariance matrix. We find the agreement with the simulations is at a 10\\% level up to $k \\sim 1 h {\\rm Mpc^{-1}}$. We show that all the connected components are dominated by the large-scale modes ($k<0.1 h {\\rm Mpc^{-1}}$), regardless of the value of the wavevectors $k,\\, k'$ of the covariance matrix, suggesting that one must be careful in applying the jackknife or bootstrap methods to the covariance matrix. We perform an eigenmode decomposition of the connected part of the covariance matrix, showing that at higher $k$ it is dominated by a single eigenmode. The full covariance matrix can be approximated as the disconnected part only, with the connected part being treated as an external nuisance parameter with a known scale dependence, and a known prior on its variance for a given survey volume. Finally, we provide a prescription for how to evaluate the covariance matrix from small box simulations without the need to simulate large volumes.
Perturbative approach to covariance matrix of the matter power spectrum
NASA Astrophysics Data System (ADS)
Mohammed, Irshad; Seljak, Uroš; Vlah, Zvonimir
2017-04-01
We evaluate the covariance matrix of the matter power spectrum using perturbation theory up to dominant terms at 1-loop order and compare it to numerical simulations. We decompose the covariance matrix into the disconnected (Gaussian) part, trispectrum from the modes outside the survey (supersample variance) and trispectrum from the modes inside the survey, and show how the different components contribute to the overall covariance matrix. We find the agreement with the simulations is at a 10 per cent level up to k ∼ 1 h Mpc-1. We show that all the connected components are dominated by the large-scale modes (k < 0.1 h Mpc-1), regardless of the value of the wave vectors k, k΄ of the covariance matrix, suggesting that one must be careful in applying the jackknife or bootstrap methods to the covariance matrix. We perform an eigenmode decomposition of the connected part of the covariance matrix, showing that at higher k, it is dominated by a single eigenmode. The full covariance matrix can be approximated as the disconnected part only, with the connected part being treated as an external nuisance parameter with a known scale dependence, and a known prior on its variance for a given survey volume. Finally, we provide a prescription for how to evaluate the covariance matrix from small box simulations without the need to simulate large volumes.
NASA Astrophysics Data System (ADS)
Jacobs, Verne; Kutana, Alex
The frequency-dependent transition rates for single-photon and multi-photon processes in quantized many-electron systems are evaluated using a reduced-density-matrix approach. We provide a fundamental quantum-mechanical foundation for systematic spectral simulations. A perturbation expansion of the frequency-domain Liouville-space self-energy operator is introduced for detailed evaluations of the spectral-line shapes. In the diagonal-resolvent (isolated-line) and short-memory-time (Markov) approximations, the lowest-order contributions to the spectral-line widths and shifts associated with environmental electron-photon and electron-phonon interactions are systematically evaluated. Our description is directly applicable to electromagnetic processes in a wide variety of many-electron systems, without premature approximations. In particular, our approach can be applied to investigate quantum optical phenomena involving electrons in both bulk and nanoscale semiconductor materials entirely from first principles, using a single-electron basis set obtained from density functional theory as a starting point for a many-electron description. Work supported by the Office of Naval Research through the Basic Research Program at The Naval Research Laboratory. A portion of this work was performed under the ASEE post doc program at NRL.
Kajzer-Bonk, Joanna; Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal
2016-01-01
The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011-12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales.
Skórka, Piotr; Nowicki, Piotr; Bonk, Maciej; Król, Wiesław; Szpiłyk, Damian; Woyciechowski, Michal
2016-01-01
The type of matrix, the landscape surrounding habitat patches, may determine the distribution and function of local populations. However, the matrix is often heterogeneous, and its various components may differentially contribute to metapopulation processes at different spatial scales, a phenomenon that has rarely been investigated. The aim of this study was to estimate the relative importance of matrix composition and spatial scale, habitat quality, and management intensity on the occurrence and density of local populations of two endangered large blue butterflies: Phengaris teleius and P. nausithous. Presence and abundance data were assessed over two years, 2011–12, in 100 local patches within two heterogeneous regions (near Kraków and Tarnów, southern Poland). The matrix composition was analyzed at eight spatial scales. We observed high occupancy rates in both species, regions and years. With the exception of area and isolation, almost all of the matrix components contributed to Phengaris sp. densities. The different matrix components acted at different spatial scales (grassland cover within 4 and 3 km, field cover within 0.4 and 0.3 km and water cover within 4 km radii for P. teleius and P. nausithous, respectively) and provided the highest independent contribution to the butterfly densities. Additionally, the effects of a 0.4 km radius of forest cover and a food plant cover on P. teleius, and a 1 km radius of settlement cover and management intensity on P. nausithous densities were observed. Contrary to former studies we conclude that the matrix heterogeneity and spatial scale rather than general matrix type are of relevance for densities of butterflies. Conservation strategies for these umbrella species should concentrate on maintaining habitat quality and managing matrix composition at the most appropriate spatial scales. PMID:28005942
NASA Astrophysics Data System (ADS)
Putaja, A.; Eich, F. G.; Baldsiefen, T.; Räsänen, E.
2016-03-01
Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced-density-matrix-functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form f (n ,n') =(nn')α for the scaling function in the exchange-correlation energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power α to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlation energy and exclude pinned states with the condition n (k )<1 for all wave vectors k . The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for α that yield the exact correlation energy and its kinetic part for both the three- and two-dimensional electron gas. In both systems, narrow regimes of validity and accuracy are found at α ≳0.6 and at rs≳10 for the density parameter, corresponding to relatively low densities.
Johnson, Christopher D; Worrall, Fred
2007-06-01
This paper reports the preparation and properties of a new low density granular absorbent material based on a zeolite/vermiculite composite. The composite prepared addresses a number of important issues relating to the use of zeolites in environmental and waste management applications. The material prepared has large particle size due to binderless adhesion of zeolite crystals within the protective lamellar matrix provided by the vermiculite granule. Additionally, the porous nature of new material ensures that it outperforms natural zeolite grains in ion-exchange tests. The material was shown to have a low bulk density (0.75 g cm(-3)) adding the benefit that the majority of grains float on water for over 15 h. The conclusion of the study is that the use of composite matrices enable the preparation of materials which show the physical properties of the host, (e.g., granular and low density), whilst maintaining the powder-like properties (e.g., high ion-exchange and small crystal size) of the active component. The resulting material can be easily handled and separated from aqueous waste streams using either flotation or exploiting its granular nature.
An Infrastructureless Approach to Estimate Vehicular Density in Urban Environments
Sanguesa, Julio A.; Fogue, Manuel; Garrido, Piedad; Martinez, Francisco J.; Cano, Juan-Carlos; Calafate, Carlos T.; Manzoni, Pietro
2013-01-01
In Vehicular Networks, communication success usually depends on the density of vehicles, since a higher density allows having shorter and more reliable wireless links. Thus, knowing the density of vehicles in a vehicular communications environment is important, as better opportunities for wireless communication can show up. However, vehicle density is highly variable in time and space. This paper deals with the importance of predicting the density of vehicles in vehicular environments to take decisions for enhancing the dissemination of warning messages between vehicles. We propose a novel mechanism to estimate the vehicular density in urban environments. Our mechanism uses as input parameters the number of beacons received per vehicle, and the topological characteristics of the environment where the vehicles are located. Simulation results indicate that, unlike previous proposals solely based on the number of beacons received, our approach is able to accurately estimate the vehicular density, and therefore it could support more efficient dissemination protocols for vehicular environments, as well as improve previously proposed schemes. PMID:23435054
Simple Approach to Renormalize the Cabibbo-Kobayashi-Maskawa Matrix
Kniehl, Bernd A.; Sirlin, Alberto
2006-12-01
We present an on-shell scheme to renormalize the Cabibbo-Kobayashi-Maskawa (CKM) matrix. It is based on a novel procedure to separate the external-leg mixing corrections into gauge-independent self-mass and gauge-dependent wave function renormalization contributions, and to implement the on-shell renormalization of the former with nondiagonal mass counterterm matrices. Diagonalization of the complete mass matrix leads to an explicit CKM counterterm matrix, which automatically satisfies all the following important properties: it is gauge independent, preserves unitarity, and leads to renormalized amplitudes that are nonsingular in the limit in which any two fermions become mass degenerate.
N-leg spin-S Heisenberg ladders: A density-matrix renormalization group study
NASA Astrophysics Data System (ADS)
Ramos, F. B.; Xavier, J. C.
2014-03-01
We investigate the N-leg spin-S Heisenberg ladders by using the density matrix renormalization group method. We present estimates of the spin gap Δs and of the ground-state energy per site e∞N in the thermodynamic limit for ladders with widths up to six legs and spin S≤5/2. We also estimate the ground-state energy per site e∞2D for the infinite two-dimensional spin-S Heisenberg model. Our results support that for ladders with semi-integer spins the spin excitation is gapless for N odd and gapped for N even, whereas for integer spin ladders the spin gap is nonzero, independent of the number of legs. Those results agree with the well-known conjectures of Haldane and Sénéchal-Sierra for chains and ladders, respectively. We also observe edge states for ladders with N odd, similar to what happens in spin chains.
NASA Astrophysics Data System (ADS)
Ghosh, Debashree; Hachmann, Johannes; Yanai, Takeshi; Chan, Garnet Kin-Lic
2008-04-01
In previous work we have shown that the density matrix renormalization group (DMRG) enables near-exact calculations in active spaces much larger than are possible with traditional complete active space algorithms. Here, we implement orbital optimization with the DMRG to further allow the self-consistent improvement of the active orbitals, as is done in the complete active space self-consistent field (CASSCF) method. We use our resulting DMRG-CASSCF method to study the low-lying excited states of the all-trans polyenes up to C24H26 as well as β-carotene, correlating with near-exact accuracy the optimized complete π-valence space with up to 24 active electrons and orbitals, and analyze our results in the light of the recent discovery from resonance Raman experiments of new optically dark states in the spectrum.
NASA Astrophysics Data System (ADS)
Hachmann, Johannes; Cardoen, Wim; Chan, Garnet Kin-Lic
2006-10-01
We have devised a local ab initio density matrix renormalization group algorithm to describe multireference correlations in large systems. For long molecules that are extended in one of their spatial dimensions, we can obtain an exact characterization of correlation, in the given basis, with a cost that scales only quadratically with the size of the system. The reduced scaling is achieved solely through integral screening and without the construction of correlation domains. We demonstrate the scaling, convergence, and robustness of the algorithm in polyenes and hydrogen chains. We converge to exact correlation energies (in the sense of full configuration interaction, with 1-10μEh precision) in all cases and correlate up to 100 electrons in 100 active orbitals. We further use our algorithm to obtain exact energies for the metal-insulator transition in hydrogen chains and compare and contrast our results with those from conventional quantum chemical methods.
Hu, Weifeng; Chan, Garnet Kin-Lic
2015-07-14
We describe and extend the formalism of state-specific analytic density matrix renormalization group (DMRG) energy gradients, first used by Liu et al. [J. Chem. Theor. Comput. 2013, 9, 4462]. We introduce a DMRG wave function maximum overlap following technique to facilitate state-specific DMRG excited-state optimization. Using DMRG configuration interaction (DMRG-CI) gradients, we relax the low-lying singlet states of a series of trans-polyenes up to C20H22. Using the relaxed excited-state geometries, as well as correlation functions, we elucidate the exciton, soliton, and bimagnon ("single-fission") character of the excited states, and find evidence for a planar conical intersection.
NASA Astrophysics Data System (ADS)
Mukhopadhyay, S.; Ramasesha, S.
2009-08-01
We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser-Parr-Pople Hamiltonian to model the interacting π electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.
A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry.
Wouters, Sebastian; Jiménez-Hoyos, Carlos A; Sun, Qiming; Chan, Garnet K-L
2016-06-14
Density matrix embedding theory (DMET) (Knizia, G.; Chan, G. K.-L. Phys. Rev. Lett. 2012, 109, 186404) provides a theoretical framework to treat finite fragments in the presence of a surrounding molecular or bulk environment, even when there is significant correlation or entanglement between the two. In this work, we give a practically oriented and explicit description of the numerical and theoretical formulation of DMET. We also describe in detail how to perform self-consistent DMET optimizations. We explore different embedding strategies with and without a self-consistency condition in hydrogen rings, beryllium rings, and a sample SN2 reaction. The source code for the calculations in this work can be obtained from https://github.com/sebwouters/qc-dmet .
Density matrix model for polarons in a terahertz quantum dot cascade laser
NASA Astrophysics Data System (ADS)
Burnett, Benjamin A.; Williams, Benjamin S.
2014-10-01
A density matrix based method is introduced for computation of steady-state dynamics in quantum cascade systems of arbitrary size, which incorporates an optical field coherently. The method is applied to a model terahertz quantum dot cascade laser system, where a means of treating coherent electron-optical-phonon coupling is also introduced. Results predict a strong increase in the upper state lifetime and operating temperature as compared to traditional well-based terahertz quantum cascade lasers. However, new complications also arise, including multiple peaks in the gain spectrum due to strong electron-phonon coupling, and strong parasitic subthreshold current channels that arise due to reduced dephasing. It is anticipated that novel design schemes will be necessary for such lasers to become a reality.
Mukhopadhyay, S; Ramasesha, S
2009-08-21
We have used the density matrix renormalization group (DMRG) method to study the linear and nonlinear optical responses of first generation nitrogen based dendrimers with donor acceptor groups. We have employed Pariser-Parr-Pople Hamiltonian to model the interacting pi electrons in these systems. Within the DMRG method we have used an innovative scheme to target excited states with large transition dipole to the ground state. This method reproduces exact optical gaps and polarization in systems where exact diagonalization of the Hamiltonian is possible. We have used a correction vector method which tacitly takes into account the contribution of all excited states, to obtain the ground state polarizibility, first hyperpolarizibility, and two photon absorption cross sections. We find that the lowest optical excitations as well as the lowest excited triplet states are localized. It is interesting to note that the first hyperpolarizibility saturates more rapidly with system size compared to linear polarizibility unlike that of linear polyenes.
Low-density, high-strength intermetallic matrix composites by XD (trademark) synthesis
NASA Technical Reports Server (NTRS)
Kumar, K. S.; Dipietro, M. S.; Brown, S. A.; Whittenberger, J. D.
1991-01-01
A feasibility study was conducted to evaluate the potential of particulate composites based on low-density, L1(sub 2) trialuminide matrices for high-temperature applications. The compounds evaluated included Al22Fe3Ti8 (as a multiphase matrix), Al67Ti25Cr8, and Al66Ti25Mn9. The reinforcement consisted of TiB2 particulates. The TiB2 composites were processed by ingot and powder metallurgy techniques. Microstructural characterization and mechanical testing were performed in the hot-pressed and hot-isostatic-pressed condition. The casting were sectioned and isothermally forged into pancakes. All the materials were tested in compression as a function of temperature, and at high temperatures as a function of strain rate. The test results are discussed.
Nakatani, Naoki; Wouters, Sebastian; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2014-01-14
Linear response theory for the density matrix renormalization group (DMRG-LRT) was first presented in terms of the DMRG renormalization projectors [J. J. Dorando, J. Hachmann, and G. K.-L. Chan, J. Chem. Phys. 130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster.
TIEG1-NULL OSTEOCYTES DISPLAY DEFECTS IN THEIR MORPHOLOGY, DENSITY AND SURROUNDING BONE MATRIX
Haddad, Oualid; Hawse, John R.; Subramaniam, Malayannan; Spelsberg, Thomas C.; Bensamoun, Sabine F.
2011-01-01
Through the development of TGFβ-inducible early gene-1 (TIEG1) knockout (KO) mice, we have demonstrated that TIEG1 plays an important role in osteoblast-mediated bone mineralization, and in bone resistance to mechanical strain. To further investigate the influence of TIEG1 in skeletal maintenance, osteocytes were analyzed by transmission electron microscopy using TIEG1 KO and wild-type mouse femurs at one, three and eight months of age. The results revealed an age-dependent change in osteocyte surface and density, suggesting a role for TIEG1 in osteocyte development. Moreover, there was a decrease in the amount of hypomineralized bone matrix surrounding the osteocytes in TIEG1 KO mice relative to wild-type controls. While little is known about the function or importance of this hypomineralized bone matrix immediately adjacent to osteocytes, this study reveals significant differences in this bone microenvironment and suggests that osteocyte function may be compromised in the absence of TIEG1 expression. PMID:22121306
NASA Astrophysics Data System (ADS)
Nakatani, Naoki; Wouters, Sebastian; Van Neck, Dimitri; Chan, Garnet Kin-Lic
2014-01-01
Linear response theory for the density matrix renormalization group (DMRG-LRT) was first presented in terms of the DMRG renormalization projectors [J. J. Dorando, J. Hachmann, and G. K.-L. Chan, J. Chem. Phys. 130, 184111 (2009)]. Later, with an understanding of the manifold structure of the matrix product state (MPS) ansatz, which lies at the basis of the DMRG algorithm, a way was found to construct the linear response space for general choices of the MPS gauge in terms of the tangent space vectors [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)]. These two developments led to the formulation of the Tamm-Dancoff and random phase approximations (TDA and RPA) for MPS. This work describes how these LRTs may be efficiently implemented through minor modifications of the DMRG sweep algorithm, at a computational cost which scales the same as the ground-state DMRG algorithm. In fact, the mixed canonical MPS form implicit to the DMRG sweep is essential for efficient implementation of the RPA, due to the structure of the second-order tangent space. We present ab initio DMRG-TDA results for excited states of polyenes, the water molecule, and a [2Fe-2S] iron-sulfur cluster.
Andrews, Lester
2004-02-20
Metal hydrides are of considerable importance in chemical synthesis as intermediates in catalytic hydrogenation reactions. Transition metal atoms react with dihydrogen to produce metal dihydrides or dihydrogen complexes and these may be trapped in solid matrix samples for infrared spectroscopic study. The MH(2) or M(H(2)) molecules so formed react further to form higher MH(4), (H(2))MH(2), or M(H(2))(2), and MH(6), (H(2))(2)MH(2), or M(H(2))(3) hydrides or complexes depending on the metal. In this critical review these transition metal and dihydrogen reaction products are surveyed for Groups 3 though 12 and the contrasting behaviour in Groups 6 and 10 is discussed. Minimum energy structures and vibrational frequencies predicted by Density Functional Theory agree with the experimental results, strongly supporting the identification of novel binary transition metal hydride species, which the matrix-isolation method is well-suited to investigate. 104 references are cited.
The variational two-electron reduced-density-matrix method for extended systems
NASA Astrophysics Data System (ADS)
Rubin, Nicholas C.
In this thesis we develop the variational two-electron reduced-density-matrix method for extended systems. Extended systems are represented in two ways: i) lattice models describing the dominant valence electronic structure with periodic boundaries to account for their extended nature and ii) a crystalline-orbital basis built from atomic orbitals using the generalization of molecular orbital theory to polymers. The first part of this thesis (Ch. 3--4) examines the performance of the variational 2-RDM method on lattice systems with tunable electron correlation. The first of these systems is the classic Hubbard model with linear and ladder lattice topologies. Because electron correlation functions, such as charge- and spin-ordering, are linear functions of the 2-RDM, the difference in electronic structure between one- and quasi-one-dimensional systems is accurately characterized. The second model contains only two-body interactions and is unique among typical spin models in that it does not have a mean-field reference wave function. The ground state wave functions from all Hamiltonians in the model have the same 1-electron reduced density matrix; consequently, one-electron theories are largely inapplicable. The superconducting eta-pairing ground states make the model a unique tool for demonstrating the necessary N-representability in highly correlated environments. The second part of this thesis (Ch. 5--6) develops a formalism for modeling materials by solving the full Schrodinger equation. Crystalline-orbital Hartree-Fock provides a set of orbitals and integral tensors for the variational 2-RDM method. We demonstrate that time-reversal symmetry, which is implicitly included in position space electronic structure calculations, must be explicitly included as an N-representability constraint on the 2-RDM when using a momentum space basis. The necessity of these equality constraints is demonstrated by the accurate recovery of the binding energy of two polymers and the
One plus two-body random matrix ensembles with parity: Density of states and parity ratios
Vyas, Manan; Srivastava, P. C.; Kota, V. K. B.
2011-06-15
One plus two-body embedded Gaussian orthogonal ensemble of random matrices with parity [EGOE(1+2)-{pi}] generated by a random two-body interaction (modeled by GOE in two-particle spaces) in the presence of a mean field for spinless identical fermion systems is defined, generalizing the two-body ensemble with parity analyzed by Papenbrock and Weidenmueller [Phys. Rev. C 78, 054305 (2008)], in terms of two mixing parameters and a gap between the positive ({pi}=+) and negative ({pi}=-) parity single-particle (sp) states. Numerical calculations are used to demonstrate, using realistic values of the mixing parameters appropriate for some nuclei, that the EGOE(1+2)-{pi} ensemble generates Gaussian form (with corrections) for fixed parity eigenvalue densities (i.e., state densities). The random matrix model also generates many features in parity ratios of state densities that are similar to those predicted by a method based on the Fermi-gas model for nuclei. We have also obtained, by applying the formulation due to Chang et al. [Ann. Phys. (NY) 66, 137 (1971)], a simple formula for the spectral variances defined over fixed-(m{sub 1},m{sub 2}) spaces, where m{sub 1} is the number of fermions in the positive parity sp states and m{sub 2} is the number of fermions in the negative parity sp states. Similarly, using the binary correlation approximation, in the dilute limit, we have derived expressions for the lowest two-shape parameters. The smoothed densities generated by the sum of fixed-(m{sub 1},m{sub 2}) Gaussians with lowest two-shape corrections describe the numerical results in many situations. The model also generates preponderance of positive parity ground states for small values of the mixing parameters, and this is a feature seen in nuclear shell-model results.
Random matrix theory for portfolio optimization: a stability approach
NASA Astrophysics Data System (ADS)
Sharifi, S.; Crane, M.; Shamaie, A.; Ruskin, H.
2004-04-01
We apply random matrix theory (RMT) to an empirically measured financial correlation matrix, C, and show that this matrix contains a large amount of noise. In order to determine the sensitivity of the spectral properties of a random matrix to noise, we simulate a set of data and add different volumes of random noise. Having ascertained that the eigenspectrum is independent of the standard deviation of added noise, we use RMT to determine the noise percentage in a correlation matrix based on real data from S&P500. Eigenvalue and eigenvector analyses are applied and the experimental results for each of them are presented to identify qualitatively and quantitatively different spectral properties of the empirical correlation matrix to a random counterpart. Finally, we attempt to separate the noisy part from the non-noisy part of C. We apply an existing technique to cleaning C and then discuss its associated problems. We propose a technique of filtering C that has many advantages, from the stability point of view, over the existing method of cleaning.
Density matrix renormalization group study of the Anyon-Hubbard model
NASA Astrophysics Data System (ADS)
Arcila-Forero, J.; Franco, R.; Silva-Valencia, J.
2016-02-01
Recently optical lattices allow us to observe phase transition without the uncertainty posed by complex materials, and the simulations of these systems are an excellent bridge between materials-based condensed matter physics and cold atoms. In this way, the computational physics related to many-body problems have increased in importance. Using the density matrix renormalization group method, we studied a Hubbard model for anyons, which is an equivalent to a variant of the Bose-Hubbard model in which the bosonic hopping depends on the local density. This is an exact mapping between anyons and bosons in one dimension. The anyons interlope between bosons and fermions. For two anyons under particle exchange, the wave function acquires a fractional phase eiθ . We conclude that this system exhibits two phases: Mott-insulator and superfluid. We present the phase diagram for some angles. The Mott lobe increases with an increase of the statistical. We observed a reentrance phase transition for all lobes. We showed that the model studied is in the same universality class as the Bose-Hubbard model with two-body interactions.
SCDM-k: Localized orbitals for solids via selected columns of the density matrix
NASA Astrophysics Data System (ADS)
Damle, Anil; Lin, Lin; Ying, Lexing
2017-04-01
The recently developed selected columns of the density matrix (SCDM) method (Damle et al. 2015, [16]) is a simple, robust, efficient and highly parallelizable method for constructing localized orbitals from a set of delocalized Kohn-Sham orbitals for insulators and semiconductors with Γ point sampling of the Brillouin zone. In this work we generalize the SCDM method to Kohn-Sham density functional theory calculations with k-point sampling of the Brillouin zone, which is needed for more general electronic structure calculations for solids. We demonstrate that our new method, called SCDM-k, is by construction gauge independent and a natural way to describe localized orbitals. SCDM-k computes localized orbitals without the use of an optimization procedure, and thus does not suffer from the possibility of being trapped in a local minimum. Furthermore, the computational complexity of using SCDM-k to construct orthogonal and localized orbitals scales as O (Nlog N) where N is the total number of k-points in the Brillouin zone. SCDM-k is therefore efficient even when a large number of k-points are used for Brillouin zone sampling. We demonstrate the numerical performance of SCDM-k using systems with model potentials in two and three dimensions.
Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
NASA Astrophysics Data System (ADS)
Ehlers, G.; White, S. R.; Noack, R. M.
2017-03-01
The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid-real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at n =0.875 filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both U /t =4.0 and 8.0 . We find that the strength of the charge ordering depends on U /t and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.
NASA Astrophysics Data System (ADS)
Gavryusev, V.; Signoles, A.; Ferreira-Cao, M.; Zürn, G.; Hofmann, C. S.; Günter, G.; Schempp, H.; Robert-de-Saint-Vincent, M.; Whitlock, S.; Weidemüller, M.
2016-08-01
We present combined measurements of the spatially resolved optical spectrum and the total excited-atom number in an ultracold gas of three-level atoms under electromagnetically induced transparency conditions involving high-lying Rydberg states. The observed optical transmission of a weak probe laser at the center of the coupling region exhibits a double peaked spectrum as a function of detuning, while the Rydberg atom number shows a comparatively narrow single resonance. By imaging the transmitted light onto a charge-coupled-device camera, we record hundreds of spectra in parallel, which are used to map out the spatial profile of Rabi frequencies of the coupling laser. Using all the information available we can reconstruct the full one-body density matrix of the three-level system, which provides the optical susceptibility and the Rydberg density as a function of spatial position. These results help elucidate the connection between three-level interference phenomena, including the interplay of matter and light degrees of freedom and will facilitate new studies of many-body effects in optically driven Rydberg gases.
Li, Zhao; Xu, Heming; Li, Shujuan; Li, Qijun; Zhang, Wenji; Ye, Tiantian; Yang, Xinggang; Pan, Weisan
2014-01-30
The study was aimed to develop a novel gastro-floating multiparticulate system based on a porous and low-density matrix core with excellent floatability. The gastro-floating pellets (GFP) were composed of a porous matrix core, a drug loaded layer (DIP and HPMC), a sub-coating layer (HPMC) and a retarding layer (Eudragit(®) NE 30D). The porous matrix cores were evaluated in specific. EC was chosen as the matrix membrane for its rigidity and minimal expansion to large extent. The porous matrix core was achieved by the complete release of the bulk water soluble excipient from the EC coated beads, and mannitol was selected as the optimal water soluble excipient. SEM photomicrographs confirmed the structure of porous matrix cores. The compositions of GFP were investigated and optimized by orthogonal array design. The optimized formulation could sustain the drug release for 12h and float on the dissolution medium for at least 12h without lag time to float. The pharmacokinetic study was conducted in beagle dogs, and the relative bioavailability of the test preparation was 193.11±3.43%. In conclusion, the novel gastro-floating pellets can be developed as a promising approach for the gastro-retentive drug delivery systems.
Random matrix approach to the distribution of genomic distance.
Alexeev, Nikita; Zograf, Peter
2014-08-01
The cycle graph introduced by Bafna and Pevzner is an important tool for evaluating the distance between two genomes, that is, the minimal number of rearrangements needed to transform one genome into another. We interpret this distance in topological terms and relate it to the random matrix theory. Namely, the number of genomes at a given 2-break distance from a fixed one (the Hultman number) is represented by a coefficient in the genus expansion of a matrix integral over the space of complex matrices with the Gaussian measure. We study generating functions for the Hultman numbers and prove that the two-break distance distribution is asymptotically normal.
A novel approach for FE-SEM imaging of wood-matrix polymer interface in a biocomposite.
Singh, Adya P; Anderson, Ross; Park, Byung-Dae; Nuryawan, Arif
2013-01-01
Understanding the interface between polymer and biomass in composite products is important for developing high performance products, as the quality of adhesion at the interface determines composite properties. For example, with greater stiffness compared to polymer matrix, such as that of high density polyethylene, the wood component enhances stiffness of wood-polymer composites, provided there is good adhesion between composite components. However, in composites made from wood flour (wood particles) and synthetic resins it is often difficult to clearly resolve particle-matrix interfaces in the conventionally employed microscopy method that involves SEM examination of fractured faces of composites. We developed a novel approach, where composites made from high density polyethylene and wood flour were examined and imaged with a FE-SEM (field emission scanning electron microscope) in transverse sections cut through the composites. Improved definition of the interface was achieved using this approach, which enabled a more thorough comparison to be made of the features of the interface between wood particles and the matrix in composites with and without a coupling agent, as it was possible to clearly resolve the interfaces for particles of all sizes, from large particles consisting of many cells down to tiny cell wall fragments, particularly in composites that did not incorporate the coupling agent used to enhance particle adhesion with the matrix polymer. The method developed would be suitable particularly for high definition SEM imaging of a wide range of composites made combining wood and agricultural residues with synthetic polymers.
Exploring multicollinearity using a random matrix theory approach.
Feher, Kristen; Whelan, James; Müller, Samuel
2012-01-01
Clustering of gene expression data is often done with the latent aim of dimension reduction, by finding groups of genes that have a common response to potentially unknown stimuli. However, what is poorly understood to date is the behaviour of a low dimensional signal embedded in high dimensions. This paper introduces a multicollinear model which is based on random matrix theory results, and shows potential for the characterisation of a gene cluster's correlation matrix. This model projects a one dimensional signal into many dimensions and is based on the spiked covariance model, but rather characterises the behaviour of the corresponding correlation matrix. The eigenspectrum of the correlation matrix is empirically examined by simulation, under the addition of noise to the original signal. The simulation results are then used to propose a dimension estimation procedure of clusters from data. Moreover, the simulation results warn against considering pairwise correlations in isolation, as the model provides a mechanism whereby a pair of genes with `low' correlation may simply be due to the interaction of high dimension and noise. Instead, collective information about all the variables is given by the eigenspectrum.
A Simple Approach to Dot Matrix Printing of Foreign Scripts.
ERIC Educational Resources Information Center
Becker, Donald A.
1985-01-01
Outlines the structure of a printer driven program that converts Romanized texts, composed with the aid of standard word-processing software, into codes that enable a dot matrix printer to produce high-quality printouts in various non-Roman scripts. (Author/SED)
Coupled Mode Formalism: Connecting Phasor, Matrix, and Geometrical Approaches
2014-05-30
the map’s cyclical re-use of a fixed range of longitude co-ordinates. This is somewhat analogous to the situation in solid state physics in which the...1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 III COUPLED STATES : MATRIX FORM...4 IV COUPLED STATES : GEOMETRIC FORM . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Normal form
Kussmann, Jörg; Luenser, Arne; Beer, Matthias; Ochsenfeld, Christian
2015-03-07
An analytical method to calculate the molecular vibrational Hessian matrix at the self-consistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulomb-type two-electron integral contractions, we show that the effect of the perturbation on the electronic structure due to the displacement of nuclei decays at least as r{sup −2} instead of r{sup −1}. The perturbation is asymptotically local, and the computation of the Hessian matrix can, in principle, be performed with O(N) complexity. Our implementation exhibits linear scaling in all time-determining steps, with some rapid but quadratic-complexity steps remaining. Sample calculations illustrate linear or near-linear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably sub-quadratic to quadratic, depending on the density of the underlying electronic structure.
Yao, Rutao; Ramachandra, Ranjith M.; Mahajan, Neeraj; Rathod, Vinay; Gunasekar, Noel; Panse, Ashish; Ma, Tianyu; Jian, Yiqiang; Yan, Jianhua; Carson, Richard E.
2012-01-01
To achieve optimal PET image reconstruction through better system modeling, we developed a system matrix that is based on the probability density function for each line of response (LOR-PDF). The LOR-PDFs are grouped by LOR-to-detector incident angles to form a highly compact system matrix. The system matrix was implemented in the MOLAR list mode reconstruction algorithm for a small animal PET scanner. The impact of LOR-PDF on reconstructed image quality was assessed qualitatively as well as quantitatively in terms of contrast recovery coefficient (CRC) and coefficient of variance (COV), and its performance was compared with a fixed Gaussian (iso-Gaussian) line spread function. The LOR-PDFs of 3 coincidence signal emitting sources, 1) ideal positron emitter that emits perfect back-to-back γ rays (γγ) in air; 2) fluorine-18 (18F) nuclide in water; and 3) oxygen-15 (15O) nuclide in water, were derived, and assessed with simulated and experimental phantom data. The derived LOR-PDFs showed anisotropic and asymmetric characteristics dependent on LOR-detector angle, coincidence emitting source, and the medium, consistent with common PET physical principles. The comparison of the iso-Gaussian function and LOR-PDF showed that: 1) without positron range and acolinearity effects, the LOR-PDF achieved better or similar trade-offs of contrast recovery and noise for objects of 4-mm radius or larger, and this advantage extended to smaller objects (e.g. 2-mm radius sphere, 0.6-mm radius hot-rods) at higher iteration numbers; and 2) with positron range and acolinearity effects, the iso-Gaussian achieved similar or better resolution recovery depending on the significance of positron range effect. We conclude that the 3-D LOR-PDF approach is an effective method to generate an accurate and compact system matrix. However, when used directly in expectation-maximization based list-mode iterative reconstruction algorithms such as MOLAR, its superiority is not clear. For this
Sener, Melih K; Schulten, Klaus
2002-03-01
We develop a random matrix model approach to study static disorder in pigment-protein complexes in photosynthetic organisms. As a case study, we examine the ring of B850 bacteriochlorophylls in the peripheral light-harvesting complex of Rhodospirillum molischianum, formulated in terms of an effective Hamiltonian describing the collective electronic excitations of the system. We numerically examine and compare various models of disorder and observe that both the density of states and the absorption spectrum of the model show remarkable spectral universality. For the case of unitary disorder, we develop a method to analytically evaluate the density of states of the ensemble using the supersymmetric formulation of random matrix theory. Succinct formulas that can be readily applied in future studies are provided in an appendix.
Open-Ended Recursive Approach for the Calculation of Multiphoton Absorption Matrix Elements.
Friese, Daniel H; Beerepoot, Maarten T P; Ringholm, Magnus; Ruud, Kenneth
2015-03-10
We present an implementation of single residues for response functions to arbitrary order using a recursive approach. Explicit expressions in terms of density-matrix-based response theory for the single residues of the linear, quadratic, cubic, and quartic response functions are also presented. These residues correspond to one-, two-, three- and four-photon transition matrix elements. The newly developed code is used to calculate the one-, two-, three- and four-photon absorption cross sections of para-nitroaniline and para-nitroaminostilbene, making this the first treatment of four-photon absorption in the framework of response theory. We find that the calculated multiphoton absorption cross sections are not very sensitive to the size of the basis set as long as a reasonably large basis set with diffuse functions is used. The choice of exchange-correlation functional, however, significantly affects the calculated cross sections of both charge-transfer transitions and other transitions, in particular, for the larger para-nitroaminostilbene molecule. We therefore recommend the use of a range-separated exchange-correlation functional in combination with the augmented correlation-consistent double-ζ basis set aug-cc-pVDZ for the calculation of multiphoton absorption properties.
Open-Ended Recursive Approach for the Calculation of Multiphoton Absorption Matrix Elements
2015-01-01
We present an implementation of single residues for response functions to arbitrary order using a recursive approach. Explicit expressions in terms of density-matrix-based response theory for the single residues of the linear, quadratic, cubic, and quartic response functions are also presented. These residues correspond to one-, two-, three- and four-photon transition matrix elements. The newly developed code is used to calculate the one-, two-, three- and four-photon absorption cross sections of para-nitroaniline and para-nitroaminostilbene, making this the first treatment of four-photon absorption in the framework of response theory. We find that the calculated multiphoton absorption cross sections are not very sensitive to the size of the basis set as long as a reasonably large basis set with diffuse functions is used. The choice of exchange–correlation functional, however, significantly affects the calculated cross sections of both charge-transfer transitions and other transitions, in particular, for the larger para-nitroaminostilbene molecule. We therefore recommend the use of a range-separated exchange–correlation functional in combination with the augmented correlation-consistent double-ζ basis set aug-cc-pVDZ for the calculation of multiphoton absorption properties. PMID:25821415
Assessing modularity using a random matrix theory approach.
Feher, Kristen; Whelan, James; Müller, Samuel
2011-09-26
Random matrix theory (RMT) is well suited to describing the emergent properties of systems with complex interactions amongst their constituents through their eigenvalue spectrums. Some RMT results are applied to the problem of clustering high dimensional biological data with complex dependence structure amongst the variables. It will be shown that a gene relevance or correlation network can be constructed by choosing a correlation threshold in a principled way, such that it corresponds to a block diagonal structure in the correlation matrix, if such a structure exists. The structure is then found using community detection algorithms, but with parameter choice guided by RMT predictions. The resulting clustering is compared to a variety of hierarchical clustering outputs and is found to the most generalised result, in that it captures all the features found by the other considered methods.
NASA Astrophysics Data System (ADS)
Lim, S. P.; Sheng, D. N.
2016-07-01
A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high-energy densities through a disorder-driven dynamic phase transition. The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target highly excited states for MBL systems. By studying the one-dimensional Heisenberg spin chain in a random field, we demonstrate the accuracy of the method in obtaining energy eigenstates and the corresponding statistical results of quantum states in the MBL phase. Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks: one at zero and another one at the quantized entropy S =ln2 with an exponential decay tail on the S >ln2 side. Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop power-law correlations. The corresponding phase diagram contains an intermediate or crossover regime, which has power-law spin-z correlations resulting from contributions of the rare events. We discuss the physical picture for the numerical observations in this regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. Our results may provide new insights for understanding the phase transition in such systems.
NASA Astrophysics Data System (ADS)
Habershon, Scott
2013-09-01
We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency.
Validation of density-functional versus density-functional+U approaches for oxide ultrathin films
NASA Astrophysics Data System (ADS)
Barcaro, Giovanni; Thomas, Iorwerth Owain; Fortunelli, Alessandro
2010-03-01
A comparison between available experimental information and the predictions of density-functional and density-functional+U approaches is presented for oxide ultrathin films grown on single-crystal metal surfaces. Prototypical examples of monolayer phases of an ionic oxide (ZnO), a late transition metal oxide (NiO), and an early transition metal oxide (TiO2) are considered. The aim is to validate the theoretical approaches, focusing on the prediction of structural features and the reproduction of scanning tunneling microscopy images, rationalized in terms of the local density of states of the systems. It is found that it is possible to reasonably estimate the optimal lattice constant of ultrathin supported films and that the inclusion of the Hubbard U term appreciably improves the accuracy of theoretical predictions, especially in the case of nonpolar ultrathin phases of a transition metal oxide. Moreover, the optimal value of U for the oxide layer at the interface with the metal support is found to differ from that appropriate for the bulk oxide, as a consequence of the intermixing of oxide and support electronic states and screening effects.
Permutationally Invariant Part of a Density Matrix and Nonseparability of N-Qubit States
NASA Astrophysics Data System (ADS)
Gao, Ting; Yan, Fengli; van Enk, S. J.
2014-05-01
We consider the concept of "the permutationally invariant (PI) part of a density matrix," which has proven very useful for both efficient quantum state estimation and entanglement characterization of N-qubit systems. We show here that the concept is, in fact, basis dependent but that this basis dependence makes it an even more powerful concept than has been appreciated so far. By considering the PI part ρPI of a general (mixed) N-qubit state ρ, we obtain (i) strong bounds on quantitative nonseparability measures, (ii) a whole hierarchy of multipartite separability criteria (one of which entails a sufficient criterion for genuine N-partite entanglement) that can be experimentally determined by just 2N +1 measurement settings, (iii) a definition of an efficiently measurable degree of separability, which can be used for quantifying a novel aspect of decoherence of N qubits, and (iv) an explicit example that shows there are, for increasing N, genuinely N-partite entangled states lying closer and closer to the maximally mixed state. Moreover, we show that if the PI part of a state is k nonseparable, then so is the actual state. We further argue to add as requirement on any multipartite entanglement measure E that it satisfy E(ρ)≥E(ρPI), even though the operation that maps ρ→ρPI is not local.
Giesbertz, K J H; Gritsenko, O V; Baerends, E J
2012-03-07
Adiabatic response time-dependent density functional theory (TDDFT) suffers from the restriction to basically an occupied → virtual single excitation formulation. Adiabatic time-dependent density matrix functional theory allows to break away from this restriction. Problematic excitations for TDDFT, viz. bonding-antibonding, double, charge transfer, and higher excitations, are calculated along the bond-dissociation coordinate of the prototype molecules H(2) and HeH(+) using the recently developed adiabatic linear response phase-including (PI) natural orbital theory (PINO). The possibility to systematically increase the scope of the calculation from excitations out of (strongly) occupied into weakly occupied ("virtual") natural orbitals to larger ranges of excitations is explored. The quality of the PINO response calculations is already much improved over TDDFT even when the severest restriction is made, to virtually the size of the TDDFT diagonalization problem (only single excitation out of occupied orbitals plus all diagonal doubles). Further marked improvement is obtained with moderate extension to allow for excitation out of the lumo and lumo+1, which become fractionally occupied in particular at longer distances due to left-right correlation effects. In the second place the interpretation of density matrix response calculations is elucidated. The one-particle reduced density matrix response for an excitation is related to the transition density matrix to the corresponding excited state. The interpretation of the transition density matrix in terms of the familiar excitation character (single excitations, double excitations of various types, etc.) is detailed. The adiabatic PINO theory is shown to successfully resolve the problematic cases of adiabatic TDDFT when it uses a proper PI orbital functional such as the PILS functional.
NASA Astrophysics Data System (ADS)
Giesbertz, K. J. H.; Gritsenko, O. V.; Baerends, E. J.
2012-03-01
Adiabatic response time-dependent density functional theory (TDDFT) suffers from the restriction to basically an occupied → virtual single excitation formulation. Adiabatic time-dependent density matrix functional theory allows to break away from this restriction. Problematic excitations for TDDFT, viz. bonding-antibonding, double, charge transfer, and higher excitations, are calculated along the bond-dissociation coordinate of the prototype molecules H2 and HeH+ using the recently developed adiabatic linear response phase-including (PI) natural orbital theory (PINO). The possibility to systematically increase the scope of the calculation from excitations out of (strongly) occupied into weakly occupied ("virtual") natural orbitals to larger ranges of excitations is explored. The quality of the PINO response calculations is already much improved over TDDFT even when the severest restriction is made, to virtually the size of the TDDFT diagonalization problem (only single excitation out of occupied orbitals plus all diagonal doubles). Further marked improvement is obtained with moderate extension to allow for excitation out of the lumo and lumo+1, which become fractionally occupied in particular at longer distances due to left-right correlation effects. In the second place the interpretation of density matrix response calculations is elucidated. The one-particle reduced density matrix response for an excitation is related to the transition density matrix to the corresponding excited state. The interpretation of the transition density matrix in terms of the familiar excitation character (single excitations, double excitations of various types, etc.) is detailed. The adiabatic PINO theory is shown to successfully resolve the problematic cases of adiabatic TDDFT when it uses a proper PI orbital functional such as the PILS functional.
