Search results for "Linear Algebra."
showing 10 items of 552 documents
Realistic Implementation of the Particle Model for the Visualization of Nanoparticle Precipitation and Growth
2019
An application for visualizing the aggregation of structureless atoms is presented. The application allows us to demonstrate on a qualitative basis, as well as by quantitatively monitoring the aggregate surface/volume ratio, that the enhanced reactivity of nanoparticles can be connected with their large specific surface. It is suggested that, along with the use of geometric analogies, this bottom-up approach can be effective in discussing the enhanced reactivity proprieties of nanoparticles. The application is based on a two-dimensional realistic dynamic model where atoms move because of their thermal and interaction potential energies, and the trajectories are determined by solving numeric…
Bounded approximation properties via integral and nuclear operators
2010
Published version of an article in the journal:Proceedings of the American Mathematical Society. Also available from the publisher, Open Access
Nuclear structure of97Yin the interacting boson fermion plus broken pair model and the nature of the 3.523 MeV high-spin isomer
1998
Nuclear structure of 97Y is described in the interacting boson fermion plus broken pair model, including quasiproton and quasiproton-two-quasineutron configurations in the basis states. In particular, the yrast bands and the decay of the 27/2- high-spin isomer are accounted for in this approach.
From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture
2020
Abstract In this paper we study the joint convexity/concavity of the trace functions Ψ p , q , s ( A , B ) = Tr ( B q 2 K ⁎ A p K B q 2 ) s , p , q , s ∈ R , where A and B are positive definite matrices and K is any fixed invertible matrix. We will give full range of ( p , q , s ) ∈ R 3 for Ψ p , q , s to be jointly convex/concave for all K. As a consequence, we confirm a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture of Audenaert and Datta and obtain the full range of ( α , z ) for α-z Renyi relative entropies to be monotone under completely positive trace preserving maps. We also give simpler proofs of many known results, including the concavity of Ψ p…
On the hyperbolicity of certain models of polydisperse sedimentation
2012
The sedimentation of a polydisperse suspension of small spherical particles dispersed in a viscous fluid, where particles belong to N species differing in size, can be described by a strongly coupled system of N scalar, nonlinear first-order conservation laws for the evolution of the volume fractions. The hyperbolicity of this system is a property of theoretical importance because it limits the range of validity of the model and is of practical interest for the implementation of numerical methods. The present work, which extends the results of R. Burger, R. Donat, P. Mulet, and C.A. Vega (SIAM Journal on Applied Mathematics 2010; 70:2186–2213), is focused on the fluxes corresponding to the …
Daugavet- and delta-points in Banach spaces with unconditional bases
2020
We study the existence of Daugavet- and delta-points in the unit sphere of Banach spaces with a 1 1 -unconditional basis. A norm one element x x in a Banach space is a Daugavet-point (resp. delta-point) if every element in the unit ball (resp. x x itself) is in the closed convex hull of unit ball elements that are almost at distance 2 2 from x x . A Banach space has the Daugavet property (resp. diametral local diameter two property) if and only if every norm one element is a Daugavet-point (resp. delta-point). It is well-known that a Banach space with the Daugavet property does not have an unconditional basis. Similarly spaces with the diametral local diameter two property do not have an un…
The barrier height of the F+H2 reaction revisited: coupled-cluster and multireference configuration-interaction benchmark calculations.
2008
Large scale coupled-cluster benchmark calculations have been carried out to determine the barrier height of the F+H2 reaction as accurately as possible. The best estimates for the barrier height of the linear and bent transition states amount to 2.16 and 1.63 kcal/mol, respectively. These values include corrections for core correlation, scalar-relativistic effects, spin-orbit effects, as well as the diagonal Born-Oppenheimer correction. The CCSD(T) basis-set limits are estimated using extrapolation techniques with augmented quintuple and sextuple-zeta basis sets, and remaining N-electron errors are determined using coupled-cluster singles, doubles, triples, quadruples calculations with up t…
Basis-set extrapolation techniques for the accurate calculation of molecular equilibrium geometries using coupled-cluster theory
2006
To reduce remaining basis-set errors in the determination of molecular equilibrium geometries, a basis-set extrapolation (BSE) scheme is suggested for the forces used in geometry optimizations. The proposed BSE scheme is based on separating the Hartree-Fock and electron-correlation contributions and uses expressions obtained by straightforward differentiation of well established extrapolation formulas for energies when using basis sets from Dunning's hierarchy of correlation-consistent basis sets. Comparison with reference data obtained at the R12 coupled-cluster level [CCSD(T)-R12] demonstrates that BSE significantly accelerates the convergence to the basis-set limit, thus leading to impro…
Implementation of transition moments between excited states in the approximate coupled-cluster singles and doubles model
2008
An implementation of transition moments between excited states for the approximate coupled-cluster singles and doubles model (CC2) using the resolution of the identity (RI) approximation is reported. The accuracy of the RI approximation is analyzed for a testset of 7 molecules and 76 transitions. The RI error is found to be very small for both transition moments and oscillator strengths. Furthermore, the performance of the CC2 model in comparison with coupled-cluster singles and doubles (CCSD) is studied for 40 transitions of the same testset, yielding deviations of about 12% for the transition moments and 24% for the oscillator strengths. In addition, for 13 transitions of the testset the …
Molecular equilibrium geometries based on coupled-cluster calculations including quadruple excitations
2005
Using analytic gradient techniques and an additivity scheme for the various electron correlation contributions, i.e. core-correlation, contribution due to full treatment of triple excitations and contributions due to quadruple excitations calculated with different basis sets, the accuracy of computed geometrical parameters are analysed in comparison with experiment. For a test set of 12 closed-shell and 5 open-shell molecules, it is found that inclusion of quadruple excitations is essential to reach agreement with experiment. The mean error of 0.002 pm and the standard deviation of 0.040 pm of the present CCSD(T)/cc-pV6Z + core(CCSD(T)/cc-pCVQZ) + T/cc-pVTZ + Q/cc-pVDZ results for the close…