scholarly journals Interaction matrix element fluctuations in ballistic quantum dots: Random wave model

2008 ◽  
Vol 78 (8) ◽  
Author(s):  
L. Kaplan ◽  
Y. Alhassid
Keyword(s):  
Quantum Dots ◽  
Matrix Element ◽  
Wave Model ◽  
Interaction Matrix ◽  
Random Wave ◽  
Interaction Matrix Element

scholarly journals Interaction matrix element fluctuations in quantum dots

2008 ◽  
Author(s):  
L. Kaplan ◽  
Y. Alhassid ◽  
Pawel Danielewicz ◽  
Piotr Piecuch ◽  
Vladimir Zelevinsky
Keyword(s):  
Quantum Dots ◽  
Matrix Element ◽  
Interaction Matrix ◽  
Interaction Matrix Element

A Multichannel “Potential Curves Hopping” Model for Inelastic Collisions

1986 ◽  
Vol 41 (5) ◽  
pp. 704-714
Author(s):  
D. Campos ◽  
J. M. Tejeiro ◽  
F. Cristancho
Keyword(s):  
Matrix Element ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Inelastic Collisions ◽  
Interaction Matrix ◽  
Quantum Mechanical ◽  
Interaction Matrix Element ◽  
S Matrix ◽  
Hopping Model ◽  
Potential Curves

We introduce a multichannel “potential curves hopping” model and obtain the exact quantum mechanical S-matrix by solving the associated set of coupled second-order ordinary differential equations that describes the inelastic collisions between atomic particles. The only assumption is that the interaction matrix element between each pair of channels (say, γ and β) is of the form Uγβ(r) = Uβγ(r) =: Uγβ δ( r - rγβ), where δ (c) is the Dirac deltafunction, and rγβ and Uγβ are parameters which can be chosen freely.Semiclassical techniques can be incorporated directly in the theory if the Schrödinger equations for the uncoupled channels allow this treatment. The formulation is particularized to the two-channel problem and illustrated with a semiclassical example the He+ + Ne problem at 70.9 eV.

scholarly journals Partial conservation law in a schematic single j shell model

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740021 ◽  
Author(s):  
Wesley Pereira ◽  
Ricardo Garcia ◽  
Larry Zamick ◽  
Alberto Escuderos ◽  
Kai Neergård
Keyword(s):  
Angular Momentum ◽  
Matrix Element ◽  
Shell Model ◽  
Linear Function ◽  
Conservation Law ◽  
Interaction Matrix ◽  
Stationary States ◽  
Interaction Matrix Element ◽  
Angular Momenta ◽  
Partial Conservation

We report the discovery of a partial conservation law obeyed by a schematic Hamiltonian of two protons and two neutrons in a [Formula: see text] shell. In our Hamiltonian, the interaction matrix element of two nucleons with combined angular momentum [Formula: see text] is linear in [Formula: see text] for even [Formula: see text] and constant for odd [Formula: see text]. It turns out that in some stationary states, the sum of the angular momenta [Formula: see text] and [Formula: see text] of the proton and neutron pairs is conserved. The energies of these states are given by a linear function of [Formula: see text]. The systematics of their occurrence is described and explained.

Interaction Matrix Element in a Shell Model

1963 ◽  
Vol 129 (6) ◽  
pp. 2643-2652 ◽  
Author(s):  
U. Fano ◽  
F. Prats ◽  
Z. Goldschmidt
Keyword(s):  
Matrix Element ◽  
Shell Model ◽  
Interaction Matrix ◽  
Interaction Matrix Element

Some Hartree–Fock Results for (3d + 4s)q+1 Configurations

1971 ◽  
Vol 49 (9) ◽  
pp. 1205-1210 ◽  
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Matrix Element ◽  
Average Energy ◽  
Interaction Matrix ◽  
Neutral Atoms ◽  
Radial Functions ◽  
Interaction Matrix Element ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

Self-consistent field calculations have been performed in three different ways for the average energy of the configurations 3dq−14s2, 3dq4s, and 3dq+1, q = 2,3,..., 9 of the neutral atoms scandium to nickel. The calculations differ in the way the radial functions depend on the configuration. Parameters which enter into the interaction matrix for states of these configurations are reported. It is shown that the lack of orthogonality of an orbital from one configuration with that of another may alter the interaction matrix element significantly, and that the parameters for radial functions independent of the configuration are significantly different from those that depend on the configuration.