Cao, Haihui; Ackerman, Jerome L; Hrovat, Mirko I; Graham, Lila; Glimcher, Melvin J; Wu, Yaotang
2008-12-01
The density of the organic matrix of bone substance is a critical parameter necessary to clinically evaluate and distinguish structural and metabolic pathological conditions such as osteomalacia in adults and rickets in growing children. Water- and fat-suppressed proton projection MRI (WASPI) was developed as a noninvasive means to obtain this information. In this study, a density calibration phantom was developed to convert WASPI intensity to true bone matrix density. The phantom contained a specifically designed poly(ethylene oxide)/poly(methyl methacrylate) (PEO/PMMA) blend, whose MRI properties (T(1), T(2), and resonance linewidth) were similar to those of solid bone matrix (collagen, tightly bound water, and other immobile molecules), minimizing the need to correct for differences in T(1) and/or T(2) relaxation between the phantom and the subject. Cortical and trabecular porcine bone specimens were imaged using WASPI with the calibration phantom in the field of view (FOV) as a stable intensity reference. Gravimetric and amino acid analyses were carried out on the same specimens after WASPI, and the chemical results were found to be highly correlated (r(2) = 0.98 and 0.95, respectively) to the WASPI intensity. By this procedure the WASPI intensity can be used to obtain the true bone matrix mass density in g cm(-3).
NASA Technical Reports Server (NTRS)
Akhundova, E. A.; Dodonov, V. V.; Manko, V. I.
1993-01-01
The exact expressions for density matrix and Wigner functions of quantum systems are known only in special cases. Corresponding Hamiltonians are quadratic forms of Euclidean coordinates and momenta. In this paper we consider the problem of one-dimensional free particle movement in the bounded region 0 is less than x is less than a (including the case a = infinity).
Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers.
Li, Huanan; Suwunnarat, Suwun; Fleischmann, Ragnar; Schanz, Holger; Kottos, Tsampikos
2017-01-27
We employ random matrix theory in order to investigate coherent perfect absorption (CPA) in lossy systems with complex internal dynamics. The loss strength γ_{CPA} and energy E_{CPA}, for which a CPA occurs, are expressed in terms of the eigenmodes of the isolated cavity-thus carrying over the information about the chaotic nature of the target-and their coupling to a finite number of scattering channels. Our results are tested against numerical calculations using complex networks of resonators and chaotic graphs as CPA cavities.
Random Matrix Approach to Quantum Adiabatic Evolution Algorithms
NASA Technical Reports Server (NTRS)
Boulatov, Alexei; Smelyanskiy, Vadier N.
2004-01-01
We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.
Approaches to 100 Gbit/sq. in. recording density
NASA Technical Reports Server (NTRS)
Kryder, Mark H.
1994-01-01
A recording density of 10 Gbit/sq. in. is being pursued by a number of companies and universities in the National Storage Industry Consortium. It is widely accepted that this goal will be achieved in the laboratory within a few years. In this paper approaches to achieving 100 Gbit/sq. in. storage densities are considered. A major obstacle to continued scaling of magnetic recording to higher densities is that as the bit size is reduced, the grain size in the magnetic media must be reduced in order that media noise does not become so large that the signal to noise ratio (SNR) degrades sufficiently to make detection impossible. At 100 Gbit/sq. in., the bit size is only 0.006 square micrometers, which, in order to achieve 30 dB SNR, requires a grain size of about 2.5 nm. Such small grains are subject to thermal instability, and the recorded information will degrade over time unless the magnetic anisotropy of the materials used is increased significantly, or the media thickness is made much larger than expected on the basis of scaling today's longitudinal media thickness.
NASA Astrophysics Data System (ADS)
DePrince, A. Eugene; Mazziotti, David A.
2010-01-01
The parametric variational two-electron reduced-density-matrix (2-RDM) method is applied to computing electronic correlation energies of medium-to-large molecular systems by exploiting the spatial locality of electron correlation within the framework of the cluster-in-molecule (CIM) approximation [S. Li et al., J. Comput. Chem. 23, 238 (2002); J. Chem. Phys. 125, 074109 (2006)]. The 2-RDMs of individual molecular fragments within a molecule are determined, and selected portions of these 2-RDMs are recombined to yield an accurate approximation to the correlation energy of the entire molecule. In addition to extending CIM to the parametric 2-RDM method, we (i) suggest a more systematic selection of atomic-orbital domains than that presented in previous CIM studies and (ii) generalize the CIM method for open-shell quantum systems. The resulting method is tested with a series of polyacetylene molecules, water clusters, and diazobenzene derivatives in minimal and nonminimal basis sets. Calculations show that the computational cost of the method scales linearly with system size. We also compute hydrogen-abstraction energies for a series of hydroxyurea derivatives. Abstraction of hydrogen from hydroxyurea is thought to be a key step in its treatment of sickle cell anemia; the design of hydroxyurea derivatives that oxidize more rapidly is one approach to devising more effective treatments.
Fragment approach to constrained density functional theory calculations using Daubechies wavelets
Ratcliff, Laura E.; Genovese, Luigi; Mohr, Stephan; Deutsch, Thierry
2015-06-21
In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.
Fragment approach to constrained density functional theory calculations using Daubechies wavelets.
Ratcliff, Laura E; Genovese, Luigi; Mohr, Stephan; Deutsch, Thierry
2015-06-21
In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.
Density matrix embedding theory studies of the two-dimensional Hubbard model
NASA Astrophysics Data System (ADS)
Zheng, Bo-Xiao
Density matrix embedding theory (DMET) provides a quantum embedding framework to compute the electronic structure in strongly correlated lattice systems. It has been applied to various model Hamiltonians and ab initio systems. In this talk, I will review the results obtained in the two-dimensional one-band Hubbard model using DMET. Over the last years, we mapped a calibrated ground-state phase diagram of the two-dimensional Hubbard model, concerning magnetic, superconducting and various inhomogeneous phases. Based on the results from this work, as well as the consistent data from other numerical methods, we are able to conclude that many parts of the Hubbard phase diagram is already settled up to an accurate energy scale of 0.001t. Recently, by using large-scale auxiliary-field quantum Monte Carlo (AFQMC) in the impurity problem, we are able to treat much larger embedded clusters at half-filling (and with the constrained path approximation at non-half-filling), which provides a deeper understanding on the finite-size effects of energy and observables in both quantum embedding and finite cluster numerical methods. Finally, we systematically investigated the putative inhomogeneous phases in the underdoped, strong coupling Hubbard model, proposing new inhomogeneous patterns as strong candidates for the ground state. Reference: [1] Bo-Xiao Zheng, Garnet K.-L. Chan, arXiv:1504.01784 [2] J.P.F. Leblanc, Andrey E. Antipov, et al., arXiv:1505.02290 We acknowledge funding from the US Department of Energy, Office of Science, through DE-SC0008624 and DE-SC0010530. This work was also performed as part of the Simons Collaboration on the Many Electron Problem, sponsored by the Simons Foundation.
Dissipative quantum molecular dynamics in gases and condensed media: A density matrix treatment
NASA Astrophysics Data System (ADS)
Leathers, Andrew S.
We present a study of dissipative quantum molecular dynamics, covering several different methods of treating the dissipation. We use a reduced density matrix framework, which leads to coupled integro-differential equations in time. We then develop a numerical algorithm for solving these equations. This algorithm is tested by comparing the results to a solved model. The method is then applied to the vibrational relaxation of adsorbates on metal surfaces. We also use this model to test approximations which transform the integro-differential equations into simpler integral equations. Our results compare well to experiment, and demonstrate the need for a full treatment without approximations. This model is then expanded to allow for electronic relaxation, as well as excitation by a light pulse. The electronic relaxation occurs on a different time scale, and is treated differently than the vibrational relaxation. Our method is shown to be general enough to handle both cases. Our next model is light-induced electron transfer in a metal cluster on a semiconductor surface. We consider both direct electronic excitation causing electron transfer, as well as indirect transfer, where there is excitation to an intermediate state which is coupled to the electron transferred state. Our results indicate vibrational relaxation plays a small role in the direct transfer dynamics, but is still important in the indirect case. Finally, we present a mixed quantum-classical study of the effect of initial conditions, with the goal of moving towards a method capable of treating dissipation in both quantum and mixed quatum-classical systems. (Full text of this dissertation may be available via the University of Florida Libraries web site. Please check http://www.uflib.ufl.edu/etd.html)
Harris, Travis V.; Morokuma, Keiji; Kurashige, Yuki; Yanai, Takeshi
2014-02-07
The applicability of ab initio multireference wavefunction-based methods to the study of magnetic complexes has been restricted by the quickly rising active-space requirements of oligonuclear systems and dinuclear complexes with S > 1 spin centers. Ab initio density matrix renormalization group (DMRG) methods built upon an efficient parameterization of the correlation network enable the use of much larger active spaces, and therefore may offer a way forward. Here, we apply DMRG-CASSCF to the dinuclear complexes [Fe{sub 2}OCl{sub 6}]{sup 2−} and [Cr{sub 2}O(NH{sub 3}){sub 10}]{sup 4+}. After developing the methodology through systematic basis set and DMRG M testing, we explore the effects of extended active spaces that are beyond the limit of conventional methods. We find that DMRG-CASSCF with active spaces including the metal d orbitals, occupied bridging-ligand orbitals, and their virtual double shells already capture a major portion of the dynamic correlation effects, accurately reproducing the experimental magnetic coupling constant (J) of [Fe{sub 2}OCl{sub 6}]{sup 2−} with (16e,26o), and considerably improving the smaller active space results for [Cr{sub 2}O(NH{sub 3}){sub 10}]{sup 4+} with (12e,32o). For comparison, we perform conventional MRCI+Q calculations and find the J values to be consistent with those from DMRG-CASSCF. In contrast to previous studies, the higher spin states of the two systems show similar deviations from the Heisenberg spectrum, regardless of the computational method.
Random matrix approach to the dynamics of stock inventory variations
NASA Astrophysics Data System (ADS)
Zhou, Wei-Xing; Mu, Guo-Hua; Kertész, János
2012-09-01
It is well accepted that investors can be classified into groups owing to distinct trading strategies, which forms the basic assumption of many agent-based models for financial markets when agents are not zero-intelligent. However, empirical tests of these assumptions are still very rare due to the lack of order flow data. Here we adopt the order flow data of Chinese stocks to tackle this problem by investigating the dynamics of inventory variations for individual and institutional investors that contain rich information about the trading behavior of investors and have a crucial influence on price fluctuations. We find that the distributions of cross-correlation coefficient Cij have power-law forms in the bulk that are followed by exponential tails, and there are more positive coefficients than negative ones. In addition, it is more likely that two individuals or two institutions have a stronger inventory variation correlation than one individual and one institution. We find that the largest and the second largest eigenvalues (λ1 and λ2) of the correlation matrix cannot be explained by random matrix theory and the projections of investors' inventory variations on the first eigenvector u(λ1) are linearly correlated with stock returns, where individual investors play a dominating role. The investors are classified into three categories based on the cross-correlation coefficients CV R between inventory variations and stock returns. A strong Granger causality is unveiled from stock returns to inventory variations, which means that a large proportion of individuals hold the reversing trading strategy and a small part of individuals hold the trending strategy. Our empirical findings have scientific significance in the understanding of investors' trading behavior and in the construction of agent-based models for emerging stock markets.
Random matrix approach to cross correlations in financial data
NASA Astrophysics Data System (ADS)
Plerou, Vasiliki; Gopikrishnan, Parameswaran; Rosenow, Bernd; Amaral, Luís A.; Guhr, Thomas; Stanley, H. Eugene
2002-06-01
We analyze cross correlations between price fluctuations of different stocks using methods of random matrix theory (RMT). Using two large databases, we calculate cross-correlation matrices
Random matrix approach to quantum adiabatic evolution algorithms
Boulatov, A.; Smelyanskiy, V.N.
2005-05-15
We analyze the power of the quantum adiabatic evolution algorithm (QAA) for solving random computationally hard optimization problems within a theoretical framework based on random matrix theory (RMT). We present two types of driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that nonadiabatic corrections in the QAA are due to the interaction of the ground state with the 'cloud' formed by most of the excited states, confirming that in driven RMT models, the Landau-Zener scenario of pairwise level repulsions is not relevant for the description of nonadiabatic corrections. We show that the QAA has a finite probability of success in a certain range of parameters, implying a polynomial complexity of the algorithm. The second model corresponds to the standard QAA with the problem Hamiltonian taken from the RMT Gaussian unitary ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. For this reason, the driven GUE model can also lead to polynomial complexity of the QAA. The main contribution to the failure probability of the QAA comes from the nonadiabatic corrections to the eigenstates, which only depend on the absolute values of the transition amplitudes. Due to the mapping between the two models, these absolute values are the same in both cases. Our results indicate that this 'phase irrelevance' is the leading effect that can make both the Markovian- and GUE-type QAAs successful.
Streubel, A; Siepmann, J; Bodmeier, R
2003-01-01
The aim of this study was to develop and physicochemically characterize single unit, floating controlled drug delivery systems consisting of (i). polypropylene foam powder, (ii). matrix-forming polymer(s), (iii). drug, and (iv). filler (optional). The highly porous foam powder provided low density and, thus, excellent in vitro floating behavior of the tablets. All foam powder-containing tablets remained floating for at least 8 h in 0.1 N HCl at 37 degrees C. Different types of matrix-forming polymers were studied: hydroxypropyl methylcellulose (HPMC), polyacrylates, sodium alginate, corn starch, carrageenan, gum guar and gum arabic. The tablets eroded upon contact with the release medium, and the relative importance of drug diffusion, polymer swelling and tablet erosion for the resulting release patterns varied significantly with the type of matrix former. The release rate could effectively be modified by varying the "matrix-forming polymer/foam powder" ratio, the initial drug loading, the tablet geometry (radius and height), the type of matrix-forming polymer, the use of polymer blends and the addition of water-soluble or water-insoluble fillers (such as lactose or microcrystalline cellulose). The floating behavior of the low density drug delivery systems could successfully be combined with accurate control of the drug release patterns.
Liquid water simulations with the density fragment interaction approach.
Hu, Xiangqian; Jin, Yingdi; Zeng, Xiancheng; Hu, Hao; Yang, Weitao
2012-06-07
We reformulate the density fragment interaction (DFI) approach [Fujimoto and Yang, J. Chem. Phys., 2008, 129, 054102.] to achieve linear-scaling quantum mechanical calculations for large molecular systems. Two key approximations are developed to improve the efficiency of the DFI approach and thus enable the calculations for large molecules: the electrostatic interactions between fragments are computed efficiently by means of polarizable electrostatic-potential-fitted atomic charges; and frozen fragment pseudopotentials, similar to the effective fragment potentials that can be fitted from interactions between small molecules, are employed to take into account the Pauli repulsion effect among fragments. Our reformulated and parallelized DFI method demonstrates excellent parallel performance based on the benchmarks for the system of 256 water molecules. Molecular dynamics simulations for the structural properties of liquid water also show a qualitatively good agreement with experimental measurements including the heat capacity, binding energy per water molecule, and the radial distribution functions of atomic pairs of O-O, O-H, and H-H. With this approach, large-scale quantum mechanical simulations for water and other liquids become feasible.
Kussmann, Jörg; Ochsenfeld, Christian
2007-11-28
A density matrix-based time-dependent self-consistent field (D-TDSCF) method for the calculation of dynamic polarizabilities and first hyperpolarizabilities using the Hartree-Fock and Kohn-Sham density functional theory approaches is presented. The D-TDSCF method allows us to reduce the asymptotic scaling behavior of the computational effort from cubic to linear for systems with a nonvanishing band gap. The linear scaling is achieved by combining a density matrix-based reformulation of the TDSCF equations with linear-scaling schemes for the formation of Fock- or Kohn-Sham-type matrices. In our reformulation only potentially linear-scaling matrices enter the formulation and efficient sparse algebra routines can be employed. Furthermore, the corresponding formulas for the first hyperpolarizabilities are given in terms of zeroth- and first-order one-particle reduced density matrices according to Wigner's (2n+1) rule. The scaling behavior of our method is illustrated for first exemplary calculations with systems of up to 1011 atoms and 8899 basis functions.
Nakatani, Naoki; Chan, Garnet Kin-Lic
2013-04-07
We investigate tree tensor network states for quantum chemistry. Tree tensor network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree tensor network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree tensor network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree tensor network states correlates 110 electrons in 110 active orbitals.
Poelmans, Ward; Van Raemdonck, Mario; Verstichel, Brecht; De Baerdemacker, Stijn; Torre, Alicia; Lain, Luis; Massaccesi, Gustavo E; Alcoba, Diego R; Bultinck, Patrick; Van Neck, Dimitri
2015-09-08
We perform a direct variational determination of the second-order (two-particle) density matrix corresponding to a many-electron system, under a restricted set of the two-index N-representability P-, Q-, and G-conditions. In addition, we impose a set of necessary constraints that the two-particle density matrix must be derivable from a doubly occupied many-electron wave function, i.e., a singlet wave function for which the Slater determinant decomposition only contains determinants in which spatial orbitals are doubly occupied. We rederive the two-index N-representability conditions first found by Weinhold and Wilson and apply them to various benchmark systems (linear hydrogen chains, He, N2, and CN(-)). This work is motivated by the fact that a doubly occupied many-electron wave function captures in many cases the bulk of the static correlation. Compared to the general case, the structure of doubly occupied two-particle density matrices causes the associate semidefinite program to have a very favorable scaling as L(3), where L is the number of spatial orbitals. Since the doubly occupied Hilbert space depends on the choice of the orbitals, variational calculation steps of the two-particle density matrix are interspersed with orbital-optimization steps (based on Jacobi rotations in the space of the spatial orbitals). We also point to the importance of symmetry breaking of the orbitals when performing calculations in a doubly occupied framework.
How Fast Can Networks Synchronize? A Random Matrix Theory Approach
NASA Astrophysics Data System (ADS)
Timme, Marc; Wolf, Fred; Geisel, Theo
2004-03-01
Pulse-coupled oscillators constitute a paradigmatic class of dynamical systems interacting on networks because they model a variety of biological systems including flashing fireflies and chirping crickets as well as pacemaker cells of the heart and neural networks. Synchronization is one of the most simple and most prevailing kinds of collective dynamics on such networks. Here we study collective synchronization [1] of pulse-coupled oscillators interacting on asymmetric random networks. Using random matrix theory we analytically determine the speed of synchronization in such networks in dependence on the dynamical and network parameters [2]. The speed of synchronization increases with increasing coupling strengths. Surprisingly, however, it stays finite even for infinitely strong interactions. The results indicate that the speed of synchronization is limited by the connectivity of the network. We discuss the relevance of our findings to general equilibration processes on complex networks. [5mm] [1] M. Timme, F. Wolf, T. Geisel, Phys. Rev. Lett. 89:258701 (2002). [2] M. Timme, F. Wolf, T. Geisel, cond-mat/0306512 (2003).
A theoretical validation of the B-matrix spatial distribution approach to diffusion tensor imaging.
Borkowski, Karol; Kłodowski, Krzysztof; Figiel, Henryk; Krzyżak, Artur Tadeusz
2017-02-01
The recently presented B-matrix Spatial Distribution (BSD) approach is a calibration technique which derives the actual distribution of the B-matrix in space. It is claimed that taking into account the spatial variability of the B-matrix improves the accuracy of diffusion tensor imaging (DTI). The purpose of this study is to verify this approach theoretically through computer simulations. Assuming three different spatial distributions of the B-matrix, diffusion weighted signals were calculated for the six orientations of a model anisotropic phantom. Subsequently two variants of the BSD calibration were performed for each of the three cases; one with the assumption of high uniformity of the model phantom (uBSD-DTI) and the other taking into account imperfections in phantom structure (BSD-DTI). Several cases of varying degrees of phantom uniformity were analyzed and the distributions of the B-matrix obtained were used for the calculation of the diffusion tensor of a model isotropic phantom. The results were compared with standard diffusion tensor calculation. The simulations confirmed the improvement of accuracy in the determination of the diffusion tensor after the calibration. BSD-DTI improves accuracy independent of both the degree of uniformity of the phantom and the inhomogeneity of the B-matrix. In cases of a relatively good uniformity of the phantom and minor distortions in the spatial distribution of the B-matrix, the uBSD-DTI approach is sufficient.
Different approaches for extracting information from the co-occurrence matrix.
Nanni, Loris; Brahnam, Sheryl; Ghidoni, Stefano; Menegatti, Emanuele; Barrier, Tonya
2013-01-01
In 1979 Haralick famously introduced a method for analyzing the texture of an image: a set of statistics extracted from the co-occurrence matrix. In this paper we investigate novel sets of texture descriptors extracted from the co-occurrence matrix; in addition, we compare and combine different strategies for extending these descriptors. The following approaches are compared: the standard approach proposed by Haralick, two methods that consider the co-occurrence matrix as a three-dimensional shape, a gray-level run-length set of features and the direct use of the co-occurrence matrix projected onto a lower dimensional subspace by principal component analysis. Texture descriptors are extracted from the co-occurrence matrix evaluated at multiple scales. Moreover, the descriptors are extracted not only from the entire co-occurrence matrix but also from subwindows. The resulting texture descriptors are used to train a support vector machine and ensembles. Results show that our novel extraction methods improve the performance of standard methods. We validate our approach across six medical datasets representing different image classification problems using the Wilcoxon signed rank test. The source code used for the approaches tested in this paper will be available at: http://www.dei.unipd.it/wdyn/?IDsezione=3314&IDgruppo_pass=124&preview=.
A space efficient flexible pivot selection approach to evaluate determinant and inverse of a matrix.
Jafree, Hafsa Athar; Imtiaz, Muhammad; Inayatullah, Syed; Khan, Fozia Hanif; Nizami, Tajuddin
2014-01-01
This paper presents new simple approaches for evaluating determinant and inverse of a matrix. The choice of pivot selection has been kept arbitrary thus they reduce the error while solving an ill conditioned system. Computation of determinant of a matrix has been made more efficient by saving unnecessary data storage and also by reducing the order of the matrix at each iteration, while dictionary notation [1] has been incorporated for computing the matrix inverse thereby saving unnecessary calculations. These algorithms are highly class room oriented, easy to use and implemented by students. By taking the advantage of flexibility in pivot selection, one may easily avoid development of the fractions by most. Unlike the matrix inversion method [2] and [3], the presented algorithms obviate the use of permutations and inverse permutations.
NASA Astrophysics Data System (ADS)
Li, Yonghui; Ullrich, Carsten
2013-03-01
The time-dependent transition density matrix (TDM) is a useful tool to visualize and interpret the induced charges and electron-hole coherences of excitonic processes in large molecules. Combined with time-dependent density functional theory on a real-space grid (as implemented in the octopus code), the TDM is a computationally viable visualization tool for optical excitation processes in molecules. It provides real-time maps of particles and holes which gives information on excitations, in particular those that have charge-transfer character, that cannot be obtained from the density alone. Some illustration of the TDM and comparison with standard density difference plots will be shown for photoexcited organic donor-acceptor molecules. This work is supported by NSF Grant DMR-1005651
Kaminski, S; Jakobi, A; Wilhelm, Chr
2014-12-01
This paper is intended to identify the uncertainties of activities in environmental samples measured with gamma-ray spectrometry that result from uncertainties in matrix composition, density and geometrical dimensions of the sample. For that purpose efficiencies were calculated for a wide range of environmental matrices such as fresh and ashed food samples, water samples and soil samples. Compositions were mainly taken from literature. Densities and geometry parameters were varied in a range occurring in practice. Considered energies cover a range from 46.5keV to 2000keV. Finally, a couple of recommendations in respect to gamma-ray spectrometric measurements of environmental samples are given.
Levorson, Erica J.; Mountziaris, Paschalia M.; Hu, Olivia; Kasper, F. Kurtis
2014-01-01
This study investigated the coculture of chondrocytes and mesenchymal stem cells (MSCs) on electrospun fibrous polymer scaffolds to produce polymer/extracellular matrix (ECM) hybrid constructs with the objective of reducing the number of chondrocytes necessary to produce ample cartilage-like ECM within the scaffolds. To generate these hybrid constructs, electrospun poly(ɛ-caprolactone) fibrous scaffolds were seeded at both high and low initial densities with five different ratios of chondrocytes to MSCs: 1:0, 1:1, 1:3, 1:5, and 0:1, and cultured for 7, 14, and 21 days. Glycosaminoglycan production and distribution within the three coculture groups was similar to quantities generated by chondrocyte-only controls. Conversely, as the concentration of chondrocytes was increased, the collagen content of the constructs also increased at each time point, with a 1:1 chondrocyte to MSC ratio approximating the collagen production of chondrocytes alone. Histological staining suggested that cocultured constructs mimicked the well-distributed ECM patterns of chondrocyte generated constructs, while improving greatly over the restricted distribution of matrix within MSC-only constructs. These results support the capacity of cocultures of chondrocytes and MSCs to generate cartilaginous matrix within a polymeric scaffold. Further, the inclusion of MSCs in these cocultures enables the reduction of chondrocytes needed to produce cell-generated ECM. PMID:24007559
NASA Technical Reports Server (NTRS)
Pototzky, Anthony S.
2008-01-01
A simple matrix polynomial approach is introduced for approximating unsteady aerodynamics in the s-plane and ultimately, after combining matrix polynomial coefficients with matrices defining the structure, a matrix polynomial of the flutter equations of motion (EOM) is formed. A technique of recasting the matrix-polynomial form of the flutter EOM into a first order form is also presented that can be used to determine the eigenvalues near the origin and everywhere on the complex plane. An aeroservoelastic (ASE) EOM have been generalized to include the gust terms on the right-hand side. The reasons for developing the new matrix polynomial approach are also presented, which are the following: first, the "workhorse" methods such as the NASTRAN flutter analysis lack the capability to consistently find roots near the origin, along the real axis or accurately find roots farther away from the imaginary axis of the complex plane; and, second, the existing s-plane methods, such as the Roger s s-plane approximation method as implemented in ISAC, do not always give suitable fits of some tabular data of the unsteady aerodynamics. A method available in MATLAB is introduced that will accurately fit generalized aerodynamic force (GAF) coefficients in a tabular data form into the coefficients of a matrix polynomial form. The root-locus results from the NASTRAN pknl flutter analysis, the ISAC-Roger's s-plane method and the present matrix polynomial method are presented and compared for accuracy and for the number and locations of roots.
NASA Astrophysics Data System (ADS)
Miura, Shinichi; Okazaki, Susumu
2001-09-01
In this paper, the path integral molecular dynamics (PIMD) method has been extended to employ an efficient approximation of the path action referred to as the pair density matrix approximation. Configurations of the isomorphic classical systems were dynamically sampled by introducing fictitious momenta as in the PIMD based on the standard primitive approximation. The indistinguishability of the particles was handled by a pseudopotential of particle permutation that is an extension of our previous one [J. Chem. Phys. 112, 10 116 (2000)]. As a test of our methodology for Boltzmann statistics, calculations have been performed for liquid helium-4 at 4 K. We found that the PIMD with the pair density matrix approximation dramatically reduced the computational cost to obtain the structural as well as dynamical (using the centroid molecular dynamics approximation) properties at the same level of accuracy as that with the primitive approximation. With respect to the identical particles, we performed the calculation of a bosonic triatomic cluster. Unlike the primitive approximation, the pseudopotential scheme based on the pair density matrix approximation described well the bosonic correlation among the interacting atoms. Convergence with a small number of discretization of the path achieved by this approximation enables us to construct a method of avoiding the problem of the vanishing pseudopotential encountered in the calculations by the primitive approximation.
Abbey, Colette A; Bayless, Kayla J
2014-09-01
This study was designed to determine the optimal conditions required for known pro-angiogenic stimuli to elicit successful endothelial sprouting responses. We used an established, quantifiable model of endothelial cell (EC) sprout initiation where ECs were tested for invasion in low (1 mg/mL) and high density (5 mg/mL) 3D collagen matrices. Sphingosine 1-phosphate (S1P) alone, or S1P combined with stromal derived factor-1α (SDF) and phorbol ester (TPA), elicited robust sprouting responses. The ability of these factors to stimulate sprouting was more effective in higher density collagen matrices. S1P stimulation resulted in a significant increase in invasion distance, and with the exception of treatment groups containing phorbol ester, invasion distance was longer in 1mg/mL compared to 5mg/mL collagen matrices. Closer examination of cell morphology revealed that increasing matrix density and supplementing with SDF and TPA enhanced the formation of multicellular structures more closely resembling capillaries. TPA enhanced the frequency and size of lumen formation and correlated with a robust increase in phosphorylation of p42/p44 Erk kinase, while S1P and SDF did not. Also, a higher number of significantly longer extended processes formed in 5mg/mL compared to 1mg/mL collagen matrices. Because collagen matrices at higher density have been reported to be stiffer, we tested for changes in the mechanosensitive protein, zyxin. Interestingly, zyxin phosphorylation levels inversely correlated with matrix density, while levels of total zyxin did not change significantly. Immunofluorescence and localization studies revealed that total zyxin was distributed evenly throughout invading structures, while phosphorylated zyxin was slightly more intense in extended peripheral processes. Silencing zyxin expression increased extended process length and number of processes, while increasing zyxin levels decreased extended process length. Altogether these data indicate that ECs
A new approach to calculate the transport matrix in RF cavities
Eidelman, Yu.; Mokhov, N.; Nagaitsev, S.; Solyak, N.; /Fermilab
2011-03-01
A realistic approach to calculate the transport matrix in RF cavities is developed. It is based on joint solution of equations of longitudinal and transverse motion of a charged particle in an electromagnetic field of the linac. This field is a given by distribution (measured or calculated) of the component of the longitudinal electric field on the axis of the linac. New approach is compared with other matrix methods to solve the same problem. The comparison with code ASTRA has been carried out. Complete agreement for tracking results for a TESLA-type cavity is achieved. A corresponding algorithm will be implemented into the MARS15 code. A realistic approach to calculate the transport matrix in RF cavities is developed. Complete agreement for tracking results with existed code ASTRA is achieved. New algorithm will be implemented into MARS15 code.
Soltan, Ahmed; McGovern, Brian; Drakakis, Emmanuel; Neil, Mark; Maaskant, Pleun; Akhter, Mahbub; Lee, Jun Su; Degenaar, Patrick
2017-04-01
Optical neuron stimulation arrays are important for both in-vitro biology and retinal prosthetic biomedical applications. Hence, in this work, we present an 8100 pixel high radiance photonic stimulator. The chip module vertically combines custom made gallium nitride μ LEDs with a CMOS application specific integrated circuit. This is designed with active pixels to ensure random access and to allow continuous illumination of all required pixels. The μLEDs have been assembled on the chip using a solder ball flip-chip bonding technique which has allowed for reliable and repeatable manufacture. We have evaluated the performance of the matrix by measuring the different factors including the static, dynamic power consumption, the illumination, and the current consumption by each LED. We show that the power consumption is within a range suitable for portable use. Finally, the thermal behavior of the matrix is monitored and the matrix proved to be thermally stable.
NASA Astrophysics Data System (ADS)
Oberhofer, Harald; Blumberger, Jochen
2010-12-01
We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q-) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, ( {< {| {H_ab } |^2 } > } )^{1/2} = 6.7 {mH}, is significantly higher than the value obtained for the minimum energy structure, | {H_ab } | = 3.8 {mH}. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q- in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.
NASA Astrophysics Data System (ADS)
Bencheikh, K.; van Zyl, B. P.; Berkane, K.
2016-08-01
The semiclassical ℏ expansion of the one-particle density matrix for a two-dimensional Fermi gas is calculated within the Wigner transform method of B. Grammaticos and A. Voros [Ann. Phys. (N.Y.) 123, 359 (1979), 10.1016/0003-4916(79)90343-9], originally developed in the context of nuclear physics. The method of Grammaticos and Voros has the virtue of preserving both the Hermiticity and idempotency of the density matrix to all orders in the ℏ expansion. As a topical application, we use our semiclassical expansion to go beyond the local-density approximation for the construction of the total dipole-dipole interaction energy functional of a two-dimensional, spin-polarized dipolar Fermi gas. We find a finite, second-order gradient correction to the Hartree-Fock energy, which takes the form ɛ (∇ρ ) 2/√{ρ } , with ɛ being small (|ɛ |≪1 ) and negative. We test the quality of the corrected energy by comparing it with the exact results available for harmonic confinement. Even for small particle numbers, the gradient correction to the dipole-dipole energy provides a significant improvement over the local-density approximation.
Quantum dynamics of finite atomic and molecular systems through density matrix methods
NASA Astrophysics Data System (ADS)
Thorndyke, Brian
We develop a mixed quantum-classical formulation to describe the dynamics of few- and many-body atomic systems by applying a partial Wigner transform over the quantum Liouville equation of motion. In this approach, the density operator becomes a function in quasiclassical phase space, while remaining an operator over a subset of quantal variables. By taking appropriate limits and introducing an effective potential, we derive equations of motion describing quasiclassical nuclear trajectories coupled to quantal electronic evolution. We also introduce a variable timestep procedure to account for the disparity between slow nuclear motion and fast electronic fluctuations. Our mixed quantum-classical method is applied to the study of three simple one-dimensional two-state models. The first model represents the photoinduced desorption of an alkali atom from a metal surface, where near-resonant electron transfer is important. A second model explores a binary collision under conditions where two avoided crossings are present. The third model follows the photoinduced dissociation of the sodium iodide complex, whose long-range attractive surface results in oscillations of internuclear distance. Quantities such as state populations and quantum coherence are computed, and found to be in excellent agreement with precise quantal results obtained through fast Fourier transform grid methods. Having validated our approach, we turn to the study of alkali atoms embedded in rare gas clusters, treating the alkali atom-rare gas interactions with l-dependent semi-local pseudopotentials. Light emission from the electronic motion of the alkali atom is derived in the semiclassical limit, and computational methods to render the simulation feasible for a many-atom cluster are discussed. The formalism is applied to lithium atoms in helium clusters, where the cluster configuration and the electronic population dynamics of the lithium atom are monitored over time. We study both the ground and
Filtered density function approach for reactive transport in groundwater
NASA Astrophysics Data System (ADS)
Suciu, Nicolae; Schüler, Lennart; Attinger, Sabine; Knabner, Peter
2016-04-01
Spatial filtering may be used in coarse-grained simulations (CGS) of reactive transport in groundwater, similar to the large eddy simulations (LES) in turbulence. The filtered density function (FDF), stochastically equivalent to a probability density function (PDF), provides a statistical description of the sub-grid, unresolved, variability of the concentration field. Besides closing the chemical source terms in the transport equation for the mean concentration, like in LES-FDF methods, the CGS-FDF approach aims at quantifying the uncertainty over the whole hierarchy of heterogeneity scales exhibited by natural porous media. Practically, that means estimating concentration PDFs on coarse grids, at affordable computational costs. To cope with the high dimensionality of the problem in case of multi-component reactive transport and to reduce the numerical diffusion, FDF equations are solved by particle methods. But, while trajectories of computational particles are modeled as stochastic processes indexed by time, the concentration's heterogeneity is modeled as a random field, with multi-dimensional, spatio-temporal sets of indices. To overcome this conceptual inconsistency, we consider FDFs/PDFs of random species concentrations weighted by conserved scalars and we show that their evolution equations can be formulated as Fokker-Planck equations describing stochastically equivalent processes in concentration-position spaces. Numerical solutions can then be approximated by the density in the concentration-position space of an ensemble of computational particles governed by the associated Itô equations. Instead of sequential particle methods we use a global random walk (GRW) algorithm, which is stable, free of numerical diffusion, and practically insensitive to the increase of the number of particles. We illustrate the general FDF approach and the GRW numerical solution for a reduced complexity problem consisting of the transport of a single scalar in groundwater
Wu, Yu-Shu; Pan, Lehua; Pruess, Karsten
2004-03-15
Modeling fracture-matrix interaction within a complex multiple phase flow system is a key issue for fractured reservoir simulation. Commonly used mathematical models for dealing with such interactions employ a dual- or multiple-continuum concept, in which fractures and matrix are represented as overlapping, different, but interconnected continua, described by parallel sets of conservation equations. The conventional single-point upstream weighting scheme, in which the fracture relative permeability is used to represent the counterpart at the fracture-matrix interface, is the most common scheme by which to estimate flow mobility for fracture-matrix flow terms. However, such a scheme has a serious flaw, which may lead to unphysical solutions or significant numerical errors. To overcome the limitation of the conventional upstream weighting scheme, this paper presents a physically based modeling approach for estimating physically correct relative permeability in calculating multiphase flow between fractures and the matrix, using continuity of capillary pressure at the fracture-matrix interface. The proposed approach has been implemented into two multiphase reservoir simulators and verified using analytical solutions and laboratory experimental data. The new method is demonstrated to be accurate, numerically efficient, and easy to implement in dual- or multiple-continuum models.
NASA Astrophysics Data System (ADS)
Hine, N. D. M.; Haynes, P. D.; Mostofi, A. A.; Payne, M. C.
2010-09-01
We present calculations of formation energies of defects in an ionic solid (Al2O3) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.
Hine, N D M; Haynes, P D; Mostofi, A A; Payne, M C
2010-09-21
We present calculations of formation energies of defects in an ionic solid (Al(2)O(3)) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes.
Very high cell density perfusion of CHO cells anchored in a non-woven matrix-based bioreactor.
Zhang, Ye; Stobbe, Per; Silvander, Christian Orrego; Chotteau, Véronique
2015-11-10
Recombinant Chinese Hamster Ovary (CHO) cells producing IgG monoclonal antibody were cultivated in a novel perfusion culture system CellTank, integrating the bioreactor and the cell retention function. In this system, the cells were harbored in a non-woven polyester matrix perfused by the culture medium and immersed in a reservoir. Although adapted to suspension, the CHO cells stayed entrapped in the matrix. The cell-free medium was efficiently circulated from the reservoir into- and through the matrix by a centrifugal pump placed at the bottom of the bioreactor resulting in highly homogenous concentrations of the nutrients and metabolites in the whole system as confirmed by measurements from different sampling locations. A real-time biomass sensor using the dielectric properties of living cells was used to measure the cell density. The performances of the CellTank were studied in three perfusion runs. A very high cell density measured as 200 pF/cm (where 1 pF/cm is equivalent to 1 × 10(6)viable cells/mL) was achieved at a perfusion rate of 10 reactor volumes per day (RV/day) in the first run. In the second run, the effect of cell growth arrest by hypothermia at temperatures lowered gradually from 37 °C to 29 °C was studied during 13 days at cell densities above 100 pF/cm. Finally a production run was performed at high cell densities, where a temperature shift to 31 °C was applied at cell density 100 pF/cm during a production period of 14 days in minimized feeding conditions. The IgG concentrations were comparable in the matrix and in the harvest line in all the runs, indicating no retention of the product of interest. The cell specific productivity was comparable or higher than in Erlenmeyer flask batch culture. During the production run, the final harvested IgG production was 35 times higher in the CellTank compared to a repeated batch culture in the same vessel volume during the same time period.
A Density-Ratio Approach to Machine Learning
2011-04-20
for computing matrix inverses: for an invertible square matrix A and vectors u and v such that v⊤A−1u 6= −1, (A+ uv ⊤)−1 = A−1 − A −1uv⊤A−1 1+ v⊤A−1u...Thus the simulation results below should be slightly in favor of OSVM. Local outlier factor (LOF): LOF is the score to detect a local outlier which...extensive simulations in covariate shift adaptation and outlier detection, and experimentally confirmed that the proposed uLSIF is computationally
A New Approach of Designing Superalloys for Low Density
NASA Technical Reports Server (NTRS)
MacKay, Rebecca A.; Gabb, Timothy P.; Smialek, James L.; Nathal, Michael V.
2010-01-01
New low-density single-crystal (LDS) alloy, have bee. developed for turbine blade applications, which have the potential for significant improvements in the thrust-to-weight ratio over current production superalloys. An innovative alloying strategy was wed to achieve alloy density reductions, high-temperature creep resistance, microstructural stability, and cyclic oxidation resistance. The alloy design relies on molybdenum as a potent. lower-density solid-solution strengthener in the nickel-based superalloy. Low alloy density was also achieved with modest rhenium levels tmd the absence of tungsten. Microstructural, physical mechanical, and environmental testing demonstrated the feasibility of this new LDS superalloy design.
Lishev, St.; Yordanov, D. Shivarova, A.
2015-04-08
Concepts for the extraction of volume-produced negative hydrogen ions from a rf matrix source (a matrix of small-radius discharges with a planar-coil inductive driving) are presented and discussed based on experimental results for the current densities of the extracted ions and the co-extracted electrons. The experiment has been carried out in a single discharge of the source: a rf discharge with a radius of 2.25 cm inductively driven by a 3.5-turn planar coil. The length of the discharge tube, the area of the reference electrode inserted in the discharge volume, the discharge modes, the magnetic filter and its position along the discharge length, the position of the permanent magnets for the separation of the co-extracted electrons from the extracted ions in the extraction device and the bias applied to its first electrode are considered as factors influencing the extracted currents of negative ions.
A Synthetic Approach to the Transfer Matrix Method in Classical and Quantum Physics
ERIC Educational Resources Information Center
Pujol, O.; Perez, J. P.
2007-01-01
The aim of this paper is to propose a synthetic approach to the transfer matrix method in classical and quantum physics. This method is an efficient tool to deal with complicated physical systems of practical importance in geometrical light or charged particle optics, classical electronics, mechanics, electromagnetics and quantum physics. Teaching…
Predicting Fish Densities in Lotic Systems: a Simple Modeling Approach
Fish density models are essential tools for fish ecologists and fisheries managers. However, applying these models can be difficult because of high levels of model complexity and the large number of parameters that must be estimated. We designed a simple fish density model and te...
Xie, Hang; Jiang, Feng; Tian, Heng; Zheng, Xiao; Kwok, Yanho; Chen, Shuguang; Yam, ChiYung; Yan, YiJing; Chen, Guanhua
2012-07-28
Basing on our hierarchical equations of motion for time-dependent quantum transport [X. Zheng, G. H. Chen, Y. Mo, S. K. Koo, H. Tian, C. Y. Yam, and Y. J. Yan, J. Chem. Phys. 133, 114101 (2010)], we develop an efficient and accurate numerical algorithm to solve the Liouville-von-Neumann equation. We solve the real-time evolution of the reduced single-electron density matrix at the tight-binding level. Calculations are carried out to simulate the transient current through a linear chain of atoms, with each represented by a single orbital. The self-energy matrix is expanded in terms of multiple Lorentzian functions, and the Fermi distribution function is evaluated via the Padè spectrum decomposition. This Lorentzian-Padè decomposition scheme is employed to simulate the transient current. With sufficient Lorentzian functions used to fit the self-energy matrices, we show that the lead spectral function and the dynamics response can be treated accurately. Compared to the conventional master equation approaches, our method is much more efficient as the computational time scales cubically with the system size and linearly with the simulation time. As a result, the simulations of the transient currents through systems containing up to one hundred of atoms have been carried out. As density functional theory is also an effective one-particle theory, the Lorentzian-Padè decomposition scheme developed here can be generalized for first-principles simulation of realistic systems.
An entropy-driven matrix completion (E-MC) approach to complex network mapping
NASA Astrophysics Data System (ADS)
Koochakzadeh, Ali; Pal, Piya
2016-05-01
Mapping the topology of a complex network in a resource-efficient manner is a challenging problem with applications in internet mapping, social network inference, and so forth. We propose a new entropy driven algorithm leveraging ideas from matrix completion, to map the network using monitors (or sensors) which, when placed on judiciously selected nodes, are capable of discovering their immediate neighbors. The main challenge is to maximize the portion of discovered network using only a limited number of available monitors. To this end, (i) a new measure of entropy or uncertainty is associated with each node, in terms of the currently discovered edges incident on that node, and (ii) a greedy algorithm is developed to select a candidate node for monitor placement based on its entropy. Utilizing the fact that many complex networks of interest (such as social networks), have a low-rank adjacency matrix, a matrix completion algorithm, namely 1-bit matrix completion, is combined with the greedy algorithm to further boost its performance. The low rank property of the network adjacency matrix can be used to extrapolate a portion of missing edges, and consequently update the node entropies, so as to efficiently guide the network discovery algorithm towards placing monitors on the nodes that can turn out to be more informative. Simulations performed on a variety of real world networks such as social networks and peer networks demonstrate the superior performance of the matrix-completion guided approach in discovering the network topology.
