Moving Point Source Research Articles

Attenuation of radiated ground motion and stresses from three‐dimensional supershear ruptures

Radiating shear and Rayleigh waves from supershear ruptures form Mach waves that transmit large‐amplitude ground motion and stresses to locations far from the fault. We simulate bilateral ruptures on a finite‐width vertical strike‐slip fault (of width W and half‐length L with L ≫ W) breaking the surface of an elastic half‐space, and focus on the wavefield out to distances comparable to L. At distances much smaller than W, two‐dimensional plane‐strain slip‐pulse models (i.e., models in which the lateral extent of the slip zone is unbounded) accurately predict the subsurface wavefield. Amplitudes in the shear Mach wedge of those models are undiminished with distance from the fault. When viewed from distances far greater than W, rupture is accurately modeled as a moving point source that produces a shear Mach cone and, on the free surface, Rayleigh‐wave Mach fronts. Geometrical spreading of the shear Mach cone occurs radially and amplitudes there decrease with the inverse square‐root of distance. The transition between these two asymptotic limits occurs at distances comparable to W. Similar considerations suggest that Rayleigh Mach waves suffer no attenuation in the ideally elastic medium studied here. The rate at which fault strength weakens at the rupture front exerts a strong influence on the off‐fault fields only in the immediate vicinity of the fault (for both sub‐Rayleigh and supershear ruptures) and at the Mach fronts of supershear ruptures. More rapid weakening generates larger amplitudes at the Mach fronts.

Solutions for modelling moving heat sources in a semi-infinite medium and applications to laser material processing

This study describes the analytical and numerical solution of the heat conduction equation for a localised moving heat source of any type for use in laser material processing, as welding, layered manufacturing and laser alloying. In this paper, the analytical solution for a uniform heat source is derived from the solution of an instantaneous point heat source. The result is evaluated numerically and is compared to existing solutions for the moving point source and a semi-ellipsoidal source. Next, the result is used to demonstrate how such model can be used to study the effect of the heat source geometry. Besides, this solution reveals that a melting efficiency higher than 0.37 (= 1/ e, a maximum value stated by Rykalin [N. Rykalin, A. Uglov, A. Kokora, O. Glebov, Laser Machining and Welding, Mir Publishers, Moscow, 1978]) can be obtained. To investigate the effect of the temperature dependence of the material parameters, in particular the latent heat of fusion, a finite difference model is implemented. It is shown that the enthalpy method is most suited to implement the latent heat of fusion. A numerical evaluation for Ti–6Al–4V, reveals that the effect of the latent heat is rather small, except when the conductivity is very low, e.g. when scanning in a loose powder bed. The results demonstrate that analytical and numerical solutions can be effectively used to calculate the temperature distribution in a semi-infinite medium for finite 3D heat sources. In this way, a tool to investigate the importance of different processing parameters in laser manufacturing is obtained.

The influence of turbulence on noise propagation from a point source above a flat ground surface

Abstract The presence of turbulence in the atmosphere affects the interaction between an acoustic wave and the ground surface. The noise attenuation by the ground in the presence of atmospheric turbulence is smaller than in non-turbulent atmosphere. A simple engineering model of noise propagation above a flat ground surface, for stationary and moving point sources, has been proposed. The model takes into account the air absorption and ground effect in the presence of turbulence. As well as parameters for type of ground and air absorption, the model introduces two adjustable parameters which must be deduced from in situ measurements at two ranges or two heights. The model’s free parameters have been obtained as a function of the resultant sound speed gradient on the basis of the field measurements performed for a stationary noise source. Also, using field data for a vehicle moving at steady speeds up to 100 km/h, the model has been verified for a moving point source.

Green functions for wave propagation on a five-dimensional manifold and the associated gauge fields generated by a uniformly moving point source

Gauge fields associated with the manifestly covariant dynamics of particles in (3,1) space time are five dimensional (5D). We provide solutions of the classical 5D gauge field equations in both (4,1) and (3,2) flat space-time metrics for the simple example of a uniformly moving point source. Green functions for the 5D field equations are obtained, which are consistent with the solutions for uniform motion obtained directly from the field equations with free asymptotic conditions.

A thermomechanical hot channel approach for friction stir welding

This paper provides a theoretical framework for developing a thermomechanical hot channel (THC) approach for augmenting the friction stir welding (FSW) process. The model follows from the Rosenthal solution for moving point sources where heat input from the tool shoulder acts as a warm source while plasmas or laser heat sources provide higher energy input. The THC approach aims at decreasing tool wear by reducing the demand for frictional heat from the tool shoulder and pin. In the proposed model, the THC processing temperature is approximately 1000 °C, which is close to the temperature required for stir welding steel.

