Search results for "PERTURBATION"
showing 10 items of 811 documents
Chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes-Renner relation
2010
The next to leading order chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes- Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order P…
Computation of conical intersections by using perturbation techniques
2005
Multiconfigurational second-order perturbation theory, both in its single-state multiconfigurational second-order perturbation theory (CASPT2) and multistate (MS-CASPT2) formulations, is used to search for minima on the crossing seams between different potential energy hypersurfaces of electronic states in several molecular systems. The performance of the procedures is tested and discussed, focusing on the problem of the nonorthogonality of the single-state perturbative solutions. In different cases the obtained structures and energy differences are compared with available complete active space self-consistent field and multireference configuration interaction solutions. Calculations on dif…
Multiconfigurational second-order perturbation study of the decomposition of the radical anion of nitromethane
2004
The doublet potential energy surfaces involved in the decomposition of the nitromethane radical anion (CH(3)NO(2) (-)) have been studied by using the multistate extension of the multiconfigurational second-order perturbation method (MS-CASPT2) in conjunction with large atomic natural orbital-type basis sets. A very low energy barrier is found for the decomposition reaction: CH(3)NO(2) (-)--[CH(3)NO(2)](-)--CH(3)+NO(2) (-). No evidence has been obtained on the existence of an isomerization channel leading to the initial formation of the methylnitrite anion (CH(3)ONO(-)) which, in a subsequent reaction, would yield nitric oxide (NO). In contrast, it is suggested that NO is formed through the …
The Magnus expansion and some of its applications
2008
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to build up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of prese…
A Perturbation Approach to Continuous-Time Portfolio Selection Under Stochastic Investment Opportunities
2013
This paper studies portfolio selection in continuous-time models with stochastic investment opportunities. We consider asset allocation problems where preferences are specified as power utility derived from terminal wealth as well as consumption-savings problems with recursive utility Epstein-Zin preferences. The paper approximates the associated dynamic programming problem by perturbing the coefficients of the stochastic dynamics. We represent the Hamilton-Jacobi-Bellman equation as a series of partial differential equations that can be solved iteratively in closed-form through computer algebra software, at any desired accuracy.
Comparison of parallel implementation of some multi-level Schwarz methods for singularly perturbed parabolic problems
1999
Abstract Parallel multi-level algorithms combining a time discretization and an overlapping domain decomposition technique are applied to the numerical solution of singularly perturbed parabolic problems. Two methods based on the Schwarz alternating procedure are considered: a two-level method with auxiliary “correcting” subproblems as well as a three-level method with auxiliary “predicting” and “correcting” subproblems. Moreover, modifications of the methods using time extrapolation on subdomain interfaces are investigated. The emphasis is given to the description of the algorithms as well as their computer realization on a distributed memory multiprocessor computer. Numerical experiments …
Density functional theory (DFT) prediction of structural and spectroscopic parameters of cytosine using harmonic and anharmonic approximations
2015
The applicability of popular and efficient B3LYP hybrid density functional and medium-size Pople-type basis set in combination with computationally expensive anharmonic model to obtain more accurate theoretical structure, vibrational frequencies and GIAO NMR parameters of cytosine was tested. We report on prediction of cytosine equilibrium (R e ) and rovibrationally averaged (R v ) structures and vibrational frequencies in the gas phase and DMSO solution using density functional theory combined with 6-311++G** basis set. The harmonic and anharmonic vibrational frequencies (using second-order vibrational perturbation theory, VPT2) were critically discussed. In comparison with initial harmoni…
Antiproton over proton and K$^-$ over K$^+$ multiplicity ratios at high $z$ in DIS
2020
The $\bar{\rm p} $ over p multiplicity ratio is measured in deep-inelastic scattering for the first time using (anti-) protons carrying a large fraction of the virtual-photon energy, $z>0.5$. The data were obtained by the COMPASS Collaboration using a 160 GeV muon beam impinging on an isoscalar $^6$LiD target. The regime of deep-inelastic scattering is ensured by requiring $Q^2$ > 1 (GeV/$c$)$^2$ for the photon virtuality and $W > 5$ GeV/$c^2$ for the invariant mass of the produced hadronic system. The range in Bjorken-$x$ is restricted to $0.01 < x < 0.40$. Protons and antiprotons are identified in the momentum range $20 ��60$ GeV/$c$. In the whole studied $z$-region, the $\…
A New Approach to Deriving Interatomic Many-Body Interactions in Metals
1998
An original method of treating the kinetic and exchange-correlation en- ergies functionals in terms of many particle interactions was developed. It is based on utilizing the local density approximation. The total electron density, extracted from the ab initio . band structure calculations, is expressed as a lin- ear superposition of contributions from the individual pseudoions embedded in the uniform background. The explicit expressions for the pair and triplet potentials are presented. The general form for the part of the pair interatomic interactions caused by the kinetic and. the exchange-correlation effects is ob- tained. Relationship between the developing approach and the perturbation…
Nonlinear vector Duffing inclusions with no growth restriction on the orientor field
2019
We consider nonlinear multivalued Dirichlet Duffing systems. We do not impose any growth condition on the multivalued perturbation. Using tools from the theory of nonlinear operators of monotone type, we prove existence theorems for the convex and the nonconvex problems. Also we show the existence of extremal trajectories and show that such solutions are $C_0^1(T,\mathbb{R}^N)$-dense in the solution set of the convex problem (strong relaxation theorem).