Nonextensive random matrix theory approach to mixed regular-chaotic dynamics.
Abul-Magd, A Y
2005-06-01
We apply Tsallis' q -indexed entropy to formulate a nonextensive random matrix theory, which may be suitable for systems with mixed regular-chaotic dynamics. The joint distribution of the matrix elements is given by folding the corresponding quantity in the conventional random matrix theory by a distribution of the inverse matrix-element variance. It keeps the basis invariance of the standard theory but violates the independence of the matrix elements. We consider the subextensive regime of q more than unity in which the transition from the Wigner to the Poisson statistics is expected to start. We calculate the level density for different values of the entropic index. Our results are consistent with an analogous calculation by Tsallis and collaborators. We calculate the spacing distribution for mixed systems with and without time-reversal symmetry. Comparing the result of calculation to a numerical experiment shows that the proposed nonextensive model provides a satisfactory description for the initial stage of the transition from chaos towards the Poisson statistics.
Wu, Yu-Shu; Pruess, Karsten
2004-05-04
Modeling fracture-matrix interaction within a multiple-phase flow system is a key issue for fractured reservoir simulation. Commonly used mathematical models for dealing with such interactions employ dual- or multiple-continuum concepts, in which fractures and matrix are represented as overlapping, different, but interconnected continua, described by parallel sets of conservation equations. The conventional single-point upstream weighting scheme is most commonly used to estimate flow mobility for fracture-matrix flow. However, such a scheme may have serious limitations or flaws, which lead to unphysical solutions or significant numerical errors. To overcome the limitations of the conventional upstream weighting scheme, this paper presents a physically based modeling approach for estimating physically correct relative permeability in calculating multiphase flow between fractures and the matrix, using continuity of capillary pressure at the fracture-matrix interface. The proposed approach has been implemented into two multiphase reservoir simulators and verified using analytical solutions and laboratory experimental data. The new method is demonstrated to be accurate, numerically efficient, and easy to implement in dual- or multiple-continuum reservoir simulators.
Parkhomenko, A I; Shalagin, Anatolii M
2011-11-30
Using the eikonal approximation, we have calculated effective collision frequencies in density-matrix kinetic equations describing nonlinear effects in the wings of spectral lines. We have established the relation between the probabilities of absorption and stimulated emission and the characteristics of the radiation and elementary scattering event. The example of the power interaction potential shows that quantum mechanical calculation of the collision frequencies in the eikonal approximation and previously known spectral line wing theory give similar results for the probability of radiation absorption.
Thorvaldsen, Andreas J; Ruud, Kenneth; Kristensen, Kasper; Jørgensen, Poul; Coriani, Sonia
2008-12-07
A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability.
NASA Astrophysics Data System (ADS)
Thorvaldsen, Andreas J.; Ruud, Kenneth; Kristensen, Kasper; Jørgensen, Poul; Coriani, Sonia
2008-12-01
A general method is presented for the calculation of molecular properties to arbitrary order at the Kohn-Sham density functional level of theory. The quasienergy and Lagrangian formalisms are combined to derive response functions and their residues by straightforward differentiation of the quasienergy derivative Lagrangian using the elements of the density matrix in the atomic orbital representation as variational parameters. Response functions and response equations are expressed in the atomic orbital basis, allowing recent advances in the field of linear-scaling methodology to be used. Time-dependent and static perturbations are treated on an equal footing, and atomic basis sets that depend on the applied frequency-dependent perturbations may be used, e.g., frequency-dependent London atomic orbitals. The 2n+1 rule may be applied if computationally favorable, but alternative formulations using higher-order perturbed density matrices are also derived. These may be advantageous in order to minimize the number of response equations that needs to be solved, for instance, when one of the perturbations has many components, as is the case for the first-order geometrical derivative of the hyperpolarizability.
Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
NASA Astrophysics Data System (ADS)
Bañuls, Mari Carmen; Cichy, Krzysztof; Cirac, J. Ignacio; Jansen, Karl; Kühn, Stefan
2017-02-01
We numerically study the zero temperature phase structure of the multiflavor Schwinger model at nonzero chemical potential. Using matrix product states, we reproduce analytical results for the phase structure for two flavors in the massless case and extend the computation to the massive case, where no analytical predictions are available. Our calculations allow us to locate phase transitions in the mass-chemical potential plane with great precision and provide a concrete example of tensor networks overcoming the sign problem in a lattice gauge theory calculation.
Influence of Hemp Fibers Pre-processing on Low Density Polyethylene Matrix Composites Properties
NASA Astrophysics Data System (ADS)
Kukle, S.; Vidzickis, R.; Zelca, Z.; Belakova, D.; Kajaks, J.
2016-04-01
In present research with short hemp fibres reinforced LLDPE matrix composites with fibres content in a range from 30 to 50 wt% subjected to four different pre-processing technologies were produced and such their properties as tensile strength and elongation at break, tensile modulus, melt flow index, micro hardness and water absorption dynamics were investigated. Capillary viscosimetry was used for fluidity evaluation and melt flow index (MFI) evaluated for all variants. MFI of fibres of two pre-processing variants were high enough to increase hemp fibres content from 30 to 50 wt% with moderate increase of water sorption capability.
NASA Astrophysics Data System (ADS)
Weisse, A.; Bursill, R. J.; Hamer, C. J.; Weihong, Zheng
2006-04-01
The phase diagram of the two-leg t-Jz ladder is explored, using the density-matrix renormalization group method. Results are obtained for energy gaps, electron density profiles, and correlation functions for the half filled and quarter filled cases. The effective Lagrangian velocity parameter vρ is shown to vanish at half filling. The behavior of the one-hole gap in the Nagaoka limit is investigated, and found to disagree with theoretical predictions. A tentative phase diagram is presented, which is quite similar to the full t-J ladder, but scaled up by a factor of about 2 in coupling. Near half filling a Luther-Emery phase is found, which may be expected to show superconducting correlations, while near quarter filling the system appears to be in a Tomonaga-Luttinger phase.
Perturbation approach to multifractal dimensions for certain critical random-matrix ensembles.
Bogomolny, E; Giraud, O
2011-09-01
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes, we obtain expressions similar to those of the critical banded random matrix ensemble extensively discussed in the literature. For certain ensembles, the leading-order term for weak multifractality can be calculated within standard perturbation theory. For other models, such a direct approach requires modifications, which are briefly discussed. Our analytical formulas are in good agreement with numerical calculations.
A Delphi-matrix approach to SEA and its application within the tourism sector in Taiwan
Kuo, N.-W. . E-mail: ibis@ntcn.edu.tw; Hsiao, T.-Y.; Yu, Y.-H.
2005-04-15
Strategic Environmental Assessment (SEA) is a procedural tool and within the framework of SEA, several different types of analytical methods can be used in the assessment. However, the impact matrix used currently in Taiwan has some disadvantages. Hence, a Delphi-matrix approach to SEA is proposed here to improve the performance of Taiwan's SEA. This new approach is based on the impact matrix combination with indicators of sustainability, and then the Delphi method is employed to collect experts' opinions. In addition, the assessment of National Floriculture Park Plan and Taiwan Flora 2008 Program is taken as an example to examine this new method. Although international exhibition is one of the important tourism (economic) activities, SEA is seldom about tourism sector. Finally, the Delphi-matrix approach to SEA for tourism development plan is established containing eight assessment topics and 26 corresponding categories. In summary, three major types of impacts: resources' usages, pollution emissions, and local cultures change are found. Resources' usages, such as water, electricity, and natural gas demand, are calculated on a per capita basis. Various forms of pollution resulting from this plan, such as air, water, soil, waste, and noise, are also identified.
Ranucci, C S; Moghe, P V
2001-02-01
The regulation of cell motility by ligand density on substrates with variable microtopography is not well understood. In this report, we studied the adhesion and motility behavior of HepG2 cells on microtextured poly(glycolic-co-lactic)acid (PGLA) copolymer substrates, whose surface bioactivity was differentially modified through the adsorption of 0-5.5 ng/cm(2) collagen. Microtextured PGLA substrates were fabricated as thin films with a uniform surface distribution of micropores of median size of 3.1 +/- 1.5 microm and three-dimensional root mean squared roughness of 0.253 microm. Even in the absence of collagen, cells on microtextured substrates responded to substrate topography by exhibiting a 200% increase in adhesion strength compared with untextured controls and ventral localization of the intracellular adhesion protein vinculin. Further enhancement in adhesion strength (420% over untextured, untreated substrates) was demonstrated with bioactivated, microtextured surfaces, indicating that cell adhesion responses to topography and surface ligand density were cooperative. Our motility studies of cells on untextured substrates adsorbed with different levels of collagen demonstrated that a classical biphasic relationship between the cell population averaged migration rate, mu, and the collagen ligand density was preserved. However, comparison of cell motility responses between untextured and microtextured substrates indicates that the motility versus ligand density curve shifted, such that equivalent levels of cell motility were achieved at lower ligand density on microtextured surfaces. Furthermore, the maximum mu values achieved on the microtextured substrates exceeded those on untextured substrates by twofold. Taken together, we show that the magnitude of subcellular scale microtexture of a polymer substrate can sensitize the cell motility responsiveness to substrate ligand concentration; we suggest that the underlying mechanisms involve alteration in the
Analytical O (αs) corrections to the beam frame double-spin density matrix elements of e+e-→t t ¯
NASA Astrophysics Data System (ADS)
Kaldamäe, L.; Groote, S.; Körner, J. G.
2016-12-01
We provide analytical results for the O (αs) corrections to the double-spin density matrix elements in the reaction e+e-→t t ¯ . These concern the elements l l , l t , l n , t t , t n , and n n of the double-spin density matrix elements where l , t , n stand for longitudinal, transverse and normal orientations with respect to the beam frame spanned by the electron and the top quark momentum.
On the scaling of avaloids and turbulence with the average density approaching the density limit
NASA Astrophysics Data System (ADS)
Antar, G. Y.; Counsell, G.; Ahn, J.-W.
2005-08-01
This article is dedicated to the characterization of turbulent transport in the scrape-off layer of the Mega Ampère Spherical Tokamak [A. Sykes et al., Phys. Plasmas 8, 2101 (2001)] as a function of the average density (nL). The aim is to answer a renewed interest in this subject since the bursty character of turbulence in the scrape-off layer was shown to be caused by large-scale events with high radial velocity reaching about 1/10th of the sound speed called avaloids [G. Antar et al., Phys. Rev. Lett 87, 065001 (2001)]. With increasing density, turbulence and transport increase nonlinearly at the midplane while remaining almost unchanged in the target region. Using various and complementary statistical analyses, the existence of a "critical" density, at nL/nG≃0.35 is emphasized; nG is the Greenwald density. Both above and below this density, intermittency decreases and avaloids play a decreasing role in the particle radial transport. This is interpreted as caused by the interplay between avaloids and the surrounding turbulent structures which mix them more efficiently with increasing density as the level of the background turbulence increases. The scaling of the different quantities with respect to the normalized density is obtained. It reveals that not only the level of turbulence and transport increase, but also the radial velocity and length scales. This increases the coupling between the hot plasma edge and the cold scrape-off layer that may explain the disruptive instability occurring at high densities.
On the scaling of avaloids and turbulence with the average density approaching the density limit
Antar, G.Y.; Counsell, G.; Ahn, J.-W.
2005-08-15
This article is dedicated to the characterization of turbulent transport in the scrape-off layer of the Mega Ampere Spherical Tokamak [A. Sykes et al., Phys. Plasmas 8, 2101 (2001)] as a function of the average density (n{sub L}). The aim is to answer a renewed interest in this subject since the bursty character of turbulence in the scrape-off layer was shown to be caused by large-scale events with high radial velocity reaching about 1/10th of the sound speed called avaloids [G. Antar et al., Phys. Rev. Lett 87, 065001 (2001)]. With increasing density, turbulence and transport increase nonlinearly at the midplane while remaining almost unchanged in the target region. Using various and complementary statistical analyses, the existence of a 'critical' density, at n{sub L}/n{sub G}{approx_equal}0.35 is emphasized; n{sub G} is the Greenwald density. Both above and below this density, intermittency decreases and avaloids play a decreasing role in the particle radial transport. This is interpreted as caused by the interplay between avaloids and the surrounding turbulent structures which mix them more efficiently with increasing density as the level of the background turbulence increases. The scaling of the different quantities with respect to the normalized density is obtained. It reveals that not only the level of turbulence and transport increase, but also the radial velocity and length scales. This increases the coupling between the hot plasma edge and the cold scrape-off layer that may explain the disruptive instability occurring at high densities.
Giesbertz, K. J. H.; Gritsenko, O. V.; Baerends, E. J.
2014-05-14
Recently, we have demonstrated that the problems finding a suitable adiabatic approximation in time-dependent one-body reduced density matrix functional theory can be remedied by introducing an additional degree of freedom to describe the system: the phase of the natural orbitals [K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, Phys. Rev. Lett. 105, 013002 (2010); K. J. H. Giesbertz, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 133, 174119 (2010)]. In this article we will show in detail how the frequency-dependent response equations give the proper static limit (ω → 0), including the perturbation in the chemical potential, which is required in static response theory to ensure the correct number of particles. Additionally we show results for the polarizability for H{sub 2} and compare the performance of two different two-electron functionals: the phase-including Löwdin–Shull functional and the density matrix form of the Löwdin–Shull functional.
Spin alignment and density matrix measurement in sup 28 Si + sup 12 C orbiting reaction
Ray, A.; Shapira, D.; Halbert, M.L.; Gomez del Campo, J.; Kim, H.J. ); Sullivan, J.P. . Cyclotron Inst.); Shivakumar, B.; Mitchell, J. . Wright Nuclear Structure Lab.)
1990-01-01
Gamma-ray angular correlations have been measured for the strongly damped reactions {sup 12}C({sup 28}Si,{sup 12}C){sup 28}Si between {theta}{sub cm} = (120{degree} {minus} 160{degree}) for E{sub cm} = 43.5 and 48 MeV. We find that the density matrices for the {sup 12}C(2{sub 1}{sup +}) and {sup 28}Si states are almost diagonal with respect to the direction of motion of the outgoing particle. The measured density matrices and spin alignments are consistent with the picture of formation of a long-lived dinuclear complex undergoing orbiting, bending and wriggling motions, but not with those obtained from statistical compound nucleus or sticking model calculations. 17 refs., 2 figs., 1 tab.
Density matrix spectra and order parameters in the 1D extended Hubbard model
NASA Astrophysics Data System (ADS)
Yu, Wing Chi; Gu, Shi-Jian; Lin, Hai-Qing
2016-09-01
Without any knowledge of the symmetry existing in a system, we derive the exact forms of the order parameters which show long-range correlations in the ground state of the one-dimensional (1D) extended Hubbard model using a quantum information approach. Our work demonstrates that the quantum information approach can help us to find the explicit form of the order parameter, which could not be derived systematically via traditional methods in the condensed matter theory.
An information theory approach to the density of the earth
NASA Technical Reports Server (NTRS)
Graber, M. A.
1977-01-01
Information theory can develop a technique which takes experimentally determined numbers and produces a uniquely specified best density model satisfying those numbers. A model was generated using five numerical parameters: the mass of the earth, its moment of inertia, three zero-node torsional normal modes (L = 2, 8, 26). In order to determine the stability of the solution, six additional densities were generated, in each of which the period of one of the three normal modes was increased or decreased by one standard deviation. The superposition of the seven models is shown. It indicates that current knowledge of the torsional modes is sufficient to specify the density in the upper mantle but that the lower mantle and core will require smaller standard deviations before they can be accurately specified.
An Extreme Learning Machine Approach to Density Estimation Problems.
Cervellera, Cristiano; Maccio, Danilo
2017-01-17
In this paper, we discuss how the extreme learning machine (ELM) framework can be effectively employed in the unsupervised context of multivariate density estimation. In particular, two algorithms are introduced, one for the estimation of the cumulative distribution function underlying the observed data, and one for the estimation of the probability density function. The algorithms rely on the concept of $F$-discrepancy, which is closely related to the Kolmogorov-Smirnov criterion for goodness of fit. Both methods retain the key feature of the ELM of providing the solution through random assignment of the hidden feature map and a very light computational burden. A theoretical analysis is provided, discussing convergence under proper hypotheses on the chosen activation functions. Simulation tests show how ELMs can be successfully employed in the density estimation framework, as a possible alternative to other standard methods.
Shrinkage covariance matrix approach based on robust trimmed mean in gene sets detection
NASA Astrophysics Data System (ADS)
Karjanto, Suryaefiza; Ramli, Norazan Mohamed; Ghani, Nor Azura Md; Aripin, Rasimah; Yusop, Noorezatty Mohd
2015-02-01
Microarray involves of placing an orderly arrangement of thousands of gene sequences in a grid on a suitable surface. The technology has made a novelty discovery since its development and obtained an increasing attention among researchers. The widespread of microarray technology is largely due to its ability to perform simultaneous analysis of thousands of genes in a massively parallel manner in one experiment. Hence, it provides valuable knowledge on gene interaction and function. The microarray data set typically consists of tens of thousands of genes (variables) from just dozens of samples due to various constraints. Therefore, the sample covariance matrix in Hotelling's T2 statistic is not positive definite and become singular, thus it cannot be inverted. In this research, the Hotelling's T2 statistic is combined with a shrinkage approach as an alternative estimation to estimate the covariance matrix to detect significant gene sets. The use of shrinkage covariance matrix overcomes the singularity problem by converting an unbiased to an improved biased estimator of covariance matrix. Robust trimmed mean is integrated into the shrinkage matrix to reduce the influence of outliers and consequently increases its efficiency. The performance of the proposed method is measured using several simulation designs. The results are expected to outperform existing techniques in many tested conditions.
Yunoki, Shunji; Sugiura, Hiroaki; Ikoma, Toshiyuki; Kondo, Eiji; Yasuda, Kazunori; Tanaka, Junzo
2011-02-01
The aim of this study was to evaluate the effects of increased collagen-matrix density on the mechanical properties and in vivo absorbability of porous hydroxyapatite (HAp)-collagen composites as artificial bone materials. Seven types of porous HAp-collagen composites were prepared from HAp nanocrystals and dense collagen fibrils. Their densities and HAp/collagen weight ratios ranged from 122 to 331 mg cm⁻³ and from 20/80 to 80/20, respectively. The flexural modulus and strength increased with an increase in density, reaching 2.46 ± 0.48 and 0.651 ± 0.103 MPa, respectively. The porous composites with a higher collagen-matrix density exhibited much higher mechanical properties at the same densities, suggesting that increasing the collagen-matrix density is an effective way of improving the mechanical properties. It was also suggested that other structural factors in addition to collagen-matrix density are required to achieve bone-like mechanical properties. The in vivo absorbability of the composites was investigated in bone defects of rabbit femurs, demonstrating that the absorption rate decreased with increases in the composite density. An exhaustive increase in density is probably limited by decreases in absorbability as artificial bones.
Simon, Aude; Iftner, Christophe; Mascetti, Joëlle; Spiegelman, Fernand
2015-03-19
The present theoretical study aims at investigating the effects of an argon matrix on the structures, energetics, dynamics, and infrared (IR) spectra of small water clusters (H2O)n (n = 1-6). The potential energy surface is obtained from a hybrid self-consistent charge density functional-based tight binding/force-field approach (SCC-DFTB/FF) in which the water clusters are treated at the SCC-DFTB level and the matrix is modeled at the FF level by a cluster consisting of ∼340 Ar atoms with a face centered cubic (fcc) structure, namely (H2O)n/Ar. With respect to a pure FF scheme, this allows a quantum description of the molecular system embedded in the matrix, along with all-atom geometry optimization and molecular dynamics (MD) simulations of the (H2O)n/Ar system. Finite-temperature IR spectra are derived from the MD simulations. The SCC-DFTB/FF scheme is first benchmarked on (H2O)Arn clusters against correlated wave function results and DFT calculations performed in the present work, and against FF data available in the literature. Regarding (H2O)n/Ar systems, the geometries of the water clusters are found to adapt to the fcc environment, possibly leading to intermolecular distortion and matrix perturbation. Several energetical quantities are estimated to characterize the water clusters in the matrix. In the particular case of the water hexamer, substitution and insertion energies for the prism, bag, and cage are found to be lower than that for the 6-member ring isomer. Finite-temperature MD simulations show that the water monomer has a quasifree rotation motion at 13 K, in agreement with experimental data. In the case of the water dimer, the only large-amplitude motion is a distortion-rotation intermolecular motion, whereas only vibration motions around the nuclei equilibrium positions are observed for clusters with larger sizes. Regarding the IR spectra, we find that the matrix environment leads to redshifts of the stretching modes and almost no shift of the
The nutrient density approach to healthy eating: challenges and opportunities
Technology Transfer Automated Retrieval System (TEKTRAN)
The term 'nutrient density' for foods/beverages has been used loosely to promote the Dietary Guidelines for Americans. The 2010 Dietary Guidelines for Americans defined 'all vegetables, fruits, whole grains, fat-free or low-fat milk and milk products, seafood, lean meats and poultry, eggs, beans and...
On the GPI approach with unknown inertia matrix in robot manipulators
NASA Astrophysics Data System (ADS)
Arteaga-Pérez, Marco A.; Gutiérrez-Giles, Alejandro
2014-04-01
This article discusses the design of generalised proportional integral observers for the tracking control of robot manipulators. The unknown, possibly state-dependent, additive nonlinearity influencing the input-output description, in terms of the tracking error dynamics is modelled for observer construction purposes, as an absolutely bounded, additive, unknown time-varying perturbation input signal. A disadvantage of the approach lies in the fact that the system inertia matrix is usually required for implementation. In this work, it is shown how the approach can be modified to avoid the use of the inertia matrix when it is unknown. A set of experiments with three different test beds is carried out to show the good performance of the proposed algorithm.
Positron accumulation effect in particles embedded in a low-density matrix
Dryzek, Jerzy; Siemek, Krzysztof
2015-02-07
Systematic studies of the so-called positron accumulation effect for samples with particles embedded in a matrix are reported. This effect is related to energetic positrons which penetrate inhomogeneous medium. Due to differences in the linear absorption coefficient, different amounts of positrons are accumulated and annihilate in the identical volume of both materials. Positron lifetime spectroscopy and Doppler broadening of the annihilation line using Na-22 positrons were applied to the studies of the epoxy resin samples with embedded micro-sized particles of transition metals, i.e., Ni, Sn, Mo, W, and nonmetal particles, i.e., Si and NaF. The significant difference between the determined fraction of positrons annihilating in the particles and the particle volume fraction indicates the positron accumulation effect. The simple phenomenological model and Monte Carlo simulations are able to describe the main features of the obtained dependencies. The aluminum alloy with embedded Sn nanoparticles is also considered for demonstration differences between the accumulation and another related effect, i.e., the positron affinity.
Positron accumulation effect in particles embedded in a low-density matrix
NASA Astrophysics Data System (ADS)
Dryzek, Jerzy; Siemek, Krzysztof
2015-02-01
Systematic studies of the so-called positron accumulation effect for samples with particles embedded in a matrix are reported. This effect is related to energetic positrons which penetrate inhomogeneous medium. Due to differences in the linear absorption coefficient, different amounts of positrons are accumulated and annihilate in the identical volume of both materials. Positron lifetime spectroscopy and Doppler broadening of the annihilation line using Na-22 positrons were applied to the studies of the epoxy resin samples with embedded micro-sized particles of transition metals, i.e., Ni, Sn, Mo, W, and nonmetal particles, i.e., Si and NaF. The significant difference between the determined fraction of positrons annihilating in the particles and the particle volume fraction indicates the positron accumulation effect. The simple phenomenological model and Monte Carlo simulations are able to describe the main features of the obtained dependencies. The aluminum alloy with embedded Sn nanoparticles is also considered for demonstration differences between the accumulation and another related effect, i.e., the positron affinity.
Charged- and neutral-pion production in the S-matrix approach
Malafaia, V.; Pena, M. T.; Elster, Ch.; Adam, J. Jr.
2006-10-15
The S-matrix approach is used to calculate both charged- and neutral-pion production in nucleon-nucleon (NN) scattering near threshold. The irreducible pion-rescattering diagram, direct production mechanism, {delta} isobars in intermediate states, and Z diagrams mediated by heavy isoscalar mesons are included in the calculation. For the NN distortions, we considered a realistic interaction, within the Bonn family of potentials, which describes the nucleonic inelasticities above the pion production energy threshold.
Unified approach to nuclear densities from exotic atoms
NASA Astrophysics Data System (ADS)
Friedman, E.
2009-09-01
Parameters of nuclear density distributions are derived from least-squares fits to strong interaction observables in exotic atoms. Global analyses of antiprotonic and pionic atoms show reasonably good agreement between the two types of probes regarding the average behaviour of root-mean-square radii of the neutron distributions. Apparent conflict regarding the shape of the neutron distribution is attributed to different radial sensitivities of these two probes.
The nutrient density approach to healthy eating: challenges and opportunities.
Nicklas, Theresa A; Drewnowski, Adam; O'Neil, Carol E
2014-12-01
The term 'nutrient density' for foods/beverages has been used loosely to promote the Dietary Guidelines for Americans. The 2010 Dietary Guidelines for Americans defined 'all vegetables, fruits, whole grains, fat-free or low-fat milk and milk products, seafood, lean meats and poultry, eggs, beans and peas (legumes), and nuts and seeds that are prepared without added solid fats, added sugars, and sodium' as nutrient dense. The 2010 Dietary Guidelines for Americans further states that nutrient-dense foods and beverages provide vitamins, minerals and other substances that may have positive health effects with relatively few (kilo)calories or kilojoules. Finally, the definition states nutrients and other beneficial substances have not been 'diluted' by the addition of energy from added solid fats, added sugars or by the solid fats naturally present in the food. However, the Dietary Guidelines Advisory Committee and other scientists have failed to clearly define 'nutrient density' or to provide criteria or indices that specify cut-offs for foods that are nutrient dense. Today, 'nutrient density' is a ubiquitous term used in the scientific literature, policy documents, marketing strategies and consumer messaging. However, the term remains ambiguous without a definitive or universal definition. Classifying or ranking foods according to their nutritional content is known as nutrient profiling. The goal of the present commentary is to address the research gaps that still exist before there can be a consensus on how best to define nutrient density, highlight the situation in the USA and relate this to wider, international efforts in nutrient profiling.
NASA Astrophysics Data System (ADS)
Kurashige, Yuki; Yanai, Takeshi
2009-06-01
This article presents an efficient and parallelized implementation of the density matrix renormalization group (DMRG) algorithm for quantum chemistry calculations. The DMRG method as a large-scale multireference electronic structure model is by nature particularly efficient for one-dimensionally correlated systems, while the present development is oriented toward applications for polynuclear transition metal compounds, in which the macroscopic one-dimensional structure of electron correlation is absent. A straightforward extension of the DMRG algorithm is proposed with further improvements and aggressive optimizations to allow its application with large multireference active space, which is often demanded for metal compound calculations. Special efficiency is achieved by making better use of sparsity and symmetry in the operator and wave function representations. By accomplishing computationally intensive DMRG calculations, the authors have found that a large number of renormalized basis states are required to represent high entanglement of the electron correlation for metal compound applications, and it is crucial to adopt auxiliary perturbative correction to the projected density matrix during the DMRG sweep optimization in order to attain proper convergence to the solution. Potential energy curve calculations for the Cr2 molecule near the known equilibrium precisely predicted the full configuration interaction energies with a correlation space of 24 electrons in 30 orbitals [denoted by (24e,30o)]. The energies are demonstrated to be accurate to 0.6mEh (the error from the extrapolated best value) when as many as 10 000 renormalized basis states are employed for the left and right DMRG block representations. The relative energy curves for [Cu2O2]2+ along the isomerization coordinate were obtained from DMRG and other correlated calculations, for which a fairly large orbital space (32e,62o) is modeled as a full correlation space. The DMRG prediction nearly overlaps
Nuclear clustering in the energy density functional approach
Ebran, J.-P.; Khan, E.; Nikšić, T.; Vretenar, D.
2015-10-15
Nuclear Energy Density Functionals (EDFs) are a microscopic tool of choice extensively used over the whole chart to successfully describe the properties of atomic nuclei ensuing from their quantum liquid nature. In the last decade, they also have proved their ability to deal with the cluster phenomenon, shedding a new light on its fundamental understanding by treating on an equal footing both quantum liquid and cluster aspects of nuclei. Such a unified microscopic description based on nucleonic degrees of freedom enables to tackle the question pertaining to the origin of the cluster phenomenon and emphasizes intrinsic mechanisms leading to the emergence of clusters in nuclei.
Das, Mousumi
2014-03-28
We studied the nature of the ground state and low-lying excited states of armchair polyacene oligomers (Polyphenanthrene) within long-range Pariser-Parr-Pople model Hamiltonian with up to 14 monomers using symmetrized density matrix renormalization group technique. The ground state of all armchair polyacenes studied is found to be singlet. The results show that lowest singlet dipole allowed excited state has higher energy for armchair polyacenes as compared to linear fused polyacenes. Moreover, unlike linear fused polyacenes, the lowest singlet excited state of these oligomers is always found to lie below the lowest dipole forbidden two-photon state indicating that these armchair polyacene oligomers strongly fluoresce. The calculations of low-lying excitations on singly and triply electron doped armchair polyacene oligomers show a low energy band with strong transition dipole moment that coupled to charge conductivity. This implies armchair polyacene posses novel field-effect transistor properties.
Shenvi, Neil; van Aggelen, Helen; Yang, Yang; Yang, Weitao; Schwerdtfeger, Christine; Mazziotti, David
2013-08-07
Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r(4)), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the standard p2RDM algorithm, somewhere between that of CCSD and CCSD(T).
Chan, Garnet Kin-Lic; Van Voorhis, Troy
2005-05-22
We describe the theory and implementation of two extensions to the density-matrix renormalization-group (DMRG) algorithm in quantum chemistry: (i) to work with an underlying nonorthogonal one-particle basis (using a biorthogonal formulation) and (ii) to use non-Hermitian and complex operators and complex wave functions, which occur naturally in biorthogonal formulations. Using these developments, we carry out ground-state calculations on ethene, butadiene, and hexatriene, in a polarized atomic-orbital basis. The description of correlation in these systems using a localized nonorthogonal basis is improved over molecular-orbital DMRG calculations, and comparable to or better than coupled-cluster calculations, although we encountered numerical problems associated with non-Hermiticity. We believe that the non-Hermitian DMRG algorithm may further become useful in conjunction with other non-Hermitian Hamiltonians, for example, similarity-transformed coupled-cluster Hamiltonians.
Transfer-matrix approach for finite-difference time-domain simulation of periodic structures.
Deinega, Alexei; Belousov, Sergei; Valuev, Ilya
2013-11-01
Optical properties of periodic structures can be calculated using the transfer-matrix approach, which establishes a relation between amplitudes of the wave incident on a structure with transmitted or reflected waves. The transfer matrix can be used to obtain transmittance and reflectance spectra of finite periodic structures as well as eigenmodes of infinite structures. Traditionally, calculation of the transfer matrix is performed in the frequency domain and involves linear algebra. In this work, we present a technique for calculation of the transfer matrix using the finite-difference time-domain (FDTD) method and show the way of its implementation in FDTD code. To illustrate the performance of our technique we calculate the transmittance spectra for opal photonic crystal slabs consisting of multiple layers of spherical scatterers. Our technique can be used for photonic band structure calculations. It can also be combined with existing FDTD methods for the analysis of periodic structures at an oblique incidence, as well as for modeling point sources in a periodic environment.
Transfer-matrix approach for finite-difference time-domain simulation of periodic structures
NASA Astrophysics Data System (ADS)
Deinega, Alexei; Belousov, Sergei; Valuev, Ilya
2013-11-01
Optical properties of periodic structures can be calculated using the transfer-matrix approach, which establishes a relation between amplitudes of the wave incident on a structure with transmitted or reflected waves. The transfer matrix can be used to obtain transmittance and reflectance spectra of finite periodic structures as well as eigenmodes of infinite structures. Traditionally, calculation of the transfer matrix is performed in the frequency domain and involves linear algebra. In this work, we present a technique for calculation of the transfer matrix using the finite-difference time-domain (FDTD) method and show the way of its implementation in FDTD code. To illustrate the performance of our technique we calculate the transmittance spectra for opal photonic crystal slabs consisting of multiple layers of spherical scatterers. Our technique can be used for photonic band structure calculations. It can also be combined with existing FDTD methods for the analysis of periodic structures at an oblique incidence, as well as for modeling point sources in a periodic environment.
Lin, Huizi A; Gupta, Michelle S; Varma, Devika M; Gilchrist, M Lane; Nicoll, Steven B
2016-01-01
Engineered constructs represent a promising treatment for replacement of nucleus pulposus (NP) tissue. Recently, photocrosslinked hydrogels comprised of methacrylated carboxymethylcellulose (CMC) were shown to support chondrogenic differentiation of encapsulated human mesenchymal stem cells (hMSCs) and promote accumulation of NP-like extracellular matrix (ECM). The objective of this study was to investigate the influence of CMC crosslinking density, by varying macromer concentration and modification (i.e., methacrylation) percentage, on NP-like differentiation of encapsulated hMSCs. Constructs of lower macromer concentration (2%, w/v) exhibited significantly greater collagen II accumulation, more homogeneous distribution of ECM macromolecules, and a temporal increase in mechanical properties compared to hydrogels of higher macromer concentration (4%, w/v). Constructs of higher modification percentage (25%) gave rise to significantly elevated collagen II content and the formation of cell clusters within the matrix relative to samples of lower modification percentage (10% and 15%). These differences in functional ECM accumulation and distribution are likely attributed to the distinct crosslinked network structures of the various hydrogel formulations. Overall, CMC constructs of lower macromer concentration and modification percentage were most promising as scaffolds for NP tissue engineering based on functional ECM assembly. Optimization of such hydrogel fabrication parameters may lead to the development of clinically relevant tissue-engineered NP replacements.
NASA Astrophysics Data System (ADS)
Leathers, Andrew S.; Micha, David A.; Kilin, Dmitri S.
2009-10-01
The interaction of an excited adsorbate with a medium undergoing electronic and vibrational transitions leads to fast dissipation due to electronic energy relaxation and slow (or delayed) dissipation from vibrational energy relaxation. A theoretical and computational treatment of these phenomena has been done in terms of a reduced density matrix satisfying a generalized Liouville-von Neumann equation, with instantaneous dissipation constructed from state-to-state transition rates, and delayed dissipation given by a memory term derived from the time-correlation function (TCF) of atomic displacements in the medium. Two representative applications are presented here, where electronic excitation may enhance vibrational relaxation of an adsorbate. They involve femtosecond excitation of (a) a CO molecule adsorbed on the Cu(001) metal surface and (b) a metal cluster on a semiconductor surface, Ag3Si(111):H, both electronically excited by visible light and undergoing electron transfer and dissipative dynamics by electronic and vibrational relaxations. Models have been parametrized in both cases from electronic structure calculations and known TCFs for the medium, which are slowly decaying in case (a) and fast decaying in case (b). This requires different numerical procedures in the solution of the integrodifferential equations for the reduced density matrix, which have been solved with an extension of the Runge-Kutta algorithm. Results for the populations of vibronic states versus time show that they oscillate due to vibrational coupling through dissipative interaction with the substrate and show quantum coherence. The total population of electronic states is, however, little affected by vibrational motions. Vibrational relaxation is important only at very long times to establish thermal equilibrium.
Tabacchi, G; Hutter, J; Mundy, C
2005-04-07
A combined linear response--frozen electron density model has been implemented in a molecular dynamics scheme derived from an extended Lagrangian formalism. This approach is based on a partition of the electronic charge distribution into a frozen region described by Kim-Gordon theory, and a response contribution determined by the instaneous ionic configuration of the system. The method is free from empirical pair-potentials and the parameterization protocol involves only calculations on properly chosen subsystems. They apply this method to a series of alkali halides in different physical phases and are able to reproduce experimental structural and thermodynamic properties with an accuracy comparable to Kohn-Sham density functional calculations.
Devarajan, Karthik; Wang, Guoli; Ebrahimi, Nader
2015-04-01
Non-negative matrix factorization (NMF) is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into the product of two nonnegative matrices, W and H, such that V ∼ W H. It has been shown to have a parts-based, sparse representation of the data. NMF has been successfully applied in a variety of areas such as natural language processing, neuroscience, information retrieval, image processing, speech recognition and computational biology for the analysis and interpretation of large-scale data. There has also been simultaneous development of a related statistical latent class modeling approach, namely, probabilistic latent semantic indexing (PLSI), for analyzing and interpreting co-occurrence count data arising in natural language processing. In this paper, we present a generalized statistical approach to NMF and PLSI based on Renyi's divergence between two non-negative matrices, stemming from the Poisson likelihood. Our approach unifies various competing models and provides a unique theoretical framework for these methods. We propose a unified algorithm for NMF and provide a rigorous proof of monotonicity of multiplicative updates for W and H. In addition, we generalize the relationship between NMF and PLSI within this framework. We demonstrate the applicability and utility of our approach as well as its superior performance relative to existing methods using real-life and simulated document clustering data.
Modeling limit languages via limit adjacency matrix and Yusof-Goode approaches
NASA Astrophysics Data System (ADS)
Lim, Wen Li, Yusof, Yuhani
2015-05-01
Limit language was introduced by Goode and Pixton in 2004 under the framework of formal language theory. It is a subset of splicing languages which is restricted to the molecules that will be presented in the splicing system after the reaction of biochemical has run to its completion. In this paper, limit adjacency matrix will be introduced to model the existence of limit languages from splicing languages. Besides, it can be used to characterize the splicing language in terms of active persistent, adult/inert and transient properties based on Yusof-Goode splicing system. In this paper, some examples and theorems that have been formulated via limit adjacency matrix approach will be presented too.
NASA Astrophysics Data System (ADS)
Nakatani, Naoki; Guo, Sheng
2017-03-01
This paper describes an interface between the density matrix renormalization group (DMRG) method and the complete active-space self-consistent field (CASSCF) method and its analytical gradient, as well as an extension to the second-order perturbation theory (CASPT2) method. This interfacing allows large active-space multi-reference computations to be easily performed. The interface and its extension are both implemented in terms of reduced density matrices (RDMs) which can be efficiently computed via the DMRG sweep algorithm. We also present benchmark results showing that, in practice, the DMRG-CASSCF calculations scale with active-space size in a polynomial manner in the case of quasi-1D systems. Geometry optimization of a binuclear iron-sulfur cluster using the DMRG-CASSCF analytical gradient is demonstrated, indicating that the inclusion of the valence p-orbitals of sulfur and double-shell d-orbitals of iron lead to non-negligible changes in the geometry compared to the results of small active-space calculations. With the exception of the selection of M values, many computational settings in these practical DMRG calculations have been tuned and black-boxed in our interface, and so the resulting DMRG-CASSCF and DMRG-CASPT2 calculations are now available to novice users as a common tool to compute strongly correlated electronic wavefunctions.
Ohyabu, Yoshimi; Yunoki, Shunji; Hatayama, Hirosuke; Teranishi, Yoshikazu
2013-11-01
Collagen-based 3-D hydrogels often lack sufficient mechanical strength for tissue engineering. We developed a method for fabrication of high-density collagen fibril matrix (CFM) gels from concentrated solutions of uncleaved gelatin (UCG). Denatured random-coil UCG exhibited more rapid and efficient renaturation into collagen triple-helix than cleaved gelatin (CG) over a broad range of setting temperatures. The UCG solution formed opaque gels with high-density reconstituted collagen fibrils at 28-32 °C and transparent gels similar to CG at <25 °C. The unique gelation properties of UCG enabled the encapsulation of cultured cells in CFM of high solid volume (>5%) and elasticity (1.28 ± 0.15 kPa at 5% and 4.82 ± 0.38 kPa at 8%) with minimal cell loss. The elastic modulus of these gels was higher than that of conventional CFM containing 0.5% collagen. High-strength CFM may provide more durable hydrogels for tissue engineering and regenerative medicine.
Hielscher, Abigail C; Gerecht, Sharon
2012-12-01
A major paradigm shift in cancer research is the emergence of multidisciplinary approaches to investigate complex cell behaviors, to elucidate regulatory mechanisms and to identify therapeutic targets. Recently, efforts are focused on the engineering of complex in vitro models, which more accurately recapitulate the growth and progression of cancer. These strategies have proven vital for investigating and targeting the events that control tumor angiogenesis. In this review, we explore how the emerging engineering approaches are being used to unlock the complex mechanisms regulating tumor angiogenesis. Emphasis is placed on models using natural and synthetic biomaterials to generate scaffolds mimicking the extracellular matrix, which is known to play a critical role in angiogenesis. While the models presented in this review are revolutionary, improvements are still necessary and concepts for advancing and perfecting engineering approaches for modeling tumor angiogenesis are proposed. Overall, the marriage between disparate scientific fields is expected to yield significant improvements in our understanding and treatment of cancer.
Matrix approach to discrete fractional calculus II: Partial fractional differential equations
NASA Astrophysics Data System (ADS)
Podlubny, Igor; Chechkin, Aleksei; Skovranek, Tomas; Chen, YangQuan; Vinagre Jara, Blas M.
2009-05-01
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny's matrix approach [I. Podlubny, Matrix approach to discrete fractional calculus, Fractional Calculus and Applied Analysis 3 (4) (2000) 359-386]. Four examples of numerical solution of fractional diffusion equation with various combinations of time-/space-fractional derivatives (integer/integer, fractional/integer, integer/fractional, and fractional/fractional) with respect to time and to the spatial variable are provided in order to illustrate how simple and general is the suggested approach. The fifth example illustrates that the method can be equally simply used for fractional differential equations with delays. A set of MATLAB routines for the implementation of the method as well as sample code used to solve the examples have been developed.
A Sparse Matrix Approach for Simultaneous Quantification of Nystagmus and Saccade
NASA Technical Reports Server (NTRS)
Kukreja, Sunil L.; Stone, Lee; Boyle, Richard D.
2012-01-01
The vestibulo-ocular reflex (VOR) consists of two intermingled non-linear subsystems; namely, nystagmus and saccade. Typically, nystagmus is analysed using a single sufficiently long signal or a concatenation of them. Saccade information is not analysed and discarded due to insufficient data length to provide consistent and minimum variance estimates. This paper presents a novel sparse matrix approach to system identification of the VOR. It allows for the simultaneous estimation of both nystagmus and saccade signals. We show via simulation of the VOR that our technique provides consistent and unbiased estimates in the presence of output additive noise.
Vernarsky, Brian J.
2014-01-01
In an effort towards a ''complete'' experiment for the ω meson, we present studies from an experiment with an unpolarized target and a circularly polarized photon beam (g1c), carried out using the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. The experiment was analyzed using an extended maximum likelihood fit with partial wave amplitudes. New likelihood functions were calculated to account for the polarization of the photon beam. Both circular and linear polarizations are explored. The results of these fits are then used to project out the spin density matrix for the {omega}. First measurements of the {rho}{sup 3} spin density matrix elements will be presented using this method.
