Search results for "Degenerate energy levels"
showing 10 items of 221 documents
Unravelling the kinetics and molecular mechanism of the degenerate Cope rearrangement of bullvalene
2020
The kinetics and molecular mechanism of the gas phase degenerate Cope rearrangement (DCR) of bullvalene have been investigated by applying quantum mechanical calculations. Highly accurate energies (CBS-QB3 and CBS-APNO) and RRKM calculations were employed to study the kinetics and ‘fall-off’ behavior. It was found that the DCR of bullvalene (C3v) occurs through a bishomoaromatic transition structure (C2v) with an energy barrier of ∼49 kJ mol−1. The calculated activation energy and enthalpy were in good agreement with the available values in the literature, but lower than those of common Cope rearrangement; this result is related to the high stabilization energy due to the interaction of the…
The minimum mean cycle-canceling algorithm for linear programs
2022
Abstract This paper presents the properties of the minimum mean cycle-canceling algorithm for solving linear programming models. Originally designed for solving network flow problems for which it runs in strongly polynomial time, most of its properties are preserved. This is at the price of adapting the fundamental decomposition theorem of a network flow solution together with various definitions: that of a cycle and the way to calculate its cost, the residual problem, and the improvement factor at the end of a phase. We also use the primal and dual necessary and sufficient optimality conditions stated on the residual problem for establishing the pricing step giving its name to the algorith…
Łojasiewicz exponents, the integral closure of ideals and Newton polyhedra
2003
We give an upper estimate for the Łojasiewicz exponent $\ell(J,I)$ of an ideal $J\subseteq A(K^{n})$ with respect to another ideal I in the ring $A(K^{n})$ of germs analytic functions $f$ : $(K^{n},\mathrm{O})\rightarrow K$ , where $K=C$ or $R$ , using Newton polyhedrons. In particular, we give a method to estimate the Łojasiewicz exponent $\alpha_{0}(f)$ of a germ $f\in A(K^{n})$ that can be applied when $f$ is Newton degenerate with respect to its Newton polyhedron.
Evidence of oblate-prolate shape coexistence in the strongly-deformed nucleus 119Cs
2021
International audience; Prolate-oblate shape coexistence close to the ground state in the strongly-deformed proton-rich A≈120 nuclei is reported for the first time. One of the four reported bands in 119Cs, built on a 11/2− state at 670 keV, consists of nearly degenerate signature partners, and has properties which unequivocally indicate the strongly-coupled πh11/2[505]11/2− configuration associated with oblate shape. Together with the decoupled πh11/2[541]3/2− band built on the 11/2− prolate state at 110 keV, for which a half-life of T1/2=55(5)μs has been measured, the new bands bring evidence of shape coexistence at low spin in the proton-rich strongly deformed A≈120 nuclei, a phenomenon p…
Continuity of solutions of linear, degenerate elliptic equations
2009
We consider the simplest form of a second order, linear, degenerate, divergence structure equation in the plane. Under an integrability condition on the degenerate function, we prove that the solutions are continuous.
Ultracold Rare-Earth Magnetic Atoms with an Electric Dipole Moment
2018
We propose a new method to produce an electric and magnetic dipolar gas of ultracold dysprosium atoms. The pair of nearly degenerate energy levels of opposite parity, at 17513.33 cm$^{-1}$ with electronic angular momentum $J=10$, and at 17514.50 cm$^{-1}$ with $J=9$, can be mixed with an external electric field, thus inducing an electric dipole moment in the laboratory frame. For field amplitudes relevant to current-day experiments, we predict a magnetic dipole moment up to 13 Bohr magnetons, and an electric dipole moment up to 0.22 Debye, which is similar to the values obtained for alkali-metal diatomics. When a magnetic field is present, we show that the electric dipole moment is strongly…
Wulff shape characterizations in overdetermined anisotropic elliptic problems
2017
We study some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and we prove the corresponding Wulff shape characterizations by using some integral identities and just one pointwise inequality. Our techniques provide a somehow unified approach to this variety of problems.
Local regularity for quasi-linear parabolic equations in non-divergence form
2018
Abstract We consider viscosity solutions to non-homogeneous degenerate and singular parabolic equations of the p -Laplacian type and in non-divergence form. We provide local Holder and Lipschitz estimates for the solutions. In the degenerate case, we prove the Holder regularity of the gradient. Our study is based on a combination of the method of alternatives and the improvement of flatness estimates.
Stress concentration for closely located inclusions in nonlinear perfect conductivity problems
2019
We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium. The governing equation may be degenerate of $p-$Laplace type, with $1<p \leq N$. We prove optimal $L^\infty$ estimates for the blow-up of the gradient of the solution as the distance between the inclusions tends to zero.
(Bounded) Traveling combustion fronts with degenerate kinetics
2022
Abstract We consider the propagation of a flame front in a solid periodic medium. It is governed by an equation of Hamilton–Jacobi type, whose front’s velocity depends on the temperature via a nonlinear degenerate kinetic rate. The temperature solves a free boundary problem subject to boundary conditions depending on the front’s velocity itself. We show the existence of nonplanar traveling wave solutions which are bounded and global. Previous results by the same authors (cf. Alibaud and Namah, 2017) were obtained for essentially positively lower bounded kinetics or eventually which have some very weak degeneracy. Here we consider very general degenerate kinetics, including for the first tim…