Stationary Point Source Research Articles

Radiative transfer of excitation: Lévy flights and self-similarity

The Green function of the Biberman–Holstein integral equation, both nonstationary (instantaneous point flash) and stationary (stationary point source) is studied. The point flash produces a self-similar spherical wave of excitation in homogenous gas medium. The transfer of excitation is due to the Lévy flights of resonance line photons. The properties of the wave – its shape, time evolution and propagation – are found for arbitrary line profile. The cases of Doppler, Lorentz and Voigt profiles are considered in some detail. For the Doppler broadened line, the structure of the self-similar wave is given by a rational function. The properties of the Green function of stationary Biberman–Holstein equation are reviewed. Some unexpected parallels with non-stationary case are found. The spherically-symmetric version of the longest flight approximation is discussed and the condition of its validity is formulated.

Life cycle assessment of CO2 conversion and storage in metal–CO2 electrochemical cells

AbstractResearchers have proposed a family of electrochemical technologies that incorporate CO2 as a gas cathode and alkali or alkaline earth metal anodes to exploit the high reactivity of CO2 with these metals. Such proposed cells operate by converting gaseous CO2 into solid carbonate, extracting value from CO2 in the form of electricity, and fixing the CO2 in solid form. Given the increasing number of these proof‐of‐concept studies, it is timely to critically examine the potential of such emerging technologies to reduce stationary point source emissions. Environmental life cycle assessment (LCA) during early research stages can inform important design decisions. In this study, we perform LCA on electrochemical conversion processes (ECPs) involving Li, Na, Mg, or Ca as a co‐reactant with CO2 sourced from a coal plant, evaluating differing scenarios. We find that a Na‐based primary ECP configuration that integrates capture with conversion of coal plant CO2 emissions to Na2CO3 can avoid almost 28% of emissions (and 74% under best‐case conditions) that are typically associated with conventional production of the same carbonate and electricity. This represents a net emissions decrease of 435 kg CO2‐eq per 1 MWh of electricity delivered by the ECP, from a baseline of 1,105 kg CO2‐eq emitted without any mitigation strategies. In contrast, all ECPs in a rechargeable configuration result in increased emissions compared to the conventional baseline, unless the ECP system energy requirements are provided by renewables and the conventional system is assumed to have high emissions intensity.

THE ANALYSIS OF THERMAL FIELDS AT THE PRIMARY STAGE OF THE STEAM-ASSISTED GRAVITY DRAINAGE PROCESS

This article analyzes the temperature distribution in a producer well at the primary stage of the steam-assisted gravity drainage process. The increase in share of hard-to-recover reserves requires using steam-assisted gravity drainage (SAGD). Its successful application, in turn, depends on warming up the inter-well zone, which demands steam circulation in both wells at the primary stage of the process. The duration of this stage affects the transition to oil production and the profitability of the process, which emphasizes the importance of analyzing thermal fields at this stage to assess its duration. The existing research does not allow estimating the temperature in the producer, using the correct formulation of the problem. This paper presents the temperature distribution in a producer for SAGD for classical and chess well patterns for the first time. The aim of the work is to choose a development system for the minimum duration of primary stage of SAGD. For this purpose, the fundamental solution of the non-stationary heat equation for a continuous stationary point source in an unbounded medium is used. The estimation of temperature, at which oil becomes mobile, allows determining the primary stage duration. The authors compare the classical and chess well patterns. In addition, they have obtained the temperature distribution in producer. The results show that classical well pattern provides faster heating of inter-well zone. It is determined that the closest injection well has the greatest influence on the temperature in the producing well.