Railway source models for integration in the new European noise prediction method proposed in Harmonoise

The purpose of the Harmonoise European project is to provide an engineering model for the propagation of road and rail traffic noise which requires, for a better accuracy than existing models, the distinction between source output and propagation. In that context, the purpose of work package 1.2 of Harmonoise is to provide the emission data for railway sources to be implemented in the engineering model for the propagation. The relevant output of the emission data that is useful as input of the propagation calculations is the sound power level of equivalent moving point sources for at most five fixed heights and the associated directivity, both in one-third octave bands. The purpose of Harmonoise is to provide source models based on the most relevant physical parameters which can describe the three main sources: rolling, traction and aerodynamic. A database structure with some examples is also provided as well as guidelines for practical data collection. The paper presents first the main investigations which have been carried out through Harmonoise to provide the source models based on their physical parameters. The paper also presents how the database is organised and linked with the Harmonoise engineering model.

Propagation of muon induced Cherenkov photons through a diffusive medium

Analytic functions are derived that describe the arrival time distribution of photons (photoelectrons) induced by the passage of a high energy muon through a detector containing a Cherenkov medium that has scattering and absorptive properties. These functions, derived in the diffusive approximation, are as yet the best analytic descriptions of photon propagation from a moving point source of photons. As such, usage of these functions within the context of likelihood or other reconstruction algorithms will increase the pointing accuracy of neutrino telescopes that are embedded in ice or submerged in water.

Transmission imaging with a moving point source: influence of crystal thickness and collimator type

Nonuniform patient attenuation maps can be acquired using an axially moving point source of a high energy isotope that emits a fanbeam of photons. We simulated the Beacon attenuation correction tool attached to multiheaded Single Photon Emission Computed Tomography (SPECT) cameras which uses this approach. We investigated the scatter order of the photons reaching the detector, and the scatter contributions from the different detector components were evaluated for different energy windows. In case of simultaneous emission and transmission scanning the spatial signals are electronically windowed to allow differentiation between photons from the attenuation and from the emission source. However, an additional correction needs to be applied for cross-contamination. When applying the Beacon device in hybrid mode [gammacamera-Positron Emission Tomography (PET)] there are no degrees of freedom for crystal and collimator. The inter-window contamination was thus examined in detail to derive possible protocol optimizations for that dedicated setup. For the case of applying Beacon-SPECT, we performed multiple types of simulations including different crystal thicknesses and different collimators to evaluate the inter-window contamination. The main conclusion of this work is that a thick crystal detector coupled to a Low Energy High Resolution (LEHR) collimator is the best solution for acquiring attenuation maps in low energy applications. For medium energy studies attenuation maps have to be rescaled to account for the low sensitivity near the center of the patient. Fully Monte Carlo simulating the system matrix for medium energy studies on low energy collimators in order to replace the Medium Energy General Purpose (MEGP) collimators by the LEHR variants appeared to be a more valuable approach. This last method is penalized by a computational burden but results in an improved image quality after reconstruction.

Entry dynamics and acoustics/infrasonic/seismic analysis for the Neuschwanstein meteorite fall

Abstract— We have analyzed several types of data associated with the well‐documented fall of the Neuschwanstein meteorites on April 6, 2002 (a total of three meteorites have been recovered). This includes ground‐based photographic and radiometer data as well as infrasound and seismic data from this very significant bolide event (Spurný et al. 2002, 2003). We have also used these data to model the entry of Neuschwanstein, including the expected dynamics, energetics, panchromatic luminosity, and associated fragmentation effects. In addition, we have calculated the differential efficiency of acoustical waves for Neuschwanstein and used these values to compare against the efficiency calculated using available ground‐based infrasound data. This new numerical technique has allowed the source height to be determined independent of ray tracing solutions. We have also carried out theoretical ray tracing for a moving point source (not strictly a cylindrical line emission) and for an infinite speed line source. In addition, we have determined the ray turning heights as a function of the source height for both initially upward and downward propagating rays, independent of the explicit ray tracing (detailed propagation path) programs. These results all agree on the origins of the acoustic emission and explicit source heights for Neuschwanstein for the strongest infrasonic signals. Calculated source energies using more than four different independent approaches agree that Neuschwanstein was certainly <500 kg in initial mass, given the initial velocity of 20.95 km/s, resulting in an initial source energy ≤0.0157‐0.0276 kt TNT equivalent (4.185 times 1012 J). Local source energies at the calculated infrasonic/seismic source altitudes are up to two orders of magnitude smaller than this initial source energy.