NASA Astrophysics Data System (ADS)
Moroz, Pavel
Growing fossil fuels consumption compels researchers to find new alternative pathways to produce energy. Along with new materials for the conversion of different types of energy into electricity innovative methods for efficient processing of energy sources are also introduced. The main criteria for the success of such materials and methods are the low cost and compelling performance. Among different types of materials semiconductor nanocrystals are considered as promising candidates for the role of the efficient and cheap absorbers for solar energy applications. In addition to the anticipated cost reduction, the integration of nanocrystals (NC) into device architectures is inspired by the possibility of tuning the energy of electrical charges in NCs via nanoparticle size. However, the stability of nanocrystals in photovoltaic devices is limited by the stability of organic ligands which passivate the surface of semiconductors to preserve quantum confinement. The present work introduces a new strategy for low-temperature processing of colloidal nanocrystals into all-inorganic films: semiconductor matrix encapsulated nanocrystal arrays (SMENA). This methodology goes beyond the traditional ligand-interlinking scheme and relies on the encapsulation of morphologically-defined nanocrystal arrays into a matrix of a wide-band gap semiconductor, which preserves optoelectronic properties of individual nanoparticles. Fabricated solids exhibit excellent thermal stability, which is attributed to the heteroepitaxial structure of nanocrystal-matrix interfaces. The main characteristics and properties of these solids were investigated and compared with ones of traditionally fabricated nanocrystal films using standard spectroscopic, optoelectronic and electronic techniques. As a proof of concept, we. We also characterized electron transport phenomena in different types of nanocrystal films using all-optical approach. By measuring excited carrier lifetimes in either ligand-linked or
Xia, Xianping; Tang, Ying; Xie, Changsheng; Wang, Yun; Cai, Shuizhou; Zhu, Changhong
2011-07-01
As a novel copper-containing intrauterine device (IUD), the prospective life-span of the copper/low-density-polyethylene (Cu/LDPE) nanocomposite IUD is very important for the future clinical use and should be given in advance. Here a novel approach, cupric ions accelerated release in diluted nitric acid solution and cupric ions concentration release in various volume of simulated uterine solution (SUS), is reported to verify the type of cupric ions release model of the cylindrical matrix-type nanocomposite IUD, and to obtain the minimal cupric ions release rate that need to ensure contraceptive efficacy and the thickness of copper particles exhausted layer of the cylindrical matrix-type nanocomposite IUD within two difficult immersion durations in experimental volume of SUS, respectively. Using these results, the prospective life-span of the cylindrical matrix-type nanocomposite IUD can be obtained. For instance, the prospective life-span of the novel γ-shape nanocomposite IUD with 25 wt% of copper nanoparticles and 2 mm of diameter and a total weight of 285 mg can be given in advance and it is about 5 years in the future clinical use.
2007-03-01
matrix element scaling were determined through the use of a training set of light atoms and molecules consisting of H2, He, Li, Be, B, C, N, O, F, Ne...as electron velocities near the nucleus become appreciable fractions of the speed of light . Electron or- bitals having high densities near the nucleus...contraction. However, the inner s- and p- orbitals nearest the nucleus experience the most contraction (108). In light -element molecules, this orbital
A practical approach to lake water density from electrical conductivity and temperature
NASA Astrophysics Data System (ADS)
Moreira, Santiago; Schultze, Martin; Rahn, Karsten; Boehrer, Bertram
2016-07-01
Density calculations are essential to study stratification, circulation patterns, internal wave formation and other aspects of hydrodynamics in lakes and reservoirs. Currently, the most common procedure is the use of CTD (conductivity, temperature and depth) profilers and the conversion of measurements of temperature and electrical conductivity into density. In limnic waters, such approaches are of limited accuracy if they do not consider lake-specific composition of solutes, as we show. A new approach is presented to correlate density and electrical conductivity, using only two specific coefficients based on the composition of solutes. First, it is necessary to evaluate the lake-specific coefficients connecting electrical conductivity with density. Once these coefficients have been obtained, density can easily be calculated based on CTD data. The new method has been tested against measured values and the most common equations used in the calculation of density in limnic and ocean conditions. The results show that our new approach can reproduce the density contribution of solutes with a relative error of less than 10 % in lake waters from very low to very high concentrations as well as in lakes of very particular water chemistry, which is better than all commonly implemented density calculations in lakes. Finally, a web link is provided for downloading the corresponding density calculator.
Rimayi, Cornelius; Odusanya, David; Mtunzi, Fanyana; Tsoka, Shepherd
2015-01-01
This paper investigates the efficiency of application of four different multivariate calibration techniques, namely matrix-matched internal standard (MMIS), matrix-matched external standard (MMES), solvent-only internal standard (SOIS) and solvent-only external standard (SOES) on the detection and quantification of 20 organochlorine compounds from high, low and blank matrix water sample matrices by Gas Chromatography-Mass Spectrometry (GC-MS) coupled to solid phase extraction (SPE). Further statistical testing, using Statistical Package for the Social Science (SPSS) by applying MANOVA, T-tests and Levene's F tests indicates that matrix composition has a more significant effect on the efficiency of the analytical method than the calibration method of choice. Matrix effects are widely described as one of the major sources of errors in GC-MS multiresidue analysis. Descriptive and inferential statistics proved that the matrix-matched internal standard calibration was the best approach to use for samples of varying matrix composition as it produced the most precise average mean recovery of 87% across all matrices tested. The use of an internal standard calibration overall produced more precise total recoveries than external standard calibration, with mean values of 77% and 64% respectively. The internal standard calibration technique produced a particularly high overall standard deviation of 38% at 95% confidence level indicating that it is less robust than the external standard calibration method which had an overall standard error of 32% at 95% confidence level. Overall, the matrix-matched external standard calibration proved to be the best calibration approach for analysis of low matrix samples which consisted of the real sample matrix as it had the most precise recovery of 98% compared to other calibration approaches for the low-matrix samples.
Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; Salinger, Andrew G.; Price, Stephen
2016-10-06
A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigrid hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.
Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; ...
2016-10-06
A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigridmore » hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.« less
Gong, Yu; Andrews, Lester
2011-11-14
Reactions of laser-ablated thorium and uranium atoms with dimethyl ether were investigated using matrix isolation infrared spectroscopy. Four types of reaction products for both uranium and thorium were identified using deuterium substituted samples as well as density functional frequency and energy calculations. Ground state uranium and thorium atoms react with dimethyl ether spontaneously to give the M(CH(3)OCH(3)) complexes (M = Th, U) on annealing, which are predicted to have C(2v) symmetry with triplet (Th) and quintet (U) ground states. Subsequent visible irradiation produces the divalent CH(3)OThCH(3) and CH(3)OUCH(3) insertion products with singlet and quintet states lowest in energy. Further UV irradiation induces isomerization of the CH(3)OMCH(3) molecules to the (CH(3))(2)MO isomers with M=O double bonds and pyramidal structures. In the presence of another dimethyl ether reagent, evidence for (CH(3)O)(2)M(CH(3))(2) molecules is also produced upon UV irradiation.
Transfer-matrix study of a hard-square lattice gas with two kinds of particles and density anomaly
NASA Astrophysics Data System (ADS)
Oliveira, Tiago J.; Stilck, Jürgen F.
2015-09-01
Using transfer matrix and finite-size scaling methods, we study the thermodynamic behavior of a lattice gas with two kinds of particles on the square lattice. Only excluded volume interactions are considered, so that the model is athermal. Large particles exclude the site they occupy and its four first neighbors, while small particles exclude only their site. Two thermodynamic phases are found: a disordered phase where large particles occupy both sublattices with the same probability and an ordered phase where one of the two sublattices is preferentially occupied by them. The transition between these phases is continuous at small concentrations of the small particles and discontinuous at larger concentrations, both transitions are separated by a tricritical point. Estimates of the central charge suggest that the critical line is in the Ising universality class, while the tricritical point has tricritical Ising (Blume-Emery-Griffiths) exponents. The isobaric curves of the total density as functions of the fugacity of small or large particles display a minimum in the disordered phase.
Bottom-up and top-down solid-state NMR approaches for bacterial biofilm matrix composition
NASA Astrophysics Data System (ADS)
Cegelski, Lynette
2015-04-01
The genomics and proteomics revolutions have been enormously successful in providing crucial "parts lists" for biological systems. Yet, formidable challenges exist in generating complete descriptions of how the parts function and assemble into macromolecular complexes and whole-cell assemblies. Bacterial biofilms are complex multicellular bacterial communities protected by a slime-like extracellular matrix that confers protection to environmental stress and enhances resistance to antibiotics and host defenses. As a non-crystalline, insoluble, heterogeneous assembly, the biofilm extracellular matrix poses a challenge to compositional analysis by conventional methods. In this perspective, bottom-up and top-down solid-state NMR approaches are described for defining chemical composition in complex macrosystems. The "sum-of-the-parts" bottom-up approach was introduced to examine the amyloid-integrated biofilms formed by Escherichia coli and permitted the first determination of the composition of the intact extracellular matrix from a bacterial biofilm. An alternative top-down approach was developed to define composition in Vibrio cholerae biofilms and relied on an extensive panel of NMR measurements to tease out specific carbon pools from a single sample of the intact extracellular matrix. These two approaches are widely applicable to other heterogeneous assemblies. For bacterial biofilms, quantitative parameters of matrix composition are needed to understand how biofilms are assembled, to improve the development of biofilm inhibitors, and to dissect inhibitor modes of action. Solid-state NMR approaches will also be invaluable in obtaining parameters of matrix architecture.
Xu, Zhengbin; Ozcelikkale, Altug; Kim, Young L; Han, Bumsoo
2013-02-01
Quality and functionality of engineered tissues are closely related to the microstructures and integrity of their extracellular matrix (ECM). However, currently available methods for characterizing ECM structures are often labor-intensive, destructive, and limited to a small fraction of the total area. These methods are also inappropriate for assessing temporal variations in ECM structures. In this study, to overcome these limitations and challenges, we propose an elastic light scattering approach to spatiotemporally assess ECM microstructures in a relatively large area in a nondestructive manner. To demonstrate its feasibility, we analyze spectroscopic imaging data obtained from acellular collagen scaffolds and dermal equivalents as model ECM structures. For spatial characterization, acellular scaffolds are examined after a freeze/thaw process mimicking a cryopreservation procedure to quantify freezing-induced structural changes in the collagen matrix. We further analyze spatial and temporal changes in ECM structures during cell-driven compaction in dermal equivalents. The results show that spectral dependence of light elastically backscattered from engineered tissue is sensitively associated with alterations in ECM microstructures. In particular, a spectral decay rate over the wavelength can serve as an indicator for the pore size changes in ECM structures, which are at nanometer scale. A decrease in the spectral decay rate suggests enlarged pore sizes of ECM structures. The combination of this approach with a whole-field imaging platform further allows visualization of spatial heterogeneity of EMC microstructures in engineered tissues. This demonstrates the feasibility of the proposed method that nano- and micrometer scale alteration of the ECM structure can be detected and visualized at a whole-field level. Thus, we envision that this spectroscopic imaging approach could potentially serve as an effective characterization tool to nondestructively, accurately
NASA Astrophysics Data System (ADS)
Xu, Hao; Shakeshaft, Robin
2011-01-01
We develop an R-matrix approach to treating collision processes which explicitly takes into account, by means of a simple energy-dependent analytic function, the out-of-phase oscillations of the incident and scattered standing waves in the interior region. Thereby we avoid the use of the Bloch operator. In place of the Bloch operator the incident wave provides the source term in an inhomogeneous equation for the scattered wave. We take those subchannels not treated exactly into account via the optical potential, which is generally non-Hermitian due to dissipation at the boundary. The optical potential is constructed on a real analytic basis using a resolvent that satisfies outgoing-wave boundary conditions. The use of an analytic basis together with the direct determination of the K matrix, rather than the R matrix, at the boundary (this is done by matching the interior wave function to the nearly exact analytic solution beyond the boundary) makes the method particularly well suited to the treatment of ultracold collisions. We have tested our method by applying it to one-photon single-ionization of (He1s2) accompanied by excitation to He+(2s) or He+(2p) for photon energies above the complete breakup threshold, where the optical potential is non-Hermitian. Excellent agreement with experiment is obtained for the cross sections for photoionization to both He+(n=1) and to He+(n=2). The 2s-to-2p branching ratio is strongly influenced by both the optical potential and, at photon energies less than a few tens of eV above the breakup threshold, the nonadiabatic dipole mixing of the 2s and 2p states.
Global financial indices and twitter sentiment: A random matrix theory approach
NASA Astrophysics Data System (ADS)
García, A.
2016-11-01
We use Random Matrix Theory (RMT) approach to analyze the correlation matrix structure of a collection of public tweets and the corresponding return time series associated to 20 global financial indices along 7 trading months of 2014. In order to quantify the collection of tweets, we constructed daily polarity time series from public tweets via sentiment analysis. The results from RMT analysis support the fact of the existence of true correlations between financial indices, polarities, and the mixture of them. Moreover, we found a good agreement between the temporal behavior of the extreme eigenvalues of both empirical data, and similar results were found when computing the inverse participation ratio, which provides an evidence about the emergence of common factors in global financial information whether we use the return or polarity data as a source. In addition, we found a very strong presumption that polarity Granger causes returns of an Indonesian index for a long range of lag trading days, whereas for Israel, South Korea, Australia, and Japan, the predictive information of returns is also presented but with less presumption. Our results suggest that incorporating polarity as a financial indicator may open up new insights to understand the collective and even individual behavior of global financial indices.
Electron Collisional Excitation Rates for OI USING the B-Spline R-Matrix Approach
NASA Technical Reports Server (NTRS)
Zatsarinny, O.; Tayal, S. S.
2003-01-01
The B-spline R-matrix approach has been used to calculate electron collisional excitation strengths and rates for transitions between the 3P, 1D, and 1S states of ground configuration and from these states to the states of the excited 2s(sup 2)2p(sup 3)ns (n = 3-5), 2s(sup 2)2p(sup 3)np (n = 3-4), 2s(sup 2)2p(sup 3)nd (n = 3-4), 2s(sup 2)2p(sup 3)4f, and 2s2p(sup 5) configurations. The nonorthogonal orbitals are used for an accurate description of both the target wave functions and the R-matrix basis functions. The thermally averaged collision strengths are obtained from the collision strengths by integrating over a Maxwellian velocity distribution of electron energies, and these are tabulated over a temperature range from 1000 to 60,000 K. The parametric functions of scaled energy have also been obtained to represent collision strengths over a wide energy range or thermally averaged collision strengths at any desired temperature.
Scattering matrix approach to the dissociative recombination of HCO+ and N2H+.
Fonseca dos Santos, S; Douguet, N; Kokoouline, V; Orel, A E
2014-04-28
We present a theoretical study of the indirect dissociative recombination of linear polyatomic ions at low collisional energies. The approach is based on the computation of the scattering matrix just above the ionization threshold and enables the explicit determination of all diabatic electronic couplings responsible for dissociative recombination. In addition, we use the multi-channel quantum-defect theory to demonstrate the precision of the scattering matrix by reproducing accurately ab initio Rydberg state energies of the neutral molecule. We consider the molecular ions N2H(+) and HCO(+) as benchmark systems of astrophysical interest and improve former theoretical studies, which had repeatedly produced smaller cross sections than experimentally measured. Specifically, we demonstrate the crucial role of the previously overlooked stretching modes for linear polyatomic ions with large permanent dipole moment. The theoretical cross sections for both ions agree well with experimental data over a wide energy range. Finally, we consider the potential role of the HOC(+) isomer in the experimental cross sections of HCO(+) at energies below 10 meV.
Current-induced forces in mesoscopic systems: A scattering-matrix approach.
Bode, Niels; Kusminskiy, Silvia Viola; Egger, Reinhold; von Oppen, Felix
2012-01-01
Nanoelectromechanical systems are characterized by an intimate connection between electronic and mechanical degrees of freedom. Due to the nanoscopic scale, current flowing through the system noticeably impacts upons the vibrational dynamics of the device, complementing the effect of the vibrational modes on the electronic dynamics. We employ the scattering-matrix approach to quantum transport in order to develop a unified theory of nanoelectromechanical systems out of equilibrium. For a slow mechanical mode the current can be obtained from the Landauer-Büttiker formula in the strictly adiabatic limit. The leading correction to the adiabatic limit reduces to Brouwer's formula for the current of a quantum pump in the absence of a bias voltage. The principal results of the present paper are the scattering-matrix expressions for the current-induced forces acting on the mechanical degrees of freedom. These forces control the Langevin dynamics of the mechanical modes. Specifically, we derive expressions for the (typically nonconservative) mean force, for the (possibly negative) damping force, an effective "Lorentz" force that exists even for time-reversal-invariant systems, and the fluctuating Langevin force originating from Nyquist and shot noise of the current flow. We apply our general formalism to several simple models that illustrate the peculiar nature of the current-induced forces. Specifically, we find that in out-of-equilibrium situations the current-induced forces can destabilize the mechanical vibrations and cause limit-cycle dynamics.
NASA Technical Reports Server (NTRS)
Cramer, Nick; Swei, Sean Shan-Min; Cheung, Kenny; Teodorescu, Mircea
2015-01-01
This paper presents a modeling and control of aerostructure developed by lattice-based cellular materials/components. The proposed aerostructure concept leverages a building block strategy for lattice-based components which provide great adaptability to varying ight scenarios, the needs of which are essential for in- ight wing shaping control. A decentralized structural control design is proposed that utilizes discrete-time lumped mass transfer matrix method (DT-LM-TMM). The objective is to develop an e ective reduced order model through DT-LM-TMM that can be used to design a decentralized controller for the structural control of a wing. The proposed approach developed in this paper shows that, as far as the performance of overall structural system is concerned, the reduced order model can be as e ective as the full order model in designing an optimal stabilizing controller.
Vibration localization in mono- and bi-coupled bladed disks - A transfer matrix approach
NASA Technical Reports Server (NTRS)
Ottarsson, Gisli; Pierre, Christophe
1993-01-01
A transfer matrix approach to the analysis of the dynamics of mistuned bladed disks is presented. The study focuses on mono-coupled systems, in which each blade is coupled to its two neighboring blades, and bi-coupled systems, where each blade is coupled to its four nearest neighbors. Transfer matrices yield the free dynamics, both the characteristic free wave and the normal modes - in closed form for the tuned assemblies. Mistuned assemblies are represented by random transfer matrices and an examination of the effect of mistuning on harmonic wave propagation yields the localization factor - the average rate of spatial wave amplitude decay per blade - in the mono-coupled assembly. Based on a comparison of the wave propagation characteristics of the mono- and bi-coupled assemblies, important conclusions are drawn about the effect of the additional coupling coordinate on the sensitivity to mistuning and the strength of mode localization predicted by a mono-coupled analysis.
NASA Astrophysics Data System (ADS)
Caballero, B.; García-Martín, A.; Cuevas, J. C.
2012-06-01
We present here a generalization of the scattering-matrix approach for the description of the propagation of electromagnetic waves in nanostructured magneto-optical systems. Our formalism allows us to describe all the key magneto-optical effects in any configuration in periodically patterned multilayer structures. The method can also be applied to describe periodic multilayer systems comprising materials with any type of optical anisotropy. We illustrate the method with the analysis of a recent experiment in which the transverse magneto-optical Kerr effect was measured in an Fe film with a periodic array of subwavelength circular holes. We show, in agreement with the experiments, that the excitation of surface plasmon polaritons in this system leads to a resonant enhancement of the transverse magneto-optical Kerr effect.
A transfer matrix approach to vibration localization in mistuned blade assemblies
NASA Technical Reports Server (NTRS)
Ottarson, Gisli; Pierre, Chritophe
1993-01-01
A study of mode localization in mistuned bladed disks is performed using transfer matrices. The transfer matrix approach yields the free response of a general, mono-coupled, perfectly cyclic assembly in closed form. A mistuned structure is represented by random transfer matrices, and the expansion of these matrices in terms of the small mistuning parameter leads to the definition of a measure of sensitivity to mistuning. An approximation of the localization factor, the spatially averaged rate of exponential attenuation per blade-disk sector, is obtained through perturbation techniques in the limits of high and low sensitivity. The methodology is applied to a common model of a bladed disk and the results verified by Monte Carlo simulations. The easily calculated sensitivity measure may prove to be a valuable design tool due to its system-independent quantification of mistuning effects such as mode localization.
Scaling laws for the largest Lyapunov exponent in long-range systems: A random matrix approach.
Anteneodo, Celia; Vallejos, Raúl O
2002-01-01
We investigate the laws that rule the behavior of the largest Lyapunov exponent (LLE) in many particle systems with long-range interactions. We consider as a representative system the so-called Hamiltonian alpha-XY model where the adjustable parameter alpha controls the range of the interactions of N ferromagnetic spins in a lattice of dimension d. In previous work the dependence of the LLE with the system size N, for sufficiently high energies, was established through numerical simulations. In the thermodynamic limit, the LLE becomes constant for alpha>d whereas it decays as an inverse power law of N for alpha
NASA Astrophysics Data System (ADS)
Sharma, Sandeep
2015-01-01
We extend our previous work [S. Sharma and G. K.-L. Chan, J. Chem. Phys. 136, 124121 (2012)], which described a spin-adapted (SU(2) symmetry) density matrix renormalization group algorithm, to additionally utilize general non-Abelian point group symmetries. A key strength of the present formulation is that the requisite tensor operators are not hard-coded for each symmetry group, but are instead generated on the fly using the appropriate Clebsch-Gordan coefficients. This allows our single implementation to easily enable (or disable) any non-Abelian point group symmetry (including SU(2) spin symmetry). We use our implementation to compute the ground state potential energy curve of the C2 dimer in the cc-pVQZ basis set (with a frozen-core), corresponding to a Hilbert space dimension of 1012 many-body states. While our calculated energy lies within the 0.3 mEh error bound of previous initiator full configuration interaction quantum Monte Carlo and correlation energy extrapolation by intrinsic scaling calculations, our estimated residual error is only 0.01 mEh, much more accurate than these previous estimates. Due to the additional efficiency afforded by the algorithm, the excitation energies (Te) of eight lowest lying excited states: a3Πu, b 3 Σg - , A1Πu, c 3 Σu + , B1Δg, B ' 1 Σg + , d3Πg, and C1Πg are calculated, which agree with experimentally derived values to better than 0.06 eV. In addition, we also compute the potential energy curves of twelve states: the three lowest levels for each of the irreducible representations 1 Σg + , 1 Σu + , 1 Σg - , and 1 Σu - , to an estimated accuracy of 0.1 mEh of the exact result in this basis.
A formulation of a matrix sparsity approach for the quantum ordered search algorithm
NASA Astrophysics Data System (ADS)
Parmar, Jupinder; Rahman, Saarim; Thiara, Jaskaran
One specific subset of quantum algorithms is Grovers Ordered Search Problem (OSP), the quantum counterpart of the classical binary search algorithm, which utilizes oracle functions to produce a specified value within an ordered database. Classically, the optimal algorithm is known to have a log2N complexity; however, Grovers algorithm has been found to have an optimal complexity between the lower bound of ((lnN‑1)/π≈0.221log2N) and the upper bound of 0.433log2N. We sought to lower the known upper bound of the OSP. With Farhi et al. MITCTP 2815 (1999), arXiv:quant-ph/9901059], we see that the OSP can be resolved into a translational invariant algorithm to create quantum query algorithm restraints. With these restraints, one can find Laurent polynomials for various k — queries — and N — database sizes — thus finding larger recursive sets to solve the OSP and effectively reducing the upper bound. These polynomials are found to be convex functions, allowing one to make use of convex optimization to find an improvement on the known bounds. According to Childs et al. [Phys. Rev. A 75 (2007) 032335], semidefinite programming, a subset of convex optimization, can solve the particular problem represented by the constraints. We were able to implement a program abiding to their formulation of a semidefinite program (SDP), leading us to find that it takes an immense amount of storage and time to compute. To combat this setback, we then formulated an approach to improve results of the SDP using matrix sparsity. Through the development of this approach, along with an implementation of a rudimentary solver, we demonstrate how matrix sparsity reduces the amount of time and storage required to compute the SDP — overall ensuring further improvements will likely be made to reach the theorized lower bound.
Cao, Haihui; Nazarian, Ara; Ackerman, Jerome L; Snyder, Brian D; Rosenberg, Andrew E; Nazarian, Rosalynn M; Hrovat, Mirko I; Dai, Guangping; Mintzopoulos, Dionyssios; Wu, Yaotang
2010-06-01
In this study, bone mineral density (BMD) of normal (CON), ovariectomized (OVX), and partially nephrectomized (NFR) rats was measured by (31)P NMR spectroscopy; bone matrix density was measured by (1)H water- and fat-suppressed projection imaging (WASPI); and the extent of bone mineralization (EBM) was obtained by the ratio of BMD/bone matrix density. The capability of these MR methods to distinguish the bone composition of the CON, OVX, and NFR groups was evaluated against chemical analysis (gravimetry). For cortical bone specimens, BMD of the CON and OVX groups was not significantly different; BMD of the NFR group was 22.1% (by (31)P NMR) and 17.5% (by gravimetry) lower than CON. For trabecular bone specimens, BMD of the OVX group was 40.5% (by (31)P NMR) and 24.6% (by gravimetry) lower than CON; BMD of the NFR group was 26.8% (by (31)P NMR) and 21.5% (by gravimetry) lower than CON. No significant change of cortical bone matrix density between CON and OVX was observed by WASPI or gravimetry; NFR cortical bone matrix density was 10.3% (by WASPI) and 13.9% (by gravimetry) lower than CON. OVX trabecular bone matrix density was 38.0% (by WASPI) and 30.8% (by gravimetry) lower than CON, while no significant change in NFR trabecular bone matrix density was observed by either method. The EBMs of OVX cortical and trabecular specimens were slightly higher than CON but not significantly different from CON. Importantly, EBMs of NFR cortical and trabecular specimens were 12.4% and 26.3% lower than CON by (31)P NMR/WASPI, respectively, and 4.0% and 11.9% lower by gravimetry. Histopathology showed evidence of osteoporosis in the OVX group and severe secondary hyperparathyroidism (renal osteodystrophy) in the NFR group. These results demonstrate that the combined (31)P NMR/WASPI method is capable of discerning the difference in EBM between animals with osteoporosis and those with impaired bone mineralization.
Spectral densities for Frenkel exciton dynamics in molecular crystals: A TD-DFTB approach.
Plötz, Per-Arno; Megow, Jörg; Niehaus, Thomas; Kühn, Oliver
2017-02-28
Effects of thermal fluctuations on the electronic excitation energies and intermonomeric Coulomb couplings are investigated for a perylene-tetracarboxylic-diimide crystal. To this end, time dependent density functional theory based tight binding (TD-DFTB) in the linear response formulation is used in combination with electronic ground state classical molecular dynamics. As a result, a parametrized Frenkel exciton Hamiltonian is obtained, with the effect of exciton-vibrational coupling being described by spectral densities. Employing dynamically defined normal modes, these spectral densities are analyzed in great detail, thus providing insight into the effect of specific intramolecular motions on excitation energies and Coulomb couplings. This distinguishes the present method from approaches using fixed transition densities. The efficiency by which intramolecular contributions to the spectral density can be calculated is a clear advantage of this method as compared with standard TD-DFT.
Spectral densities for Frenkel exciton dynamics in molecular crystals: A TD-DFTB approach
NASA Astrophysics Data System (ADS)
Plötz, Per-Arno; Megow, Jörg; Niehaus, Thomas; Kühn, Oliver
2017-02-01
Effects of thermal fluctuations on the electronic excitation energies and intermonomeric Coulomb couplings are investigated for a perylene-tetracarboxylic-diimide crystal. To this end, time dependent density functional theory based tight binding (TD-DFTB) in the linear response formulation is used in combination with electronic ground state classical molecular dynamics. As a result, a parametrized Frenkel exciton Hamiltonian is obtained, with the effect of exciton-vibrational coupling being described by spectral densities. Employing dynamically defined normal modes, these spectral densities are analyzed in great detail, thus providing insight into the effect of specific intramolecular motions on excitation energies and Coulomb couplings. This distinguishes the present method from approaches using fixed transition densities. The efficiency by which intramolecular contributions to the spectral density can be calculated is a clear advantage of this method as compared with standard TD-DFT.
Gudur, Madhu Sudhan Reddy; Hara, Wendy; Le, Quynh-Thu; Wang, Lei; Xing, Lei; Li, Ruijiang
2014-01-01
MRI significantly improves the accuracy and reliability of target delineation in radiation therapy for certain tumors due to its superior soft tissue contrast compared to CT. A treatment planning process with MRI as the sole imaging modality will eliminate systematic CT/MRI co-registration errors, reduce cost and radiation exposure, and simplify clinical workflow. However, MRI lacks the key electron density information necessary for accurate dose calculation and generating reference images for patient setup. The purpose of this work is to develop a unifying method to derive electron density from standard T1-weighted MRI. We propose to combine both intensity and geometry information into a unifying probabilistic Bayesian framework for electron density mapping. For each voxel, we compute two conditional probability density functions (PDFs) of electron density given its: (1) T1-weighted MRI intensity, and (2) geometry in a reference anatomy, obtained by deformable image registration between the MRI of the atlas and test patient. The two conditional PDFs containing intensity and geometry information are combined into a unifying posterior PDF, whose mean value corresponds to the optimal electron density value under the mean-square error criterion. We evaluated the algorithm's accuracy of electron density mapping and its ability to detect bone in the head for 8 patients, using an additional patient as the atlas or template. Mean absolute HU error between the estimated and true CT, as well as ROC's for bone detection (HU>200) were calculated. The performance was compared with a global intensity approach based on T1 and no density correction (set whole head to water). The proposed technique significantly reduced the errors in electron density estimation, with a mean absolute HU error of 126, compared with 139 for deformable registration (p=2×10-4), 283 for the intensity approach (p=2×10-6) and 282 without density correction (p=5×10-6). For 90% sensitivity in bone
Gudur, Madhu Sudhan Reddy; Hara, Wendy; Le, Quynh-Thu; Wang, Lei; Xing, Lei; Li, Ruijiang
2014-11-07
MRI significantly improves the accuracy and reliability of target delineation in radiation therapy for certain tumors due to its superior soft tissue contrast compared to CT. A treatment planning process with MRI as the sole imaging modality will eliminate systematic CT/MRI co-registration errors, reduce cost and radiation exposure, and simplify clinical workflow. However, MRI lacks the key electron density information necessary for accurate dose calculation and generating reference images for patient setup. The purpose of this work is to develop a unifying method to derive electron density from standard T1-weighted MRI. We propose to combine both intensity and geometry information into a unifying probabilistic Bayesian framework for electron density mapping. For each voxel, we compute two conditional probability density functions (PDFs) of electron density given its: (1) T1-weighted MRI intensity, and (2) geometry in a reference anatomy, obtained by deformable image registration between the MRI of the atlas and test patient. The two conditional PDFs containing intensity and geometry information are combined into a unifying posterior PDF, whose mean value corresponds to the optimal electron density value under the mean-square error criterion. We evaluated the algorithm's accuracy of electron density mapping and its ability to detect bone in the head for eight patients, using an additional patient as the atlas or template. Mean absolute HU error between the estimated and true CT, as well as receiver operating characteristics for bone detection (HU > 200) were calculated. The performance was compared with a global intensity approach based on T1 and no density correction (set whole head to water). The proposed technique significantly reduced the errors in electron density estimation, with a mean absolute HU error of 126, compared with 139 for deformable registration (p = 2 × 10(-4)), 283 for the intensity approach (p = 2 × 10(-6)) and 282 without density
NASA Astrophysics Data System (ADS)
Sudhan Reddy Gudur, Madhu; Hara, Wendy; Le, Quynh-Thu; Wang, Lei; Xing, Lei; Li, Ruijiang
2014-11-01
MRI significantly improves the accuracy and reliability of target delineation in radiation therapy for certain tumors due to its superior soft tissue contrast compared to CT. A treatment planning process with MRI as the sole imaging modality will eliminate systematic CT/MRI co-registration errors, reduce cost and radiation exposure, and simplify clinical workflow. However, MRI lacks the key electron density information necessary for accurate dose calculation and generating reference images for patient setup. The purpose of this work is to develop a unifying method to derive electron density from standard T1-weighted MRI. We propose to combine both intensity and geometry information into a unifying probabilistic Bayesian framework for electron density mapping. For each voxel, we compute two conditional probability density functions (PDFs) of electron density given its: (1) T1-weighted MRI intensity, and (2) geometry in a reference anatomy, obtained by deformable image registration between the MRI of the atlas and test patient. The two conditional PDFs containing intensity and geometry information are combined into a unifying posterior PDF, whose mean value corresponds to the optimal electron density value under the mean-square error criterion. We evaluated the algorithm’s accuracy of electron density mapping and its ability to detect bone in the head for eight patients, using an additional patient as the atlas or template. Mean absolute HU error between the estimated and true CT, as well as receiver operating characteristics for bone detection (HU > 200) were calculated. The performance was compared with a global intensity approach based on T1 and no density correction (set whole head to water). The proposed technique significantly reduced the errors in electron density estimation, with a mean absolute HU error of 126, compared with 139 for deformable registration (p = 2 × 10-4), 283 for the intensity approach (p = 2 × 10-6) and 282 without density
NASA Astrophysics Data System (ADS)
Manthe, Uwe; Ellerbrock, Roman
2016-05-01
A new approach for the quantum-state resolved analysis of polyatomic reactions is introduced. Based on the singular value decomposition of the S-matrix, energy-dependent natural reaction channels and natural reaction probabilities are defined. It is shown that the natural reaction probabilities are equal to the eigenvalues of the reaction probability operator [U. Manthe and W. H. Miller, J. Chem. Phys. 99, 3411 (1993)]. Consequently, the natural reaction channels can be interpreted as uniquely defined pathways through the transition state of the reaction. The analysis can efficiently be combined with reactive scattering calculations based on the propagation of thermal flux eigenstates. In contrast to a decomposition based straightforwardly on thermal flux eigenstates, it does not depend on the choice of the dividing surface separating reactants from products. The new approach is illustrated studying a prototypical example, the H + CH4 → H2 + CH3 reaction. The natural reaction probabilities and the contributions of the different vibrational states of the methyl product to the natural reaction channels are calculated and discussed. The relation between the thermal flux eigenstates and the natural reaction channels is studied in detail.
Mueller matrix approach for probing multifractality in the underlying anisotropic connective tissue
NASA Astrophysics Data System (ADS)
Das, Nandan Kumar; Dey, Rajib; Ghosh, Nirmalya
2016-09-01
Spatial variation of refractive index (RI) in connective tissues exhibits multifractality, which encodes useful morphological and ultrastructural information about the disease. We present a spectral Mueller matrix (MM)-based approach in combination with multifractal detrended fluctuation analysis (MFDFA) to exclusively pick out the signature of the underlying connective tissue multifractality through the superficial epithelium layer. The method is based on inverse analysis on selected spectral scattering MM elements encoding the birefringence information on the anisotropic connective tissue. The light scattering spectra corresponding to the birefringence carrying MM elements are then subjected to the Born approximation-based Fourier domain preprocessing to extract ultrastructural RI fluctuations of anisotropic tissue. The extracted RI fluctuations are subsequently analyzed via MFDFA to yield the multifractal tissue parameters. The approach was experimentally validated on a simple tissue model comprising of TiO2 as scatterers of the superficial isotropic layer and rat tail collagen as an underlying anisotropic layer. Finally, the method enabled probing of precancer-related subtle alterations in underlying connective tissue ultrastructural multifractality from intact tissues.
Manthe, Uwe; Ellerbrock, Roman
2016-05-28
A new approach for the quantum-state resolved analysis of polyatomic reactions is introduced. Based on the singular value decomposition of the S-matrix, energy-dependent natural reaction channels and natural reaction probabilities are defined. It is shown that the natural reaction probabilities are equal to the eigenvalues of the reaction probability operator [U. Manthe and W. H. Miller, J. Chem. Phys. 99, 3411 (1993)]. Consequently, the natural reaction channels can be interpreted as uniquely defined pathways through the transition state of the reaction. The analysis can efficiently be combined with reactive scattering calculations based on the propagation of thermal flux eigenstates. In contrast to a decomposition based straightforwardly on thermal flux eigenstates, it does not depend on the choice of the dividing surface separating reactants from products. The new approach is illustrated studying a prototypical example, the H + CH4 → H2 + CH3 reaction. The natural reaction probabilities and the contributions of the different vibrational states of the methyl product to the natural reaction channels are calculated and discussed. The relation between the thermal flux eigenstates and the natural reaction channels is studied in detail.
NASA Astrophysics Data System (ADS)
Müller, Silvia; Brockmann, Jan Martin; Schuh, Wolf-Dieter
2015-04-01
final product is accomplished. In conclusion, the developed integrated approach allows for estimating the dynamic topography and its inverse covariance matrix on arbitrary grids in space and time. The inverse covariance matrix contains the appropriate weights for model-data misfits in least-squares ocean model inversions. The focus of this study is on the North Atlantic Ocean. We will present the conceptual design and dynamic topography estimates based on time variable data from seven satellite altimeter missions (Jason-1, Jason-2, Topex/Poseidon, Envisat, ERS-2, GFO, Cryosat2) in combination with the latest GOCE gravity field model and in-situ data from the Argo floats and near-surface drifting buoys.
Schwerdtfeger, Christine A; Mazziotti, David A
2009-06-14
Quantum phase transitions in N-particle systems can be identified and characterized by the movement of the two-particle reduced density matrix (2-RDM) along the boundary of its N-representable convex set as a function of the Hamiltonian parameter controlling the phase transition [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 74, 012501 (2006)]. For the one-dimensional transverse Ising model quantum phase transitions as well as their finite-lattice analogs are computed and characterized by the 2-RDM movement with respect to the transverse magnetic field strength g. The definition of a 2-RDM "speed" quantifies the movement of the 2-RDM per unit of g, which reaches its maximum at the critical point of the phase transition. For the infinite lattice the convex set of 2-RDMs and the 2-RDM speed are computed from the exact solution of the 2-RDM in the thermodynamic limit of infinite N [P. Pfeuty, Ann. Phys. 57, 79 (1970)]. For the finite lattices we compute the 2-RDM convex set and its speed by the variational 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] in which approximate ground-state 2-RDMs are calculated without N-particle wave functions by using constraints, known as N-representability conditions, to restrict the 2-RDMs to represent quantum system of N fermions. Advantages of the method include: (i) rigorous lower bounds on the ground-state energies, (ii) polynomial scaling of the calculation with N, and (iii) independence of the N-representability conditions from a reference wave function, which enables the modeling of multiple quantum phases. Comparing the 2-RDM convex sets for the finite- and infinite-site lattices reveals that the variational 2-RDM method accurately captures the shape of the convex set and the signature of the phase transition in the 2-RDM movement. From the 2-RDM all one- and two-particle expectation values (or order parameters) of the quantum Ising model can also be computed including the pair correlation function, which
NASA Astrophysics Data System (ADS)
Aguayo, M.; Marshall, H.; McNamara, J. P.; Mead, J.; Flores, A. N.
2013-12-01
Estimation of snowpack parameters such as depth, density and grain structure is a central focus of hydrology in seasonally snow-covered lands. These parameters are directly estimated by field observations, indirectly estimated from other parameters using statistical correlations, or simulated with a model. Difficulty in sampling thin layers and uncertainty in the transition between layers can cause significant uncertainty in measurements of these parameters. Snow density is one of the most important parameters to measure because it is strictly related with snow water content, an important component of the global water balance. We develop a mathematical framework to estimate snow density from measurements of temperature and thickness of snowpack layers over a particular time period, in conjunction with a physics-based model of snowpack evolution. We formulate a Bayesian approach to estimate the snowpack density profile, using a full range of possible simulations that incorporate key sources of uncertainty to build in prior snowpack knowledge. The posterior probability density function of the snow density, conditioned on snowpack temperature measurements, is computed by multiplying the likelihoods and assumed prior distribution function. Random sampling is used to generate a range of densities with same probability when prior uniform probability function is assumed. A posterior probability density function calculated directly via Bayes' theorem is used to calculate the probability of every sample generated. The forward model is a 1D, multilayer snow energy and mass balance model, which solves for snow temperature, density, and liquid water content on a finite element mesh. The surface and ground temperature data of snowpack (boundary conditions), are provided by the Center for Snow and Avalanche Studies (CSAS), Silverton CO, from snow pits made at Swamp Angel and Senator Beck study plot sites. Standard errors between field observations and results computed denote the
Bone Mineral 31P and Matrix-Bound Water Densities Measured by Solid-State 1H and 31P MRI
Seifert, Alan C.; Li, Cheng; Rajapakse, Chamith S.; Bashoor- Zadeh, Mahdieh; Bhagat, Yusuf A.; Wright, Alexander C.; Zemel, Babette S.; Zavaliangos, Antonios; Wehrli, Felix W.
2014-01-01
Bone is a composite material consisting of mineral and hydrated collagen fractions. MRI of bone is challenging due to extremely short transverse relaxation times, but solid-state imaging sequences exist that can acquire the short-lived signal from bone tissue. Previous work to quantify bone density via MRI used powerful experimental scanners. This work seeks to establish the feasibility of MRI-based measurement on clinical scanners of bone mineral and collagen-bound water densities, the latter as a surrogate of matrix density, and to examine the associations of these parameters with porosity and donors’ age. Mineral and matrix-bound water images of reference phantoms and cortical bone from 16 human donors, ages 27-97 years, were acquired by zero-echo-time 31P and 1H MRI on whole body 7T and 3T scanners, respectively. Images were corrected for relaxation and RF inhomogeneity to obtain density maps. Cortical porosity was measured by micro-CT, and apparent mineral density by pQCT. MRI-derived densities were compared to x-ray-based measurements by least-squares regression. Mean bone mineral 31P density was 6.74±1.22 mol/L (corresponding to 1129±204 mg/cc mineral), and mean bound water 1H density was 31.3±4.2 mol/L (corresponding to 28.3±3.7 %v/v). Both 31P and bound water (BW) densities were correlated negatively with porosity (31P: R2 = 0.32, p < 0.005; BW: R2 = 0.63, p < 0.0005) and age (31P: R2 = 0.39, p < 0.05; BW: R2 = 0.70, p < 0.0001), and positively with pQCT density (31P: R2 = 0.46, p < 0.05; BW: R2 = 0.50, p < 0.005). In contrast, the bone mineralization ratio (expressed here as the ratio of 31P density to bound water density), which is proportional to true bone mineralization, was found to be uncorrelated with porosity, age, or pQCT density. This work establishes the feasibility of image-based quantification of bone mineral and bound water densities using clinical hardware. PMID:24846186
Morgan, Steven W.; Oganesyan, Vadim; Boutis, Gregory S.
2013-01-01
Quantum unitary evolution typically leads to thermalization of generic interacting many-body systems. There are very few known general methods for reversing this process, and we focus on the magic echo, a radio-frequency pulse sequence known to approximately “rewind” the time evolution of dipolar coupled homonuclear spin systems in a large magnetic field. By combining analytic, numerical, and experimental results we systematically investigate factors leading to the degradation of magic echoes, as observed in reduced revival of mean transverse magnetization. Going beyond the conventional analysis based on mean magnetization we use a phase encoding technique to measure the growth of spin correlations in the density matrix at different points in time following magic echoes of varied durations and compare the results to those obtained during a free induction decay (FID). While considerable differences are documented at short times, the long-time behavior of the density matrix appears to be remarkably universal among the types of initial states considered – simple low order multispin correlations are observed to decay exponentially at the same rate, seeding the onset of increasingly complex high order correlations. This manifestly athermal process is constrained by conservation of the second moment of the spectrum of the density matrix and proceeds indefinitely, assuming unitary dynamics. PMID:23710125
Eulerian Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows
NASA Technical Reports Server (NTRS)
He, Guowei; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
The Eulerian mapping closure approach is developed for uncertainty propagation in computational fluid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear flow. An analytical argument shows that fluctuation of the concentration field at one point in space is non-Gaussian and exhibits stretched exponential form. An Eulerian mapping approach provides an appropriate approximation to both convection and diffusion terms and leads to a closed mapping equation. The results obtained describe the evolution of the initial Gaussian field, which is in agreement with direct numerical simulations.
Podlubny, Igor; Skovranek, Tomas; Vinagre Jara, Blas M; Petras, Ivo; Verbitsky, Viktor; Chen, YangQuan
2013-05-13
In this paper, we further develop Podlubny's matrix approach to discretization of integrals and derivatives of non-integer order. Numerical integration and differentiation on non-equidistant grids is introduced and illustrated by several examples of numerical solution of differential equations with fractional derivatives of constant orders and with distributed-order derivatives. In this paper, for the first time, we present a variable-step-length approach that we call 'the method of large steps', because it is applied in combination with the matrix approach for each 'large step'. This new method is also illustrated by an easy-to-follow example. The presented approach allows fractional-order and distributed-order differentiation and integration of non-uniformly sampled signals, and opens the way to development of variable- and adaptive-step-length techniques for fractional- and distributed-order differential equations.
