One-dimensional Gaussian Model Research Articles

Influence of Salinity Gradient Changes on Phytoplankton Growth Caused by Sluice Construction in Yongjiang River Estuary Area

Though the number of sluices and dams in coastal areas has increased rapidly in recent years, the influence of their construction on phytoplankton in estuary areas is hardly known. This paper aims to provide a reference for quantitative research on the ecological influence of sluice construction and give ecological justifications for the setting of environmental standards in the estuary areas. The survey data gained at the lower reach of the Yongjiang River and its estuarine areas in June 2015 were used in MIKE21 software (Danish Hydraulic Institute (DHI), Denmark)) for establishing a two-dimensional numerical model to simulate the salinity field distribution after sluice construction. Based on the simulation results, the salinity gradient changes caused by the construction were analyzed. The one-dimensional Gaussian model was applied to calculated the phytoplankton’s ecological threshold interval over the salinity changes, which helped predict the influence of salinity changes on phytoplankton cell density. The study shows that salinity in the Yongjiang estuary increases obviously, beyond the phytoplankton ecological threshold, after sluice construction without water discharge. Salinity will become a restriction factor to phytoplankton growth after sluice construction in the study area, which may cause a sharp decrease of certain phytoplankton species.

Bi-Gaussian Mathematical Model of Radio-Frequency Radiation Sources in Information Environment in Telecommunication Systems

This paper analyzes the reasons why the one-dimensional Gaussian model is inapplicable for the analysis and synthesis of the measurements of parameters of complex signals. It also describes the bi-Gaussian mathematical model of signals of radio-frequency radiation sources.

Explicit schemes for time propagating many-body wave functions

Accurate theoretical data on many time-dependent processes in atomic and molecular physics and in chemistry require the direct numerical ab initio solution of the time-dependent Schr\"odinger equation, thereby motivating the development of very efficient time propagators. These usually involve the solution of very large systems of first-order differential equations that are characterized by a high degree of stiffness. In this contribution, we analyze and compare the performance of the explicit one-step algorithms of Fatunla and Arnoldi. Both algorithms have exactly the same stability function, therefore sharing the same stability properties that turn out to be optimum. Their respective accuracy, however, differs significantly and depends on the physical situation involved. In order to test this accuracy, we use a predictor-corrector scheme in which the predictor is either Fatunla's or Arnoldi's algorithm and the corrector, a fully implicit four-stage Radau IIA method of order 7. In this contribution, we consider two physical processes. The first one is the ionization of an atomic system by a short and intense electromagnetic pulse; the atomic systems include a one-dimensional Gaussian model potential as well as atomic hydrogen and helium, both in full dimensionality. The second process is the decoherence of two-electron quantum states when a time-independent perturbation is applied to a planar two-electron quantum dot where both electrons are confined in an anharmonic potential. Even though the Hamiltonian of this system is time independent the corresponding differential equation shows a striking stiffness which makes the time integration extremely difficult. In the case of the one-dimensional Gaussian potential we discuss in detail the possibility of monitoring the time step for both explicit algorithms. In the other physical situations that are much more demanding in term of computations, we show that the accuracy of both algorithms depends strongly on the degree of stiffness of the problem.

Optical conductivity of high-temperature superconductors: Exact solution for a “spin - bag” model

Exact summation of all Feynman diagrams for two-particle Green's function is performed for the one-dimensional Gaussian model of static fluctuations of short-range (antiferromagnetic) order with Lorentzian correlator analogous to “spin-bag” model of Schrieffer et al. We obtain the general picture of frequency dependence of conductivity for different ranges of correlation length of short-range order. For specific values of parameters we get good qualitative agreement with experimental data on optical absorption in high-Tc superconductors.

Ion-surface scattering in the time-dependent mean-field approximation

The exchange of electrons between a jellium surface and an energetic ion is illustrated via time-dependent mean-field theory. We use a one-dimensional Gaussian model potential to simulate the ion's effect upon the surface in this initial study. The results of our numerical simulation show the effects of energy resonances, finite and velocity-dependent resonance widths, and charge transfer from the jellium to the reflected ion. The self-consistent reaction of the surface and bulk electrons to the ion scattering is easily seen in time-dependent density profiles.