Aeroacoustic noise calculation of noncompact bodies with time-domain scattered green’s function

In view of the scattering effect induced by non-compact bodies, and the growing time cost of the noise calculation with high-order methods, tailored green function methods gradually become effective means to study acoustic noise of noncompact bodies. With the help of free-space green function and convective wave equation, time-domain integral method is presented to calculate scattered green function under arbitrary boundary condition. In order to verify the present method, the cylinder noise under solid wall condition is firstly calculated with stationary point source. The scattered green functions are in good agreement with Gloerfelt’s analytical solution and Takaishi’s frequency method. The pressure distribution demonstrates that the pressure appears as circle shape at low frequency but petal-like pattern at high frequency. Furthermore, point sources in parabolic moving form is chosen to study the influence of scattering effect to far field noise. Numerical results illustrate that the scattering effect is closely related to cylinder radius and the location of sound sources, large body size and sound sources adjacent closely to body surface could lead to serious scattered noise. Besides, time-domain method overcomes the limit that noise calculations have to be performed in relative coordinate system, and it can calculate scattered noise accurately and instantaneous.

Estimation of source location and ground impedance using a hybrid multiple signal classification and Levenberg–Marquardt approach

A microphone array signal processing method for locating a stationary point source over a locally reactive ground and for estimating ground impedance is examined in detail in the present study. A non-linear least square approach using the Levenberg–Marquardt method is proposed to overcome the problem of unknown ground impedance. The multiple signal classification method (MUSIC) is used to give the initial estimation of the source location, while the technique of forward backward spatial smoothing is adopted as a pre-processer of the source localization to minimize the effects of source coherence. The accuracy and robustness of the proposed signal processing method are examined. Results show that source localization in the horizontal direction by MUSIC is satisfactory. However, source coherence reduces drastically the accuracy in estimating the source height. The further application of Levenberg–Marquardt method with the results from MUSIC as the initial inputs improves significantly the accuracy of source height estimation. The present proposed method provides effective and robust estimation of the ground surface impedance.

A method of providing directionality for ionising radiation detectors — RadICAL

A novel method for providing directionality for radiation detection is presented. The idea is based upon the fact that detector response depends upon two properties of the active component in the detector: the radiation pathlength and the area presented to a particle flux. Thus a rotating slab of detector gives a characteristic temporal response that can be used to identify the direction of the photon flux. A model of the detector system is used to design and build a detector which is then evaluated. It is shown that a rotating detector of this nature can produce a characteristic curve which can be used to determine the location of a single stationary point source.

Sedeonic Equations of Massive Fields

Prior work on space-time sedeon algebra models relativistic quantum mechanical equation of motion with corresponding field equations, mediated by massive or massless spin-1 or spin-1/2 particles. In the massless spin-1 case, such exchange particles mediate fields in analogy to Maxwell’s equations in Lorentz gauge. This paper demonstrates fundamental aspects of massive field’s theory, such as gauge invariance, charge conservation, Poynting’s theorem, potential of a stationary scalar point source, plane wave solution, and interaction between point sources. We briefly discuss some aspects of sedeonic algebra and their potential physical applications.

An explicit solution of Burgers equation with stationary point source

Existence, uniqueness and regularity of the global weak solution to the Burgers equation with a reaction term is shown when the reaction term is given as a time independent point source and produces heat constantly. An explicit solution is obtained and used to show the long time asymptotic convergence of the solution to a steady state. For the heat equation case without any convection the solution diverges everywhere as time increases and hence it is the first order convection term that gives the compactness of the solution trajectory of the Burgers equation with reaction.

Local immobilization of particles in mass transfer described by a Jeffreys-type equation

We consider the Jeffreys-type equation as the foundation in three different models of mass transfer, namely, the Jeffreys-type and two-phase models and the D(1) approximation to the linear Boltzmann equation. We study two classic (1+1)-dimensional problems in the framework of each model. The first problem is the transfer of a substance initially confined at a point. The second problem is the transfer of a substance from a stationary point source. We calculate the mean-square displacement (MSD) for the solutions of the first problem. The temporal behavior of the MSD in the framework of the first and third models is found to be the same as that in the Brownian motion described by the standard Langevin equation. In addition, we find a remarkable phenomenon when a portion of the substance does not move.