Inter-frame filtering for list-mode EM reconstruction in high-resolution 4-D PET

Dynamic (4-D) PET imaging is a routinely used technique applied in clinical studies, and is now also finding application for high resolution animal PET systems. The usual method of implementing the image reconstruction involves separating the acquired data out into lower count discrete time frames, resulting in increased image noise. This paper presents two further developments for one-pass 4-D list-mode expectation-maximization (EM) reconstruction, which has already demonstrated enhanced reconstruction quality for image sequences compared to conventional strategies, as well as significantly reducing reconstruction time. The technique, which is an extension of one-pass 3-D list-mode EM, filters a previously reconstructed frame, which is then used as a starting image for the following frame, thus including prior object information. A new approach to post-reconstruction smoothing is also proposed, which in some cases is able to reduce noise without loss of resolution. Using measured quad-HIDAC data from a moving point source and a specially designed liquid flow experiment, and a rat scan, the two approaches are compared to the uniform image initialization method in terms of spatial and temporal resolution, noise, and accuracy of time-activity curves. Preliminary results, using resolution recovery, indicate the potential of achieving ultra-high spatial resolution with good temporal resolution, arising from improving the use of otherwise wasted prior information.

Surface effects of internal wave generated by a moving source in a two-layer fluid of finite depth

Based on the potential flow theory of water waves, the interaction mechanism between the free-surface and internal waves generated by a moving point source in the lower layer of a two-layer fluid was studied. By virtue of the method of Green's function, the properties of the divergence field at the free surface were obtained, which plays an important role in the SAR (Synthetic Aperture Radar) image. It is shown that the coupling interaction between the surface-wave mode and internal-wave mode must be taken into account for the cases of large density difference between two layers, the source approaching to the pynocline and the total Froude number Fr close to the critical number Fr2. The theoretical analysis is qualitatively consistent with the experimental results presented by Ma Hui-yang.

The spectrum of water waves produced by moving point sources, and a related inverse problem

Parameters of moving sources on the sea surface are recovered by spectral analysis of the induced surface waves. The method can be an alternative to the standard way of seeing the ship directly, in particular, when the direct observation is impossible.

The Sound Field of a Source That Executes in a Liquid Layer a Motion Represented as the Sum of a Subsonic Uniform Rectilinear Motion and a Periodic Motion. Exact (Explicit) Solutions

The problem on the sound field generated in a liquid layer by a moving point source that was turned on at a moment infinitely distant in the past is considered. Properties of the layer and the source under consideration are chosen in such a way that the solution of the problem can be constructed in the form of a triple series, separating variables in a moving coordinate system. The expressions obtained for the terms of this series (for normal waves) are not only exact but also explicit outside a neighborhood of the source in the sense that they are products of elementary and known functions of coordinates and time. Bibliography: 10 titles.

Bacterial tracking of motile algae

Abstract We investigated whether bacterial motility and chemotaxis in the ocean enables bacteria to approach and follow microscopic, moving, point sources of nutrients. The turbulent nature of the ocean combined with the imprecision of run and tumble chemotaxis has led to the assumption that marine bacteria cannot cluster around microscopic point sources. Recent work, however, shows that marine bacteria use a run and reverse strategy. We examine the ability of marine bacteria that use run and reverse chemotaxis to respond to and follow a moving point source. The addition of the 6 mum in diameter motile algae Pavlova lutheri to cultures of the marine bacteria Pseudoalteromonas haloplanktis and Shewanella putrefaciens revealed bacterial tracking individual free-swimming algae. The marine bacteria travelled at up to 445 mum s(-1) when tracking, up to 237 mum s(-1) when not tracking and up to 126 mum s(-1) in cultures without the algae. Tracking maintained bacteria within one run length of an alga. The bacteria appeared able to steer, consecutively turning up to 12 times toward the motile algae. They recovered from the occasional incorrect turn to continue moving around the swimming alga, indicating that marine bacteria can track moving point sources and form transient phyto-bacterial associations. Our analysis suggests tracking increases nutrient uptake by bringing cells into regions of high nutrient concentrations and by increased advection from high speeds. This result describes what is, apparently, one of the tightest spatial and temporal links between free-living primary and secondary producers in planktonic ecosystems.