Forced canonical thermalization in a hadronic transport approach at high density
NASA Astrophysics Data System (ADS)
Oliinychenko, Dmytro; Petersen, Hannah
2017-03-01
Hadronic transport approaches based on an effective solution of the relativistic Boltzmann equation are widely applied for the dynamical description of heavy ion reactions at low beam energies. At high densities, the assumption of binary interactions often used in hadronic transport approaches may not be applicable anymore. Therefore, we effectively simulate the high-density regime using the local forced canonical thermalization. This framework provides the opportunity to interpolate in a dynamical way between two different limits of kinetic theory: the dilute gas approximation and the ideal fluid case. This approach will be important for studies of the dynamical evolution of heavy ion collisions at low and intermediate energies as experimentally investigated at the beam energy scan program at RHIC, and in the future at FAIR and NICA. On the other hand, this new way of modeling hot and dense strongly interacting matter might be relevant for small systems at high energies (LHC and RHIC) as well.
Zhang, Xian-Ming; Han, Qing-Long
2014-06-01
This paper is concerned with global asymptotic stability for a class of generalized neural networks with interval time-varying delays by constructing a new Lyapunov-Krasovskii functional which includes some integral terms in the form of ∫(t-h)(t)(h-t-s)(j)ẋ(T)(s)Rjẋ(s)ds(j=1,2,3). Some useful integral inequalities are established for the derivatives of those integral terms introduced in the Lyapunov-Krasovskii functional. A matrix-based quadratic convex approach is introduced to prove not only the negative definiteness of the derivative of the Lyapunov-Krasovskii functional, but also the positive definiteness of the Lyapunov-Krasovskii functional. Some novel stability criteria are formulated in two cases, respectively, where the time-varying delay is continuous uniformly bounded and where the time-varying delay is differentiable uniformly bounded with its time-derivative bounded by constant lower and upper bounds. These criteria are applicable to both static neural networks and local field neural networks. The effectiveness of the proposed method is demonstrated by two numerical examples.
Deng, Bai-chuan; Yun, Yong-huan; Liang, Yi-zeng; Yi, Lun-zhao
2014-10-07
In this study, a new optimization algorithm called the Variable Iterative Space Shrinkage Approach (VISSA) that is based on the idea of model population analysis (MPA) is proposed for variable selection. Unlike most of the existing optimization methods for variable selection, VISSA statistically evaluates the performance of variable space in each step of optimization. Weighted binary matrix sampling (WBMS) is proposed to generate sub-models that span the variable subspace. Two rules are highlighted during the optimization procedure. First, the variable space shrinks in each step. Second, the new variable space outperforms the previous one. The second rule, which is rarely satisfied in most of the existing methods, is the core of the VISSA strategy. Compared with some promising variable selection methods such as competitive adaptive reweighted sampling (CARS), Monte Carlo uninformative variable elimination (MCUVE) and iteratively retaining informative variables (IRIV), VISSA showed better prediction ability for the calibration of NIR data. In addition, VISSA is user-friendly; only a few insensitive parameters are needed, and the program terminates automatically without any additional conditions. The Matlab codes for implementing VISSA are freely available on the website: https://sourceforge.net/projects/multivariateanalysis/files/VISSA/.
Naccarato, Attilio; Pawliszyn, Janusz
2016-09-01
This work proposes the novel PDMS/DVB/PDMS fiber as a greener strategy for analysis by direct immersion solid phase microextraction (SPME) in vegetables. SPME is an established sample preparation approach that has not yet been adequately explored for food analysis in direct immersion mode due to the limitations of the available commercial coatings. The robustness and endurance of this new coating were investigated by direct immersion extractions in raw blended vegetables without any further sample preparation steps. The PDMS/DVB/PDMS coating exhibited superior features related to the capability of the external PDMS layer to protect the commercial coating, and showed improvements in terms of extraction capability and in the cleanability of the coating surface. In addition to having contributed to the recognition of the superior features of this new fiber concept before commercialization, the outcomes of this work serve to confirm advancements in the matrix compatibility of the PDMS-modified fiber, and open new prospects for the development of greener high-throughput analytical methods in food analysis using solid phase microextraction in the near future.
We used data collected from Common Loon Gavia immer populations in two Canadian provinces to demonstrate a matrix population modeling approach for evaluating population-level responses to stressors and to understand how these populations may have responded to mercury contaminatio...
A comprehensive approach for the assessment of in-situ pavement density using GPR technique
NASA Astrophysics Data System (ADS)
Plati, Christina; Georgiou, Panos; Loizos, Andreas
2013-04-01
electromagnetic mixing (EM) theory, through the utilization of proper models. These models enable the prediction of asphalt mixture density dependent on its bulk dielectric constant as measured by the GPR, the dielectric properties of the asphalt mix materials, as well as other material information. The goal of the present study is to attempt to verify the prediction performance of various density models. To accomplish this goal GPR surveys were carried out in the field during asphalt pavement construction to evaluate the density results due to different compaction modes. The GPR data was analyzed to calculate the appropriate asphalt mix dielectric properties needed for the activation of the considered density prediction models. Predicted densities were compared with densities of the field cores extracted from the as-built asphalt pavement prior to trafficking. It was found that the predicted density values were significantly lower when compared to the ground truth data. A further investigation of the effect of temperature on GPR readings showed that GPR seems to overestimate the in-situ density. However, this approach could be used effectively to evaluate the performance of different compaction methods and set up the compaction pattern that is needed to achieve the desired asphalt pavement density.
A new approach to calculate Plant Area Density (PAD) using 3D ground-based lidar
NASA Astrophysics Data System (ADS)
Taheriazad, Leila; Moghadas, Hamid; Sanchez-Azofeifa, Arturo
2016-10-01
This paper presents a novel algorithm for calculation of plant area density based on surface and volume convex hull which is applied to each horizontal cut of a point cloud data. This method can be used as an alternative to conventional voxelization approaches to improve accuracy and computation efficiency. The terrestrial data was collected from a boreal forest at Peace River, Alberta, Canada during summer and fall in 2014. This technique can be applied to an arbitrary point cloud data to calculate all other metrics of forests including plant area index, leaf area density, and also leaf area index.
Making a Minimalist Approach to Codeswitching Work: Adding the Matrix Language.
ERIC Educational Resources Information Center
Jake, Janice L.; Myers-Scotton, Carol; Gross, Steven
2002-01-01
Discusses the Matrix Language Frame model. Analysis of noun phrases in a Spanish-English corpus illustrates this compatibility and shows how recent minimalist proposals can explain the distribution of nouns and determiners in the data if they adopt the notion of matrix language as bilingual instantiation of structural uniformity in a CP.…
NASA Astrophysics Data System (ADS)
Li, Yuli; Wang, Wenxian; Zhou, Jun; Chen, Hongsheng; Zhang, Peng
2017-04-01
In this paper, a novel approach to evaluate the neutron shielding performance of a boron-containing neutron absorbing material was proposed for the first time through the establishment of a direct relationship between 10B areal density (10BAD) of the material and its neutron absorption ratio. It is found when the 10BAD of a material is greater than 0.034 g/cm2, the material will achieve a good neutron shielding performance. Based on this proposed approach, B4C/6061Al composite plates with different B4C content (10 wt%, 20 wt%, 30 wt%) were successfully fabricated using vacuum hot pressing followed by hot-extrusion. The characteristics of the B4C/Al interface were studied in details using transmission electron microscopy (TEM), and the effects of B4C particle content on microstructure and mechanical properties of the Al matrix were investigated. Through current studies, B4C/6061Al composite plates possessing good neutron shielding performance and tensile strength are found to be able to be fabricated using either 20 wt% of B4C content with a plate thickness of 4.5 mm or 30 wt% B4C content with a plate thickness of 3 mm.
NASA Astrophysics Data System (ADS)
Keiser, Dennis D.; Jue, Jan-Fong; Miller, Brandon D.; Gan, Jian; Robinson, Adam B.; Medvedev, Pavel G.; Madden, James W.; Moore, Glenn A.
2016-06-01
Low-enriched (U-235 <20 pct) U-Mo dispersion fuel is being developed for use in research and test reactors. In most cases, fuel plates with Al or Al-Si alloy matrices have been tested in the Advanced Test Reactor to support this development. In addition, fuel plates with Mg as the matrix have also been tested. The benefit of using Mg as the matrix is that it potentially will not chemically interact with the U-Mo fuel particles during fabrication or irradiation, whereas with Al and Al-Si alloys such interactions will occur. Fuel plate R9R010 is a Mg matrix fuel plate that was aggressively irradiated in ATR. This fuel plate was irradiated as part of the RERTR-8 experiment at high temperature, high fission rate, and high power, up to high fission density. This paper describes the results of the scanning electron microscopy (SEM) analysis of an irradiated fuel plate using polished samples and those produced with a focused ion beam. A follow-up paper will discuss the results of transmission electron microscopy (TEM) analysis. Using SEM, it was observed that even at very aggressive irradiation conditions, negligible chemical interaction occurred between the irradiated U-7Mo fuel particles and Mg matrix; no interconnection of fission gas bubbles from fuel particle to fuel particle was observed; the interconnected fission gas bubbles that were observed in the irradiated U-7Mo particles resulted in some transport of solid fission products to the U-7Mo/Mg interface; the presence of microstructural pathways in some U-9.1 Mo particles that could allow for transport of fission gases did not result in the apparent presence of large porosity at the U-7Mo/Mg interface; and, the Mg-Al interaction layers that were present at the Mg matrix/Al 6061 cladding interface exhibited good radiation stability, i.e. no large pores.
The effect of dynamic changes in soil bulk density on hydraulic properties: modeling approaches
NASA Astrophysics Data System (ADS)
Assouline, Shmuel
2014-05-01
Natural and artificial processes, like rainfall-induced soil surface sealing or mechanical compaction, disturb the soil structure and enhance dynamic changes of the related pore size distribution. These changes may influence many aspects of the soil-water-plant-atmosphere system. One of the easiest measurable variables is the soil bulk density. Approaches are suggested that could model the effect of the change in soil bulk density on soil permeability, water retention curve (WRC) and unsaturated hydraulic conductivity function (HCF). The resulting expressions were calibrated and validated against experimental data corresponding to different soil types at various levels of compaction, and enable a relatively good prediction of the effect of bulk density on the soil hydraulic properties. These models allow estimating the impact of such changes on flow processes and on transport properties of heterogeneous soil profiles.
Assessing REDD+ performance of countries with low monitoring capacities: the matrix approach
NASA Astrophysics Data System (ADS)
Bucki, M.; Cuypers, D.; Mayaux, P.; Achard, F.; Estreguil, C.; Grassi, G.
2012-03-01
Estimating emissions from deforestation and degradation of forests in many developing countries is so uncertain that the effects of changes in forest management could remain within error ranges (i.e. undetectable) for several years. Meanwhile UNFCCC Parties need consistent time series of meaningful performance indicators to set credible benchmarks and allocate REDD+ incentives to the countries, programs and activities that actually reduce emissions, while providing social and environmental benefits. Introducing widespread measuring of carbon in forest land (which would be required to estimate more accurately changes in emissions from degradation and forest management) will take time and considerable resources. To ensure the overall credibility and effectiveness of REDD+, parties must consider the design of cost-effective systems which can provide reliable and comparable data on anthropogenic forest emissions. Remote sensing can provide consistent time series of land cover maps for most non-Annex-I countries, retrospectively. These maps can be analyzed to identify the forests that are intact (i.e. beyond significant human influence), and whose fragmentation could be a proxy for degradation. This binary stratification of forests biomes (intact/non-intact), a transition matrix and the use of default carbon stock change factors can then be used to provide initial estimates of trends in emission changes. A proof-of-concept is provided for one biome of the Democratic Republic of the Congo over a virtual commitment period (2005-2010). This approach could allow assessment of the performance of the five REDD+ activities (deforestation, degradation, conservation, management and enhancement of forest carbon stocks) in a spatially explicit, verifiable manner. Incentives could then be tailored to prioritize activities depending on the national context and objectives.
Financial Distress Prediction Using Discrete-time Hazard Model and Rating Transition Matrix Approach
NASA Astrophysics Data System (ADS)
Tsai, Bi-Huei; Chang, Chih-Huei
2009-08-01
Previous studies used constant cut-off indicator to distinguish distressed firms from non-distressed ones in the one-stage prediction models. However, distressed cut-off indicator must shift according to economic prosperity, rather than remains fixed all the time. This study focuses on Taiwanese listed firms and develops financial distress prediction models based upon the two-stage method. First, this study employs the firm-specific financial ratio and market factors to measure the probability of financial distress based on the discrete-time hazard models. Second, this paper further focuses on macroeconomic factors and applies rating transition matrix approach to determine the distressed cut-off indicator. The prediction models are developed by using the training sample from 1987 to 2004, and their levels of accuracy are compared with the test sample from 2005 to 2007. As for the one-stage prediction model, the model in incorporation with macroeconomic factors does not perform better than that without macroeconomic factors. This suggests that the accuracy is not improved for one-stage models which pool the firm-specific and macroeconomic factors together. In regards to the two stage models, the negative credit cycle index implies the worse economic status during the test period, so the distressed cut-off point is adjusted to increase based on such negative credit cycle index. After the two-stage models employ such adjusted cut-off point to discriminate the distressed firms from non-distressed ones, their error of misclassification becomes lower than that of one-stage ones. The two-stage models presented in this paper have incremental usefulness in predicting financial distress.
Accurate ab Initio Spin Densities.
Boguslawski, Katharina; Marti, Konrad H; Legeza, Ors; Reiher, Markus
2012-06-12
We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as a basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys.2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insight into chemically interesting features of the molecule under study such as the distribution of α and β electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput.2011, 7, 2740].
An Approach to Calculate Mineralś Bulk Moduli KS from Chemical Composition and Density ρ
NASA Astrophysics Data System (ADS)
Breuer, S.; Schilling, F. R.; Mueller, B.; Drüppel, K.
2015-12-01
The elastic properties of minerals are fundamental parameters for technical and geotechnical applications and an important research topic towards a better understanding of the Earth's interior. Published elastic properties, chemical composition, and density data of 86 minerals (total of 258 data including properties of minerals at various p, T conditions) were collected into a database. It was used to test different hypotheses about relationships between these properties (e.g. water content in minerals and their Poisson's ratio). Furthermore, a scheme to model the average elastic properties, i.e. the bulk modulus KS, based on mineral density and composition was developed. Birch's law, a linearity between density ρ and wave velocity (e.g. vp.), is frequently used in seismic and seismology to derive density of the Earth's interior from seismic velocities. Applying the compiled mineral data contradicts the use of a simple velocity-density relation (e.g. Gardneŕs relation, 1974). The presented model-approach to estimate the mineralś bulk moduli Ks (as Voigt-Reuss-Hill average) is based on the idea of pressure-temperature (p-T) dependent ionś bulk moduli. Using a multi-exponential regression to ascertain the ionś bulk moduli and by applying an exponential scaling with density ρ, their bulk moduli could be modelled. As a result, > 88 % of the 258 bulk moduli data are predicted with an uncertainty of < 20 % compared to published values. Compared to other models (e.g. Anderson et al. 1970 and Anderson & Nafe 1965), the here presented approach to model the bulk moduli only requires the density ρ and chemical composition of the mineral and is not limited to a specific group of minerals, composition, or structure. In addition to this, by using the pressure and temperature dependent density ρ(p, T), it is possible to predict bulk moduli for varying p-T conditions. References:Gardner, G.H.F, Gardner, L.W. and Gregory, A.R. (1974). Geophysics, 39, No. 6, 770
NASA Astrophysics Data System (ADS)
Dorfner, F.; Heidrich-Meisner, F.
2016-06-01
We study properties of the single-site reduced density matrix in the Bose-Bose resonance model as a function of system parameters. This model describes a single-component Bose gas with a resonant coupling to a diatomic molecular state, here defined on a lattice. A main goal is to demonstrate that the eigenstates of the single-site reduced density matrix have structures that are characteristic for the various quantum phases of this system. Since the Hamiltonian conserves only the global particle number but not the number of bosons and molecules individually, these eigenstates, referred to as optimal modes, can be nontrivial linear combinations of bare eigenstates of the molecular and boson particle number. We numerically analyze the optimal modes and their weights, the latter giving the importance of the corresponding state, in the ground state of the Bose-Bose resonance model. We find that the single-site von Neumann entropy is sensitive to the location of the phase boundaries. We explain the structure of the optimal modes and their weight spectra using perturbation theory and via a comparison to results for the single-component Bose-Hubbard model. We further study the dynamical evolution of the optimal modes and of the single-site entanglement entropy in two quantum quenches that cross phase boundaries of the model and show that these quantities are thermal in the steady state. For our numerical calculations, we use the density-matrix renormalization group method for ground-state calculations and time evolution in a Krylov subspace for the quench dynamics as well as exact diagonalization.
NASA Astrophysics Data System (ADS)
van Meer, R.; Gritsenko, O. V.; Baerends, E. J.
2014-01-01
Time dependent density matrix functional theory in its adiabatic linear response formulation delivers exact excitation energies ωα and oscillator strengths fα for two-electron systems if extended to the so-called phase including natural orbital (PINO) theory. The Löwdin-Shull expression for the energy of two-electron systems in terms of the natural orbitals and their phases affords in this case an exact phase-including natural orbital functional (PILS), which is non-primitive (contains other than just J and K integrals). In this paper, the extension of the PILS functional to N-electron systems is investigated. With the example of an elementary primitive NO functional (BBC1) it is shown that current density matrix functional theory ground state functionals, which were designed to produce decent approximations to the total energy, fail to deliver a qualitatively correct structure of the (inverse) response function, due to essential deficiencies in the reconstruction of the two-body reduced density matrix (2RDM). We now deduce essential features of an N-electron functional from a wavefunction Ansatz: The extension of the two-electron Löwdin-Shull wavefunction to the N-electron case informs about the phase information. In this paper, applications of this extended Löwdin-Shull (ELS) functional are considered for the simplest case, ELS(1): one (dissociating) two-electron bond in the field of occupied (including core) orbitals. ELS(1) produces high quality ωα(R) curves along the bond dissociation coordinate R for the molecules LiH, Li2, and BH with the two outer valence electrons correlated. All of these results indicate that response properties are much more sensitive to deficiencies in the reconstruction of the 2RDM than the ground state energy, since derivatives of the functional with respect to both the NOs and the occupation numbers need to be accurate.
NASA Technical Reports Server (NTRS)
Bates, Kevin R.; Daniels, Andrew D.; Scuseria, Gustavo E.
1998-01-01
We report a comparison of two linear-scaling methods which avoid the diagonalization bottleneck of traditional electronic structure algorithms. The Chebyshev expansion method (CEM) is implemented for carbon tight-binding calculations of large systems and its memory and timing requirements compared to those of our previously implemented conjugate gradient density matrix search (CG-DMS). Benchmark calculations are carried out on icosahedral fullerenes from C60 to C8640 and the linear scaling memory and CPU requirements of the CEM demonstrated. We show that the CPU requisites of the CEM and CG-DMS are similar for calculations with comparable accuracy.
Kadek, Marius; Konecny, Lukas; Gao, Bin; Repisky, Michal; Ruud, Kenneth
2015-09-21
The solution of the Liouville-von Neumann equation in the relativistic Dirac-Kohn-Sham density matrix formalism is presented and used to calculate X-ray absorption cross sections. Both dynamical relaxation effects and spin-orbit corrections are included, as demonstrated by calculations of the X-ray absorption of SF6 near the sulfur L2,3-edges. We also propose an analysis facilitating the interpretation of spectral transitions from real-time simulations, and a selective perturbation that eliminates nonphysical excitations that are artifacts of the finite basis representation.
An adaptive finite element approach to modelling sediment laden density currents
NASA Astrophysics Data System (ADS)
Parkinson, S.; Hill, J.; Allison, P. A.; Piggott, M. D.
2012-04-01
Modelling sediment-laden density currents at real-world scales is a challenging task. Here we present Fluidity, which uses dynamic adaptive re-meshing to reduce computational costs whilst maintaining sufficient resolution where and when it is required. This allows small-scale processes to be captured in large scale simulations. Density currents, also known as gravity or buoyancy currents, occur wherever two fluids with different densities meet. They can occur at scales of up to hundred kilometres in the ocean when continental shelves collapse. This process releases large quantities of sediment into the ocean which increase the bulk density of the fluid to form a density current. These currents can carry sediment hundreds of kilometres, at speeds of up to a hundred kilometres per hour, over the sea bed. They can be tsunamigenic and they have the potential to cause significant damage to submarine infrastructure, such as submarine telecommunications cables or oil and gas infrastructure. They are also a key process for movement of organic material into the depths of the ocean. Due to this, they play an important role in the global carbon cycle on the Earth, forming a significant component of the stratigraphic record, and their deposits can form useful sources of important hydrocarbons. Modelling large scale sediment laden density currents is a very challenging problem. Particles within the current are suspended by turbulence that occurs at length scales that are several orders of magnitude smaller than the size of the current. Models that resolve the vertical structure of the flow require a very large, highly resolved mesh, and substantial computing power to solve. Here, we verify our adaptive model by comparison with a set of laboratory experiments by Gladstone et al. [1998] on the propagation and sediment deposition of bidisperse gravity currents. Comparisons are also made with fixed mesh solutions, and it is shown that accuracy can be maintained with fewer elements
NASA Astrophysics Data System (ADS)
Smithey, D. T.; Beck, M.; Cooper, J.; Raymer, M. G.; Faridani, A.
1993-01-01
We have used the recently demonstrated method of optical homodyne tomography (OHT) to measure the Wigner quasiprobability distribution (Wigner function) and the density matrix for both a squeezed-vacuum and a vacuum state of a single spatial-temporal mode of the electromagnetic field. This method consists of measuring a set of probability distributions for many different Hilbert-space representations of the field-quadrature amplitude, using balanced homodyne detection, and then using tomography to obtain the Wigner function. Once the Wigner function is obtained, one can acquire the density matrix, including its complex phase. In the case of a pure state, this technique yields an experimentally determined complex wavefunction, as demonstrated here for the vacuum. The density matrix represents a complete quantum mechanical characterization of the state. From the measured density matrix we have obtained the Pegg-Barnett optical phase distribution, and from the Wigner function, the Wigner optical phase distribution.
A matrix safety frame approach to robot safety for space applications. Thesis
NASA Technical Reports Server (NTRS)
Montgomery, T. D.; Lauderbaugh, L. Ken
1988-01-01
The planned use of autonomous robots in space applications has generated many new safety problems. This thesis assesses safety of autonomous robot systems through the structure of a proposed three-dimensional matrix safety frame. By identifying the common points of accidents and fatalities involving terrestrial robots, reviewing terrestrial robot safety standards, and modifying and extending these results to space applications, hazards are identified and their associated risks assessed. Three components of the safeguarding dimension of the matrix safety frame, safeguarding through design and operation for intrinsic safety, and incorporation of add-on safety systems are explained through examples for both terrestrial and space robots. A space robot hazard identification checklist, a qualitative tool for robot systems designers, is developed using the structure imparted by the matrix safety frame. The development of an expert system from the contents of the checklist is discussed.
NASA Astrophysics Data System (ADS)
He, Cenlin; Takano, Yoshi; Liou, Kuo-Nan; Yang, Ping; Li, Qinbin; Mackowski, Daniel W.
2016-11-01
We perform a comprehensive intercomparison of the geometric-optics surface-wave (GOS) approach, the superposition T-matrix method, and laboratory measurements for optical properties of fresh and coated/aged black carbon (BC) particles with complex structures. GOS and T-matrix calculations capture the measured optical (i.e., extinction, absorption, and scattering) cross sections of fresh BC aggregates, with 5-20% differences depending on particle size. We find that the T-matrix results tend to be lower than the measurements, due to uncertainty in theoretical approximations of realistic BC structures, particle property measurements, and numerical computations in the method. On the contrary, the GOS results are higher than the measurements (hence the T-matrix results) for BC radii <100 nm, because of computational uncertainty for small particles, while the discrepancy substantially reduces to 10% for radii >100 nm. We find good agreement (differences <5%) between the two methods in asymmetry factors for various BC sizes and aggregating structures. For aged BC particles coated with sulfuric acid, GOS and T-matrix results closely match laboratory measurements of optical cross sections. Sensitivity calculations show that differences between the two methods in optical cross sections vary with coating structures for radii <100 nm, while differences decrease to 10% for radii >100 nm. We find small deviations (≤10%) in asymmetry factors computed from the two methods for most BC coating structures and sizes, but several complex structures have 10-30% differences. This study provides the foundation for downstream application of the GOS approach in radiative transfer and climate studies.
Vom Eyser, C; Palmu, K; Otterpohl, R; Schmidt, T C; Tuerk, J
2015-01-01
Producing valuable biochar from waste materials using thermal processes like hydrothermal carbonization (HTC) has gained attention in recent years. However, the fate of micropollutants present in these waste sources have been neglected, although they might entail the risk of environmental pollution. Thus, an HPLC-MS/MS method was developed for 12 pharmaceuticals to determine the micropollutant load of biochar, which was made from sewage sludge via HTC within 4 h at 210 °C. Pressurized liquid extraction was applied to extract the compounds. Because of the high load of co-extracted matter, matrix effects in HPLC-MS/MS were investigated using matrix effect profiles. Interfering compounds suppressed 50% of the phenazone signal in sewage sludge and 70% in biochar, for example. The quantification approaches external calibration, internal standard analysis, and standard addition were compared considering recovery rates, standard deviations, and measurement uncertainties. The external analysis resulted in decreased or enhanced recovery rates. Spiking before LC-MS/MS compensated instrumental matrix effects. Still, recovery rates remained below 70% for most compounds because this approach neglects sample losses during the extraction. Internal standards compensated for the matrix effects sufficiently for up to five compounds. The standard addition over the whole procedure proved to compensate for the matrix effects for 11 compounds and achieved recovery rates between 85 and 125%. Additionally, results showed good reproducibility and validity. Only sulfamethoxazole recovery rate remained below 70% in sewage sludge. Real sample analysis showed that three pharmaceuticals were detected in the biochar, while the corresponding sewage sludge source contained 8 of the investigated compounds.
Medina, F.; Horno, M.
1985-10-01
In this paper, a set of simple recurrence formulas to evaluate the Green's function matrix for a generic multiconductor and multidielectric planar transmission system with arbitrary rectangular boundary conditions is obtained. Combining these formulas with the variational technique in the spectral domain, two useful algorithms to calculate the capacitance matrix of a very wide range of practical configurations are proposed. Upper and lower bounds on mode capacitances are obtained by using both algorithms. A number of practical structures have been analyzed and their most interesting features discussed. The method is very versatile and can handle a large class of MIC configurations, no matter how complex the planar structure.
Density-functional theory for polymer-carbon dioxide mixtures: A perturbed-chain SAFT approach
NASA Astrophysics Data System (ADS)
Xu, Xiaofei; Cristancho, Diego E.; Costeux, Stéphane; Wang, Zhen-Gang
2012-08-01
We propose a density-functional theory (DFT) describing inhomogeneous polymer-carbon dioxide mixtures based on a perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). The weight density functions from fundamental measure theory are used to extend the bulk excess Helmholtz free energy to the inhomogeneous case. The additional long-range dispersion contributions are included using a mean-field approach. We apply our DFT to the interfacial properties of polystyrene-CO2 and poly(methyl methacrylate) CO2 systems. Calculated values for both solubility and interfacial tension are in good agreement with experimental data. In comparison with our earlier DFT based on the Peng-Robinson-SAFT EOS, the current DFT produces quantitatively superior agreement with experimental data and is free of the unphysical behavior at high pressures (>35 MPa) in the earlier theory.
Wang, Huiyuan; Cai, Lei; Paul, Alexandra; Enejder, Annika; Heilshorn, Sarah C
2014-09-08
Hydrogels have been developed as extracellular matrix (ECM) mimics both for therapeutic applications and basic biological studies. In particular, elastin-like polypeptide (ELP) hydrogels, which can be tuned to mimic several biochemical and physical characteristics of native ECM, have been constructed to encapsulate various types of cells to create in vitro mimics of in vivo tissues. However, ELP hydrogels become opaque at body temperature because of ELP's lower critical solution temperature behavior. This opacity obstructs light-based observation of the morphology and behavior of encapsulated cells. In order to improve the transparency of ELP hydrogels for better imaging, we have designed a hybrid ELP-polyethylene glycol (PEG) hydrogel system that rapidly cross-links with tris(hydroxymethyl) phosphine (THP) in aqueous solution via Mannich-type condensation. As expected, addition of the hydrophilic PEG component significantly improves the light transmittance. Coherent anti-Stokes Raman scattering (CARS) microscopy reveals that the hybrid ELP-PEG hydrogels have smaller hydrophobic ELP aggregates at 37 °C. Importantly, this hydrogel platform enables independent tuning of adhesion ligand density and matrix stiffness, which is desirable for studies of cell-matrix interactions. Human fibroblasts encapsulated in these hydrogels show high viability (>98%) after 7 days of culture. High-resolution confocal microscopy of encapsulated fibroblasts reveals that the cells adopt a more spread morphology in response to higher RGD ligand concentrations and softer gel mechanics.
Innovative User Defined Density Profile Approach To FSW Of Aluminium Foam
Contorno, Dorotea; Fratini, Livan; Filice, Luigino; Gagliardi, Francesco; Umbrello, Domenico; Shivpuri, Rajiv
2007-04-07
Metallic foams are one of the most exciting materials in the world of mechanical industry due to their reduced mass and the good mechanical, thermal and acoustic characteristics. Consequently, their application, is increasing day by day even with the important drawbacks that reduce their suitability and diffusion such as high manufacturing cost and difficulty in processing. An innovative approach is outlined in this paper that enables the production of complex shapes taking advantage of deformation processing and friction stir welding (FSW). The aim is to create customized tailored manufactured parts. The cellular construction of foams makes this approach rather challenging as the cell walls are extremely thin and deform unpredictably especially in the presence of rotating and moving hard tool. In this paper, an integrated approach to overcome some of the above challenges is proposed. The initial density is modified by using simple deformation processes, in order to obtained the desired 'crushed density', customized for the intended application. Then, the panels are joined to specially designed solid blocks by using FSW process with a proper set-up. Finally, the obtained specimens are evaluated for mechanical performance and the quality of the joint.
Information Architecture for the Web: The IA Matrix Approach to Designing Children's Portals.
ERIC Educational Resources Information Center
Large, Andrew; Beheshti, Jamshid; Cole, Charles
2002-01-01
Presents a matrix that can serve as a tool for designing the information architecture of a Web portal in a logical and systematic manner. Highlights include interfaces; metaphors; navigation; interaction; information retrieval; and an example of a children's Web portal to provide access to museum information. (Author/LRW)
A Transfer Learning Approach for Applying Matrix Factorization to Small ITS Datasets
ERIC Educational Resources Information Center
Voß, Lydia; Schatten, Carlotta; Mazziotti, Claudia; Schmidt-Thieme, Lars
2015-01-01
Machine Learning methods for Performance Prediction in Intelligent Tutoring Systems (ITS) have proven their efficacy; specific methods, e.g. Matrix Factorization (MF), however suffer from the lack of available information about new tasks or new students. In this paper we show how this problem could be solved by applying Transfer Learning (TL),…
Random-matrix-theory approach to mesoscopic fluctuations of heat current.
Schmidt, Martin; Kottos, Tsampikos; Shapiro, Boris
2013-08-01
We consider an ensemble of fully connected networks of N oscillators coupled harmonically with random springs and show, using random-matrix-theory considerations, that both the average phonon heat current and its variance are scale invariant and take universal values in the large N limit. These anomalous mesoscopic fluctuations is the hallmark of strong correlations between normal modes.
Karami, Samaneh; Imani, Mohammad; Farahmandghavi, Farhid
2013-10-25
Nowadays, there is a lot of interest in developing long-acting drug delivery devices for human or veterinary applications including monolithic systems. Drug content uniformity of a monolithic device is highly dependent on the uniform distribution of drug particles within the polymeric matrix both in dispersion and distribution levels. Here, a range of formulations were prepared which consisted of progesterone (1%w/w) and estradiol benzoate (0.1%w/w) dispersed in a silicone rubber matrix. Blend uniformity of the compounds was analyzed by image analysis of SEM micrographs obtained from the cross-sections of the devices by a new image processing approach. Efficiency of mixing was investigated at the dispersion level by plotting the relative frequency of drug particles versus "projected area diameter" of their aggregates. Based on the particle size distribution results, a significant improvement was observed in the dispersion pattern of drug particles by adding silicone oil (9%w/w). Distribution pattern of the particles was investigated by transforming the micrographs into algebraic matrices. An "ideal matrix" was developed by assumption of uniform localization of the drug particles. Real matrices obtained for all of the formulations were compared with this ideal matrix as a reference. Closer similarity between the two matrices was observed for silicone oil-containing (9%w/w) samples showing the best dispersive and distributive mixing quality.
NASA Astrophysics Data System (ADS)
Hanselman, D. S.; Sesi, N. N.; Huang, M.; Hieftje, G. M.
1994-05-01
Spatially-resolved electron temperature ( Te), electron number density ( ne) and gas-kinetic temperature ( Tg) maps of the inductively coupled plasma (ICP) have been obtained for two central-gas flow rates, four heights above the load coil (ALC) and in the presence and absence of interferants with a wide range of first ionization potentials. The radial profiles demonstrate how the directly measured fundamental parameters neTe and Tg can be significantly enhanced and/or depressed with added interferent, depending upon plasma operating conditions and observation region. In general, the magnitude of ne, and Te change is found to be an inverse function of interferent ionization potential; furthermore, ne enhancements in the central channel might be the result of electron redistribution from high to low electron density regions rather than from ionization of the matrix. The large measured increases in ne cannot be attributed solely to matrix ionization, especially when measurement uncertainties and the probable over-estimation in calculated ne, enhancements are taken into account. Changes in ne and Te have been correlated with axial Ca atom and ion emission profiles. A brief review of the mechanisms most likely involved in interelement matrix interferences is given within the context of the present study. This article is an electronic publication in Spectrochimica Acta Electronica (SAE), the electronic section of Spectrochimica Acta Part B (SAB). The hardcopy text is accompanied by a disk for the Macintosh computer with data files stored in ASCII format. The main article discusses the scientific aspects of the subject and gives an interpretation of the results contained in the data files.
Study of lattice QCD at finite baryon density using the canonical approach
NASA Astrophysics Data System (ADS)
Bornyakov, V. G.; Boyda, D. L.; Goy, V. A.; Molochkov, A. V.; Nakamura, Atsushi; Nikolaev, A. A.; Zakharov, V. I.
2017-03-01
At finite baryon density lattice QCD first-principle calculations can not be performed due to the sign problem. In order to circumvent this problem, we use the canonical approach, which provides reliable analytical continuation from the imaginary chemical potential region to the real chemical potential region. We briefly present the canonical partition function method, describe our formulation, and show the results, obtained for two temperatures: T/Tc = 0:93 and T/Tc = 0:99 in lattice QCD with two flavors of improved Wilson fermions.
A Dynamic Density Functional Theory Approach to Diffusion in White Dwarfs and Neutron Star Envelopes
NASA Astrophysics Data System (ADS)
Diaw, A.; Murillo, M. S.
2016-09-01
We develop a multicomponent hydrodynamic model based on moments of the Born-Bogolyubov-Green-Kirkwood-Yvon hierarchy equations for physical conditions relevant to astrophysical plasmas. These equations incorporate strong correlations through a density functional theory closure, while transport enters through a relaxation approximation. This approach enables the introduction of Coulomb coupling correction terms into the standard Burgers equations. The diffusive currents for these strongly coupled plasmas is self-consistently derived. The settling of impurities and its impact on cooling can be greatly affected by strong Coulomb coupling, which we show can be quantified using the direct correlation function.
Network trending; leadership, followership and neutrality among companies: A random matrix approach
NASA Astrophysics Data System (ADS)
Mobarhan, N. S. Safavi; Saeedi, A.; Roodposhti, F. Rahnamay; Jafari, G. R.
2016-11-01
In this article, we analyze the cross-correlation between returns of different stocks to answer the following important questions. The first one is: If there exists collective behavior in a financial market, how could we detect it? And the second question is: Is there a particular company among the companies of a market as the leader of the collective behavior? Or is there no specified leadership governing the system similar to some complex systems? We use the method of random matrix theory to answer the mentioned questions. Cross-correlation matrix of index returns of four different markets is analyzed. The participation ratio quantity related to each matrices' eigenvectors and the eigenvalue spectrum is calculated. We introduce shuffled-matrix created of cross correlation matrix in such a way that the elements of the later one are displaced randomly. Comparing the participation ratio quantities obtained from a correlation matrix of a market and its related shuffled-one, on the bulk distribution region of the eigenvalues, we detect a meaningful deviation between the mentioned quantities indicating the collective behavior of the companies forming the market. By calculating the relative deviation of participation ratios, we obtain a measure to compare the markets according to their collective behavior. Answering the second question, we show there are three groups of companies: The first group having higher impact on the market trend called leaders, the second group is followers and the third one is the companies who have not a considerable role in the trend. The results can be utilized in portfolio construction.
NASA Astrophysics Data System (ADS)
Duarte-Filho, G. C.; Macedo-Junior, A. F.; Macêdo, A. M. S.
2007-08-01
We introduce a random-matrix description of full counting statistics of charge transfer through a quantum mesoscopic system at finite temperature in the presence two nonideal contacts. Using the exact map between random-matrix theory and the supersymmetric nonlinear σ model, we demonstrate, via explicit calculations, that the saddle-point equation, derived by applying the variational principle to the supersymmetric action, can be cast in the form of the two-terminal version of Nazarov’s circuit theory, thus giving it the status of a controlled approximation. For the case in which the mesoscopic system is a quantum dot at zero temperature, this circuit theory has recently been shown [A. L. R. Barbosa and A. M. S. Macêdo, Phys. Rev. B 71, 235307 (2005)] to reproduce exactly the asymptotic semiclassical limit of the Poisson kernel in perfect agreement with a diagrammatic approach for averaging over the unitary group. We report applications of our formalism to the description of charge transfer through a quantum dot, a quantum chain, and a quantum wire. We also discuss the role of different symmetry classes (orthogonal, unitary, and symplectic) and show how to use known exact connections between the supersymmetric nonlinear σ model and random scattering matrix theories to perform both perturbative and nonperturbative calculations. We believe that our results will help unify the various approaches being currently used in mesoscopic physics of hybrid devices within a single physically sound and mathematically rigorous theoretical scheme.
Hofmann, Douglas C.; Suh, Jin-Yoo; Wiest, Aaron; Lind, Mary-Laura; Demetriou, Marios D.; Johnson, William L.
2008-01-01
The mechanical properties of bulk metallic glasses (BMGs) and their composites have been under intense investigation for many years, owing to their unique combination of high strength and elastic limit. However, because of their highly localized deformation mechanism, BMGs are typically considered to be brittle materials and are not suitable for structural applications. Recently, highly-toughened BMG composites have been created in a Zr–Ti-based system with mechanical properties comparable with high-performance crystalline alloys. In this work, we present a series of low-density, Ti-based BMG composites with combinations of high strength, tensile ductility, and excellent fracture toughness. PMID:19074287
NASA Astrophysics Data System (ADS)
Kuijlaars, A. B. J.
2001-08-01
The asymptotic behavior of polynomials that are orthogonal with respect to a slowly decaying weight is very different from the asymptotic behavior of polynomials that are orthogonal with respect to a Freud-type weight. While the latter has been extensively studied, much less is known about the former. Following an earlier investigation into the zero behavior, we study here the asymptotics of the density of states in a unitary ensemble of random matrices with a slowly decaying weight. This measure is also naturally connected with the orthogonal polynomials. It is shown that, after suitable rescaling, the weak limit is the same as the weak limit of the rescaled zeros.
Garcia-Aldea, David; Alvarellos, J. E.
2008-02-15
We propose a kinetic energy density functional scheme with nonlocal terms based on the von Weizsaecker functional, instead of the more traditional approach where the nonlocal terms have the structure of the Thomas-Fermi functional. The proposed functionals recover the exact kinetic energy and reproduce the linear response function of homogeneous electron systems. In order to assess their quality, we have tested the total kinetic energies as well as the kinetic energy density for atoms. The results show that these nonlocal functionals give as good results as the most sophisticated functionals in the literature. The proposed scheme for constructing the functionals means a step ahead in the field of fully nonlocal kinetic energy functionals, because they are capable of giving better local behavior than the semilocal functionals, yielding at the same time accurate results for total kinetic energies. Moreover, the functionals enjoy the possibility of being evaluated as a single integral in momentum space if an adequate reference density is defined, and then quasilinear scaling for the computational cost can be achieved.
A new approach on seismic mortality estimations based on average population density
NASA Astrophysics Data System (ADS)
Zhu, Xiaoxin; Sun, Baiqing; Jin, Zhanyong
2016-12-01
This study examines a new methodology to predict the final seismic mortality from earthquakes in China. Most studies established the association between mortality estimation and seismic intensity without considering the population density. In China, however, the data are not always available, especially when it comes to the very urgent relief situation in the disaster. And the population density varies greatly from region to region. This motivates the development of empirical models that use historical death data to provide the path to analyze the death tolls for earthquakes. The present paper employs the average population density to predict the final death tolls in earthquakes using a case-based reasoning model from realistic perspective. To validate the forecasting results, historical data from 18 large-scale earthquakes occurred in China are used to estimate the seismic morality of each case. And a typical earthquake case occurred in the northwest of Sichuan Province is employed to demonstrate the estimation of final death toll. The strength of this paper is that it provides scientific methods with overall forecast errors lower than 20 %, and opens the door for conducting final death forecasts with a qualitative and quantitative approach. Limitations and future research are also analyzed and discussed in the conclusion.
A reduced rank approach for covariance matrix estimation in EEG signal classification.
Tomida, Naoki; Yamagishi, Masao; Yamada, Isao; Tanaka, Toshihisa
2014-01-01
Common Spatial Pattern (CSP) methods are widely used to extract the brain activity for brain machine interfacing (BMI) based on electroencephalogram (EEG). For each mental task, CSP methods estimate a covariance matrix of EEG signals and adopt the uniform average of the sample covariance matrices over trials. However, the uniform average is sensitive to outliers caused by e.g. unrelated brain activity. In this paper, we propose an improvement of the estimated covariance matrix utilized in CSP methods by reducing the influence of the outliers as well as guaranteeing positive definiteness. More precisely, our estimation is the projection of the uniform average onto the intersection of two convex sets: the first set is a special reduced dimensional subspace which alleviates the influence of the outliers; the second is the positive definite cone. A numerical experiment supports the effectiveness of the proposed technique.
Quantum-statistical T-matrix approach to line broadening of hydrogen in dense plasmas
Lorenzen, Sonja; Wierling, August; Roepke, Gerd; Reinholz, Heidi; Zammit, Mark C.; Fursa, Dmitry V.; Bray, Igor
2010-10-29
The electronic self-energy {Sigma}{sup e} is an important input in a quantum-statistical theory for spectral line profile calculations. It describes the influence of plasma electrons on bound state properties. In dense plasmas, the effect of strong, i.e. close, electron-emitter collisions can be considered by three-particle T-matrix diagrams. These digrams are approximated with the help of an effective two-particle T-matrix, which is obtained from convergent close-coupling calculations with Debye screening. A comparison with other theories is carried out for the 2p level of hydrogen at k{sub B}T = 1 eV and n{sub e} = 2{center_dot}10{sup 23} m{sup -3}, and results are given for n{sub e} = 1{center_dot}10{sup 25} m{sup -3}.