Morphological characterization of bicontinuous structures in polymer blends and microemulsions by the inverse-clipping method in the context of the clipped-random-wave model

2000 ◽  
Vol 61 (6) ◽  
pp. 6773-6780 ◽  
Author(s):  
Hiroshi Jinnai ◽  
Yukihiro Nishikawa ◽  
Sow-Hsin Chen ◽  
Satoshi Koizumi ◽  
Takeji Hashimoto
Keyword(s):  
Polymer Blends ◽  
Wave Model ◽  
Morphological Characterization ◽  
Random Wave

Numerical and Experimental Analysis of Extreme Slamming Loads on FPSO Bows

2002 ◽  
Author(s):  
Ole A. Hermundstad ◽  
Carl T. Stansberg ◽  
O̸yvind Hellan
Keyword(s):  
Wave Model ◽  
Element Model ◽  
Practical Method ◽  
Second Order ◽  
Random Wave ◽  
Fe Model ◽  
Time Step ◽  
Scaled Model ◽  
Structural Responses ◽  
Relative Motions

A practical method for prediction of slamming loads and structural responses in the bow of an FPSO is presented. Incoming waves are simulated by a second-order random wave model, which describes the water elevation and kinematics. Vessel motions are calculated by linear analysis. The diffracted wave field is calculated taking into account linear 3D diffraction. Relative motions are then estimated by combining the linear vessel motions, second-order incoming waves and linear diffraction. The relative motions and velocities at the bow are used as input to numerical slamming calculations. The bow is divided into 2D sections and a boundary value problem is solved for each section applying the generalized Wagner-method of Zhao & Faltinsen (1993) and Zhao et al (1996). The 2D slamming calculations account for the local pile-up of water on each side of the section during impact. Structural responses are calculated from a finite-element model of the bow using the exact pressure distribution from the slamming calculations. This is achieved by automatic mapping of pressures onto the outer surface of the FE-model and performing a quasi-static structural analysis for each time-step. The methods are implemented into a package of computer tools, allowing the user to perform the various steps in the process with little manual editing of data. The system runs easily on a standard PC. Measurements on a 1:55 scaled model of an FPSO are used for validation of the bow slamming calculations. The model was equipped with five 3.85m × 1.65m (full-scale) panels in the upper part of the bow for slamming force measurements. The tests were run in storm conditions with steep waves. The calculated slamming force on a panel located at the foremost tip of the bulwark, 12.8 meters above the mean waterline, is compared with measured results for selected extreme slamming events. Considering the complexity of this problem and the relative simplicity of the approach, the agreement is very good.

Numerical Simulation of Non-Gaussian Wave Elevation and Kinematics Based on Two-Dimensional Fourier Transform

2006 ◽  
Author(s):  
Xiang Yuan Zheng ◽  
Torgeir Moan ◽  
Ser Tong Quek
Keyword(s):  
Fourier Transform ◽  
Wave Interaction ◽  
Wave Theory ◽  
Two Dimensions ◽  
Second Order ◽  
Interaction Matrix ◽  
Random Wave ◽  
Two Dimensional ◽  
Near Surface ◽  
Wave Elevation

The one-dimensional Fast Fourier Transform (FFT) has been extensively applied to efficiently simulate Gaussian wave elevation and water particle kinematics. The actual sea elevation/kinematics exhibit non-Gaussianities that mathematically can be represented by the second-order random wave theory. The elevation/kinematics formulation contains double-summation frequency sum and difference terms which in computation make the dynamic analysis of offshore structural response prohibitive. This study aims at a direct and efficient two-dimensional FFT algorithm for simulating the frequency sum terms. For the frequency difference terms, inverse FFT and FFT are respectively implemented across the two dimensions of the wave interaction matrix. Given specified wave conditions, not only the wave elevation but kinematics and associated Morison force are simulated. Favorable agreements are achieved when the statistics of elevation/kinematics are compared with not only the empirical fits but the analytical solutions developed based on modified eigenvalue/eigenvector approach, while the computation effort is very limited. In addition, the stochastic analyses in both time-and frequency domains show that the near-surface Morison force and induced linear oscillator response exhibits stronger non-Gaussianities by involving the second-order wave effects.

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