Solute transport with longitudinal and transverse diffusion in temporally and spatially dependent flow from a pulse type source

Molecular transverse diffusion through unsteady and heterogeneous medium is accounted for in solute mass transport originating from a uniform pulse-type stationary point-source. The corresponding two-dimensional advection–dispersion equation with variable coefficients is solved by the explicit finite difference method. The heterogeneity of the medium is described by a position dependent linear non-homogeneous expression for velocity with unsteady exponential variation with time. Variation of the dispersion parameter due to heterogeneity is considered proportional to square of the velocity. Results are compared to analytical solutions reported in the literature and good agreement is found. The explicit finite difference method is shown to be effective and accurate for solving the related two-dimensional advection–dispersion equation with variable coefficients in semi-infinite media, which is especially important when arbitrary initial and boundary conditions are required.

Directional recording of swell from distant storms

Almost fifteen years ago in the pages of this Journal, one of us presented power spectra of ocean waves and swell off Pendeen and Perranporth in north Cornwall (Barber & Ursell 1948). The outstanding feature of these spectra is the successive shift of peaks toward higher frequencies. This is the expected behaviour of dispersive wave trains from rather well-defined sources. Storms generate a broad spectrum of frequencies; the low frequencies are associated with the largest group velocity and accordingly are the first to arrive at distant stations. The time rate of increase in the frequency of peaks determines the distance and time of origin. In this way Barber & Ursell were able to identify the dispersive arrivals with a low pressure area in the North Atlantic, a tropical storm off Florida, and a storm off Cape Horn, at distances of 1200, 2800, and 6000 miles, respectively, from the Cornish stations. The measurements were consistent with the simple classical result that each frequency,/, is propagated with its appropriate group velocity, V = g/(47[/*). The present study is in a sense a refinement to the work of Barber & Ursell. The frequency resolution and sensitivity have each been increased by an order of m agnitude, and this makes it possible to detect and resolve meteorological sources that have previously been out of reach. The antipodal swell from the Indian Ocean is a case in point

A moving medium formulation for prediction of propeller noise at incidence

This paper presents a time domain formulation for the sound field radiated by moving bodies in a uniform steady flow with arbitrary orientation. The aim is to provide a formulation for prediction of noise from body so that effects of crossflow on a propeller can be modeled in the time domain. An established theory of noise generation by a moving source is combined with the moving medium Green's function for derivation of the formulation. A formula with Doppler factor is developed because it is more easily interpreted and is more helpful in examining the physic of systems. Based on the technique presented, the source of asymmetry of the sound field can be explained in terms of physics of a moving source. It is shown that the derived formulation can be interpreted as an extension of formulation 1 and 1A of Farassat based on the Ffowcs Williams and Hawkings (FW–H) equation for moving medium problems. Computational results for a stationary monopole and dipole point source in moving medium, a rotating point force in crossflow, a model of helicopter blade at incidence and a propeller case with subsonic tips at incidence verify the formulation.

Identification of strength and location of stationary point source of atmospheric pollutant in urban conditions using computational fluid dynamics model

Abstract In this paper a method is presented which allows for estimation of the location and rate of an unknown point stationary source of passive atmospheric pollutant in a complex urban geometry. The variational formulation is used in which the cost function characterizing difference of the calculated and measured concentrations is minimized with respect to source coordinates and rate. The minimization problem is solved by a direct algorithm using a source-receptor function which is calculated by solving adjoint equation. The algorithm has been implemented in ADREA-HF computational fluid dynamics code and has been applied in complex urban geometry. Validation of the algorithm has been performed by simulation of a wind tunnel experiment on atmospheric dispersion among an array of rectangular obstacles. Good results of source parameters estimation have been achieved. The measuring sensors to be used in source estimation had been randomly selected out of 244 available sensors by a specially designed random sampling algorithm which allowed for estimation of the probability of ‘good’ source term estimation with the given number of sensors. In case of ‘perfect model’ (when synthetic measurements were used for source estimation) good results were achieved with 90% or higher probability for arbitrary measurement networks consisting of 15 or more sensors even though prior estimation of source location was not used in this case. Several tests had been performed with the use of real measurements which differed by prior estimation of source location. In all cases 90% or higher probability of obtaining good solution was reached only for measurement networks consisting of 150 or more sensors. Hence further improvement of the source estimation algorithm can be achieved first of all by improving the performance of forward model.