Majumdar, Angshul; Gogna, Anupriya; Ward, Rabab
2014-08-25
We address the problem of acquiring and transmitting EEG signals in Wireless Body Area Networks (WBAN) in an energy efficient fashion. In WBANs, the energy is consumed by three operations: sensing (sampling), processing and transmission. Previous studies only addressed the problem of reducing the transmission energy. For the first time, in this work, we propose a technique to reduce sensing and processing energy as well: this is achieved by randomly under-sampling the EEG signal. We depart from previous Compressed Sensing based approaches and formulate signal recovery (from under-sampled measurements) as a matrix completion problem. A new algorithm to solve the matrix completion problem is derived here. We test our proposed method and find that the reconstruction accuracy of our method is significantly better than state-of-the-art techniques; and we achieve this while saving sensing, processing and transmission energy. Simple power analysis shows that our proposed methodology consumes considerably less power compared to previous CS based techniques.
The local projection in the density functional theory plus U approach: A critical assessment.
Wang, Yue-Chao; Chen, Ze-Hua; Jiang, Hong
2016-04-14
Density-functional theory plus the Hubbard U correction (DFT + U) method is widely used in first-principles studies of strongly correlated systems, as it can give qualitatively (and sometimes, semi-quantitatively) correct description of energetic and structural properties of many strongly correlated systems with similar computational cost as local density approximation or generalized gradient approximation. On the other hand, the DFT + U approach is limited both theoretically and practically in several important aspects. In particular, the results of DFT + U often depend on the choice of local orbitals (the local projection) defining the subspace in which the Hubbard U correction is applied. In this work we have systematically investigated the issue of the local projection by considering typical transition metal oxides, β-MnO2 and MnO, and comparing the results obtained from different implementations of DFT + U. We found that the choice of the local projection has significant effects on the DFT + U results, which are more significant for systems with stronger covalent bonding (e.g., MnO2) than those with more ionic bonding (e.g., MnO). These findings can help to clarify some confusion arising from the practical use of DFT + U and may also provide insights for the development of new first-principles approaches beyond DFT + U.
NASA Astrophysics Data System (ADS)
Kastening, Boris
2002-11-01
A recent simplified transfer matrix solution of the two-dimensional Ising model on a square lattice with periodic boundary conditions is generalized to periodic-antiperiodic, antiperiodic-periodic, and antiperiodic-antiperiodic boundary conditions. It is suggested to employ linear combinations of the resulting partition functions to investigate finite-size scaling. An exact relation of such a combination to the partition function corresponding to Brascamp-Kunz boundary conditions is found.
Exploring Eddy-Covariance Measurements Using a Spatial Approach: The Eddy Matrix
NASA Astrophysics Data System (ADS)
Engelmann, Christian; Bernhofer, Christian
2016-10-01
Taylor's frozen turbulence hypothesis states that "standard" eddy-covariance measurements of fluxes at a fixed location can replace a spatial ensemble of instantaneous values at multiple locations. For testing this hypothesis, a unique turbulence measurement set-up was used for two measurement campaigns over desert (Namibia) and grassland (Germany) in 2012. This "Eddy Matrix" combined nine ultrasonic anemometer-thermometers and 17 thermocouples in a 10 m × 10 m regular grid with 2.5-m grid distance. The instantaneous buoyancy flux derived from the spatial eddy covariance of the Eddy Matrix was highly variable in time (from -0.3 to 1 m K s^{-1}). However, the 10-min average reflected 83 % of the reference eddy-covariance flux with a good correlation. By introducing a combined eddy-covariance method (the spatial eddy covariance plus the additional flux of the temporal eddy covariance of the spatial mean values), the mean flux increases by 9 % relative to the eddy-covariance reference. Considering the typical underestimation of fluxes by the standard eddy-covariance method, this is seen as an improvement. Within the limits of the Eddy Matrix, Taylor's hypothesis is supported by the results.
Metric-space approach to potentials and its relevance to density-functional theory
NASA Astrophysics Data System (ADS)
Sharp, P. M.; D'Amico, I.
2016-12-01
External potentials play a crucial role in modeling quantum systems, since, for a given interparticle interaction, they define the system Hamiltonian. We use the metric-space approach to quantum mechanics to derive, from the energy conservation law, two natural metrics for potentials. We show that these metrics are well defined for physical potentials, regardless of whether the system is in an eigenstate or if the potential is bounded. In addition, we discuss the gauge freedom of potentials and how to ensure that the metrics preserve physical relevance. Our metrics for potentials, together with the metrics for wave functions and densities from I. D'Amico et al. [Phys. Rev. Lett. 106, 050401 (2011), 10.1103/PhysRevLett.106.050401] paves the way for a comprehensive study of the two fundamental theorems of density-functional theory. We explore these by analyzing two many-body systems for which the related exact Kohn-Sham systems can be derived. First we consider the information provided by each of the metrics, and we find that the density metric performs best in distinguishing two many-body systems. Next we study for the systems at hand the one-to-one relationships among potentials, ground-state wave functions, and ground-state densities defined by the Hohenberg-Kohn theorem as relationships in metric spaces. We find that, in metric space, these relationships are monotonic and incorporate regions of linearity, at least for the systems considered. Finally, we use the metrics for wave functions and potentials in order to assess quantitatively how close the many-body and Kohn-Sham systems are: We show that, at least for the systems analyzed, both metrics provide a consistent picture, and for large regions of the parameter space the error in approximating the many-body wave function with the Kohn-Sham wave function lies under a threshold of 10%.
Rao, Rekha R.; Mondy, Lisa Ann; Noble, David R.; Brunini, Victor; Roberts, Christine Cardinal; Long, Kevin Nicholas; Soehnel, Melissa Marie; Celina, Mathias C.; Wyatt, Nicholas B.; Thompson, Kyle R.; Tinsley, James
2015-09-01
We are studying PMDI polyurethane with a fast catalyst, such that filling and polymerization occur simultaneously. The foam is over-packed to tw ice or more of its free rise density to reach the density of interest. Our approach is to co mbine model development closely with experiments to discover new physics, to parameterize models and to validate the models once they have been developed. The model must be able to repres ent the expansion, filling, curing, and final foam properties. PMDI is chemically blown foam, wh ere carbon dioxide is pr oduced via the reaction of water and isocyanate. The isocyanate also re acts with polyol in a competing reaction, which produces the polymer. A new kinetic model is developed and implemented, which follows a simplified mathematical formalism that decouple s these two reactions. The model predicts the polymerization reaction via condensation chemis try, where vitrification and glass transition temperature evolution must be included to correctly predict this quantity. The foam gas generation kinetics are determined by tracking the molar concentration of both water and carbon dioxide. Understanding the therma l history and loads on the foam due to exothermicity and oven heating is very important to the results, since the kinetics and ma terial properties are all very sensitive to temperature. The conservation eq uations, including the e quations of motion, an energy balance, and thr ee rate equations are solved via a stabilized finite element method. We assume generalized-Newtonian rheology that is dependent on the cure, gas fraction, and temperature. The conservation equations are comb ined with a level set method to determine the location of the free surface over time. Results from the model are compared to experimental flow visualization data and post-te st CT data for the density. Seve ral geometries are investigated including a mock encapsulation part, two configur ations of a mock stru ctural part, and a bar geometry to
Warner, G P; Hubbard, H L; Lloyd, G C; Wuthier, R E
1983-05-01
Matrix vesicle-enriched fractions were isolated from different zones of epiphyseal cartilage by nonenzymatic methods involving tissue homogenization, differential centrifugation, and isosmotic Percoll gradient fractionation. Uptakes of both 32Pi and 45Ca were studied concomitantly over periods from 20 min to 24 h. Percoll density gradients separated epiphyseal microsomes into two alkaline phosphatase-rich fractions: a low-density noncalcifiable fraction (P-I), and a higher-density fraction (P-II) which readily mineralized. The P-II fraction was found only in calcifying regions of the growth plate. Based on chemical and physical properties and enzyme activities, both fractions were similar except that P-II contained significantly higher levels of mineral ions than did P-I, and had lower levels of alkaline phosphatase. The mineral appeared to be primarily in a noncrystalline form. Metabolism of 32Pi and 45Ca by P-II followed a complex kinetic pattern in which accumulation of large amounts of both ions was preceded by an initial limited burst of uptake and a lag-phase of variable duration. During mineral ion loading, the density of the P-II fraction progressively increased as evidenced by co-migration of 45Ca, 32Pi, and alkaline phosphatase to increasingly higher densities. During the period of early mineral deposition (1-5 h), Ca/P uptake ratios were very low (1.0-1.2) and X-ray diffraction patterns showed a predominantly amorphous pattern. This suggests that the mineral accumulated in matrix vesicles is initially some form of noncrystalline calcium monohydrogenphosphate. L-tetramisole, a potent inhibitor of alkaline phosphatase, inhibited accumulation of both 45Ca and 32Pi in the absence of organic P substrates, 32Pi being preferentially inhibited over 45Ca. This finding, coupled with recent studies on the behavior of alkaline phosphatase at physiological pH, suggests that the protein is not acting as a phosphohydrolase, but rather as a Pi-binding or transport agent
Ponzoni, Chiara; Lancellotti, Isabella; Barbieri, Luisa; Spinella, Alberto; Saladino, Maria Luisa; Martino, Delia Chillura; Caponetti, Eugenio; Armetta, Francesco; Leonelli, Cristina
2015-04-09
A class of inorganic binders, also known as geopolymers, can be obtained by alkali activation of aluminosilicate powders at room temperature. The process is affected by many parameters (curing time, curing temperature, relative humidity etc.) and leads to a resistant matrix usable for inertization of hazardous waste. In this study an industrial liquid waste containing a high amount of chromium (≈ 2.3 wt%) in the form of metalorganic salts is inertized into a metakaolin based geopolymer matrix. One of the innovative aspects is the exploitation of the water contained in the waste for the geopolymerization process. This avoided any drying treatment, a common step in the management of liquid hazardous waste. The evolution of the process--from the precursor dissolution to the final geopolymer matrix hardening--of different geopolymers containing a waste amount ranging from 3 to 20%wt and their capability to inertize chromium cations were studied by: i) the leaching tests, according to the EN 12,457 regulation, at different curing times (15, 28, 90 and 540 days) monitoring releases of chromium ions (Cr(III) and Cr(VI)) and the cations constituting the aluminosilicate matrix (Na, Si, Al); ii) the humidity variation for different curing times (15 and 540 days); iii) SEM characterization at different curing times (28 and 540 days); iv) the trend of the solution conductivity and pH during the leaching test; v) the characterization of the short-range ordering in terms of TOT bonds (where T is Al or Si) by (29)Si and (27)Al solid state magic-angle spinning nuclear magnetic resonance (ss MAS NMR) for geopolymers containing high amounts of waste (10-20%wt). The results show the formation of a stable matrix after only 15 days independently on the waste amount introduced; the longer curing times increase the matrices stabilities and their ability to immobilize chromium cations. The maximum amount of waste that can be inertized is around 10 wt% after a curing time of 28 days.
Tanahashi, Kuniaki; Natsume, Atsushi; Ohka, Fumiharu; Motomura, Kazuya; Alim, Adiljan; Tanaka, Ichidai; Senga, Takeshi; Harada, Ichiro; Fukuyama, Ryuichi; Sumiyoshi, Naoyuki; Sekido, Yoshitaka; Wakabayashi, Toshihiko
2015-07-01
The NF2 gene product Merlin is a protein containing ezrin, radixin, and moesin domains; it is a member of the 4.1 protein superfamily associated with the membrane cytoskeleton and also interacts with cell surface molecules. The mammalian Hippo cascade, a downstream signaling cascade of merlin, inactivates the Yes-associated protein (YAP). Yes-associated protein is activated by loss of the NF2 gene and functions as an oncogene in meningioma cells; however, the factors controlling YAP expression, phosphorylation, and subcellular localization in meningiomas have not been fully elucidated. Here, we demonstrate that merlin expression is heterogeneous in 1 NF2 gene-negative and 3 NF2 gene-positive World Health Organization grade I meningiomas. In the NF2 gene-positive meningiomas, regions with low levels of merlin (tumor rims) had greater numbers of cells with nuclear YAP versus regions with high merlin levels (tumor cores). Merlin expression and YAP phosphorylation were also affected by cell density in the IOMM-Lee and HKBMM human meningioma cell lines; nuclear localization of YAP was regulated by cell density and extracellular matrix (ECM) stiffness in IOMM-Lee cells. These results suggest that cell density and ECM stiffness may contribute to the heterogeneous loss of merlin and increased nuclear YAP expression in human meningiomas.
Das, Mousumi
2010-05-21
We studied the nature of the ground and low-lying excited states of poly-fused thiophene oligomers within long-range Pariser-Parr-Pople (PPP) model Hamiltonian with up to 14 monomers using symmetrized density matrix renormalization group technique. Our results show that the lowest dipole-allowed state lies below the lowest dipole forbidden two-photon state, indicating that poly-fused thiophenes are strongly fluorescent. The lowest triplet state lies below the two-photon state, which is in agreement with the general trend in conjugated polymers. The charge density and bond order calculations of three low-lying excited states, along with the ground state of fused thiophene oligomers, show a significant transfer of charge from sulfur to adjacent carbon atom in the middle of the largest system size and these excitations are localized. The charge density and bond order calculations on singly and doubly doped states show that bipolarons are not stable entity in these systems. The calculations of low-lying excitations on radical cation and anion of fused thiophene oligomers show a new energy band in the low energy region, which is strongly coupled to its hole and electron conductivity. This implies that poly-fused thiophenes posses novel field-effect transistor properties.
Time-dependent analytical R-matrix approach for strong-field dynamics. I. One-electron systems
NASA Astrophysics Data System (ADS)
Torlina, Lisa; Smirnova, Olga
2012-10-01
We develop a flexible analytical approach to describe strong-field dynamics in atoms and molecules. The approach is based on the ideas of the R-matrix method. Here, we illustrate and validate our approach by applying it to systems with one active electron bound by the Coulomb potential and benchmark our results against the standard theory of Perelomov, Popov, and Terent'ev [Sov. Phys. JETP0021-903710.1007/BF01132710 23, 924 (1966)]. We discuss corrections to the ionization amplitude associated with the interplay of the Coulomb potential and the laser field on the sub-laser cycle time scale and the shape of the tunneling wave packets associated with different instants of ionization.
Zhang, Yachao
2014-12-07
A first-principles study of critical temperatures (T{sub c}) of spin crossover (SCO) materials requires accurate description of the strongly correlated 3d electrons as well as much computational effort. This task is still a challenge for the widely used local density or generalized gradient approximations (LDA/GGA) and hybrid functionals. One remedy, termed density functional theory plus U (DFT+U) approach, introduces a Hubbard U term to deal with the localized electrons at marginal computational cost, while treats the delocalized electrons with LDA/GGA. Here, we employ the DFT+U approach to investigate the T{sub c} of a pair of iron(II) SCO molecular crystals (α and β phase), where identical constituent molecules are packed in different ways. We first calculate the adiabatic high spin-low spin energy splitting ΔE{sub HL} and molecular vibrational frequencies in both spin states, then obtain the temperature dependent enthalpy and entropy changes (ΔH and ΔS), and finally extract T{sub c} by exploiting the ΔH/T − T and ΔS − T relationships. The results are in agreement with experiment. Analysis of geometries and electronic structures shows that the local ligand field in the α phase is slightly weakened by the H-bondings involving the ligand atoms and the specific crystal packing style. We find that this effect is largely responsible for the difference in T{sub c} of the two phases. This study shows the applicability of the DFT+U approach for predicting T{sub c} of SCO materials, and provides a clear insight into the subtle influence of the crystal packing effects on SCO behavior.
NASA Astrophysics Data System (ADS)
Zhang, Yachao
2014-12-01
A first-principles study of critical temperatures (Tc) of spin crossover (SCO) materials requires accurate description of the strongly correlated 3d electrons as well as much computational effort. This task is still a challenge for the widely used local density or generalized gradient approximations (LDA/GGA) and hybrid functionals. One remedy, termed density functional theory plus U (DFT+U) approach, introduces a Hubbard U term to deal with the localized electrons at marginal computational cost, while treats the delocalized electrons with LDA/GGA. Here, we employ the DFT+U approach to investigate the Tc of a pair of iron(II) SCO molecular crystals (α and β phase), where identical constituent molecules are packed in different ways. We first calculate the adiabatic high spin-low spin energy splitting ΔEHL and molecular vibrational frequencies in both spin states, then obtain the temperature dependent enthalpy and entropy changes (ΔH and ΔS), and finally extract Tc by exploiting the ΔH/T - T and ΔS - T relationships. The results are in agreement with experiment. Analysis of geometries and electronic structures shows that the local ligand field in the α phase is slightly weakened by the H-bondings involving the ligand atoms and the specific crystal packing style. We find that this effect is largely responsible for the difference in Tc of the two phases. This study shows the applicability of the DFT+U approach for predicting Tc of SCO materials, and provides a clear insight into the subtle influence of the crystal packing effects on SCO behavior.
Zhang, Yachao
2014-12-07
A first-principles study of critical temperatures (T(c)) of spin crossover (SCO) materials requires accurate description of the strongly correlated 3d electrons as well as much computational effort. This task is still a challenge for the widely used local density or generalized gradient approximations (LDA/GGA) and hybrid functionals. One remedy, termed density functional theory plus U (DFT+U) approach, introduces a Hubbard U term to deal with the localized electrons at marginal computational cost, while treats the delocalized electrons with LDA/GGA. Here, we employ the DFT+U approach to investigate the T(c) of a pair of iron(II) SCO molecular crystals (α and β phase), where identical constituent molecules are packed in different ways. We first calculate the adiabatic high spin-low spin energy splitting ΔE(HL) and molecular vibrational frequencies in both spin states, then obtain the temperature dependent enthalpy and entropy changes (ΔH and ΔS), and finally extract T(c) by exploiting the ΔH/T - T and ΔS - T relationships. The results are in agreement with experiment. Analysis of geometries and electronic structures shows that the local ligand field in the α phase is slightly weakened by the H-bondings involving the ligand atoms and the specific crystal packing style. We find that this effect is largely responsible for the difference in T(c) of the two phases. This study shows the applicability of the DFT+U approach for predicting T(c) of SCO materials, and provides a clear insight into the subtle influence of the crystal packing effects on SCO behavior.
Rogers, Caitlyn A; Stockham, Peter C; Nash, Christine M; Martin, Sheridan M; Kostakis, Chris; Lenehan, Claire E
2016-03-01
We report the use of auto-sampler programmable functions to co-inject analyte standard solution and matrix extract to assess ion enhancement and suppression (matrix effects) in LC-MS. This is effectively an automated post-extraction addition (APEA) procedure, emulating the manual post-extraction addition (PEA) approach widely adopted for assessment of matrix effects. To verify that APEA was comparable to the conventional PEA approach, matrix effects were determined using both methods for a selection of 31 illicit and pharmaceutical drugs in 10 different human urine extracts. Matrix effects measured using APEA were statistically indistinguishable from manual PEA methodology for 27 of the 31 drugs. Of the four drugs that showed significant differences using the two methods, three differed by less than 2 %, which is within the expected accuracy limits required for matrix effect determinations. The remaining analyte, trimeprazine, was found to degrade in the spiked PEA matrix extract, accounting for the difference between matrix effects measured by the PEA and APEA approaches. APEA enables a single matrix extract to be assessed at multiple analyte concentrations, resulting in a considerable reduction in sample preparation time. In addition, APEA can reduce the quantity of analyte-free sample matrix required for matrix effect assessment, which is an important consideration in certain analytical and bioanalytical fields. This work shows that APEA may be considered as an acceptable alternative to PEA for the assessment of matrix effects in LC-MS method validation and may be applicable to a variety of matrices such as environmental samples.
Superstatistical random-matrix-theory approach to transition intensities in mixed systems.
Abul-Magd, A Y
2006-05-01
We study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory, which is based on Beck and Cohen's superstatistics. We obtain an analytic expression for the distribution of the reduced transition probabilities that applies to systems undergoing a transition out of chaos. The obtained distribution fits the results of a previous nuclear shell model calculations for some electromagnetic transitions that deviate from the Porter-Thomas distribution. It agrees with the experimental reduced transition probabilities for the nucleus better than the commonly used chi(2) distribution.
Random matrix approach to collective behavior and bulk universality in protein dynamics.
Potestio, Raffaello; Caccioli, Fabio; Vivo, Pierpaolo
2009-12-31
Covariance matrices of amino acid displacements, commonly used to characterize the large-scale movements of proteins, are investigated through the prism of random matrix theory. Bulk universality is detected in the local spacing statistics of noise-dressed eigenmodes, which is well described by a Brody distribution with parameter beta approximately = 0.8. This finding, supported by other consistent indicators, implies a novel quantitative criterion to single out the collective degrees of freedom of the protein from the majority of high-energy, localized vibrations.
Developing a Health Information Technology Systems Matrix: A Qualitative Participatory Approach
Chavez, Margeaux; Nazi, Kim M; Antinori, Nicole
2016-01-01
Background The US Department of Veterans Affairs (VA) has developed various health information technology (HIT) resources to provide accessible veteran-centered health care. Currently, the VA is undergoing a major reorganization of VA HIT to develop a fully integrated system to meet consumer needs. Although extensive system documentation exists for various VA HIT systems, a more centralized and integrated perspective with clear documentation is needed in order to support effective analysis, strategy, planning, and use. Such a tool would enable a novel view of what is currently available and support identifying and effectively capturing the consumer’s vision for the future. Objective The objective of this study was to develop the VA HIT Systems Matrix, a novel tool designed to describe the existing VA HIT system and identify consumers’ vision for the future of an integrated VA HIT system. Methods This study utilized an expert panel and veteran informant focus groups with self-administered surveys. The study employed participatory research methods to define the current system and understand how stakeholders and veterans envision the future of VA HIT and interface design (eg, look, feel, and function). Directed content analysis was used to analyze focus group data. Results The HIT Systems Matrix was developed with input from 47 veterans, an informal caregiver, and an expert panel to provide a descriptive inventory of existing and emerging VA HIT in four worksheets: (1) access and function, (2) benefits and barriers, (3) system preferences, and (4) tasks. Within each worksheet is a two-axis inventory. The VA’s existing and emerging HIT platforms (eg, My HealtheVet, Mobile Health, VetLink Kiosks, Telehealth), My HealtheVet features (eg, Blue Button, secure messaging, appointment reminders, prescription refill, vet library, spotlight, vitals tracker), and non-VA platforms (eg, phone/mobile phone, texting, non-VA mobile apps, non-VA mobile electronic devices, non
NASA Astrophysics Data System (ADS)
Sanchez, Dario F.; Marmitt, Gabriel; Marin, Cristiane; Baptista, Daniel L.; de M. Azevedo, Gustavo; Grande, Pedro L.; Fichtner, Paulo F. P.
2013-12-01
In this work we demonstrate that Medium Energy Ion Scattering (MEIS) measurements in combination with Transmission Electron Microscopy (TEM) or Grazing Incidence Small Angle X-Ray Scattering (GISAXS) can provide a complete characterization of nanoparticle (NP) systems embedded into dielectric films. This includes the determination of the nanoparticle characteristics (location, size distribution and number concentration) as well as the depth distribution and concentration of the NP atomic components dispersed in the matrix. Our studies are performed considering a model case system consisting of planar arrangements of Au NPs (size range from 1 to 10 nm) containing three distinct Au concentrations embedded in a SiO2 film.
ERIC Educational Resources Information Center
Sousa, Joao Carlos; Costa, Manuel Joao; Palha, Joana Almeida
2010-01-01
The biochemistry and molecular biology of the extracellular matrix (ECM) is difficult to convey to students in a classroom setting in ways that capture their interest. The understanding of the matrix's roles in physiological and pathological conditions study will presumably be hampered by insufficient knowledge of its molecular structure.…
NASA Astrophysics Data System (ADS)
Zheng, Bo-Xiao; Kretchmer, Joshua S.; Shi, Hao; Zhang, Shiwei; Chan, Garnet Kin-Lic
2017-01-01
We investigate the cluster size convergence of the energy and observables using two forms of density matrix embedding theory (DMET): the original cluster form (CDMET) and a new formulation motivated by the dynamical cluster approximation (DCA-DMET). Both methods are applied to the half-filled one- and two-dimensional Hubbard models using a sign-problem free auxiliary-field quantum Monte Carlo impurity solver, which allows for the treatment of large impurity clusters of up to 100 sites. While CDMET is more accurate at smaller impurity cluster sizes, DCA-DMET exhibits faster asymptotic convergence towards the thermodynamic limit. We use our two formulations to produce new accurate estimates for the energy and local moment of the two-dimensional Hubbard model for U /t =2 ,4 ,6 . These results compare favorably with the best data available in the literature, and help resolve earlier uncertainties in the moment for U /t =2 .
PWA with full rank density matrix of the π+π-π- and π-π0π0 systems at VES setup
NASA Astrophysics Data System (ADS)
Kachaev, Igor; Ryabchikov, Dmitry
2016-11-01
Partial Wave Analysis of the π+π-π- and π-π0π0 final states produced by 29GeV/c π- beam on beryllium target is presented. About 42 · 106 events for the first system and 22 · 106 events for the second one are collected with VES setup. The statistics for 3π neutral is known to be the largest in the world while statistics for 3π charged is next to largest. The t' range for the analysis is 0 < |t'| < 0.8 GeV2/c2. The data are analysed using formalism of full rank density matrix. The comparison of the analysis results for two systems is presented.
Mazziotti, David A
2016-10-07
A central challenge of physics is the computation of strongly correlated quantum systems. The past ten years have witnessed the development and application of the variational calculation of the two-electron reduced density matrix (2-RDM) without the wave function. In this Letter we present an orders-of-magnitude improvement in the accuracy of 2-RDM calculations without an increase in their computational cost. The advance is based on a low-rank, dual formulation of an important constraint on the 2-RDM, the T2 condition. Calculations are presented for metallic chains and a cadmium-selenide dimer. The low-scaling T2 condition will have significant applications in atomic and molecular, condensed-matter, and nuclear physics.
NASA Astrophysics Data System (ADS)
Mazziotti, David A.
2016-10-01
A central challenge of physics is the computation of strongly correlated quantum systems. The past ten years have witnessed the development and application of the variational calculation of the two-electron reduced density matrix (2-RDM) without the wave function. In this Letter we present an orders-of-magnitude improvement in the accuracy of 2-RDM calculations without an increase in their computational cost. The advance is based on a low-rank, dual formulation of an important constraint on the 2-RDM, the T 2 condition. Calculations are presented for metallic chains and a cadmium-selenide dimer. The low-scaling T 2 condition will have significant applications in atomic and molecular, condensed-matter, and nuclear physics.
Fogel, Paul; Gaston-Mathé, Yann; Hawkins, Douglas; Fogel, Fajwel; Luta, George; Young, S. Stanley
2016-01-01
Often data can be represented as a matrix, e.g., observations as rows and variables as columns, or as a doubly classified contingency table. Researchers may be interested in clustering the observations, the variables, or both. If the data is non-negative, then Non-negative Matrix Factorization (NMF) can be used to perform the clustering. By its nature, NMF-based clustering is focused on the large values. If the data is normalized by subtracting the row/column means, it becomes of mixed signs and the original NMF cannot be used. Our idea is to split and then concatenate the positive and negative parts of the matrix, after taking the absolute value of the negative elements. NMF applied to the concatenated data, which we call PosNegNMF, offers the advantages of the original NMF approach, while giving equal weight to large and small values. We use two public health datasets to illustrate the new method and compare it with alternative clustering methods, such as K-means and clustering methods based on the Singular Value Decomposition (SVD) or Principal Component Analysis (PCA). With the exception of situations where a reasonably accurate factorization can be achieved using the first SVD component, we recommend that the epidemiologists and environmental scientists use the new method to obtain clusters with improved quality and interpretability. PMID:27213413
Fogel, Paul; Gaston-Mathé, Yann; Hawkins, Douglas; Fogel, Fajwel; Luta, George; Young, S Stanley
2016-05-18
Often data can be represented as a matrix, e.g., observations as rows and variables as columns, or as a doubly classified contingency table. Researchers may be interested in clustering the observations, the variables, or both. If the data is non-negative, then Non-negative Matrix Factorization (NMF) can be used to perform the clustering. By its nature, NMF-based clustering is focused on the large values. If the data is normalized by subtracting the row/column means, it becomes of mixed signs and the original NMF cannot be used. Our idea is to split and then concatenate the positive and negative parts of the matrix, after taking the absolute value of the negative elements. NMF applied to the concatenated data, which we call PosNegNMF, offers the advantages of the original NMF approach, while giving equal weight to large and small values. We use two public health datasets to illustrate the new method and compare it with alternative clustering methods, such as K-means and clustering methods based on the Singular Value Decomposition (SVD) or Principal Component Analysis (PCA). With the exception of situations where a reasonably accurate factorization can be achieved using the first SVD component, we recommend that the epidemiologists and environmental scientists use the new method to obtain clusters with improved quality and interpretability.
Karami, Samaneh; Imani, Mohammad; Farahmandghavi, Farhid
2014-01-02
Nowadays, there is a lot of interest in developing long-acting drug delivery devices for human or veterinary applications including monolithic systems. Drug content uniformity of a monolithic device is highly dependent on the uniform distribution of drug particles within the polymeric matrix both in dispersion and distribution levels. Here, a range of formulations were prepared which consisted of progesterone (1%w/w) and estradiol benzoate (0.1%w/w) dispersed in a silicone rubber matrix. Blend uniformity of the compounds was analyzed by image analysis of SEM micrographs obtained from the cross-sections of the devices by a new image processing approach. Efficiency of mixing was investigated at the dispersion level by plotting the relative frequency of drug particles versus “projected area diameter” of their aggregates. Based on the particle size distribution results, a significant improvement was observed in the dispersion pattern of drug particles by adding silicone oil (9%w/w). Distribution pattern of the particles was investigated by transforming the micrographs into algebraic matrices. An “ideal matrix” was developed by assumption of uniform localization of the drug particles. Real matrices obtained for all of the formulations were compared with this ideal matrix as a reference. Closer similarity between the two matrices was observed for silicone oil-containing (9%w/w) samples showing the best dispersive and distributive mixing quality.
Huang, Yongfei; Zhao, Yanying; Zheng, Xuming; Zhou, Mingfei
2010-02-25
Reactions of scandium and yttrium monoxide molecules (ScO and YO) with monochloromethane have been studied in solid argon by infrared absorption spectroscopy and density functional theoretical calculations. The metal monoxide molecules were prepared by laser-evaporation of bulk metal oxide targets. The results show that the ground state scandium and yttrium monoxide molecules reacted with CH(3)Cl to form two MO(CH(3)Cl) (M = Sc, Y) complex isomers spontaneously on annealing. Broad-band UV-visible irradiation initiated the addition of the Cl-C bond to the M=O bond to form the CH(3)OMCl molecule and the addition of the C-H bond to the M=O bond to give the CH(2)ClMOH isomer, both of which are more stable than the MO(CH(3)Cl) complex structures. The CH(2)ClMOH molecule was predicted to involve agnostic interaction between the chlorine atom and the metal atom.
Pelzer, Kenley; Greenman, Loren; Gidofalvi, Gergely; Mazziotti, David A
2011-06-09
Polyaromatic hydrocarbons (PAHs) are a class of organic molecules with importance in several branches of science, including medicine, combustion chemistry, and materials science. The delocalized π-orbital systems in PAHs require highly accurate electronic structure methods to capture strong electron correlation. Treating correlation in PAHs has been challenging because (i) traditional wave function methods for strong correlation have not been applicable since they scale exponentially in the number of strongly correlated orbitals, and (ii) alternative methods such as the density-matrix renormalization group and variational two-electron reduced density matrix (2-RDM) methods have not been applied beyond linear acene chains. In this paper we extend the earlier results from active-space variational 2-RDM theory [Gidofalvi, G.; Mazziotti, D. A. J. Chem. Phys. 2008, 129, 134108] to the more general two-dimensional arrangement of rings--acene sheets--to study the relationship between geometry and electron correlation in PAHs. The acene-sheet calculations, if performed with conventional wave function methods, would require wave function expansions with as many as 1.5 × 10(17) configuration state functions. To measure electron correlation, we employ several RDM-based metrics: (i) natural-orbital occupation numbers, (ii) the 1-RDM von Neumann entropy, (iii) the correlation energy per carbon atom, and (iv) the squared Frobenius norm of the cumulant 2-RDM. The results confirm a trend of increasing polyradical character with increasing molecular size previously observed in linear PAHs and reveal a corresponding trend in two-dimensional (arch-shaped) PAHs. Furthermore, in PAHs of similar size they show significant variations in correlation with geometry. PAHs with the strictly linear geometry (chains) exhibit more electron correlation than PAHs with nonlinear geometries (sheets).
Pham, Thi-Thu-Hien; Lo, Yu-Lung
2012-09-01
An analytical technique based on Stokes polarimetry and the Mueller matrix method is proposed for extracting the effective linear birefringence, linear dichroism, circular birefringence, circular dichroism, linear depolarization, and circular depolarization properties of turbid media. In contrast to existing analytical models, the model proposed extracts the effective parameters in a decoupled manner and considers not only the circular dichroism properties of the sample, but also the depolarization properties. The results show that the proposed method enables all of the effective parameters to be measured over the full range. Moreover, it is shown that the extracted value of the depolarization index is unaffected by the order in which the depolarizing Mueller matrix is decomposed during the extraction procedure. Finally, a method is proposed for calibrating the optical rotation angle of a polystyrene microsphere suspension containing dissolved D-glucose (C6H12O6) powder in accordance with the distance between the sample and the detector. The experimental results show that the sensitivity of the resulting D-glucose measurement is equal to approximately 1.73 deg/M.
Agata, Yasuyoshi; Iwao, Yasunori; Shiino, Kai; Miyagishima, Atsuo; Itai, Shigeru
2011-07-29
To predict drug dissolution and understand the mechanisms of drug release from wax matrix dosage forms containing glyceryl monostearate (GM; a wax base), aminoalkyl methacrylate copolymer E (AMCE; a pH-dependent functional polymer), and acetaminophen (APAP; a model drug), we tried to derive a novel mathematical model with respect to erosion and diffusion theory. Our model exhibited good agreement with the whole set of experimentally obtained values pertaining to APAP release at pH 4.0 and pH 6.5. In addition, this model revealed that the eroding speed of wax matrices was strongly influenced by the loading content of AMCE, but not that of APAP, and that the diffusion coefficient increased as APAP loading decreased and AMCE loading increased, thus directly defining the physicochemical properties of erosion and diffusion. Therefore, this model might prove a useful equation for the precise prediction of dissolution and for understanding the mechanisms of drug release from wax matrix dosage forms.
A Density Functional Approach to Para-hydrogen at Zero Temperature
NASA Astrophysics Data System (ADS)
Ancilotto, Francesco; Barranco, Manuel; Navarro, Jesús; Pi, Marti
2016-10-01
We have developed a density functional (DF) built so as to reproduce either the metastable liquid or the solid equation of state of bulk para-hydrogen, as derived from quantum Monte Carlo zero temperature calculations. As an application, we have used it to study the structure and energetics of small para-hydrogen clusters made of up to N=40 molecules. We compare our results for liquid clusters with diffusion Monte Carlo (DMC) calculations and find a fair agreement between them. In particular, the transition found within DMC between hollow-core structures for small N values and center-filled structures at higher N values is reproduced. The present DF approach yields results for (pH_2)_N clusters indicating that for small N values a liquid-like character of the clusters prevails, while solid-like clusters are instead energetically favored for N ≥ 15.
NASA Astrophysics Data System (ADS)
Yan, Hua; Wu, Junyong; Dai, Guoliang; Zhong, Aiguo; Yang, Jianguo; Liang, Huading; Pan, Fuyou
2010-04-01
Spectroscopic approach and density functional theory (DFT) have been employed to investigate the interaction between melamine (MA) and bovine serum albumin (BSA). The UV absorption difference spectra show the MA-BSA complexes can form under physiological conditions. Furthermore, the B3LYP/6-311++G(d,p) calculations indicate that the protonated melamine (MAH +) bond to Asp, Glu, Asn, Gln, Ser, Thr amino acid residues or peptide groups via N sbnd H(MAH +)…O dbnd C(BSA) or N sbnd H(MAH +)…O sbnd C(BSA) hydrogen bonds, in agreement with the results of UV absorption difference spectra, and the interaction energies of them decrease in the order Asp, Glu > Pep > Asn, Gln > Ser, Thr. The fluorescence spectra, synchronous fluorescence spectra and FT-IR spectra demonstrate that this interaction has no obvious effect on the secondary structure of BSA.
Mixtures of ions and amphiphilic molecules in slit-like pores: A density functional approach
Pizio, O.; Rżysko, W. Sokołowski, S.; Sokołowska, Z.
2015-04-28
We investigate microscopic structure and thermodynamic properties of a mixture that contains amphiphilic molecules and charged hard spheres confined in slit-like pores with uncharged hard walls. The model and the density functional approach are the same as described in details in our previous work [Pizio et al., J. Chem. Phys. 140, 174706 (2014)]. Our principal focus is in exploring the effects brought by the presence of ions on the structure of confined amphiphilic particles. We have found that for some cases of anisotropic interactions, the change of the structure of confined fluids occurs via the first-order transitions. Moreover, if anions and cations are attracted by different hemispheres of amphiphiles, a charge at the walls appears at the zero value of the wall electrostatic potential. For a given thermodynamic state, this charge is an oscillating function of the pore width.
The late-type stellar density profile in the Galactic Center: A statistical approach
NASA Astrophysics Data System (ADS)
Chappell, S. N.; Ghez, A. M.; Do, T.; Martinez, G. D.; Yelda, S.; Sitarski, B. N.; Lu, J. R.; Morris, M. R.
2017-01-01
The late-type stellar population in the Galactic Center was first predicted to reside in a dynamically relaxed cusp (power law slope ranging from 3/2 to 7/4). However, other works - which rely on models to correct for projection effects - have suggested a flat distribution instead. The need for this correction is due to the lack of information regarding the line-of-sight distances. With a two decade long baseline in astrometric measurements, we are now able to measure significant projected radial accelerations, six of which are newly reported here, which directly constrain line-of-sight distances. Here we present a statistical approach to take advantage of this information and more accurately constrain the shape of the radial density profile of the late-type stellar population in the Galactic Center.
Springer, Nora L; Fischbach, Claudia
2016-08-01
Tumors are characterized by aberrant extracellular matrix (ECM) remodeling and chronic inflammation. While advances in biomaterials and tissue engineering strategies have led to important new insights regarding the role of ECM composition, structure, and mechanical properties in cancer in general, the functional link between these parameters and macrophage phenotype is poorly understood. Nevertheless, increasing experimental evidence suggests that macrophage behavior is similarly controlled by physicochemical properties of the ECM and consequential changes in mechanosignaling. Here, we will summarize the current knowledge of macrophage biology and ECM-mediated differences in mechanotransduction and discuss future opportunities of biomaterials and tissue engineering platforms to interrogate the functional relationship between these parameters and their relevance to cancer.
A micro to macro approach to polymer matrix composites damage modeling : final LDRD report.
English, Shawn Allen; Brown, Arthur A.; Briggs, Timothy M.
2013-12-01
Capabilities are developed, verified and validated to generate constitutive responses using material and geometric measurements with representative volume elements (RVE). The geometrically accurate RVEs are used for determining elastic properties and damage initiation and propagation analysis. Finite element modeling of the meso-structure over the distribution of characterizing measurements is automated and various boundary conditions are applied. Plain and harness weave composites are investigated. Continuum yarn damage, softening behavior and an elastic-plastic matrix are combined with known materials and geometries in order to estimate the macroscopic response as characterized by a set of orthotropic material parameters. Damage mechanics and coupling effects are investigated and macroscopic material models are demonstrated and discussed. Prediction of the elastic, damage, and failure behavior of woven composites will aid in macroscopic constitutive characterization for modeling and optimizing advanced composite systems.
An NDE Approach for Characterizing Quality Problems in Polymer Matrix Composites
NASA Technical Reports Server (NTRS)
Roth, Don J.; Baaklini, George Y.; Sutter, James K.; Bodis, James R.; Leonhardt, Todd A.; Crane, Elizabeth A.
1994-01-01
Polymer matrix composite (PMC) materials are periodically identified appearing optically uniform but containing a higher than normal level of global nonuniformity as indicated from preliminary ultrasonic scanning. One such panel was thoroughly examined by nondestructive (NDE) and destructive methods to quantitatively characterize the nonuniformity. The NDE analysis of the panel was complicated by the fact that the panel was not uniformly thick. Mapping of ultrasonic velocity across a region of the panel in conjunction with an error analysis was necessary to (1) characterize properly the porosity gradient that was discovered during destructive analyses and (2) account for the thickness variation effects. Based on this study, a plan for future NDE characterization of PMC's is presented to the PMC community.
Transfer matrix approach for the Kerr and Faraday rotation in layered nanostructures.
Széchenyi, Gábor; Vigh, Máté; Kormányos, Andor; Cserti, József
2016-09-21
To study the optical rotation of the polarization of light incident on multilayer systems consisting of atomically thin conductors and dielectric multilayers we present a general method based on transfer matrices. The transfer matrix of the atomically thin conducting layer is obtained using the Maxwell equations. We derive expressions for the Kerr (Faraday) rotation angle and for the ellipticity of the reflected (transmitted) light as a function of the incident angle and polarization of the light. The method is demonstrated by calculating the Kerr (Faraday) angle for bilayer graphene in the quantum anomalous Hall state placed on the top of dielectric multilayers. The optical conductivity of the bilayer graphene is calculated in the framework of a four-band model.
NASA Technical Reports Server (NTRS)
Rodriguez, G.; Kreutz, K.
1988-01-01
This report advances a linear operator approach for analyzing the dynamics of systems of joint-connected rigid bodies.It is established that the mass matrix M for such a system can be factored as M=(I+H phi L)D(I+H phi L) sup T. This yields an immediate inversion M sup -1=(I-H psi L) sup T D sup -1 (I-H psi L), where H and phi are given by known link geometric parameters, and L, psi and D are obtained recursively by a spatial discrete-step Kalman filter and by the corresponding Riccati equation associated with this filter. The factors (I+H phi L) and (I-H psi L) are lower triangular matrices which are inverses of each other, and D is a diagonal matrix. This factorization and inversion of the mass matrix leads to recursive algortihms for forward dynamics based on spatially recursive filtering and smoothing. The primary motivation for advancing the operator approach is to provide a better means to formulate, analyze and understand spatial recursions in multibody dynamics. This is achieved because the linear operator notation allows manipulation of the equations of motion using a very high-level analytical framework (a spatial operator algebra) that is easy to understand and use. Detailed lower-level recursive algorithms can readily be obtained for inspection from the expressions involving spatial operators. The report consists of two main sections. In Part 1, the problem of serial chain manipulators is analyzed and solved. Extensions to a closed-chain system formed by multiple manipulators moving a common task object are contained in Part 2. To retain ease of exposition in the report, only these two types of multibody systems are considered. However, the same methods can be easily applied to arbitrary multibody systems formed by a collection of joint-connected regid bodies.
Virial coefficients for trapped Bose and Fermi gases beyond the unitary limit: An S -matrix approach
NASA Astrophysics Data System (ADS)
Marcelino, Edgar; Nicolai, André; Roditi, Itzhak; LeClair, André
2014-11-01
We study the virial expansion for three-dimensional Bose and Fermi gases at finite temperature using an approximation that only considers two-body processes and is valid for high temperatures and low densities. The first virial coefficients are computed and the second is exact. The results are obtained for the full range of values of the scattering length, and the unitary limit is recovered as a particular case. A weak coupling expansion is performed and the free case is also obtained as a proper limit. The influence of an anisotropic harmonic trap is considered using the local density approximation (LDA), analytical results are obtained, and the special case of the isotropic trap is discussed in detail.
