Transverse Spread Research Articles

Modeling the Coarse Fraction of Solid Fertilizer Deposition from a Fixed-Wing Aircraft: 1. A Ballistics Model

A particle ballistics model is proposed to predict the landing position of granular fertilizer particles ejected from fixed-wing agricultural aircraft. The model is a single-particle model that predicts flight trajectory from the particle force balance based on the aircraft ground speed, axial and tangential propeller wash, wind characteristics, and particle properties including sphericity. As an input, the model relies on known exit velocities from the spreader device mounted underneath the aircraft. When simplified, the mathematics for a particle falling vertically in quiescent air is the same as that developed by Grift et al., 1997 [Trans. ASAE 40(1): 13-20]. Without the propeller wash model, comparison is made to the lateral prediction of Bansal et al., 1998 [Trans. ASAE 41(3): 537-544], who used a simpler model for which similar results and similar trends are obtained. Lastly, with the propeller wash model turned on, model predictions are compared to predictions from AGDISP 8.15. Again, results and trends are similar. The model takes the first step in creating a system to evaluate the performance of agricultural aircraft with respect to delivering variable-rate application technology. The next step is to include a gatebox/distributor model so that a transverse spread distribution pattern can be generated by running the model multiple times, and then to validate this against field measurements.

Pore‐scale simulation of dispersion and reaction along a transverse mixing zone in two‐dimensional porous media

Several studies have demonstrated that the success of natural and engineered in situ remediation of groundwater pollutants relies on the transverse mixing of reactive chemicals or nutrients along plume margins. Efforts to predict reactions in groundwater generally rely on dispersion coefficients obtained from nonreactive tracer experiments to determine the amount of mixing, but these coefficients may be affected by spreading, which does not contribute to reaction. Mixing is controlled only by molecular diffusion in pore spaces, and the length scale of transverse mixing zones can be small, often on the order of millimeters to centimeters. We use 2D pore‐scale simulation to investigate whether classical transverse dispersion coefficients can be applied to model mixing‐controlled reactive transport in three different porous media geometries: periodic, random, and macroscopically trending. The lattice‐Boltzmann method is used to solve the steady flow field; a finite volume code is used to solve for reactive transport. Nonreactive dispersion coefficients are determined from the transverse spreading of a conservative tracer. Reactive dispersion coefficients are determined by fitting a continuum model which calculates the total product formation as a function of distance to the results from our pore scale simulation. Nonreactive and reactive dispersion coefficients from these simulations are compared. Results indicate that, regardless of the geometrical properties of the media, product formation can be predicted using transverse dispersion coefficients determined from a conservative tracer, provided dispersion coefficients are determined beyond some critical distance downgradient where the plume has spread over a sufficiently large transverse distance compared to the mean grain diameter. This result contrasts with other studies where reactant mixing was controlled by longitudinal hydrodynamic dispersion; in those studies longitudinal dispersion coefficients determined from nonreactive tracer experiments over‐estimated the extent of reaction and product formation. Additional work is called for in order to confirm that these findings hold for a wider variety of grain sizes and geometries.

Spatial amplification of a laser wave and the transverse spread of electrons in an undulator with a noncollinear configuration

The spatial amplification of a wave in a magnetostatic undulator with noncollinear electron and laser beams is studied in the framework of the dispersion relation for single-frequency and collective regimes. The dependence of the gain on the electron beam width is estimated with regard to the spatial boundedness of the beams. The laser power threshold at which the selection with respect to the transverse velocity is possible is obtained for a free-electron laser without inversion.

Analysis of Aberrations in Laser-Focused Nanofabrication

Based on the semi-classical model,we analyse the motion equation of chromium atoms in the laserstanding wave field under the condition of low intensity light fieldusing fourth-order Adams–Moulton algorithm. The trajectory of theatoms is obtained in the standing wave field by analytical simulation.The image distortion coming from aberrations is analysedand the effects on focal beam features are also discussed. Besidesthese influences, we also discuss the effects on contrast as well asthe feature width of the atomic beam due to laser power and laser beamwaist. The simulation results have shown that source imperfection,especially the transverse velocity spread, plays a critical role inbroadening the feature width. Based on these analyse, we present somesuggestions to minimize these influences.