One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

The one-dimensional linear advection–diffusion equation is solved analytically by using the Laplace integral transform. The solute transport as well as the flow field is considered to be unsteady, both of independent patterns. The solute dispersion occurs through an inhomogeneous semi-infinite medium. Hence, velocity is considered to be an increasing function of the space variable, linearly interpolated in a finite domain in which solute dispersion behaviour is studied. Dispersion is considered to be proportional to the square of the spatial linear function. Thus, the coefficients of the advection–diffusion equation are functions of both the independent variables, but the expression for each coefficient is considered in degenerate form. These coefficients are reduced into constant coefficients with the help of a new space variable, introduced in our earlier works, and new time variables. The source of the solute is considered to be a stationary uniform point source of pulse type.

Horizontal solute transport from a pulse type source along temporally and spatially dependent flow: Analytical solution

Summary Transport of solute mass transport, originating from a uniform pulse-type stationary point source through a heterogeneous semi-infinite horizontal medium, is studied. The heterogeneity is described by position dependent linear non-homogeneous expression for the velocity. The exponential unsteady variation in velocity of decreasing/increasing is also considered. The variation in dispersion parameter due to heterogeneity is considered proportional to square of that in the velocity. But the same due to unsteadiness is proportional to a power of the velocity which may take any value between 1 and 2 or outside this range. The variable coefficients of the two-dimensional advection–diffusion equation are put in degenerate form. These are reduced into constant coefficients with the help of new independent variables introduced at different stages, paving the way for using Laplace transformation technique to get the desired solution.

Modeling of influencing parameters in active noise control on an enclosure wall

This paper investigates, by means of a numerical model, the possibility of using an active noise barrier to virtually reduce the acoustic transparency of a partition wall inside an enclosure. The room is modeled with the image method as a rectangular enclosure with a stationary point source; the active barrier is set up by an array of loudspeakers and error microphones and is meant to minimize the squared sound pressure on a wall with the use of a decentralized control. Simulations investigate the effects of the enclosure characteristics and of the barrier geometric parameters on the sound pressure attenuation on the controlled partition, on the whole enclosure potential energy and on the diagonal control stability. Performances are analyzed in a frequency range of 25–300 Hz at discrete 25 Hz steps. Influencing parameters and their effects on the system performances are identified with a statistical inference procedure. Simulation results have shown that it is possible to averagely reduce the sound pressure on the controlled partition. In the investigated configuration, the surface attenuation and the diagonal control stability are mainly driven by the distance between the loudspeakers and the error microphones and by the loudspeakers directivity; minor effects are due to the distance between the error microphones and the wall, by the wall reflectivity and by the active barrier grid meshing. Room dimensions and source position have negligible effects. Experimental results point out the validity of the model and the efficiency of the barrier in the reduction of the wall acoustic transparency.

On the correspondence between creeping flows of viscous and viscoelastic fluids

From the wealth of exact solutions for Stokes flow of simple viscous fluids [C. Pozrikidis, Introduction to Theoretical and Computational Fluid Dynamics, Oxford University Press, Oxford, 1997, pp. 222–311], the classical “viscous–viscoelastic correspondence” between creeping flows of viscous and linear viscoelastic materials yields exact viscoelastic creeping flow solutions. The correspondence is valid for an arbitrary prescribed source: of force, flow, displacement or stress; local or nonlocal; steady or oscillatory. Two special Stokes singularities, extended to viscoelasticity in this way, form the basis of modern microrheology [T.G. Mason, D.A. Weitz, Optical measurements of the linear viscoelastic moduli of complex fluids, Phys. Rev. Lett. 74 (1995) 1250–1253]: the Stokeslet (for a stationary point source of force) and the solution for a driven sphere. We amplify these viscoelastic creeping flow solutions with a detailed focus on experimentally measurable signatures: of elastic and viscous responses to steady and time-periodic driving forces; and of unsteady (inertial) effects. We also assess the point force approximation for micron-size driven beads. Finally, we illustrate the generality in source geometry by analyzing the linear response for a nonlocal, planar source of unsteady stress.