Shourijeh, Mohammad S; Flaxman, Teresa E; Benoit, Daniel L
2016-02-01
The aim of this study was to evaluate non-negative matrix factorization (NMF) and concatenated NMF (CNMF) to analyze and reliably extract muscle synergies. NMF and CNMF were used to extract knee joint muscle synergies from surface EMGs collected during a weight bearing, force matching task. Repeatability and between subject similarity were evaluated for each method using intra-class correlation coefficients (ICCs). High repeatability was found for CNMF (>0.99; 0.99-1.0) compared to NMF (>0.26; range 0.26-0.98). Reasonable consistency across subjects was improved using the CNMF over the NMF approach. CNMF was found to be a more reliable approach than NMF and suitable for between subject comparison of muscle synergies.
Clement, T Prabhakar
2014-06-01
We propose a rational method for addressing an important question-who deserves to be an author of a scientific article? We review various contentious issues associated with this question and recommend that the scientific community should view authorship in terms of contributions and responsibilities, rather than credits. We propose a new paradigm that conceptually divides a scientific article into four basic elements: ideas, work, writing, and stewardship. We employ these four fundamental elements to modify the well-known International Committee of Medical Journal Editors (ICMJE) authorship guidelines. The modified ICMJE guidelines are then used as the basis to develop an approach to quantify individual contributions and responsibilities in multi-author articles. The outcome of the approach is an authorship matrix, which can be used to answer several nagging questions related to authorship.
NASA Astrophysics Data System (ADS)
Kharrat, M.; Ramasso, E.; Placet, V.; Boubakar, M. L.
2016-03-01
Structural elements made of Organic Matrix Composites (OMC) under complex loading may suffer from high Acoustic Emission (AE) activity caused by the emergence of different emission sources at high rates with high noise level, which finally engender continuous emissions. The detection of hits in this situation becomes a challenge particularly during fatigue tests. This work suggests an approach based on the Discrete Wavelet Transform (DWT) denoising applied on signal segments. A particular attention is paid to the adjustment of the denoising parameters based on pencil lead breaks and their influence on the quality of the denoised AE signals. The validation of the proposed approach is performed on a ring-shaped Carbon Fiber Reinforced Plastics (CFRP) under in-service-like conditions involving continuous emissions with superimposed damage-related transients. It is demonstrated that errors in hit detection are greatly reduced leading to a better identification of the natural damage scenario based on AE signals.
Nelson, Clarke; Khan, Yusuf; Laurencin, Cato T
2014-11-01
Bone is an essential organ for health and quality of life. Due to current shortfalls in therapy for bone tissue engineering, scientists have sought the application of synthetic materials as bone graft substitutes. As a composite organic/inorganic material with significant extra cellular matrix (ECM), one way to improve bone graft substitutes may be to engineer a synthetic matrix that is influenced by the physical appearance of natural ECM networks. In this work, the authors evaluate composite, hybrid scaffolds for bone tissue engineering based on composite ceramic/polymer microsphere scaffolds with synthetic ECM-mimetic networks in their pore spaces. Using thermally induced phase separation, nanoscale fibers were deposited in the pore spaces of structurally sound microsphere-based scaffold with a density proportionate to the initial polymer concentration. Porosimetry and mechanical testing indicated no significant changes in overall pore characteristics or mechanical integrity as a result of the fiber deposition process. These scaffolds displayed adequate mechanical integrity on the scale of human trabecular bone and supported the adhesion and proliferation of cultured mouse calvarial osteoblasts. Drawing from natural cues, these scaffolds may represent a new avenue forward for advanced bone tissue engineering scaffolds.
The symptom matrix: Using a formalism-based approach to address complex syndromes systematically.
Skillen, Jennifer D
2016-12-01
Complex rheumatological syndromes such as Systemic lupus erythematosus, Sjogren's Syndrome and many connective tissue disorders can be a challenge to classify and diagnose, due to their wide-ranging signs and symptoms, not all of which will necessarily be present in all patients. This can result in difficulties for the clinician, patient and researcher if signs and symptoms are either overlooked or are incorrectly included in the nosology or classification of diseases. This article presents a formalism-based approach to describing syndromes. This approach offers a more systematic way of representing signs and symptoms, to aid in diagnosis and classification of complex, heterogeneous and little understood syndromes. To illustrate this approach, Ehlers-Danlos Syndrome - Hypermobility Type is used as a worked example. This approach can also be applied to other syndromes in both clinical and educational settings, to assist with research, diagnosis, choice of treatment or intervention and nosology revision.
Wu, Sau-Ching; Wang, Chris; Hansen, Dave; Wong, Sui-Lam
2017-01-01
SAVSBPM18 is an engineered streptavidin for affinity purification of both biotinylated biomolecules and recombinant proteins tagged with streptavidin binding peptide (SBP) tags. To develop a user-friendly approach for the preparation of the SAVSBPM18-based affinity matrices, a designer fusion protein containing SAVSBPM18 and a galactose binding domain was engineered. The galactose binding domain derived from the earthworm lectin EW29 was genetically modified to eliminate a proteolytic cleavage site located at the beginning of the domain. This domain was fused to the C-terminal end of SAVSBPM18. It allows the SAVSBPM18 fusions to bind reversibly to agarose and can serve as an affinity handle for purification of the fusion. Fluorescently labeled SAVSBPM18 fusions were found to be stably immobilized on Sepharose 6B-CL. The enhanced immobilization capability of the fusion to the agarose beads results from the avidity effect mediated by the tetrameric nature of SAVSBPM18. This approach allows the consolidation of purification and immobilization of SAVSBPM18 fusions to Sepharose 6B-CL in one step for affinity matrix preparation. The resulting affinity matrix has been successfully applied to purify both SBP tagged β-lactamase and biotinylated proteins. No significant reduction in binding capacity of the column was observed for at least six months. PMID:28220817
NASA Astrophysics Data System (ADS)
Babilotte, P.; Nunes Henrique Silva, V.; Sathaye, K.; Dubreuil, M.; Rivet, S.; Dupont, L.; de Bougrenet de la Tocnaye, J. L.; Le Jeune, B.
2014-01-01
A low frequency and high amplitude rectangular voltage V has been applied during different increased duration to Twisted Surface Stabilized Ferroelectric Liquid crystal (TwFLC) samples in which the alignment layers of the two substrates were rubbed along two different directions between 0° and 90°. The optical bistability properties have been evaluated using the specific Mueller Matrix formalism that allows a simultaneous access, through a single-shot measurement, to different polarimetric coefficients. In this new approach, the ellipticity ɛR and the azimuthal αR polarimetric parameters, extracted from the birefringence Mueller Matrix MR will be considered in priority. Several significant parameters, such as the horizontal offset ΔV, the degree of asymmetry DA, the characteristic area S of the hysteresis loop, are used to characterize the degradation observed into the hysteretic behaviour of the samples, for different values of ψ, at different duration T of exposure to V, before reaching the so-called stripes regime, giving a new experimental point of view concerning the evolution of the dynamic properties of the samples studied. The αR(V) and the ɛR(V) hysteresis loops are specifically examined. Static mapping related to ɛR(T) is given too. Among the different possible physical origins of the observed degradation, the in-plane anchoring energy contribution will be particularly examined, and a theoretical model is proposed that also gives access to different physical parameters, through a new approach.
NASA Astrophysics Data System (ADS)
Rashdan, M.
2015-05-01
Sub-barrier fusion cross sections for reactions involving stable and very neutron-rich nuclei, which may be important in determining the composition and heating of the crust of accreting neutron stars, are calculated using internuclear potentials derived from the microscopic Brueckner G -matrix and Skyrme SKM* and SLy4 energy density functionals. Microscopic Skyrme-Hartree-Fock proton and neutron density distributions are used. No parameters have been fit to fusion data. Calculations are performed for the isotopic reactions 16O+16O,16O+24O,16O+28O,24O+24O,12C+16O,12C+24O , and 12C+12C , which are of great astrophysical importance for the understanding of the time scale and the nucleosynthesis during late stellar evolution. The coupling to the low lying excited states is considered through the ccfull code. I compare my results with the time-dependent-Hartree-Fock calculations and with the São Paulo model as well as the experimental data. I found a remarkable agreement with the fusion cross sections for stable nuclei.
A numerical spectral approach to solve the dislocation density transport equation
NASA Astrophysics Data System (ADS)
Djaka, K. S.; Taupin, V.; Berbenni, S.; Fressengeas, C.
2015-09-01
A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme.
Koppen, Jessica V.; Szczęśniak, Małgorzata M.; Hapka, Michał; Modrzejewski, Marcin; Chałasiński, Grzegorz
2014-06-28
Donor-acceptor interactions are notoriously difficult and unpredictable for conventional density functional theory (DFT) methodologies. This work presents a reliable computational treatment of gold-ligand interactions of the donor-acceptor type within DFT. These interactions require a proper account of the ionization potential of the electron donor and electron affinity of the electron acceptor. This is accomplished in the Generalized Kohn Sham framework that allows one to relate these properties to the frontier orbitals in DFT via the tuning of range-separated functionals. A donor and an acceptor typically require different tuning schemes. This poses a problem when the binding energies are calculated using the supermolecular method. A two-parameter tuning for the monomer properties ensures that a common functional, optimal for both the donor and the acceptor, is found. A reliable DFT approach for these interactions also takes into account the dispersion contribution. The approach is validated using the water dimer and the (HAuPH{sub 3}){sub 2} aurophilic complex. Binding energies are computed for Au{sub 4} interacting with the following ligands: SCN{sup −}, benzenethiol, benzenethiolate anion, pyridine, and trimethylphosphine. The results agree for the right reasons with coupled-cluster reference values.
Gudur, M; Hara, W; Wang, L; Xing, L; Li, R
2014-06-15
Purpose: MRI significantly improves the accuracy and reliability of target delineation for patient simulation and treatment planning in radiation therapy, due to its superior soft tissue contrast as compared to CT. An MRI based simulation will reduce cost and simplify clinical workflow with zero ionizing radiation. However, MRI lacks the key electron density information. The purpose of this work is to develop a reliable method to derive electron density from MRI. Methods: We adopt a probabilistic Bayesian approach for electron density mapping based on T1-weighted head MRI. For each voxel, we compute conditional probability of electron densities given its: (1) T1 intensity and (2) geometry in a reference anatomy, obtained by deformable image registration between the MRI of test patient and atlas. Intensity and geometry information are combined into a unifying posterior probability density function whose mean gives the electron density. Mean absolute HU error between the estimated and true CT, as well as ROC's for bone detection (HU>200) were calculated for 8 patients. The performance was compared with a global intensity approach based on T1 and no density correction (set whole head to water). Results: The proposed technique significantly reduced the errors in electron density estimation, with a mean absolute HU error of 132, compared with 139 for deformable registration (p=10{sup −3}), 371 for the intensity approach (p=10{sup −5}) and 282 without density correction (p=2×10{sup −4}). For 90% sensitivity in bone detection, the proposed method had a specificity of 85% and that for deformable registration, intensity and without density correction are 80%, 24% and 10% respectively. Conclusion: The proposed unifying method provides accurate electron density estimation and bone detection from MRI of the head with highly heterogeneous regions. This paves the way for accurate dose calculation and generating reference images for patient setup in MRI-based treatment
An improved theoretical approach to the empirical corrections of density functional theory
NASA Astrophysics Data System (ADS)
Lii, Jenn-Huei; Hu, Ching-Han
2012-02-01
An empirical correction to density functional theory (DFT) has been developed in this study. The approach, called correlation corrected atomization-dispersion (CCAZD), involves short- and long-range terms. Short-range correction consists of bond ( 1,2-) and angle ( 1,3-) interactions, which remedies the deficiency of DFT in describing the proto-branching stabilization effects. Long-range correction includes a Buckingham potential function aiming to account for the dispersion interactions. The empirical corrections of DFT were parameterized to reproduce reported Δ H f values of the training set containing alkane, alcohol and ether molecules. The Δ H f of the training set molecules predicted by the CCAZD method combined with two different DFT methods, B3LYP and MPWB1K, with a 6-31G* basis set agreed well with the experimental data. For 106 alkane, alcohol and ether compounds, the average absolute deviations (AADs) in Δ H f were 0.45 and 0.51 kcal/mol for B3LYP- and MPWB1K-CCAZD, respectively. Calculations of isomerization energies, rotational barriers and conformational energies further validated the CCAZD approach. The isomerization energies improved significantly with the CCAZD treatment. The AADs for 22 energies of isomerization reactions were decreased from 3.55 and 2.44 to 0.55 and 0.82 kcal/mol for B3LYP and MPWB1K, respectively. This study also provided predictions of MM4, G3, CBS-QB3 and B2PLYP-D for comparison. The final test of the CCAZD approach on the calculation of the cellobiose analog potential surface also showed promising results. This study demonstrated that DFT calculations with CCAZD empirical corrections achieved very good agreement with reported values for various chemical reactions with a small basis set as 6-31G*.
Solid waste bin level detection using gray level co-occurrence matrix feature extraction approach.
Arebey, Maher; Hannan, M A; Begum, R A; Basri, Hassan
2012-08-15
This paper presents solid waste bin level detection and classification using gray level co-occurrence matrix (GLCM) feature extraction methods. GLCM parameters, such as displacement, d, quantization, G, and the number of textural features, are investigated to determine the best parameter values of the bin images. The parameter values and number of texture features are used to form the GLCM database. The most appropriate features collected from the GLCM are then used as inputs to the multi-layer perceptron (MLP) and the K-nearest neighbor (KNN) classifiers for bin image classification and grading. The classification and grading performance for DB1, DB2 and DB3 features were selected with both MLP and KNN classifiers. The results demonstrated that the KNN classifier, at KNN = 3, d = 1 and maximum G values, performs better than using the MLP classifier with the same database. Based on the results, this method has the potential to be used in solid waste bin level classification and grading to provide a robust solution for solid waste bin level detection, monitoring and management.
SURVEY DESIGN FOR SPECTRAL ENERGY DISTRIBUTION FITTING: A FISHER MATRIX APPROACH
Acquaviva, Viviana; Gawiser, Eric; Bickerton, Steven J.; Grogin, Norman A.; Guo Yicheng; Lee, Seong-Kook
2012-04-10
The spectral energy distribution (SED) of a galaxy contains information on the galaxy's physical properties, and multi-wavelength observations are needed in order to measure these properties via SED fitting. In planning these surveys, optimization of the resources is essential. The Fisher Matrix (FM) formalism can be used to quickly determine the best possible experimental setup to achieve the desired constraints on the SED-fitting parameters. However, because it relies on the assumption of a Gaussian likelihood function, it is in general less accurate than other slower techniques that reconstruct the probability distribution function (PDF) from the direct comparison between models and data. We compare the uncertainties on SED-fitting parameters predicted by the FM to the ones obtained using the more thorough PDF-fitting techniques. We use both simulated spectra and real data, and consider a large variety of target galaxies differing in redshift, mass, age, star formation history, dust content, and wavelength coverage. We find that the uncertainties reported by the two methods agree within a factor of two in the vast majority ({approx}90%) of cases. If the age determination is uncertain, the top-hat prior in age used in PDF fitting to prevent each galaxy from being older than the universe needs to be incorporated in the FM, at least approximately, before the two methods can be properly compared. We conclude that the FM is a useful tool for astronomical survey design.
The SAGE Cross-Culture Matrix Approach to the Study of Global Environments and Human Inhabitants.
ERIC Educational Resources Information Center
Peters, Richard
The Humans and Environment Learning Program (HELP) and the Student Awareness of Global Environments (SAGE) approach are designed to directly and vicariously expose students to natural and social environments and develop their awareness of the character and nature of the different environments in which each individual functions throughout a…
A New Approach to Modeling Densities and Equilibria of Ice and Gas Hydrate Phases
NASA Astrophysics Data System (ADS)
Zyvoloski, G.; Lucia, A.; Lewis, K. C.
2011-12-01
, and NaCl in permafrost conditions are presented to illustrate the predictive capabilities of the multi-scale GHC equation. In particular, we show that the GHC equation correctly predicts 1) The density of 1h ice and methane hydrate to within 1%. 2) The melting curve for hexagonal ice. 3) The hydrate-gas phase co-existence curve. 4) Various phase equilibrium involving ice and hydrate phases. We also show that the GHC equation approach can be readily incorporated into subsurface flow simulation programs like FEHM to predict the behavior of permafrost and other reservoirs where ice and/or hydrates are present. Many geometric illustrations are used to elucidate key concepts. References A. Lucia, A Multi-Scale Gibbs Helmholtz Constrained Cubic Equation of State. J. Thermodynamics: Special Issue on Advances in Gas Hydrate Thermodynamics and Transport Properties. Available on-line [doi:10.1155/2010/238365]. A. Lucia, B.M. Bonk, A. Roy and R.R. Waterman, A Multi-Scale Framework for Multi-Phase Equilibrium Flash. Comput. Chem. Engng. In press.
Detecting Cracks in Ceramic Matrix Composites by Electrical Resistance
NASA Technical Reports Server (NTRS)
Smith, Craig; Gyekenyesi, Andrew
2011-01-01
The majority of damage in SiC/SiC ceramic matrix composites subjected to monotonic tensile loads is in the form of distributed matrix cracks. These cracks initiate near stress concentrations, such as 90o fiber tows or large matrix pores and continue to accumulate with additional stress until matrix crack saturation is achieved. Such damage is difficult to detect with conventional nondestructive evaluation techniques (immersion ultrasonics, x-ray, etc.). Monitoring a specimen.s electrical resistance change provides an indirect approach for monitoring matrix crack density. Sylramic-iBN fiber- reinforced SiC composites with a melt infiltrated (MI) matrix were tensile tested at room temperature. Results showed an increase in resistance of more than 500% prior to fracture, which can be detected either in situ or post-damage. A relationship between resistance change and matrix crack density was also determined.
Detecting Damage in Ceramic Matrix Composites Using Electrical Resistance
NASA Technical Reports Server (NTRS)
Smith, Craig E.; Gyekenyesi, Andrew
2011-01-01
The majority of damage in SiC/SiC ceramic matrix composites subjected to monotonic tensile loads is in the form of distributed matrix cracks. These cracks initiate near stress concentrations, such as 90 deg fiber tows or large matrix pores and continue to accumulate with additional stress until matrix crack saturation is achieved. Such damage is difficult to detect with conventional nondestructive evaluation techniques (immersion ultrasonics, x-ray, etc.). Monitoring a specimen.s electrical resistance change provides an indirect approach for monitoring matrix crack density. Sylramic-iBN fiber- reinforced SiC composites with a melt infiltrated (MI) matrix were tensile tested at room temperature. Results showed an increase in resistance of more than 500% prior to fracture, which can be detected either in situ or post-damage. A relationship between resistance change and matrix crack density was also determined.
Chi, Won Seok; Kim, Sang Jin; Lee, Seung-Joon; Bae, Youn-Sang; Kim, Jong Hak
2015-02-01
Herein, a high performance mixed-matrix membrane (MMM) is reported with simultaneously large improvements in the CO2 permeability by 880 % from 70.2 to 687.7 Barrer (1 Barrer=1×10(-10) cm(3) cm cm(-2) s(-1) cmHg(-1) ) and CO2 /N2 selectivity by 14.4 % from 30.5 to 34.9. These findings represent one of the most dramatic improvements ever reported for MMMs. These improvements are obtained through an interface and interaction tuning approach based on an amphiphilic grafted copolymer. Poly(vinyl chloride)-g-poly(oxyethylene methacrylate) (PVC-g-POEM) graft copolymer plays a key role as a soft organic matrix to provide good permeation properties, uniform distribution of zeolite imidazole frameworks-8 (ZIF-8), and better interfacial contact with inorganic compounds. In particular, the CO2 /C3 H8 and CO2 /C3 H6 selectivities reached 10.5 and 42.7, respectively, for PVC-g-POEM/ZIF (40 %) MMMs; this indicates that it could be a promising membrane material for the purification of C3 hydrocarbons.
Nanni, Loris; Lumini, Alessandra; Brahnam, Sheryl
2013-03-01
Many domains have a stake in the development of reliable systems for automatic protein classification. Of particular interest in recent studies of automatic protein classification is the exploration of new methods for extracting features from a protein that enhance classification for specific problems. These methods have proven very useful in one or two domains, but they have failed to generalize well across several domains (i.e. classification problems). In this paper, we evaluate several feature extraction approaches for representing proteins with the aim of sequence-based protein classification. Several protein representations are evaluated, those starting from: the position specific scoring matrix (PSSM) of the proteins; the amino-acid sequence; a matrix representation of the protein, of dimension (length of the protein) ×20, obtained using the substitution matrices for representing each amino-acid as a vector. A valuable result is that a texture descriptor can be extracted from the PSSM protein representation which improves the performance of standard descriptors based on the PSSM representation. Experimentally, we develop our systems by comparing several protein descriptors on nine different datasets. Each descriptor is used to train a support vector machine (SVM) or an ensemble of SVM. Although different stand-alone descriptors work well on some datasets (but not on others), we have discovered that fusion among classifiers trained using different descriptors obtains a good performance across all the tested datasets. Matlab code/Datasets used in the proposed paper are available at http://www.bias.csr.unibo.it\
Scattering matrix approach to the dissociative recombination of HCO{sup +} and N{sub 2}H{sup +}
Fonseca dos Santos, S.; Douguet, N.; Orel, A. E.; Kokoouline, V.
2014-04-28
We present a theoretical study of the indirect dissociative recombination of linear polyatomic ions at low collisional energies. The approach is based on the computation of the scattering matrix just above the ionization threshold and enables the explicit determination of all diabatic electronic couplings responsible for dissociative recombination. In addition, we use the multi-channel quantum-defect theory to demonstrate the precision of the scattering matrix by reproducing accurately ab initio Rydberg state energies of the neutral molecule. We consider the molecular ions N{sub 2}H{sup +} and HCO{sup +} as benchmark systems of astrophysical interest and improve former theoretical studies, which had repeatedly produced smaller cross sections than experimentally measured. Specifically, we demonstrate the crucial role of the previously overlooked stretching modes for linear polyatomic ions with large permanent dipole moment. The theoretical cross sections for both ions agree well with experimental data over a wide energy range. Finally, we consider the potential role of the HOC{sup +} isomer in the experimental cross sections of HCO{sup +} at energies below 10 meV.
NASA Astrophysics Data System (ADS)
Fotin, Sergei V.; Yin, Yin; Haldankar, Hrishikesh; Hoffmeister, Jeffrey W.; Periaswamy, Senthil
2016-03-01
Computer-aided detection (CAD) has been used in screening mammography for many years and is likely to be utilized for digital breast tomosynthesis (DBT). Higher detection performance is desirable as it may have an impact on radiologist's decisions and clinical outcomes. Recently the algorithms based on deep convolutional architectures have been shown to achieve state of the art performance in object classification and detection. Similarly, we trained a deep convolutional neural network directly on patches sampled from two-dimensional mammography and reconstructed DBT volumes and compared its performance to a conventional CAD algorithm that is based on computation and classification of hand-engineered features. The detection performance was evaluated on the independent test set of 344 DBT reconstructions (GE SenoClaire 3D, iterative reconstruction algorithm) containing 328 suspicious and 115 malignant soft tissue densities including masses and architectural distortions. Detection sensitivity was measured on a region of interest (ROI) basis at the rate of five detection marks per volume. Moving from conventional to deep learning approach resulted in increase of ROI sensitivity from 0:832 +/- 0:040 to 0:893 +/- 0:033 for suspicious ROIs; and from 0:852 +/- 0:065 to 0:930 +/- 0:046 for malignant ROIs. These results indicate the high utility of deep feature learning in the analysis of DBT data and high potential of the method for broader medical image analysis tasks.
Modeling solvation effects in real-space and real-time within density functional approaches.
Delgado, Alain; Corni, Stefano; Pittalis, Stefano; Rozzi, Carlo Andrea
2015-10-14
The Polarizable Continuum Model (PCM) can be used in conjunction with Density Functional Theory (DFT) and its time-dependent extension (TDDFT) to simulate the electronic and optical properties of molecules and nanoparticles immersed in a dielectric environment, typically liquid solvents. In this contribution, we develop a methodology to account for solvation effects in real-space (and real-time) (TD)DFT calculations. The boundary elements method is used to calculate the solvent reaction potential in terms of the apparent charges that spread over the van der Waals solute surface. In a real-space representation, this potential may exhibit a Coulomb singularity at grid points that are close to the cavity surface. We propose a simple approach to regularize such singularity by using a set of spherical Gaussian functions to distribute the apparent charges. We have implemented the proposed method in the Octopus code and present results for the solvation free energies and solvatochromic shifts for a representative set of organic molecules in water.
NASA Astrophysics Data System (ADS)
Kirchner, Tom
2013-05-01
Ion-impact induced ionization and fragmentation of complex molecules have important applications in many branches of science. If the molecule is H2O an obvious topic to address is the radiobiological relevance of these processes, e.g. in the context of hadron therapy, to name just one example. From a more fundamental physics viewpoint ion-molecule collision systems constitute interesting many-body systems, whose analysis poses challenges to both experimentalists and theorists. This talk will describe a theoretical approach to ion-molecule collisions, which is based on density functional theory to describe the nonperturbative electron dynamics. The basis generator method applied in the past successfully to ion-atom collisions is adapted to deal with the multi-center problem one faces when one considers molecular targets. Cross sections for single- and multiple-electron processes (capture and transfer to the continuum) are obtained directly from solving time-dependent Kohn-Sham-type orbital equations and using a Slater determinant based analysis. Fragmentation yields are predicted on the basis of a semi-phenomenological model which uses the calculated cross sections as input. Results will be presented for various ions impacting on water molecules in the energy range of 10-5000 keV/amu and compared with experimental data and previous theoretical calculations where available. First applications of the model to collisions involving CH4 molecules will also be discussed. This work has been supported by SHARCNET and NSERC Canada.
Modeling solvation effects in real-space and real-time within density functional approaches
Delgado, Alain; Corni, Stefano; Pittalis, Stefano; Rozzi, Carlo Andrea
2015-10-14
The Polarizable Continuum Model (PCM) can be used in conjunction with Density Functional Theory (DFT) and its time-dependent extension (TDDFT) to simulate the electronic and optical properties of molecules and nanoparticles immersed in a dielectric environment, typically liquid solvents. In this contribution, we develop a methodology to account for solvation effects in real-space (and real-time) (TD)DFT calculations. The boundary elements method is used to calculate the solvent reaction potential in terms of the apparent charges that spread over the van der Waals solute surface. In a real-space representation, this potential may exhibit a Coulomb singularity at grid points that are close to the cavity surface. We propose a simple approach to regularize such singularity by using a set of spherical Gaussian functions to distribute the apparent charges. We have implemented the proposed method in the OCTOPUS code and present results for the solvation free energies and solvatochromic shifts for a representative set of organic molecules in water.
Modeling solvation effects in real-space and real-time within density functional approaches
NASA Astrophysics Data System (ADS)
Delgado, Alain; Corni, Stefano; Pittalis, Stefano; Rozzi, Carlo Andrea
2015-10-01
The Polarizable Continuum Model (PCM) can be used in conjunction with Density Functional Theory (DFT) and its time-dependent extension (TDDFT) to simulate the electronic and optical properties of molecules and nanoparticles immersed in a dielectric environment, typically liquid solvents. In this contribution, we develop a methodology to account for solvation effects in real-space (and real-time) (TD)DFT calculations. The boundary elements method is used to calculate the solvent reaction potential in terms of the apparent charges that spread over the van der Waals solute surface. In a real-space representation, this potential may exhibit a Coulomb singularity at grid points that are close to the cavity surface. We propose a simple approach to regularize such singularity by using a set of spherical Gaussian functions to distribute the apparent charges. We have implemented the proposed method in the Octopus code and present results for the solvation free energies and solvatochromic shifts for a representative set of organic molecules in water.
Madjarova, G; Tadjer, A; Cholakova, Tz P; Dobrev, A A; Mineva, T
2005-01-20
Density functional (DF) based numerical approaches for computing orbital and atomic reactivity indices were employed in the study of selectivity descriptors for the 1,4 Michael addition reaction. To this aim, atomic and orbital Fukui indices and atomic softnesses for 2-arylmethylene-1,4-butanolides and N,N-disubstituted phenylacetamides were computed. Further on, these local selectivity descriptors have been rationalized in terms of the Pearson's hard-soft-acid-base principle to explain the observed regioselectivity. It is shown that the methods employed for local (atomic and orbital) reactivity index computations are useful and reliable for prediction of the regioselectivity upon conjugate addition of ambident nucleophiles to 2,3-unsaturated carboxylic esters. All the results reveal similar degree of localization/hardness of the 1,4-butanolides C4 and active alpha-carbon belonging to the N,N-dimethyl-phenylacetamide, while the soft alpha-carbon in LiCH2CN reacts with the soft C2 1,4-butanolide center.
Khan, Muntazir S; Krupadam, Reddithota J
2013-11-01
Molecular imprinting is an interesting technique for preparation of molecular recognition materials with discriminating similar molecules from complex systems. In particular, imprinting more than one molecule has immense application in remediation of industrial waste. Major difficulty in molecular imprinting is the selection of suitable polymer precursors. In this article, authors have proposed a new computational approach for combinatorial screening of polymer precursor library to select appropriate polymer precursors to prepare imprinted polymer capable of selectively binding carcinogenic polycyclic aromatic hydrocarbons (PAHs). Molecular Dynamics (MD) and Quantum Mechanics (QM) models were used to compute interaction energy scores between polymer precursors and PAHs in a simulated solvent box. A self-designed virtual library of functional monomers has been prepared, and then used for MD simulations to screen the best functional monomers. Initially, molecules used in the study were geometrically optimized and then interaction energies were computed using density functional theory (DFT) in Becke 3-Parameter Exchange Correlation Function (B3LYP) level with 6-31G*basis set on Gaussian 4.1 Ver. software. Complimentary to theoretical predictions, selected polymers were prepared in laboratory and compared theoretically computed binding score with the binding capacity of the polymer on spectrofluorimetry. The computer simulations used in this research paper are rapid and reliable for the combinatorial screening of polymer precursors in experimental-free way to design of multi-template imprinted polymers.
Fischbach, Claudia
2014-01-01
Tumor-stroma interactions have emerged as critical determinants of drug efficacy. However, the underlying biological and physicochemical mechanisms by which the microenvironment regulates therapeutic response remain unclear, due in part to a lack of physiologically relevant in vitro platforms to accurately interrogate tissue-level phenomena. Tissue-engineered tumor models are beginning to address this shortcoming. By allowing selective incorporation of microenvironmental complexity, these platforms afford unique access to tumor-associated signaling and transport dynamics. This review will focus on engineering approaches to study drug delivery as a function of tumor-associated changes of the vasculature and extracellular matrix (ECM). First, we review current biological understanding of these components and discuss their impact on transport processes. Then, we evaluate existing microfluidic, tissue engineering, and materials science strategies to recapitulate vascular and ECM characteristics of tumors, and finish by outlining challenges and future directions of the field that may ultimately improve anti-cancer therapies. PMID:24309015
Seo, Bo Ri; Delnero, Peter; Fischbach, Claudia
2014-04-01
Tumor-stroma interactions have emerged as critical determinants of drug efficacy. However, the underlying biological and physicochemical mechanisms by which the microenvironment regulates therapeutic response remain unclear, due in part to a lack of physiologically relevant in vitro platforms to accurately interrogate tissue-level phenomena. Tissue-engineered tumor models are beginning to address this shortcoming. By allowing selective incorporation of microenvironmental complexity, these platforms afford unique access to tumor-associated signaling and transport dynamics. This review will focus on engineering approaches to study drug delivery as a function of tumor-associated changes of the vasculature and extracellular matrix (ECM). First, we review current biological understanding of these components and discuss their impact on transport processes. Then, we evaluate existing microfluidic, tissue engineering, and materials science strategies to recapitulate vascular and ECM characteristics of tumors, and finish by outlining challenges and future directions of the field that may ultimately improve anti-cancer therapies.
Badawi, Mohamed S; Gouda, Mona M; Nafee, Sherif S; El-Khatib, Ahmed M; El-Mallah, Ekram A
2012-12-01
To calibrate the co-axial HPGe semiconductor detectors, we introduce a new theoretical approach based on the Direct Statistical method proposed by Selim and Abbas (1995, 1996) to calculate the full-energy peak efficiency for cylindrical detectors. The present method depends on the accurate analytical calculation of the average path length covered by the photon inside the detector active volume and the geometrical solid angle Ω, to obtain a simple formula for the efficiency. In addition, the self attenuation coefficient of the source matrix (with a radius greater than the detector's radius), the attenuation factors of the source container and the detector housing materials are also treated by calculating the average path length within these materials. (152)Eu aqueous radioactive sources covering the energy range from 121 to 1408 keV were used. Remarkable agreement between the measured and the calculated efficiencies was achieved with discrepancies less than 2%.
NASA Astrophysics Data System (ADS)
Mak, Rachel Y. C.
2014-09-01
X-ray absorption spectromicroscopy combines microscopy and spectroscopy to provide rich information about the chemical organization of materials down to the nanoscale. But with richness also comes complexity: natural materials such as biological or environmental science specimens can be composed of complex spectroscopic mixtures of different materials. The challenge becomes how we could meaningfully simplify and interpret this information. Approaches such as principal component analysis and cluster analysis have been used in previous studies, but with some limitations that we will describe. This leads us to develop a new approach based on a development of non-negative matrix approximation (NNMA) analysis with both sparseness and spectra similarity regularizations. We apply this new technique to simulated spectromicroscopy datasets as well as a preliminary study of the large-scale biochemical organization of a human sperm cell. NNMA analysis is able to select major features of the sperm cell without the physically erroneous negative weightings or thicknesses in the calculated image which appeared in previous approaches.
NASA Astrophysics Data System (ADS)
Hewett, Caspar J. M.; Quinn, Paul; Wilkinson, Mark
2014-05-01
Intense farming plays a key role in contributing to problems such as increased flood risk, soil erosion and poor water quality. This means that there is great potential for agricultural practitioners to play a major part in reducing multiple risks through better land-use management. Greater understanding by farmers, land managers, practitioners and policy-makers of the ways in which farmed landscapes contribute to risks and the ways in which those risks might be mitigated can be an essential component in improving practice. The Decision Support Matrix (DSM) approach involves the development of a range of visualization and communication tools to help compare the risks associated with different farming practices and explore options to manage runoff. DSMs are simple decision support systems intended for use by the non-expert which combine expert hydrological evidence with local knowledge of runoff patterns. They are developed through direct engagement with stakeholders, ensuring that the examples and language used makes sense to end-users. A key element of the tools is that they show the current conditions of the land and describe extremes of land-use management within a hydrological and agricultural land-management context. The tools include conceptual models of a series of pre-determined runoff scenarios, providing the end-user with a variety of potential land management practices and runoff management options. Visual examples of different farming practices are used to illustrate the impact of good and bad practice on specific problems such as nutrient export or risk of flooding. These show both how current conditions cause problems downstream and how systems are vulnerable to changes in climate and land-use intensification. The level of risk associated with a particular land management option is represented by a mapping on a two- or three-dimensional matrix. Interactive spreadsheet-based tools are developed in which multiple questions allow the user to explore
Bertels, Luke W.; Mazziotti, David A.
2014-07-28
Multireference correlation in diradical molecules can be captured by a single-reference 2-electron reduced-density-matrix (2-RDM) calculation with only single and double excitations in the 2-RDM parametrization. The 2-RDM parametrization is determined by N-representability conditions that are non-perturbative in their treatment of the electron correlation. Conventional single-reference wave function methods cannot describe the entanglement within diradical molecules without employing triple- and potentially even higher-order excitations of the mean-field determinant. In the isomerization of bicyclobutane to gauche-1,3-butadiene the parametric 2-RDM (p2-RDM) method predicts that the diradical disrotatory transition state is 58.9 kcal/mol above bicyclobutane. This barrier is in agreement with previous multireference calculations as well as recent Monte Carlo and higher-order coupled cluster calculations. The p2-RDM method predicts the Nth natural-orbital occupation number of the transition state to be 0.635, revealing its diradical character. The optimized geometry from the p2-RDM method differs in important details from the complete-active-space self-consistent-field geometry used in many previous studies including the Monte Carlo calculation.
NASA Astrophysics Data System (ADS)
Dutta, Tirthankar; Ramasesha, S.
2012-01-01
In this paper we investigate the effect of terminal substituents on the dynamics of spin and charge transport in donor-acceptor substituted polyenes [D-(CH)x-A] chains, also known as push-pull polyenes. We employ a long-range correlated model Hamiltonian for the D-(CH)x-A system, and time-dependent density matrix renormalization group technique for time propagating the wave packet obtained by injecting a hole at a terminal site, in the ground state of the system. Our studies reveal that the end groups do not affect spin and charge velocities in any significant way, but change the amount of charge transported. We have compared these push-pull systems with donor-acceptor substituted polymethine imine (PMI), D-(CHN)x-A, systems in which besides electron affinities, the nature of pz orbitals in conjugation also alternate from site to site. We note that spin and charge dynamics in the PMIs are very different from that observed in the case of push-pull polyenes, and within the time scale of our studies, transport of spin and charge leads to the formation of a “quasi-static” state.
Sand, Andrew M; Mazziotti, David A
2013-06-28
Different sets of molecular orbitals and the rotations connecting them are of great significance in molecular electronic structure. Most electron correlation methods depend on a reference wave function that separates the orbitals into occupied and unoccupied spaces. Energies and properties from these methods depend upon rotations between the spaces. Some electronic structure methods, such as modified coupled electron pair approximations and the recently developed parametric two-electron reduced density matrix (2-RDM) methods [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], also depend upon rotations between occupied orbitals and rotations between unoccupied orbitals. In this paper, we explore the sensitivity of the ground-state energies from the parametric 2-RDM method to rotations within the occupied space and within the unoccupied space. We discuss the theoretical origin of the rotational dependence and provide computational examples at both equilibrium and non-equilibrium geometries. We also study the effect of these rotations on the size extensivity of the parametric 2-RDM method. Computations show that the orbital rotations have a small effect upon the parametric 2-RDM energies in comparison to the energy differences observed between methodologies such as coupled cluster and parametric 2-RDM. Furthermore, while the 2-RDM method is rigorously size extensive in a local molecular orbital basis set, calculations reveal negligible deviations in nonlocal molecular orbital basis sets such as those from canonical Hartree-Fock calculations.
A New Approach to Minimize Acellular Dermal Matrix Use in Prosthesis-based Breast Reconstruction
Hadad, Ivan; Liu, Allen S.
2015-01-01
Background: Acellular dermal matrices (ADMs) are often used to improve lower-pole contour, as well as allow for single-stage reconstruction, but numerous studies have shown an increased complication rate using ADM. As such, our group has developed a minimal-ADM-use technique to lower complications while effectively recreating lower-pole contour. Methods: A total of 380 postmastectomy prosthesis-based breast reconstructions were performed in 265 patients by a single surgeon. One hundred eight reconstructions were performed using the traditional ADM technique, with a large piece of ADM along the entire inferior and lateral borders. Two hundred twenty-five reconstructions were performed with the minimal-use technique, patching only the lateral area of the reconstruction. Thirty-five reconstructions were performed without the use of any ADM for high-risk reconstructions, most often in morbidly obese patients. Results: Comparing the traditional technique with the minimal-use technique, the seroma rate dropped from 3% to 0%. The rate of infection and reconstruction loss fell from 9% to 1%. Upon greatly reducing or eliminating the use of ADM use in obese patients, the seroma rate decreased from 15.4% to 5.7%, and the reconstruction loss rate decreased from 38% to 9%. Conclusions: This article describes a new surgical approach to minimize the amount of ADM necessary to create an aesthetically pleasing breast reconstruction. We believe that this approach helps avoid the complications of seroma, infection, and loss of the reconstruction. In certain obese patients, total avoidance of ADM may be the better choice. PMID:26301161
Akkelin, S.V.; Sinyukov, Yu.M.
2004-12-01
A method allowing analysis of the overpopulation of phase space in heavy ion collisions in a model-independent way is proposed within the hydrodynamic approach. It makes it possible to extract a chemical potential of thermal pions at freeze-out, irrespective of the form of freeze-out (isothermal) hypersurface in Minkowski space and transverse flows on it. The contributions of resonance (with masses up to 2 GeV) decays to spectra, interferometry volumes, and phase-space densities are calculated and discussed in detail. The estimates of average phase-space densities and chemical potentials of thermal pions are obtained for SPS and RHIC energies. They demonstrate that multibosonic phenomena at those energies might be considered as a correction factor rather than as a significant physical effect. The analysis of the evolution of the pion average phase-space density in chemically frozen hadron systems shows that it is almost constant or slightly increases with time while the particle density and phase-space density at each space point decreases rapidly during the system's expansion. We found that, unlike the particle density, the average phase-space density has no direct link to the freeze-out criterion and final thermodynamic parameters, being connected rather to the initial phase-space density of hadronic matter formed in relativistic nucleus-nucleus collisions.
A density functional theory based approach for predicting melting points of ionic liquids.
Chen, Lihua; Bryantsev, Vyacheslav S
2017-02-01
Accurate prediction of melting points of ILs is important both from the fundamental point of view and from the practical perspective for screening ILs with low melting points and broadening their utilization in a wider temperature range. In this work, we present an ab initio approach to calculate melting points of ILs with known crystal structures and illustrate its application for a series of 11 ILs containing imidazolium/pyrrolidinium cations and halide/polyatomic fluoro-containing anions. The melting point is determined as a temperature at which the Gibbs free energy of fusion is zero. The Gibbs free energy of fusion can be expressed through the use of the Born-Fajans-Haber cycle via the lattice free energy of forming a solid IL from gaseous phase ions and the sum of the solvation free energies of ions comprising IL. Dispersion-corrected density functional theory (DFT) involving (semi)local (PBE-D3) and hybrid exchange-correlation (HSE06-D3) functionals is applied to estimate the lattice enthalpy, entropy, and free energy. The ions solvation free energies are calculated with the SMD-generic-IL solvation model at the M06-2X/6-31+G(d) level of theory under standard conditions. The melting points of ILs computed with the HSE06-D3 functional are in good agreement with the experimental data, with a mean absolute error of 30.5 K and a mean relative error of 8.5%. The model is capable of accurately reproducing the trends in melting points upon variation of alkyl substituents in organic cations and replacement one anion by another. The results verify that the lattice energies of ILs containing polyatomic fluoro-containing anions can be approximated reasonably well using the volume-based thermodynamic approach. However, there is no correlation of the computed lattice energies with molecular volume for ILs containing halide anions. Moreover, entropies of solid ILs follow two different linear relationships with molecular volume for halides and polyatomic fluoro
Kessler, Eva M. V.; Schmitt, Sebastian; Wüllen, Christoph van
2013-11-14
The broken symmetry approach to the calculation of zero field splittings (or magnetic anisotropies) of multinuclear transition metal complexes is further developed. A procedure is suggested how to extract spin Hamiltonian parameters for anisotropic exchange from a set of broken symmetry density functional calculations. For isotropic exchange coupling constants J{sub ij}, the established procedure is retrieved, and anisotropic (or pseudodipolar) exchange coupling tensors D{sub ij} are obtained analogously. This procedure only yields the sum of the individual single-ion zero field splitting tensors D{sub i}. Therefore, a procedure based on localized orbitals has been developed to extract the individual single-ion contributions. With spin Hamiltonian parameters at hand, the zero field splittings of the individual spin multiplets are calculated by an exact diagonalization of the isotropic part, followed by a spin projection done numerically. The method is applied to the binuclear cation [LCr(OH){sub 3}CrL]{sup 3+} (L = 1,4,7-trimethyl-1,4,7-triazanonane) for which experimental zero field splittings for all low-energy spin states are known, and to the single-molecule magnet [Fe{sub 4}(CH{sub 3}C(CH{sub 2}O){sub 3}){sub 2}(dpm){sub 6}] (Hdpm = 2,2,6,6-tetramethylheptane-3,5-dione). In both these 3d compounds, the single-ion tensors mainly come from the spin-orbit interaction. Anisotropic exchange is dominated by the spin-dipolar interaction only for the chromium compound. Despite the rather small isotropic exchange couplings in the iron compound, spin-orbit and spin-dipolar contributions to anisotropic exchange are of similar size here.