Numerical Simulation Study of Double-Beam Magnetron-Injection Guns for High-Power Gyrotrons

This paper describes the detailed design of the double-beam coaxial magnetron-injection gun (DBMIG) for use in Ka-band coaxial gyrotron with two beams operating in the harmonic mode. The DBMIG operating voltage is 70 kV with a total beam current of 20 A, evenly divided among the beamlets, and provides two 70-kV 10-A beams with a velocity ratio of 1.5. The minimum of the transverse velocity spread and the axial velocity spread are about 3% and 5%, respectively. The emitter current density has been kept below 10 Amiddotcm-2 (space-charge limited). The primary computational tools used in the design process were the self-consistent particle-in-cell simulation code MAGIC

Estimation of the in‐field variation in fertiliser application

Variation in field application from a centrifugal fertiliser spreader has, in the past, been difficult to assess due to the intensive field testing required. However, with the application of current technologies such as Global Positioning Systems and Geographic Information Systems, the assessment of field application variation is now possible. The aim of this research was to develop a method to assess field application variation using basic transverse spread pattern test and vehicle tracking data. The information was used to measure and compare the effect of spread pattern, driving accuracy, driving method and paddock shape. Two differently shaped paddocks were used for analysis, one rectangular, the other triangular. A simple analysis method was initially used to calculate which areas of the paddock received nil, single, or double application. An advanced assessment method was also developed to measure application variation within the paddock and to calculate field application variation. Transverse spread pattern data was averaged at 2 m increments and linked to GPS tracking data from the spreading vehicle using ArcGIS 9.1©. The dataset was then analysed and a field application map produced. The field coefficient of variation (CV) was then calculated from the application map. Three simulations of perfect driving width and perfect application pattern were also conducted as a means of comparison to the actual field data. Simple analysis results showed, in both paddocks, the area receiving the correct application rate was between 70 and 80%, with 5–15% of the area receiving nil application. Using the advanced analysis method, the calculated field CV was 32.9 and 43.0% for the triangular and rectangular paddocks, respectively. However, when simulated “perfect driving” tracking data were used, the average field CV was reduced to 24.8 and 23.5%, respectively. When both perfect driving and a perfect spread pattern were used field application variation could be reduced to less than 20% for either shaped paddock. The results concluded that there is far greater variation in field application of fertiliser than that measured from a single transverse test, with the single biggest gain in calculated field CV being from driver accuracy and driving method.

On the complex three‐dimensional amplitude point spread function of lenses and microscope objectives: theoretical aspects, simulations and measurements by digital holography

The point spread function is widely used to characterize the three-dimensional imaging capabilities of an optical system. Usually, attention is paid only to the intensity point spread function, whereas the phase point spread function is most often neglected because the phase information is not retrieved in noninterferometric imaging systems. However, phase point spread functions are needed to evaluate phase-sensitive imaging systems and we believe that phase data can play an essential role in the full aberrations' characterization. In this paper, standard diffraction models have been used for the computation of the complex amplitude point spread function. In particular, the Debye vectorial model has been used to compute the amplitude point spread function of x63/0.85 and x100/1.3 microscope objectives, exemplifying the phase point spread function specific for each polarization component of the electromagnetic field. The effect of aberrations on the phase point spread function is then analyzed for a microscope objective used under nondesigned conditions, by developing the Gibson model (Gibson & Lanni, 1991), modified to compute the three-dimensional amplitude point spread function in amplitude and phase. The results have revealed a novel anomalous phase behaviour in the presence of spherical aberration, providing access to the quantification of the aberrations. This work mainly proposes a method to measure the complex three-dimensional amplitude point spread function of an optical imaging system. The approach consists in measuring and interpreting the amplitude point spread function by evaluating in amplitude and phase the image of a single emitting point, a 60-nm-diameter tip of a Near Field Scanning Optical Microscopy fibre, with an original digital holographic experimental setup. A single hologram gives access to the transverse amplitude point spread function. The three-dimensional amplitude point spread function is obtained by performing an axial scan of the Near Field Scanning Optical Microscopy fibre. The phase measurements accuracy is equivalent to lambda/60 when the measurement is performed in air. The method capability is demonstrated on an Achroplan x20 microscope objective with 0.4 numerical aperture. A more complete study on a x100 microscope objective with 1.3 numerical aperture is also presented, in which measurements performed with our setup are compared with the prediction of an analytical aberrations model.