Optimisation of ground attenuation for moving sound sources

In an earlier study, Attenborough and Li [Attenborough K, Li, KM. Ground effect for A-weighted noise in the presence of turbulence and refraction. J Acoust Soc Am 102:1997;1013–22] derived a closed form analytical formula to calculate optimum ground parameters for reducing the A-weighted noise due to a stationary point source. This paper extends this earlier study by deriving an expression to calculate the sound field due to a source moving at a constant speed above a ground surface. An A-weighted mean-square sound pressure has been derived that enables one to estimate the sound exposure levels of a moving source. Numerical calculations for a realistic range of speeds show the influence of the source motion on the noise levels. Although the predicted effects on the ground attenuation are moderate, they are significant at a relatively low Mach number. In addition, the sensitivity to the atmospheric turbulence and the geometrical parameters tends to be altered by the source motion. On the other hand, it is demonstrated that the optimum ground parameters are similar for stationary and moving sources.

Neutrophil microtubules suppress polarity and enhance directional migration

How do microtubules, which maintain and direct polarity of many eukaryotic cells, regulate polarity of blood neutrophils? In sharp contrast to most cells, disrupting a neutrophil's microtubule network with nocodazole causes it to polarize and migrate [Niggli, V. (2003) J. Cell Sci. 116, 813-822]. Nocodazole induces the same responses in differentiated HL-60 cells, a model neutrophil cell line, and reduces their chemotactic prowess by causing them to pursue abnormally circuitous paths in migrating toward a stationary point source of an attractant, f-Met-Leu-Phe (fMLP). The chemotactic defect stems from dramatic nocodazole-induced imbalance between the divergent, opposed fMLP-induced "backness" and "frontness" signals responsible for neutrophil polarity. Nocodazole (i) stimulates backness by increasing Rho- and actomyosin-dependent contractility, as reported by Niggli, and also (ii) impairs fMLP-dependent frontness: pseudopods are flatter, contain less F-actin, and show decreased membrane translocation of PH-Akt-GFP, a fluorescent marker for 3'-phosphoinositide lipids. Inhibiting backness with a pharmacologic inhibitor of a Rho-dependent kinase substantially reverses nocodazole's effects on chemotaxis, straightness of migration paths, morphology, and PH-Akt-GFP translocation. Thus, microtubules normally balance backness vs. frontness signals, preventing backness from reducing the strength of pseudopods and from impairing directional migration.

Broadband performance of a moving time reversing array.

Acoustic time reversal exploits reciprocity between sources and receivers to generate backward propagating waves that automatically focus at their point of origin. In underwater acoustics, an array of transducers that can both transmit and receive, referred to as a time reversing array (TRA) or time reversal mirror (TRM), generates the back-propagating waves. Such arrays have been shown to spatially and temporally focus sound in unknown complicated multipath environments, and are therefore of interest for active sonar and underwater communication applications. Although stationary vertical linear TRAs have been favored in prior studies, practical applications of acoustic time reversal in underwater environments are likely to involve towed, tilted, horizontal, or bottom-mounted arrays. In particular, array motion introduces Doppler effects and eliminates source-receiver reciprocity, two factors that potentially impact the automatic focusing capability of TRAs. This paper presents the results from a theoretical and computational investigation into how array motion and orientation influence TRA retrofocusing in the shallow ocean. Here, the TRA tow speed is assumed constant, and the array is assumed to be straight and linear (vertical, horizontal, or tilted). And, for simplicity, the TRA is assumed to respond to a stationary point source emitting a broadband pulse. When a TRA moves, the retrofocus is predicted to shift in the direction of array motion due to the translation of the array between its reception and broadcast times. In addition, the performance of a towed horizontal TRA is predicted to degrade more rapidly with towing speed than that of an equivalent (but clearly idealized) towed vertical array because of range-dependent Doppler phase differences that do not influence the vertical array. However, short tilted arrays may approach vertical array performance and appear to be a potentially versatile compromise for implementing TRA concepts in active sonar or underwater communication systems.