On the shape of invading population in anisotropic environments

Mathematical Modelling of Natural Phenomena ◽

10.1051/mmnp/2019046 ◽

2020 ◽

Vol 15 ◽

pp. 4

Author(s):

Viktoria Blavatska

Keyword(s):

Lattice Model ◽

Transition Probabilities ◽

Spatial Anisotropy ◽

Random Walkers ◽

Shape Characteristics ◽

Instantaneous Configuration

We analyze the properties of population spreading in environments with spatial anisotropy within the frames of a lattice model of asymmetric (biased) random walkers. The expressions for the universal shape characteristics of the instantaneous configuration of population, such as asphericity A and prolateness S are found analytically and proved to be dependent only on the asymmetric transition probabilities in different directions. The model under consideration is shown to capture, in particular, the peculiarities of invasion in presence of an array of oriented tubes (fibers) in the environment.

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NUCLEAR ALTERNATING-PARITY BANDS AND TRANSITION RATES IN A MODEL OF COHERENT QUADRUPOLE–OCTUPOLE MOTION

International Journal of Modern Physics E ◽

10.1142/s0218301312500218 ◽

2012 ◽

Vol 21 (05) ◽

pp. 1250021 ◽

Cited By ~ 1

Author(s):

N. MINKOV ◽

S. DRENSKA ◽

M. STRECKER ◽

W. SCHEID

Keyword(s):

Complex Shape ◽

Transition Probabilities ◽

Negative Parity ◽

Transition Rates ◽

Angular Momenta ◽

State Band ◽

Electric Transition ◽

Reduced Transition Probabilities ◽

Transition Operators ◽

Shape Characteristics

A further extension of a model of coherent quadrupole–octupole vibrations and rotations and its application to alternating-parity spectra in heavy even–even nuclei is presented. Within the model the yrast alternating-parity sequence includes the ground state band and the lowest negative parity levels with odd angular momenta, while the non-yrast sequences include excited β-bands and higher negative-parity levels. Electric transition operators reflecting the complex shape characteristics associated with the quadrupole–octupole vibration modes are introduced. By using them B(E1), B(E2) and B(E3) reduced transition probabilities within and between the different energy sequences are calculated. It is shown that the model successfully reproduces yrast and non-yrast alternating-parity bands together with the attendant B(E1)–B(E3) transition rates in the nuclei 154 Sm , 156 Gd and 100 Mo .

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EELS white line intensities calculated for the 3d and 4d metals

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100153919 ◽

1989 ◽

Vol 47 ◽

pp. 388-389

Author(s):

C. C. Ahn ◽

D. H. Pearson ◽

P. Rez ◽

B. Fultz

Keyword(s):

Experimental Data ◽

Line Intensity ◽

Transition Probabilities ◽

Initial Increase ◽

White Line ◽

Hartree Fock ◽

Line Intensities ◽

Integrated Intensity ◽

X Ray Absorption ◽

The Continuum

Previous experimental measurements of the total white line intensities from L2,3 energy loss spectra of 3d transition metals reported a linear dependence of the white line intensity on 3d occupancy. These results are inconsistent, however, with behavior inferred from relativistic one electron Dirac-Fock calculations, which show an initial increase followed by a decrease of total white line intensity across the 3d series. This inconsistency with experimental data is especially puzzling in light of work by Thole, et al., which successfully calculates x-ray absorption spectra of the lanthanide M4,5 white lines by employing a less rigorous Hartree-Fock calculation with relativistic corrections based on the work of Cowan. When restricted to transitions allowed by dipole selection rules, the calculated spectra of the lanthanide M4,5 white lines show a decreasing intensity as a function of Z that was consistent with the available experimental data.Here we report the results of Dirac-Fock calculations of the L2,3 white lines of the 3d and 4d elements, and compare the results to the experimental work of Pearson et al. In a previous study, similar calculations helped to account for the non-statistical behavior of L3/L2 ratios of the 3d metals. We assumed that all metals had a single 4s electron. Because these calculations provide absolute transition probabilities, to compare the calculated white line intensities to the experimental data, we normalized the calculated intensities to the intensity of the continuum above the L3 edges. The continuum intensity was obtained by Hartree-Slater calculations, and the normalization factor for the white line intensities was the integrated intensity in an energy window of fixed width and position above the L3 edge of each element.

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