Effective dispersion in a chemically heterogeneous medium under temporally fluctuating flow conditions

We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the equilibrium adsorption properties, the corresponding fluctuating retardation factor is modeled as a stationary random space function. The temporal variability of the flow is represented by a stationary temporal random process. Solute spreading is quantified by effective dispersion coefficients, which are derived from the ensemble average of the second centered moments of the normalized solute distribution in a single disorder realization. Using first-order expansions in the variances of the respective random fields, we derive explicit compact expressions for the time behavior of the disorder induced contributions to the effective dispersion coefficients. Focusing on the contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady flow fields, evolves to a disorder-induced macroscopic value (i.e., independent of local dispersion). At the same time, the asymptotic longitudinal dispersion coefficient can decrease. Under certain conditions the contribution to the longitudinal effective dispersion coefficient shows superdiffusive behavior, similar to that observed for transport in s stratified porous medium, before it decreases to its asymptotic value. The presented compact and easy to use expressions for the longitudinal and transverse effective dispersion coefficients can be used for the quantification of effective spreading and mixing in the context of the groundwater remediation based on hydraulic manipulation and for the effective modeling of reactive transport in heterogeneous media in general.

A GIS Methodology to Calculate In-Field Dispersion of Fertilizer from a Spinning-Disc Spreader

A model was developed within a GIS environment using the transverse spread pattern and GPS driving track during spreading to map actual fertilizer application at any point in a paddock. The spreading vehicle required a GPS of sufficient accuracy in order to provide proof of placement and guidance assistance to the driver. The method was used to assess the effect of field size and shape on actual application rate and application variation. At a target application rate of 80 kg ha-1, measured application rates ranged from 51.8 to 106.7 kg ha-1 of urea (46% N) fertilizer over 102 paddocks on four farms. Average field variation calculated over all paddocks was 37.9%. Irregular-shaped paddocks were found to have higher application variation (40.8%) compared to regular-shaped paddocks (35.9%). Hot spot analysis was performed to identify areas receiving statistically significant high and low application rates (s < 2.0). Over all paddocks, 7.4% of the total area received significantly high application rates, while 10.2 % received significantly low application rates. This information, collected over a number of applications, could be incorporated into subsequent variable-rate application maps whereby rates could be adjusted on areas that have received incorrect quantities of fertilizer in previous applications. This system will improve sustainability for a farm by ensuring that nutrient management plans can be followed, as well as providing a means of traceability and proof of placement.

Numerical analysis of flow and transport from a multiple‐source system in a partially saturated heterogeneous soil under cropped conditions

Field‐scale solute transport in a three‐dimensional, heterogeneous, variably saturated soil, originating from multiple planar sources (MS) is analyzed and compared with its counterpart originating from a single planar source (SS). The case under consideration is a citrus grove planted on a Hamra Red Mediterranean soil (Rhodoxeralf) in the central part of the coastal region of Israel, with a distinct rainy period during the winter and irrigations during the rest of the year. Results of the analyses show that for both the MS and the SS cases, solute transport during the irrigation season is characterized by a restricted downward movement and spread and by a considerable increase in concentration, while the opposite situation occurs during the rain season. In addition, results of the analyses suggest that as compared with the SS case, the MS case is characterized by a larger uncertainty in the concentration point values, by a slower solute convection and a smaller longitudinal solute spread, by a larger transverse solute spread, and by larger skewness and uncertainty in the solute breakthrough curve (BTC). Regarding the solute sampling design problem, our findings suggest that for both cases a pair of sampling points located in the horizontal plane of the field may be sufficient in order to provide relatively accurate estimates of characteristics of the transport (i.e., displacement and spread of the solute plume in the direction of the mean flow and mean solute BTC) for the entire spatially heterogeneous domain. To achieve these desirable results, in the MS case the first sampling point must be located within the wetted area in the vicinity of one of the planar sources, while in the SS case these results are independent of the location of the first sampling point. For both cases, however, an effort to quantify the uncertainty in the mean solute BTC requires few additional sampling points.

Experimental and theoretical investigation into the effect of the electron velocity distribution on chaotic oscillations in an electron beam under virtual cathode formation conditions

The effect of the electron transverse and longitudinal velocity spread at the entrance to the interaction space on wide-band chaotic oscillations in intense multiple-velocity beams is studied theoretically and numerically under the conditions of formation of a virtual cathode. It is found that an increase in the electron velocity spread causes chaotization of virtual cathode oscillations. An insight into physical processes taking place in a virtual-cathode multiple-velocity beam is gained by numerical simulation. The chaotization of the oscillations is shown to be associated with additional electron structures, which were separated out by constructing charged particle distribution functions.

