Search results for "potential function"

Superlinear Robin Problems with Indefinite Linear Part

2018

We consider a semilinear Robin problem with an indefinite linear part and a superlinear reaction term, which does not satisfy the usual in such cases AR condition. Using variational methods, together with truncation–perturbation techniques and Morse theory (critical groups), we establish the existence of three nontrivial solutions. Our result extends in different ways the multiplicity theorem of Wang.

On the determination of the intramolecular potential energy surface of polyatomic molecules: Hydrogen sulfide and formaldehyde as an illustration

2009

International audience; We present here an approach for determining the Hamiltonian of polyatomic molecules that allows one to successfully solve the problem of potential energy surface (PES) determination via construction and diagonalization of a Hamiltonian matrix of large dimension. In the suggested approach, the Hamiltonian is very simple and can be used both for any "normal" polyatomic molecule and for any isotopic species of a molecule. Molecules with two to four equivalent X-Y bonds are considered, and for illustration of the efficiency of the suggested approach, numerical calculations are made for the three-atomic (hydrogen sulfide) and four-atomic (formaldehyde) molecules.

Bayesian Smoothing in the Estimation of the Pair Potential Function of Gibbs Point Processes

1999

A flexible Bayesian method is suggested for the pair potential estimation with a high-dimensional parameter space. The method is based on a Bayesian smoothing technique, commonly applied in statistical image analysis. For the calculation of the posterior mode estimator a new Monte Carlo algorithm is developed. The method is illustrated through examples with both real and simulated data, and its extension into truly nonparametric pair potential estimation is discussed.

Stimulated Raman and Cars Spectroscopy of ν1 and 2ν2 (A1) Bands of 12CF4

1994

Two experimental coherent Raman techniques, stimulated Raman and coherent anti-Stokes Raman spectroscopy (CARS), were employed to study the Raman spectrum of CF 4 in the 900 cm −1 region. The stimulated Raman and CARS spectra of the ν 1 band of CF 4 were recorded at high resolution. The analysis of these spectra enabled some spectroscopic constants of this band to be refined and higher order constants to be determined for the first time. The first high-resolution CARS spectrum of the 2ν 2 (A 1 ) harmonic band is also presented. The rotational transitions of this band up to J = 40 were assigned and the first set of spectroscopic constants for this sub-level were determined. These results imp…

LEM for twisted re-entrant angle sections

2014

In this paper an innovative numerical method named as line element-less method, LEM, for finding solution of torsion problem has been extended to all shaped sections, including sections possessing re-entrant angles at their boundary. The response solution in terms of shear stress field or Prandtl function or warping function in all domain and for any kind of domain with arbitrary contour, may be performed quickly, calculating line integrals only. The method takes full advantage of the theory of analytic complex function and is robust in the sense that returns exact solution if this exists. Numerical implementation of LEM has been developed using Mathematica software without resorting to any…

Oб определении внутримолекулярной потенциальной функции многоатомной молекулы H2S

2008

In modern molecular physics, there are two basic methods of determining the intramolecular potential function of polyatomic molecules. The first method is ab initio calculations and the second is the so-called semi-empirical method in which the Hamiltonian parameters are varied by direct construction of the Hamiltonian matrix. In the present work, the second approach is discussed on the example of the XY2 three-atomic molecule of the C2v symmetry. On the one hand, it is extremely simple for implementation, and on the other hand, it considerably extends the capability of application of the traditional semi-empirical methods. The approach suggested involves two aspects that make it advantageo…

Complex analysis for the solution of torsion problems: a comparison among three methods

2009

Normalized Solutions to the Fractional Schrödinger Equation with Potential

2023

AbstractThis paper is concerned with the existence of normalized solutions to a class of Schrödinger equations driven by a fractional operator with a parametric potential term. We obtain minimization of energy functional associated with that equations assuming basic conditions for the potential. Our work offers a partial extension of previous results to the non-local case.

"Expanded" local mode approach and isotopic effect in polyatomic molecules

2014

In this thesis, on the base of the "expanded", local mode approach and general isotopic substitution theory we obtain sets of simple analytical relations between spectroscopic parameters (harmonic frequencies, anharmonic coefficients, ro-vibrational parameters, different kinds of Fermi and Coriolis-type interaction parameters) of the CH2D2, CH3D and CHD3 molecules. All of them are expressed as simple functions of spectroscopic parameters of the mother CH4 molecule. Test calculations with the isotopic relations show that even without including prior informations about the isotopic species, numerical results of calculations are in a good agreement both with experimental data and results of ab…

On the high resolution spectroscopy and intramolecular potential function of SO2

2009

Abstract Two weak stretching bands, ν 1  + 3 ν 3 and 3 ν 1  +  ν 3 , of the sulfur dioxide molecule have been recorded at high resolution and analyzed for the first time with using a Fourier transform Bruker IFS-120 HR interferometer. About 1000 transitions with J max .  = 51, K a max . = 16 , and 900 transitions with J max .  = 53, K a max . = 16 have been assigned to the bands ν 1  + 3 ν 3 and 3 ν 1  +  ν 3 , respectively. Analysis of the recorded spectra was made using the model of isolated vibrational states. Parameters obtained from the fit reproduce the initial experimental ro-vibrational energies with the rms deviation of 0.0006 and 0.0012 cm −1 for the bands, 3 ν 1  +  ν 3 and ν 1  …