Time-dependent Point Source Research Articles

The recovery of a time-dependent point source in a linear transport equation: application to surface water pollution

The aim of this paper is to localize the position of a point source and recover the history of its time-dependent intensity function that is both unknown and constitutes the right-hand side of a 1D linear transport equation. Assuming that the source intensity function vanishes before reaching the final control time, we prove that recording the state with respect to the time at two observation points framing the source region leads to the identification of the source position and the recovery of its intensity function in a unique manner. Note that at least one of the two observation points should be strategic. We establish an identification method that determines quasi-explicitly the source position and transforms the task of recovering its intensity function into solving directly a well-conditioned linear system. Some numerical experiments done on a variant of the water pollution BOD model are presented.

Vortex simulation of leading-edge separation bubble with local forcing

A numerical study is made of the flow control of leading-edge separation bubbles in a two-dimensional semi-infinite blunt plate, which is aligned parallel to the main stream. A version of thediscrete-vortex method is utilized. A time-dependent point source of small magnitude is introduced near the separation edge. The effect of local source forcing on the evolution of a leading-edge separation bubble is scrutinized by varying the strength and the forcing frequency of the source. It is found that the reattachment length attains a single minimum at lower forcing levels, while it shows double minima at moderately high forcing levels. Based on the numerical results, the mechanism of decreasing reattachment length is pursued. These findings are qualitatively consistent with the existing experimental results for a blunt circular cylinder.

Unsteady-state dispersion of a reactive gaseous species from an elevated time-dependent point source forming secondary species

The dispersion of a reactive gaseous species emitted from an elevated time-dependent point source undergoing a first-order chemical reaction removal process such as rainout/washout and forming secondary species has been studied by solving unsteady-state three-dimensional diffusion equation by prescribing different forms of fluxes at the source. By using the method of images, the solutions have also been obtained when the source is located at (0, 0, h s) and the ground is acting as a reflecting plane. The effects of removal processes on the dispersion of primary and secondary species have been discussed.

Time-dependent radiative transfer in a spherical vacuum

Abstract We consider an isotropic time-dependent point source of radiation at the center of a spherical vacuum Hohlraum. The inner surface of the sphere scatters radiation isotropically back into the Hohlraum with known albedo, initially assumed averaged over all frequencies. The flux, f, at any point on the sphere is dependent on time only. The function f (t) is known to satisfy a Volterra integral equation. A recursive algorithm for the solution of this equation is presented. Smoothness properties of f are considered in detail. Asymptotic behaviors, as suggested by calculations are discussed but are not yet fully understood. The flux seems to have one of two possible behaviors depending on the strength of the source for longer time. The more general problem in which the albedo is a function of frequency is then considered. The frequencies are binned into groups. The analysis parallels that for the frequency averaged case. Numerical examples are given in all cases.

Complex source pulsed beam representation of transient radiation

A new exact representation of transient radiation is presented, wherein the time-dependent point source field is modeled by an equivalent distribution of impulsive complex sources located on a spherical surface that encloses the source, and which may therefore be interpreted as a time-dependent complex Huygens' principle. Physically, each one of the equivalent sources launches a pulsed beam field in the radial direction. A new spectral representation for transient radiation is thereby obtained in terms of a continuum of pulsed beam fields emanating radially from the source in all directions. The convergence of the representation, and in particular the conditions under which a given source field may be represented only by paraxial contributions from neighboring pulsed beams are explored. In this latter approximation, our representation is the time-domain analogue of the Gaussian beam summation method which has recently been introduced as an efficient tool for computing time-harmonic fields in a complicated environment.

Some properties of the scalar field in a Schwarzschild space-time

The scalar field due to a point source at rest in the vicinity of a Schwarzschild space-time is studied. For the static scalar field ψ it is proved that as a solution of the Laplace equation it converges absolutely and uniformly and its limit is calculated explicitly on the horizonrs. It is proved also that ∇ψ = 0 atr = 0.5rs, ϑ = π/2 and that the function ψ satisfies certain symmetries which are independent of the source position. For the time-dependent scalar field we study the wave fronts of a perturbation due to a time-dependent point source and derive analytically the first correction to the field ψ(t, r, ϑ, ϕ) due to the Schwarzschild space-time.

Unsteady state dispersion of air pollutant from a time dependent point source forming a secondary pollutant

In this paper, the dispersion of air pollutant from a time dependent point source forming a secondary pollutant has been investigated by taking into account the dry and wet deposition on the ground. The unsteady state three-dimensional diffusion equation has been solved for prescribed forms of time dependent flux at the source. The case when the flux is given by the step function has been applied to study the dispersion of an episode like the MIC leakage in Bhopal, India.

Atmospheric dispersion model of removal mechanism with integral term

A general mathematical model for atmospheric dispersion is suggest, in the form of an integro-partial differential equation, the integral term characterizing the removal mechanism which may arise due to absorption of air pollutant in fog or rain droplets present in the atmosphere. This model is applied to the study of the effects of instantaneous and delayed removal on dispersion of air pollutant from an elevated time-dependent point source. It has been shown that the concentration of the pollutant along the central line at a given time and point decreases due to the removal process and the concentration of pollutant with a delayed removal process may be greater than that for an instantaneous removal case.

Determination of an Unknown Heat Source from Overspecified Boundary Data

Determination of an Unknown Heat Source from Overspecified Boundary Data