A novel simplified two-dimensional magneto-optical trap as an intense source of slow cesium atoms

We describe the design and performance of a slow atom source based on a 2D magneto-optical trap (MOT) that uses an innovative simple optical configuration. Metal-coated retro-reflecting prisms replace mirrors and quarter-wave plates so the optical power of the cooling laser beam is recycled. This source has been characterised for three different configurations: with and without transverse magnetic field gradient, and with a pusher beam to obtain a 2D + -MOT. The longitudinal velocity is of the order of 25 m·s −1 , with a transverse velocity spread ≤1 m·s −1 , while the typical atomic flux density obtained is up to 1.3×10 14 at ·s −1 ·m −2 for a cesium vapour pressure of ~4×10 −8 mbar in the source. We use this slow atom beam, instead of cesium vapour, to load a 3D moving optical molasses that feeds a continuous cold atom fountain. We obtain a gain of a factor ~20 in the atomic flux launched by the fountain.

CONCEPTUAL DESIGN OF BESSEL BEAM CAVITY FOR FREE-ELECTRON LASER

The conventional cavity for a free-electron laser (FEL) oscillator usually forms an optical beam of Gaussian mode, which undergoes transverse spread along the interaction region. The transverse divergence of an optical beam will induce reduction of the FEL gain from three aspects: degenerating filling factor, causing diffraction loss and limiting the effective interaction distance. Bessel optical beam has been experimentally demonstrated diffraction-free characteristics in its propagation, which provides a possibility of improvement of FEL gain. In this paper, we present a conceptual design of a Bessel beam cavity for the free-electron laser oscillator. This cavity generates nondiffracting optical beam in the wiggler, resulting in improving the filling factor, decreasing the diffraction loss and elongating the effective interaction distance.

Efficiency of closed stiffener orthotropic deck panels for railway bridges

Closed stiffener orthotropic decks can be advantageous for ballasted or non-ballasted railway bridges. This has been achieved successfully on a number of tied arch railway bridges for the high-speed railway network in Belgium. In these bridges, the orthotropic plate contributes to both the deck plate action and the main load carrying system as the horizontal lower chord or arch tie. Although the basic structural action is comparable to that of road bridges, specific differences exist. These differences, which originate from a substantial discrepancy of the load transfer, are addressed in this paper. Railway loads considerably exceed applicable loads for road bridges, which result in significantly larger rib and floor beam dimensions. This has a significant impact on the transverse load spreading in the plate and on the moment redistribution due to floor beam flexibility. Load spreading describes the phenomenon in which a concentrated load is spread throughout a continuous medium. For typical railway bridg...

Ion manipulation with cooled and bunched beams

Ion beam properties are often critical to experiments with rare isotopes. The ability to cool transverse motion and energy spread in a beam or modify its time structure can significantly improve many types of experiments. This ability is now a common feature in existing low-energy facilities and will play a central role in a number of next generation radioactive beam facilities. The basic physics underpinning the operation of these beam cooling devices is introduced below together with the key technical evolutions that have occurred since the previous ENAM conference. Examples of operating devices for various sources of radioactive ions are given, together with the performance presently achieved and improvements expected in the near future.

Effective solute transport in temporally fluctuating flow through heterogeneous media

We investigate the effective spreading of a passive solute evolving from a finite source in temporally fluctuating flow through a heterogeneous porous medium. To this end, we distinguish between two stochastic processes: one to represent the spatial variability of hydraulic conductivity (K) and one to model the temporal fluctuations of the hydraulic gradient (J). In a second‐order perturbation approach we systematically investigate the time evolution of “effective” dispersion coefficients, which quantify solute spreading in response to longitudinal and transverse fluctuations of the hydraulic gradient, spatial heterogeneity, and local dispersion. The effective dispersion coefficients consist of three contributions that reflect (1) local dispersion, (2) the interaction between local dispersion and spatial heterogeneity, and (3) the interaction of local dispersion, spatial heterogeneity, and temporal fluctuations (i.e., time fluctuations enhance spreading only as a consequence of the interplay with spatial heterogeneity). Furthermore, longitudinal and transverse temporal fluctuations of the hydraulic gradient induce macroscopic contributions to the longitudinal as well as the transverse effective dispersion coefficients, which can both be comparable to the contributions to longitudinal dispersion due to steady flow, i.e., large. An application to a field‐scale tracer experiment gives evidence that temporal fluctuations help in explaining observed macroscopic transverse solute spreading. Furthermore, aquifer remediation techniques that rely on the mixing of injected reactants with resident contaminants, or simply on dissolving these, can benefit from forcing velocity fluctuations. The presented results provide a quantitative basis for the design of such hydraulic manipulation techniques.