Bacterial tracking of motile algae

We investigated whether bacterial motility and chemotaxis in the ocean enables bacteria to approach and follow microscopic, moving, point sources of nutrients. The turbulent nature of the ocean combined with the imprecision of run and tumble chemotaxis has led to the assumption that marine bacteria cannot cluster around microscopic point sources. Recent work, however, shows that marine bacteria use a run and reverse strategy. We examine the ability of marine bacteria that use run and reverse chemotaxis to respond to and follow a moving point source. The addition of the 6 μm in diameter motile algae Pavlova lutheri to cultures of the marine bacteria Pseudoalteromonas haloplanktis and Shewanella putrefaciens revealed bacterial tracking individual free-swimming algae. The marine bacteria travelled at up to 445 μm s −1 when tracking, up to 237 μm s −1 when not tracking and up to 126 μm s −1 in cultures without the algae. Tracking maintained bacteria within one run length of an alga. The bacteria appeared able to steer, consecutively turning up to 12 times toward the motile algae. They recovered from the occasional incorrect turn to continue moving around the swimming alga, indicating that marine bacteria can track moving point sources and form transient phyto-bacterial associations. Our analysis suggests tracking increases nutrient uptake by bringing cells into regions of high nutrient concentrations and by increased advection from high speeds. This result describes what is, apparently, one of the tightest spatial and temporal links between free-living primary and secondary producers in planktonic ecosystems.

Self-induced field model for crystal twisting in spherulites

The observed twisting of crystals about the growth direction in spherulites is modeled as a response to fields generated during the crystal growth process. These fields can be compositional or mechanical. In either case, the high local field value in the melt near the interface acts to reduce the growth velocity. Twisting of the crystal about the growth direction places all portions of the growth surface in contact with melt of lower field value than would be the case for untwisted growth, thereby increasing the growth velocity. The effect of a compositional field is analyzed here, using an extension of the moving point source to compute the composition in the melt ahead of a twisting crystal. The retarding effect of the elastic twisting of the crystal is included in the analysis. Simulations using parameters for a crystallizable/uncrystallizable polyethylene blend are carried out for a crystal with thin, rectangular cross-section. The results are quantitatively and qualitatively consistent with observation. Comments on simplifications within and implications of the model are given.

On transient waves in dispersive media produced by moving point sources

A solution for the inhomogeneous telegraph equation for a point source moving with the velocity of light is constructed. We find relations describing both the transient and steady-state wave processes. The solutions obtained are used to define electromagnetic waves in a conductive medium. The case of a source moving faster than light is also given.

Optimization of Systems with a Moving Control

We study a functioning model of a linear system with a moving point source. The existence of optimal moving controls is proved.

Moving point source—A simple model for predicting statistical sound levels in the neighborhood

When predicting the noise produced by moving sound sources (e.g., vehicles, airplanes, etc.) sound-level statistics can be helpful to describe the situation. However, the common sound models only yield the average sound level, and under special circumstances, also the maximum sound level. The calculation model moving sound source also gives sound level and the level-versus-time diagram. For the calculation, first the paths of the sound sources have to be digitalized and divided into parts. Each part will be represented as a point sound source which is active during a certain time slot, which again is based upon the velocities of the moving objects. Sound propagation from all point sources to the point of emission is calculated by using ISO or equivalent standards. This leads to the time versus level diagram and (when the steps from one to another point source are small enough) to the desired statistical levels. The described model, named the moving sound source, has no limitations. It could be easily integrated in commercial sound propagation calculation programs. It was successfully used for the approval of a new racetrack in Germany. Also, the new DIN 45684 (noise of small aircraft) is based on it.

FLULA2: Aircraft noise prediction and measurements

Aircraft noise predictions of the program FLULA2 are compared with airport noise monitor measurements and with single flight events. Further, the versatility of using a point source model for simulation is discussed and the implications of accurate noise predictions on land use planning are outlined. The aircraft noise simulation program FLULA2, developed at EMPA, uses a point source with a directivity characteristic in contrast to many other models which use line segments and correction terms. With the powerful model of a moving point source, the level-time history of a single flight can be reconstructed. Thus all acoustic effects (topography, spectral air absorption, ground effects,...) may be included and any noise metrics can be calculated. The program is validated by comparing single events (the level-time history of measurements and of calculations) and by comparing the yearly average of measurements at monitoring stations around airports with the Leq predictions. There are variations, but there is no systematic under- or overestimation of the noise calculations compared with the monitors.