Search results for "PERTURBATION"
showing 10 items of 811 documents
Coupled-cluster methods including noniterative corrections for quadruple excitations
2005
A new method is presented for treating the effects of quadruple excitations in coupled-cluster theory. In the approach, quadruple excitation contributions are computed from a formula based on a non-Hermitian perturbation theory analogous to that used previously to justify the usual noniterative triples correction used in the coupled cluster singles and doubles method with a perturbative treatment of the triple excitations (CCSD(T)). The method discussed in this paper plays a parallel role in improving energies obtained with the full coupled-cluster singles, doubles, and triples method (CCSDT) by adding a perturbative treatment of the quadruple excitations (CCSDT(Q)). The method is tested fo…
Second sound propagation in laminar and turbulent superfluid 4He via extended thermodynamics
2012
In this work, previous results on the complex propagation of second sound in laminar and turbulent superfluid 4He are reported. Furthermore the case of inhomogeneous superfluid turbulence is examined and, in particular, the wave propagation is investigated in the presence of an anisotropic vortex tangle. Two cases of physical interest are considered: wave front collinear and orthogonal to the heat flux.
MS-CASPT2 analysis of the UV thermochromism of octamethyltrisilane
2006
We interpret the reversal of the direction of the thermochromic shift of the first absorption band of peralkylated oligosilanes as the silicon chain is extended, based on multistate complete active space second-order perturbation theory (MS-CASPT2) calculations for octamethyltrisilane, Si3Me8. The observed shift is attributed to the effect of b1 distortions from ground state equilibrium geometry on vertical excited state energies and intensities. A generally contracted basis set of atomic natural orbitals (ANOs) at a ground state geometry optimized in the second-order Moller–Plesset perturbation theory (MP2) approximation with Dunning's correlation consistent triple-zeta basis set (cc-pVTZ)…
Strong-coupling expansions for the -symmetric oscillators
1998
We study the traditional problem of convergence of perturbation expansions when the hermiticity of the Hamiltonian is relaxed to a weaker symmetry. An elementary and quite exceptional cubic anharmonic oscillator is chosen as an illustrative example of such models. We describe its perturbative features paying particular attention to the strong-coupling regime. Efficient numerical perturbation theory proves suitable for such a purpose.
A proof of bistability for the dual futile cycle
2014
Abstract The multiple futile cycle is an important building block in networks of chemical reactions arising in molecular biology. A typical process which it describes is the addition of n phosphate groups to a protein. It can be modelled by a system of ordinary differential equations depending on parameters. The special case n = 2 is called the dual futile cycle. The main result of this paper is a proof that there are parameter values for which the system of ODE describing the dual futile cycle has two distinct stable stationary solutions. The proof is based on bifurcation theory and geometric singular perturbation theory. An important entity built of three coupled multiple futile cycles is…
Smooth Feshbach map and operator-theoretic renormalization group methods
2003
Abstract A new variant of the isospectral Feshbach map defined on operators in Hilbert space is presented. It is constructed with the help of a smooth partition of unity, instead of projections, and is therefore called smooth Feshbach map . It is an effective tool in spectral and singular perturbation theory. As an illustration of its power, a novel operator-theoretic renormalization group method is described and applied to analyze a general class of Hamiltonians on Fock space. The main advantage of the new renormalization group method over its predecessors is its technical simplicity, which it owes to the use of the smooth Feshbach map.
Simplification of Models
2016
In practical applications the “complete” model, i.e., a model that contains all features that the experts in the application domain consider important, is often quite complicated and difficult to analyse mathematically. A straightforward numerical realization is often costly and may give very little qualitative understanding of the situation. It is therefore important to study if the model can be systematically simplified in order to enhance a qualitative analysis/understanding.
Geometric Singular Perturbation Theory Beyond Normal Hyperbolicity
2001
Geometric Singular Perturbation theory has traditionally dealt only with perturbation problems near normally hyperbolic manifolds of singularities. In this paper we want to show how blow up techniques can permit enlarging the applicability to non-normally hyperbolic points. We will present the method on well chosen examples in the plane and in 3-space.
Multiple Canard Cycles in Generalized Liénard Equations
2001
AbstractThe paper treats multiple limit cycle bifurcations in singular perturbation problems of planar vector fields. The results deal with any number of parameters. Proofs are based on the techniques introduced in “Canard Cycles and Center Manifolds” (F. Dumortier and R. Roussarie, 1996, Mem. Amer. Math. Soc., 121). The presentation is limited to generalized Liénard equations εx+α(x, c)x+β(x, c)=0.
Proof I: Upper Bounds
2019
In this chapter we study upper bounds on singular values and determinants of certain operators related to Pδ. The bounds are not probabilistic; they only depend on a certain smallness of the perturbation.