Theory of cathode trajectory characterization by canonical mapping transformation

The paraxial lens theory cannot directly be applied to the cathode trajectories inside the gun. This inconvenience makes the interpretation of cathode trajectories difficult since one cannot use the physical concepts familiar in the paraxial lens theory, such as focal length and magnification factor. We have proposed the canonical mapping transformation (CMT) to describe the electron trajectories inside the gun by relating the ray conditions on the cathode surface to those in the crossover plane. The method takes as variables the distance along the surface and the sine of the ray angle with respect to the surface normal to define ray conditions. It has been shown that the CMT can be characterized by a small number of optical parameters. One of the parameters is the 'electron gun focal length', an extension of the image side focal length in the paraxial lens theory. The crossover size of a triode gun can be calculated from the electron gun focal length and the initial transverse energy spread. The calculation predicts the dependence of the crossover size on the grid voltage due to the change in the electron gun focal length. The prediction is compared with the measurement and shows good agreement with it. Since the CMT optical parameters can be calculated from the representative trajectories only and as they predict practically all the necessary source properties of guns, the CMT can be used as a practical tool in the designing of various types of electron guns.

Nicht-traumatische akute Querschnittsyndrome

Differential diagnosis of non-traumatic, acute transverse spinal cord syndromes should cover compressive myelopathy (mostly hematomas or tumors), inflammatory myelitis and vascular myelopathies. Since acute pathologies of the spinal cord primarily result in flaccid para- or tetraparesis accompanied by areflexia or hyporeflexia (spinal shock), acute polyradiculoneuritis and the cauda equina syndrome must also be weighed into the differential diagnosis. Paraplegia may ultimately also be of psychogenic origin. The clinical picture is characterized by the rapidity of progression, the possible involvement of pain, and the specific pattern of the deficits. When the latter occurs, localization of the rostrocaudal level and transverse spread are crucial factors. Depending on the affected structure, one differentiates between anterior spinal cord syndromes (anterior spinal artery syndrome, selective involvement of the anterior horn, centromedullary syndromes), long pathway syndrome (isolated in the posterior bundle or combined with pyramidal pathways) and the unilateral Brown-Séquard's syndrome. Infectious myelitis is usually caused by neurotropic viruses or mycoplasmata in conjunction with meningitis or encephalitis; these in turn either induce transverse myelitis accompanied by severe sensomotor deficits or chiefly affect the gray matter, then producing a pattern similar to anterior spinal artery syndrome. In the case of non-infectious inflammatory myelitis, one must differentiate between multiple sclerosis, acute disseminated encephalomyelitis (ADEM), idiopathic transverse myelitis and that of the neuromyelitis optica or Devic's disease. Symptomatic transverse myelitis can also be present in association with connective tissue diseases (e.g. SLE, Behçet's disease, Sjögren's syndrome) or sarcoidosis. Notably, when ischemic spinal infarcts are involved, their onset is frequently painful and their manifestation typically subacute, rather than apoplectiform.

Transverse kinematics of ions stored in an electrostatic ion beam trap

We present experimental results, as well as numerical simulations, for the transverse velocity distribution of ions stored in an electrostatic ion beam trap. The measurements indicate that the transverse velocity spread is about 1% of the longitudinal velocity, and that the ions fill the whole transverse stable phase space. We also demonstrate that ion losses from the trap due to multiple scattering with molecules from the residual gas is an important factor limiting the lifetime of the beam.

Can we determine the transverse macrodispersivity by using the method of moments?

One of the main assumptions that renders the stochastic theories applicable to real aquifers is the ergodic hypothesis, i.e. the possibility to exchange ensemble and spatial averages of a variable of interest. The principal aim of this paper is to elucidate the conditions that allow for an exchange between ensemble and spatially averaged second moments of concentration field ( S ij ); the fulfillment of the ergodic condition underlies the applicability of the dispersion coefficients or other related quantities obtained by the stochastic theories to actual aquifers. The fulfillment of the ergodic hypothesis is assessed here by analyzing the diminishing of the variance of S ij as the initial size of the plume V 0 grows, i.e. the tendency of S ij toward its expected value 〈 S ij 〉. It is shown that it is not always possible to assume ergodicity for solute plumes in heterogeneous aquifers. For the typical plume configurations encountered in applications, transverse and vertical spreading are the most problematic in this respect. In particular, satisfying the ergodic hypothesis depends largely on the initial plume configuration and size, on one hand, and the direction of the moment of interest, on the other. Numerical simulations based on the analytic element method elucidate the results. The relevance of the results is mostly felt for the inference of macrodispersive parameters, which are often derived through S ij . The work indicates that S ij may be a distorted and inadequate measure of the plume spread. This should serve as a warning against application of results based on ensemble averages to real-life plumes, particularly when estimating macrodispersion coefficient from field experiment.