Rios, Lorena P.; Khan, Aliya; Sultan, Muhammad; McAssey, Karen; Fouda, Mona A.; Armstrong, David
2013-01-01
Abstract Objective To provide clinicians with an update on the diagnosis of celiac disease (CD) and to make recommendations on the indications to screen for CD in patients presenting with low bone mineral density (BMD) or fragility fractures. Quality of evidence A multidisciplinary task force developed clinically relevant questions related to the diagnosis of CD as the basis for a literature search of the MEDLINE, EMBASE, and CENTRAL databases (January 2000 to January 2009) using the key words celiac disease, osteoporosis, osteopenia, low bone mass, and fracture. The existing literature consists of level I and II studies. Main message The estimated prevalence of asymptomatic CD is 2% to 3% in individuals with low BMD. Routine screening for CD is not justified in patients with low BMD. However, targeted screening for CD is recommended for patients who have T-scores of −1.0 or less at the spine or hip, or a history of fragility fractures in association with any CD-related symptoms or conditions; family history of CD; or low urinary calcium levels, vitamin D insufficiency, and raised parathyroid hormone levels despite adequate intake of calcium and vitamin D. Celiac disease testing should be performed while the subject is consuming a gluten-containing diet; initial screening should be performed with human recombinant immunoglobulin (Ig) A tissue transglutaminase or other IgA tissue transglutaminase assays, in association with IgA endomysial antibody immunofluorescence. Duodenal biopsy is necessary to confirm the diagnosis of CD. Human leukocyte antigen typing might assist in confirming or ruling out the diagnosis of CD in cases where serology and histology are discordant. Definitive diagnosis is based on clinical, serologic, and histologic features, combined with a positive response to a gluten-free diet. Conclusion Current evidence does not support routine screening for CD in all patients with low BMD. A targeted case-finding approach is appropriate for patients
NASA Astrophysics Data System (ADS)
Tarana, Michal; Čurík, Roman
2016-05-01
We introduce a computational method developed for study of long-range molecular Rydberg states of such systems that can be approximated by two electrons in a model potential of the atomic cores. The method is based on a two-electron R-matrix approach inside a sphere centered on one of the atoms. The wave function is then connected to a Coulomb region outside the sphere via a multichannel version of the Coulomb Green's function. This approach is applied to a study of Rydberg states of Rb2 for internuclear separations R from 40 to 320 bohrs and energies corresponding to n from 7 to 30. We report bound states associated with the low-lying 3Po resonance and with the virtual state of the rubidium atom that turn into ion-pair-like bound states in the Coulomb potential of the atomic Rydberg core. The results are compared with previous calculations based on single-electron models employing a zero-range contact-potential and short-range modele potential. Czech Science Foundation (Project No. P208/14-15989P).
ERIC Educational Resources Information Center
Smith, Carol; And Others
The concept of the density of a material has an important role in elementary and secondary school science curricula, but it is a difficult concept to grasp. This project explores why this should be and whether there are some simpler, more accessible notions which can serve as the basis for building a concept of density in students' minds during…
Wolfenden, A.; Tang, H.H.; Chawla, K.; Hermel, T.
1999-07-01
The effects of thermal cycling on the mechanical and physical properties, namely, the density, dynamic elastic modulus and vibrational damping, were measured for a particular reinforced metal matrix composite (MMC). The material was made by Duralcan. Specimens were exposed to up thermal cycles from room temperature to 300 C. The density of the material was measured by the Archimedes technique. The dynamic Young`s Modulus and vibrational damping of the material were determined by the piezoelectric ultrasonic composite oscillator technique (PUCOT). The results showed that the density and elastic modulus of the material increased only slightly due to the thermal cycling while the damping increased significantly. An increase in dislocation concentration near the particle/matrix interfaces caused by the thermal cycling could account for the measured results.
THE COLUMN DENSITY VARIANCE IN TURBULENT INTERSTELLAR MEDIA: A FRACTAL MODEL APPROACH
Seon, Kwang-Il
2012-12-20
Fractional Brownian motion structures are used to investigate the dependency of column density variance ({sigma}{sup 2}{sub lnN}) in the turbulent interstellar medium on the variance of three-dimensional density ({sigma}{sup 2}{sub ln{rho}}) and the power-law slope of the density power spectrum. We provide quantitative expressions to infer the three-dimensional density variance, which is not directly observable, from the observable column density variance and spectral slope. We also investigate the relationship between the column density variance and sonic Mach number (M{sub s}) in the hydrodynamic (HD) regime by assuming the spectral slope and density variance to be functions of sonic Mach number, as obtained from the HD turbulence simulations. They are related by the expression {sigma}{sup 2}{sub lnN} = A{sigma}{sub ln{rho}} {sup 2} = Aln (1 + b {sup 2} M{sup 2}{sub s}), suggested by Burkhart and Lazarian for the magnetohydrodynamic case. The proportional constant A varies from Almost-Equal-To 0.2 to Almost-Equal-To 0.4 in the HD regime as the turbulence forcing parameter b increases from 1/3 (purely solenoidal forcing) to 1 (purely compressive forcing). It is also discussed that the parameter A is lowered in the presence of a magnetic field.
Ding, Jiarui; Shah, Sohrab; Condon, Anne
2016-01-01
Motivation: Many biological data processing problems can be formalized as clustering problems to partition data points into sensible and biologically interpretable groups. Results: This article introduces densityCut, a novel density-based clustering algorithm, which is both time- and space-efficient and proceeds as follows: densityCut first roughly estimates the densities of data points from a K-nearest neighbour graph and then refines the densities via a random walk. A cluster consists of points falling into the basin of attraction of an estimated mode of the underlining density function. A post-processing step merges clusters and generates a hierarchical cluster tree. The number of clusters is selected from the most stable clustering in the hierarchical cluster tree. Experimental results on ten synthetic benchmark datasets and two microarray gene expression datasets demonstrate that densityCut performs better than state-of-the-art algorithms for clustering biological datasets. For applications, we focus on the recent cancer mutation clustering and single cell data analyses, namely to cluster variant allele frequencies of somatic mutations to reveal clonal architectures of individual tumours, to cluster single-cell gene expression data to uncover cell population compositions, and to cluster single-cell mass cytometry data to detect communities of cells of the same functional states or types. densityCut performs better than competing algorithms and is scalable to large datasets. Availability and Implementation: Data and the densityCut R package is available from https://bitbucket.org/jerry00/densitycut_dev. Contact: condon@cs.ubc.ca or sshah@bccrc.ca or jiaruid@cs.ubc.ca Supplementary information: Supplementary data are available at Bioinformatics online. PMID:27153661
NASA Astrophysics Data System (ADS)
Chumakov, E. S.; Fomin, Y. D.; Shangina, E. L.; Tareyeva, E. E.; Tsiok, E. N.; Ryzhov, V. N.
2015-08-01
In the framework of the density functional theory of freezing proposed in our previous works, we calculate the phase diagram of two-dimensional system of particles interacting through the repulsive shoulder potential. This potential consists of the hard core and repulsive shoulder of the larger radius. It is shown that at low densities the system melts through the continuous transition in accordance with the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) scenario, while at high densities the conventional first order transition takes place.
NASA Astrophysics Data System (ADS)
Patel, Niravkumar D.; Nocera, Alberto; Alvarez, Gonzalo; Arita, Ryotaro; Moreo, Adriana; Dagotto, Elbio
2016-08-01
The recent discovery of superconductivity under high pressure in the two-leg ladder compound BaFe2S3 [H. Takahashi et al., Nat. Mater. 14, 1008 (2015), 10.1038/nmat4351] opens a broad avenue of research, because it represents the first report of pairing tendencies in a quasi-one-dimensional iron-based high-critical-temperature superconductor. Similarly, as in the case of the cuprates, ladders and chains can be far more accurately studied using many-body techniques and model Hamiltonians than their layered counterparts, particularly if several orbitals are active. In this publication, we derive a two-orbital Hubbard model from first principles that describes individual ladders of BaFe2S3 . The model is studied with the density matrix renormalization group. These first reported results are exciting for two reasons: (i) at half-filling, ferromagnetic order emerges as the dominant magnetic pattern along the rungs of the ladder, and antiferromagnetic order along the legs, in excellent agreement with neutron experiments; and (ii) with hole doping, pairs form in the strong coupling regime, as found by studying the binding energy of two holes doped on the half-filled system. In addition, orbital selective Mott phase characteristics develop with doping, with only one Wannier orbital receiving the hole carriers while the other remains half-filled. These results suggest that the analysis of models for iron-based two-leg ladders could clarify the origin of pairing tendencies and other exotic properties of iron-based high-critical-temperature superconductors in general.
NASA Astrophysics Data System (ADS)
Dey, B.; Meyer, C. A.; Bellis, M.; Williams, M.; Adhikari, K. P.; Adikaram, D.; Aghasyan, M.; Amaryan, M. J.; Anderson, M. D.; Anefalos Pereira, S.; Ball, J.; Baltzell, N. A.; Battaglieri, M.; Bedlinskiy, I.; Biselli, A. S.; Bono, J.; Boiarinov, S.; Briscoe, W. J.; Brooks, W. K.; Burkert, V. D.; Carman, D. S.; Celentano, A.; Chandavar, S.; Colaneri, L.; Cole, P. L.; Contalbrigo, M.; Cortes, O.; Crede, V.; D'Angelo, A.; Dashyan, N.; De Vita, R.; De Sanctis, E.; Deur, A.; Djalali, C.; Doughty, D.; Dugger, M.; Dupre, R.; El Alaoui, A.; El Fassi, L.; Elouadrhiri, L.; Fedotov, G.; Fegan, S.; Fleming, J. A.; Garçon, M.; Gevorgyan, N.; Ghandilyan, Y.; Gilfoyle, G. P.; Giovanetti, K. L.; Girod, F. X.; Glazier, D. I.; Goetz, J. T.; Gothe, R. W.; Griffioen, K. A.; Guidal, M.; Hafidi, K.; Hanretty, C.; Harrison, N.; Hattawy, M.; Hicks, K.; Ho, D.; Holtrop, M.; Hyde, C. E.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Jenkins, D.; Jo, H. S.; Joo, K.; Keller, D.; Khandaker, M.; Kim, A.; Kim, W.; Klein, A.; Klein, F. J.; Koirala, S.; Kubarovsky, V.; Kuhn, S. E.; Kuleshov, S. V.; Lenisa, P.; Livingston, K.; Lu, H.; MacGregor, I. J. D.; Markov, N.; Mayer, M.; McCracken, M. E.; McKinnon, B.; Mineeva, T.; Mirazita, M.; Mokeev, V.; Montgomery, R. A.; Moriya, K.; Moutarde, H.; Munevar, E.; Munoz Camacho, C.; Nadel-Turonski, P.; Niccolai, S.; Niculescu, G.; Niculescu, I.; Osipenko, M.; Pappalardo, L. L.; Paremuzyan, R.; Park, K.; Pasyuk, E.; Peng, P.; Phillips, J. J.; Pisano, S.; Pogorelko, O.; Pozdniakov, S.; Price, J. W.; Procureur, S.; Protopopescu, D.; Puckett, A. J. R.; Rimal, D.; Ripani, M.; Ritchie, B. G.; Rizzo, A.; Rossi, P.; Roy, P.; Sabatié, F.; Saini, M. S.; Schott, D.; Schumacher, R. A.; Seder, E.; Senderovich, I.; Sharabian, Y. G.; Simonyan, A.; Smith, E. S.; Sober, D. I.; Sokhan, D.; Stepanyan, S. S.; Stoler, P.; Strakovsky, I. I.; Strauch, S.; Sytnik, V.; Taiuti, M.; Tang, W.; Tkachenko, S.; Ungaro, M.; Vernarsky, B.; Vlassov, A. V.; Voskanyan, H.; Voutier, E.; Walford, N. K.; Watts, D. P.; Zachariou, N.; Zana, L.; Zhang, J.; Zhao, Z. W.; Zonta, I.; CLAS Collaboration
2014-05-01
High-statistics measurements of differential cross sections and spin density matrix elements for the reaction γp →ϕp have been made using the CLAS detector at Jefferson Lab. We cover center-of-mass energies (√s ) from 1.97 to 2.84 GeV, with an extensive coverage in the ϕ production angle. The high statistics of the data sample made it necessary to carefully account for the interplay between the ϕ natural lineshape and effects of the detector resolution, that are found to be comparable in magnitude. We study both the charged- (ϕ →K+K-) and neutral- (ϕ →KS0KL0) KK ¯ decay modes of the ϕ. Further, for the charged mode, we differentiate between the cases where the final K- track is directly detected or its momentum reconstructed as the total missing momentum in the event. The two charged-mode topologies and the neutral-mode have different resolutions and are calibrated against each other. Extensive usage is made of kinematic fitting to improve the reconstructed ϕ mass resolution. Our final results are reported in 10- and mostly 30-MeV-wide √s bins for the charged- and the neutral-modes, respectively. Possible effects from K+Λ* channels with pKK ¯ final states are discussed. These present results constitute the most precise and extensive ϕ photoproduction measurements to date and in conjunction with the ω photoproduction results recently published by CLAS, will greatly improve our understanding of low energy vector meson photoproduction.
Patel, Niravkumar D.; Nocera, Alberto; Alvarez, Gonzalo; ...
2016-08-10
The recent discovery of superconductivity under high pressure in the two-leg ladder compound BaFe2S3 [H. Takahashi et al., Nat. Mater. 14, 1008 (2015)] opens a broad avenue of research, because it represents the first report of pairing tendencies in a quasi-one-dimensional iron-based high-critical-temperature superconductor. Similarly, as in the case of the cuprates, ladders and chains can be far more accurately studied using many-body techniques and model Hamiltonians than their layered counterparts, particularly if several orbitals are active. In this publication, we derive a two-orbital Hubbard model from first principles that describes individual ladders of BaFe2S3. The model is studied withmore » the density matrix renormalization group. These first reported results are exciting for two reasons: (i) at half-filling, ferromagnetic order emerges as the dominant magnetic pattern along the rungs of the ladder, and antiferromagnetic order along the legs, in excellent agreement with neutron experiments; and (ii) with hole doping, pairs form in the strong coupling regime, as found by studying the binding energy of two holes doped on the half-filled system. In addition, orbital selective Mott phase characteristics develop with doping, with only oneWannier orbital receiving the hole carriers while the other remains half-filled. Lastly, these results suggest that the analysis of models for iron-based two-leg ladders could clarify the origin of pairing tendencies and other exotic properties of iron-based high-critical-temperature superconductors in general.« less
Dey, B.; Meyer, C. A.; Bellis, M.; ...
2014-05-27
High-statistics measurements of differential cross sections and spin density matrix elements for the reaction γ p → Φp have been made using the CLAS detector at Jefferson Lab. We cover center-of-mass energies (√s) from 1.97 to 2.84 GeV, with an extensive coverage in the Φ production angle. The high statistics of the data sample made it necessary to carefully account for the interplay between the Φ natural lineshape and effects of the detector resolution, that are found to be comparable in magnitude. We study both the charged- (Φ → K⁺K⁻) and neutral- (Φ → K0SK0L)more » $$K\\bar{K}$$ decay modes of the Φ. Further, for the charged mode, we differentiate between the cases where the final K⁻ track is directly detected or its momentum reconstructed as the total missing momentum in the event. The two charged-mode topologies and the neutral-mode have different resolutions and are calibrated against each other. Extensive usage is made of kinematic fitting to improve the reconstructed Φ mass resolution. Our final results are reported in 10- and mostly 30-MeV-wide √s bins for the charged- and the neutral-mode, respectively. Possible effects from K⁺Λ* channels with p$$K\\bar{K}$$ final-states are discussed. These present results constitute the most precise and extensive Φ photoproduction measurements to date and in conjunction with the ω photoproduction results recently published by CLAS, will greatly improve our understanding of low energy vector meson photoproduction.« less
Mazziotti, David A.
2010-06-15
An improved parametrization of the two-electron reduced density matrix (2-RDM) [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)] was recently shown to yield energies and properties that are markedly better than those calculated by traditional ab initio methods of similar computational scaling. In this paper a family of such energy functionals, generalizing the ones obtained previously, is derived through the use of (i) p-particle contraction relations based on the contraction of the cumulant expansions of p-particle RDMs and (ii) Cauchy-Schwarz relations that arise from an important set of N-representability constraints known as the two-positivity conditions. The 2-RDMs are explicitly parameterized in terms of the first-order part of the cumulant 2-RDM and, for the inclusion of single excitations, a second-order part of the 1-RDM. In contrast to earlier formulations based on the coefficients from configuration interaction with single and double excitations (CISD), the cumulant-based parametric 2-RDM methods, from the properties of cumulants, are rigorously size extensive. We also show that writing the energy functionals in terms of correlated 1-RDMs and cumulant 2-RDMs reduces the computational cost of the parametric 2-RDM methods to that of CISD. Applications are made to ground-state energies of several molecules, equilibrium bond distances, and frequencies of HF, F{sub 2}, and CO, the relative energy of the cis and trans isomers of HO{sub 3}{sup -}, and the HCN-HNC isomerization reaction. For bond breaking in hydrogen fluoride the improved and more efficient parametric 2-RDM methods yield energies with similar accuracies at both equilibrium and nonequilibrium geometries in 6-31G** and polarized valence quadruple-{zeta} basis sets. Computed 2-RDMs very nearly satisfy well-known N-representability conditions.
Dey, B.; Meyer, C. A.; Bellis, M.; Williams, M.; Adhikari, K. P.; Adikaram, D.; Aghasyan, M.; Amaryan, M. J.; Anderson, M. D.; Anefalos Pereira, S.; Ball, J.; Baltzell, N. A.; Battaglieri, M.; Bedlinskiy, I.; Biselli, A. S.; Bono, J.; Boiarinov, S.; Briscoe, W. J.; Brooks, W. K.; Burkert, V. D.; Carman, D. S.; Celentano, A.; Chandavar, S.; Colaneri, L.; Cole, P. L.; Contalbrigo, M.; Cortes, O.; Crede, V.; D'Angelo, A.; Dashyan, N.; De Vita, R.; De Sanctis, E.; Deur, A.; Djalali, C.; Doughty, D.; Dugger, M.; Dupre, R.; El Alaoui, A.; El Fassi, L.; Elouadrhiri, L.; Fedotov, G.; Fegan, S.; Fleming, J. A.; Garçon, M.; Gevorgyan, N.; Ghandilyan, Y.; Gilfoyle, G. P.; Giovanetti, K. L.; Girod, F. X.; Glazier, D. I.; Goetz, J. T.; Gothe, R. W.; Griffioen, K. A.; Guidal, M.; Hafidi, K.; Hanretty, C.; Harrison, N.; Hattawy, M.; Hicks, K.; Ho, D.; Holtrop, M.; Hyde, C. E.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Jenkins, D.; Jo, H. S.; Joo, K.; Keller, D.; Khandaker, M.; Kim, A.; Kim, W.; Klein, A.; Klein, F. J.; Koirala, S.; Kubarovsky, V.; Kuhn, S. E.; Kuleshov, S. V.; Lenisa, P.; Livingston, K.; Lu, H.; MacGregor, I. J.D.; Markov, N.; Mayer, M.; McCracken, M. E.; McKinnon, B.; Mineeva, T.; Mirazita, M.; Mokeev, V.; Montgomery, R. A.; Moriya, K.; Moutarde, H.; Munevar, E.; Munoz Camacho, C.; Nadel-Turonski, P.; Niccolai, S.; Niculescu, G.; Niculescu, I.; Osipenko, M.; Pappalardo, L. L.; Paremuzyan, R.; Park, K.; Pasyuk, E.; Peng, P.; Phillips, J. J.; Pisano, S.; Pogorelko, O.; Pozdniakov, S.; Price, J. W.; Procureur, S.; Protopopescu, D.; Puckett, A. J. R.; Rimal, D.; Ripani, M.; Ritchie, B. G.; Rizzo, A.; Rossi, P.; Roy, P.; Sabatié, F.; Saini, M. S.; Schott, D.; Schumacher, R. A.; Seder, E.; Senderovich, I.; Sharabian, Y. G.; Simonyan, A.; Smith, E. S.; Sober, D. I.; Sokhan, D.; Stepanyan, S. S.; Stoler, P.; Strakovsky, I. I.; Strauch, S.; Sytnik, V.; Taiuti, M.; Tang, W.; Tkachenko, S.; Ungaro, M.; Vernarsky, B.; Vlassov, A. V.; Voskanyan, H.; Voutier, E.; Watts, D. P.; Zachariou, N.; Zana, L.; Zhang, J.; Zhao, Z. W.; Zonta, I.
2014-05-27
High-statistics measurements of differential cross sections and spin density matrix elements for the reaction γ p → Φp have been made using the CLAS detector at Jefferson Lab. We cover center-of-mass energies (√s) from 1.97 to 2.84 GeV, with an extensive coverage in the Φ production angle. The high statistics of the data sample made it necessary to carefully account for the interplay between the Φ natural lineshape and effects of the detector resolution, that are found to be comparable in magnitude. We study both the charged- (Φ → K⁺K⁻) and neutral- (Φ → K^{0}_{S}K^{0}_{L}) $K\\bar{K}$ decay modes of the Φ. Further, for the charged mode, we differentiate between the cases where the final K⁻ track is directly detected or its momentum reconstructed as the total missing momentum in the event. The two charged-mode topologies and the neutral-mode have different resolutions and are calibrated against each other. Extensive usage is made of kinematic fitting to improve the reconstructed Φ mass resolution. Our final results are reported in 10- and mostly 30-MeV-wide √s bins for the charged- and the neutral-mode, respectively. Possible effects from K⁺Λ* channels with p$K\\bar{K}$ final-states are discussed. These present results constitute the most precise and extensive Φ photoproduction measurements to date and in conjunction with the ω photoproduction results recently published by CLAS, will greatly improve our understanding of low energy vector meson photoproduction.
2012-10-01
material obtained through a microfluidic approach is shown on figure 1. In this approach, one can vary the average size and droplets volume fraction in the...AFRL-AFOSR-UK-TR-2012-0049 Acoustic metamaterials through a microfluidic , bottom-up approach: Toward highly attenuating, negative...2012 Final Report 26 Apr 2011 - 26 Sep 2012 Acoustic metamaterials through a microfluidic , bottom-up approach: Toward highly attenuating, negative
Weber, Valéry; Laino, Teodoro; Pozdneev, Alexander; Fedulova, Irina; Curioni, Alessandro
2015-07-14
In this paper, we present a novel, highly efficient, and massively parallel implementation of the sparse matrix-matrix multiplication algorithm inspired by the midpoint method that is suitable for matrices with decay. Compared with the state of the art in sparse matrix-matrix multiplications, the new algorithm heavily exploits data locality, yielding better performance and scalability, approaching a perfect linear scaling up to a process box size equal to a characteristic length that is intrinsic to the matrices. Moreover, the method is able to scale linearly with system size reaching constant time with proportional resources, also regarding memory consumption. We demonstrate how the proposed method can be effectively used for the construction of the density matrix in electronic structure theory, such as Hartree-Fock, density functional theory, and semiempirical Hamiltonians. We present the details of the implementation together with a performance analysis up to 185,193 processes, employing a Hamiltonian matrix generated from a semiempirical NDDO scheme.
NASA Astrophysics Data System (ADS)
Nava, Andrea; Giuliano, Rosa; Campagnano, Gabriele; Giuliano, Domenico
2016-11-01
Using the properties of the transfer matrix of one-dimensional quantum mechanical systems, we derive an exact formula for the persistent current across a quantum mechanical ring pierced by a magnetic flux Φ as a single integral of a known function of the system's parameters. Our approach provides exact results at zero temperature, which can be readily extended to a finite temperature T . We apply our technique to exactly compute the persistent current through p -wave and s -wave superconducting-normal hybrid rings, deriving full plots of the current as a function of the applied flux at various system's scales. Doing so, we recover at once a number of effects such as the crossover in the current periodicity on increasing the size of the ring and the signature of the topological phase transition in the p -wave case. In the limit of a large ring size, resorting to a systematic expansion in inverse powers of the ring length, we derive exact analytic closed-form formulas, applicable to a number of cases of physical interest.
Gavan, Alexandru; Porfire, Alina; Marina, Cristina; Tomuta, Ioan
2017-03-01
The main objective of the present study was to apply QbD methodology in the development of once-a-day sustained release quetiapine tablets. The quality target product profile (QTPP) was defined after the pharmaceutical properties and kinetic release of the innovator product, Seroquel XR 200 mg. For the D-optimal experimental design, the level and ratio of matrix forming agents and the type of extragranular diluent were chosen as independent inputs, which represented critical formulation factors. The critical quality attributes (CQAs) studied were the cumulative percentages of quetiapine released after certain time intervals. After the analysis of the experimental design, optimal formulas and the design space were defined. Optimal formulas demonstrated zero-order release kinetics and a dissolution profile similar to the innovator product, with f2 values of 74.53 and 83.74. It was concluded that the QbD approach allowed fast development of sustained release tablets with similar dissolution behavior as the innovator product.
Archer, A J
2009-01-07
In recent years, a number of dynamical density functional theories (DDFTs) have been developed for describing the dynamics of the one-body density of both colloidal and atomic fluids. In the colloidal case, the particles are assumed to have stochastic equations of motion and theories exist for both the case when the particle motion is overdamped and also in the regime where inertial effects are relevant. In this paper, we extend the theory and explore the connections between the microscopic DDFT and the equations of motion from continuum fluid mechanics. In particular, starting from the Kramers equation, which governs the dynamics of the phase space probability distribution function for the system, we show that one may obtain an approximate DDFT that is a generalization of the Euler equation. This DDFT is capable of describing the dynamics of the fluid density profile down to the scale of the individual particles. As with previous DDFTs, the dynamical equations require as input the Helmholtz free energy functional from equilibrium density functional theory (DFT). For an equilibrium system, the theory predicts the same fluid one-body density profile as one would obtain from DFT. Making further approximations, we show that the theory may be used to obtain the mode coupling theory that is widely used for describing the transition from a liquid to a glassy state.
NASA Astrophysics Data System (ADS)
MacDonald, R.; Savina, M. E.
2003-12-01
One approach to curriculum review and development is to construct a matrix of the desired skills versus courses in the departmental curriculum. The matrix approach requires faculty to articulate their goals, identify specific skills, and assess where in the curriculum students will learn and practice these skills and where there are major skills gaps. Faculty members in the Geology Department at Carleton College developed a matrix of skills covered in geology courses with the following objectives: 1) Geology majors should begin their "senior integrative exercise" having practiced multiple times all of the formal steps in the research process (recognizing problems, writing proposals, carrying out a project, reporting a project in several ways); 2) Geology majors should learn and practice a variety of professional and life skills life (e.g. computer skills, field skills, lab skills, and interpretive skills).The matrix was used to identify where in the curriculum various research methods and skills were addressed and to map potential student experiences to the objectives. In Carleton's non-hierarchical curriculum, the matrix was used to verify that students have many opportunities to practice research and life skills regardless of the path they take to completion of the major. In William and Mary's more structured curriculum, the matrix was used to ensure that skills build upon each other from course to course. Faculty members in the Geology Department at the College of William and Mary first used this approach to focus on teaching quantitative skills across the geology curriculum, and later used it in terms of teaching research, communication, and information literacy skills. After articulating goals and skills, faculty members in both departments developed more specific skill lists within each category of skills, then described the current assignments and activities in each course relative to the specific components of the matrix and discussed whether to add
A simple approach for determining detonation velocity of high explosive at any loading density.
Keshavarz, Mohammad Hossein
2005-05-20
A simple empirical relationship is introduced between detonation velocity at any loading density and chemical composition of high explosive as well as its gas phase heat of formation, which is calculated by group additivity rules. The present work may be applied to any explosive that contains the elements of carbon, hydrogen, nitrogen and oxygen with no difficulties. The new correlation can easily be applied for determining detonation velocity of explosives with loading densities less than 1g/cm3 as well as greater than 1g/cm3. Calculated detonation velocities by this procedure for both pure and explosive formulations show good agreement with respect to measured detonation velocity over a wide range of loading density.
Exploration of Plasma Jets Approach to High Energy Density Physics. Final report
Chen, Chiping
2013-08-26
High-energy-density laboratory plasma (HEDLP) physics is an emerging, important area of research in plasma physics, nuclear physics, astrophysics, and particle acceleration. While the HEDLP regime occurs at extreme conditions which are often found naturally in space but not on the earth, it may be accessible by colliding high intensity plasmas such as high-energy-density plasma jets, plasmoids or compact toroids from plasma guns. The physics of plasma jets is investigated in the context of high energy density laboratory plasma research. This report summarizes results of theoretical and computational investigation of a plasma jet undergoing adiabatic compression and adiabatic expansion. A root-mean-squared (rms) envelope theory of plasma jets is developed. Comparison between theory and experiment is made. Good agreement between theory and experiment is found.
Linear density drift instabilities in very low beta plasmas A different approach
NASA Technical Reports Server (NTRS)
Gary, S. P.
1983-01-01
This paper reports a study of the linear Vlasov electromagnetic dispersion equation for density drift instabilities in very low beta plasmas. A uniform magnetic field and a weak uniform density gradient are assumed. This paper differs from most other studies of this topic in three important ways: (1) no low frequency or long wavelength approximations are made, (2) no gauge condition is imposed and (3) a modification of the local approximation is used which is argued to be less arbitrary than the usual local approximation. Numerical solution of the resulting dispersion equation yields stabilization of the universal density drift instability at values of beta somewhat higher than those obtained from the local approximation, and near maximum growth shows no evidence of coupling between the universal and Alfven modes.
Areal Crater Density Analysis of Volcanic Smooth Plains: A New Approach to Distinguishing Age Units
NASA Astrophysics Data System (ADS)
Ostrach, L. R.; Robinson, M. S.
2013-12-01
It is well documented that the lunar maria were emplaced over an extended period of time [e.g., 1-3], and mare units exhibit significant color differences in multispectral data that are interpreted to correlate with distinct mineralogical compositions and ages [e.g., 3-7]. Areal crater density (ACD) analysis is used as a novel approach to identify resurfacing boundaries within Mare Imbrium as a test case for mercurian studies. Absolute model age dating and measures of ACD from crater counts on Lunar Reconnaissance Orbiter Wide Angle Camera (LRO WAC) mosaics reveal two spatially expansive, statistically separable units in Mare Imbrium. The older, spectrally red unit (~15-18 wt% FeO, ~2-5 wt% TiO2 [8]) in the east is ~3.3 Ga, and the younger, spectrally blue unit (~17-20 wt% FeO, ~7-10 wt% TiO2 [8]) in the west is ~2.2 Ga. ACD measurements show a regional boundary at the contact between these two regions. The geologic contact is confidently observed in ACD maps derived for regions with model age differences >300-500 million years and spatial extents >1 × 104 km2. The older, spectrally red unit exhibits higher ACD (>35000 craters with diameters ≥500 m per 106 km2) and the younger, spectrally blue unit has a lower ACD (<26000 craters with diameters ≥500 m per 106 km2); the absolute model ages and ACD results agree with other dating studies of this region [5, 9-12]. Thus, ACD measurements provide a reliable technique to distinguish relative ages among geologic units as well as a means to explore the statistical significance of published absolute model ages. Moreover, the ability to distinguish surface units of different ages from measures of crater frequencies in Mare Imbrium, when spectral information is not available or units do not exhibit spectral contrasts, shows that the ACD technique may be applied to other planetary bodies to search for age boundaries within contiguous smooth plains units. For example, multispectral differences within volcanic units (age
NASA Astrophysics Data System (ADS)
Kimura, I.; Kasahara, Y.; Oya, H.
2001-07-01
It has been necessary requirements to determine the global electron density distribution in the plasmasphere with time resolutions, of less than a day. We have provided solutions to this requirement using the wave normal directions, delay time of Omega signals and the in situ electron density observed on-board the Japanese satellite Akebono (Sawada et al., Journal of Geophysical Research 98(11) (1993) 267, Kimura et al., Advance Space Research 15(2) (1995) 103, Advance Space Research 18(6) (1996) 279, Journal of Atmospheric and Solar-Terrestrial Physics 59 (1997) 1569). The present paper is intended to review our earlier studies.
NASA Astrophysics Data System (ADS)
Sangsawong, Supharart; Waiyawat, Weerawan; Shiowatana, Juwadee; Siripinyanond, Atitaya
2011-06-01
An on-line coupling between a continuous-flow sequential extraction (CFSE) unit and flow field-flow fractionation with cross flow matrix removal (FlFFF/CFM) with ICP-OES detection was developed for determination of metal leachability from soil. The use of high concentration of Mg(NO 3) 2 in exchangeable phase can cause undesirable matrix effects by shifting ionization equilibrium in the plasma, etc., resulting in a clear need for matrix removal. Therefore, the capability of FlFFF/CFM to remove Mg matrix ion from soil extract was evaluated. Poly(ethylene imine) (PEI) having molecular weight of 25,000 Da was added to form complexes with analyte elements (Cu, Mn, Pb, and Zn) but not the matrix element (Mg). The free Mg matrix ions were then removed by filtering off through the ultrafiltration membrane, having a 1000-Da molecular weight cut-off, inside the FlFFF channel. With the use of FlFFF/CFM, matrix removal efficiency was approximately 83.5%, which was equivalent to approximately 6-fold dilution of the matrix ion. The proposed hyphenated system of CFSE and FlFFF/CFM with ICP-OES detection was examined for its reliability by checking with SRM 2710 (a highly contaminated soil from Montana). The metal contents determined by the proposed method were not significantly different (at 95% confidence) from the certified values.
Santoro, R.J.
1996-09-01
Significant advantages can be gained by the use of high energy density fuels in volume limited applications. However, excessive soot formation that accompanies the combustion of these fuels presently limits their application. Fuel additive approaches prove attractive as they require minimal modifications to already existing equipment. In the present study, a variety of flame configurations were used to study the additive effects on soot formation. Through tests conducted on laminar diffusion flames carbon disulfide (CS2) and methanol (CH3OH) were found to be the most effective soot suppressants. Chemical interaction by either additive was found to far surpass the physical influences. However, the exact nature of the chemical action could not be established with the current set of experiments. Additionally, both of these additives were found to reduce soot formation in at least one high energy density fuel - quadricyclane (C7H8). To further validate this approach, studies were conducted using droplet flames and high-pressure spray flames.
A consumer-resource approach to the density-dependent population dynamics of mutualism
Holland, J. Nathaniel; DeAngelis, Donald L.
2010-01-01
Like predation and competition, mutualism is now recognized as a consumer resource (C-R) interaction, including, in particular, bi-directional (e.g., coral, plant- mycorrhizae) and uni-directional (e.g., ant-plant defense, plant-pollinator) C-R mutualisms. Here, we develop general theory for the density-dependent population dynamics of mutualism based on the C-R mechanism of interspecific interaction. To test the influence of C-R interactions on the dynamics and stability of bi- and uni-directional C-R mutualisms, we developed simple models that link consumer functional response of one mutualistic species with the resources supplied by another. Phase-plane analyses show that the ecological dynamics of C-R mutualisms are stable in general. Most transient behavior leads to an equilibrium of mutualistic coexistence, at which both species densities are greater than in the absence of interactions. However, due to the basic nature of C-R interactions, certain density-dependent conditions can lead to C-R dynamics characteristic of predator-prey interactions, in which one species overexploits and causes the other to go extinct. Consistent with empirical phenomena, these results suggest that the C-R interaction can provide a broad mechanism for understanding density-dependent population dynamics of mutualism. By unifying predation, competition, and mutualism under the common ecological framework of consumer-resource theory, we may also gain a better understanding of the universal features of interspecific interactions in general.
The structure of mixed {sup 3}He-{sup 4}He droplets doped with OCS: A density functional approach
Leal, Antonio; Mateo, David; Pi, Martí; Barranco, Manuel; Navarro, Jesús
2013-11-07
We have investigated the structure and energetics of mixed {sup 3}He-{sup 4}He droplets doped with a carbonyl sulfide molecule within a density functional approach considering a small but finite temperature of 0.1 K. The molecule is treated as an external field to which the helium droplet is attached. The energetics and appearance of these droplets are discussed for selected numbers of helium atoms, identifying the first magic numbers of the fermionic component.
Abrams, Peter A
2009-09-01
Consumer-resource models are used to deduce the functional form of density dependence in the consumer population. A general approach to determining the form of consumer density dependence is proposed; this involves determining the equilibrium (or average) population size for a series of different harvest rates. The relationship between a consumer's mortality and its equilibrium population size is explored for several one-consumer/one-resource models. The shape of density dependence in the resource and the shape of the numerical and functional responses all tend to be "inherited" by the consumer's density dependence. Consumer-resource models suggest that density dependence will very often have both concave and convex segments, something that is impossible under the commonly used theta-logistic model. A range of consumer-resource models predicts that consumer population size often declines at a decelerating rate with mortality at low mortality rates, is insensitive to or increases with mortality over a wide range of intermediate mortalities, and declines at a rapidly accelerating rate with increased mortality when mortality is high. This has important implications for management and conservation of natural populations.
Density matters: Review of approaches to setting organism-based ballast water discharge standards
Lee II,; Frazier,; Ruiz,
2010-01-01
As part of their effort to develop national ballast water discharge standards under NPDES permitting, the Office of Water requested that WED scientists identify and review existing approaches to generating organism-based discharge standards for ballast water. Six potential approaches were identified and the utility and uncertainties of each approach was evaluated. During the process of reviewing the existing approaches, the WED scientists, in conjunction with scientists at the USGS and Smithsonian Institution, developed a new approach (per capita invasion probability or "PCIP") that addresses many of the limitations of the previous methodologies. THE PCIP approach allows risk managers to generate quantitative discharge standards using historical invasion rates, ballast water discharge volumes, and ballast water organism concentrations. The statistical power of sampling ballast water for both the validation of ballast water treatment systems and ship-board compliance monitoring with the existing methods, though it should be possible to obtain sufficient samples during treatment validation. The report will go to a National Academy of Sciences expert panel that will use it in their evaluation of approaches to developing ballast water discharge standards for the Office of Water.
NASA Astrophysics Data System (ADS)
Lougovski, A.; Hofheinz, F.; Maus, J.; Schramm, G.; Will, E.; van den Hoff, J.
2014-02-01
The aim of this study is the evaluation of on-the-fly volume of intersection computation for system’s geometry modelling in 3D PET image reconstruction. For this purpose we propose a simple geometrical model in which the cubic image voxels on the given Cartesian grid are approximated with spheres and the rectangular tubes of response (ToRs) are approximated with cylinders. The model was integrated into a fully 3D list-mode PET reconstruction for performance evaluation. In our model the volume of intersection between a voxel and the ToR is only a function of the impact parameter (the distance between voxel centre to ToR axis) but is independent of the relative orientation of voxel and ToR. This substantially reduces the computational complexity of the system matrix calculation. Based on phantom measurements it was determined that adjusting the diameters of the spherical voxel size and the ToR in such a way that the actual voxel and ToR volumes are conserved leads to the best compromise between high spatial resolution, low noise, and suppression of Gibbs artefacts in the reconstructed images. Phantom as well as clinical datasets from two different PET systems (Siemens ECAT HR+ and Philips Ingenuity-TF PET/MR) were processed using the developed and the respective vendor-provided (line of intersection related) reconstruction algorithms. A comparison of the reconstructed images demonstrated very good performance of the new approach. The evaluation showed the respective vendor-provided reconstruction algorithms to possess 34-41% lower resolution compared to the developed one while exhibiting comparable noise levels. Contrary to explicit point spread function modelling our model has a simple straight-forward implementation and it should be easy to integrate into existing reconstruction software, making it competitive to other existing resolution recovery techniques.
Míguez-Framil, Martha; Cabarcos, Pamela; Tabernero, María Jesús; Bermejo, Ana María; Bermejo-Barrera, Pilar; Moreda-Piñeiro, Antonio
2013-11-05
The possibility of assisting enzymatic hydrolysis (EH) procedures by sample disruption mechanisms inherent to matrix solid phase dispersion (MSPD) has been explored in the current study. EH of hair specimens from poly-drug abusers was assisted by dispersing/blending the sample (0.05 g) with alumina (2.25 g) before loading the dissolved enzyme (6 mL of 1 mg mL(-1) Pronase E in 1.4 M/1.4 M Tris/HCl, pH 7.3) through the hair-alumina solid phase packaged inside a disposable MSPD syringe. The MSPD-EH method was developed, and it proved to offer quantitative results when isolating cocaine, benzoylecgonine (BZE), codeine, morphine and 6-monoacethylmorphine (6-MAM) from human hair samples. The procedure allows an on column clean-up/pre-concentration procedure of the isolated targets by attaching a previously conditioned Oasis HLB cartridge to the end of the MSPD syringe. The EH procedure of human hair with Pronase E can therefore be shortened to approximately 30 min. Within this time, sample blending/dispersion, MSPD syringe package, elution (EH when dissolved Pronase E is passing through the sample-dispersant bed), and extract clean-up and target pre-concentration stages are achieved. Gas chromatography-mass spectrometry (GC-MS) was used for determining each target after elution from the Oasis HLB cartridges with 2 mL of 2% (v/v) acetic acid in methanol, concentration by N2 stream evaporation, and dried extract derivatization with N-methyl-tert-butylsilyltrifluoroacetamide (BSTFA) and chlorotrimethylsilane (TMCS). The method was validated according to the guidance for bioanalytical method validation of the US Department of Health and Human Services, Food and Drug Administration. The simplicity of the proposed approach makes it a useful procedure for screening/quantifying drugs of abuse in hair specimens from poly-drug abusers.
NASA Technical Reports Server (NTRS)
Sorini, Chris; Chattopadhyay, Aditi; Goldberg, Robert K.; Kohlman, Lee W.
2016-01-01
Understanding the high velocity impact response of polymer matrix composites with complex architectures is critical to many aerospace applications, including engine fan blade containment systems where the structure must be able to completely contain fan blades in the event of a blade-out. Despite the benefits offered by these materials, the complex nature of textile composites presents a significant challenge for the prediction of deformation and damage under both quasi-static and impact loading conditions. The relatively large mesoscale repeating unit cell (in comparison to the size of structural components) causes the material to behave like a structure rather than a homogeneous material. Impact experiments conducted at NASA Glenn Research Center have shown the damage patterns to be a function of the underlying material architecture. Traditional computational techniques that involve modeling these materials using smeared homogeneous, orthotropic material properties at the macroscale result in simulated damage patterns that are a function of the structural geometry, but not the material architecture. In order to preserve heterogeneity at the highest length scale in a robust yet computationally efficient manner, and capture the architecturally dependent damage patterns, a previously-developed subcell modeling approach where the braided composite unit cell is approximated as a series of four adjacent laminated composites is utilized. This work discusses the implementation of the subcell methodology into the commercial transient dynamic finite element code LS-DYNA (Livermore Software Technology Corp.). Verification and validation studies are also presented, including simulation of the tensile response of straight-sided and notched quasi-static coupons composed of a T700/PR520 triaxially braided [0deg/60deg/-60deg] composite. Based on the results of the verification and validation studies, advantages and limitations of the methodology as well as plans for future work
A universal approach for template-directed assembly of ultrahigh density magnetic nanodot arrays.
Xia, Guodong; Wang, Sumei; Jeong, Seong-Jun
2010-12-03
L1(0) ordered alloys, such as FePt, CoPt and FePd alloys with high magnetocrystalline anisotropy, have attracted much attention due to their potential applications in ultrahigh density data storage. The assembly or organization of nanoparticle arrays is necessary for device application. A facile and general method to fabricate highly ordered ferromagnetic nanostructure arrays was demonstrated. It is found that simple oxygen plasma can make a hydrophilic polymer template, which would easily integrate with the widely used spin-coating process. With simple block copolymer lithography and spin-coating process, uniform ferromagnetic nanoparticle arrays can be easily fabricated over a large area. It is also significant that a very high coercivity up to 10 kOe was obtained in CoPt nanodot arrays. This method can find attractive applications in ultrahigh density storage media.