Reverse Trajectory Research Articles

Exact reconstruction of volumetric images in reverse helical cone-beam CT.

Helical scanning configuration has been used widely in diagnostic cone-beam computed tomography (CBCT) for acquiring data sufficient for exact image reconstruction over an extended volume. In image-guided radiation therapy (IGRT) and other applications of CBCT, it can be difficult, if not impossible, to implement mechanically a multiple-turn helical trajectory on the imaging systems due to hardware constraints. However, imaging systems in these applications often allow for the implementation of a reverse helical trajectory in which the rotation direction changes between two consecutive turns. Because the reverse helical trajectory satisfies Tuy's condition, when projections of the imaged object are nontruncated, it yields data sufficient for exact image reconstruction within the reverse helix volume. The recently developed chord-based algorithms such as the backprojection filtration (BPF) algorithm can readily be applied to reconstructing images on chords of a reverse helical trajectory, and they can thus reconstruct an image within a volume covered by the chords. Conversely, the chord-based algorithms cannot reconstruct images within regions that are not intersected by chords. In a reverse helix volume, as shown below, chordless regions exist in which no images can thus be reconstructed by use of the chord-based algorithms. In this work, based upon Pack-Noo's formula, a shift-invariant filtered backprojection (FBP) algorithm is derived for exact image reconstruction within the reverse helix volume, including the chordless region. Numerical studies have also been conducted to demonstrate the chordless region in a reverse helix volume and to validate the FBP algorithm for image reconstruction within the chordless region. Results of the numerical studies confirm that the FBP algorithm can exactly reconstruct an image within the entire reverse helix volume, including the chordless region. It is relatively straightforward to extend the FBP algorithm to reconstruct images for general trajectories, including reverse helical trajectories with variable pitch, tilted axis, and/or additional segments between turns.

Symmetry based mechanism for hand-over-hand molecular motors

Many bio-molecular motors are dimers that move by a “hand-over-hand” mechanism along polar bio-polymeric tracks. Examples include kinesin, that “walks” on microtubule and myosin V that “walks” on actin. These molecular motors share two important symmetries. Typically the motor dimers have approximate mirror symmetry, and their tracks have translational, but not mirror, symmetry. Here we use a trajectory approach to analyze a minimal model for a generic dimeric motor that moves on a polymer track incorporating these two symmetry features. The analysis focuses of the relative probabilities of forward, reverse, backward, backward reverse trajectories and provides an experimentally accessible measure of the relative importance of a “Brownian motor” vs. “Power stroke” mechanism. Reciprocal relations, similar to those derived for the linear regime by Onsager for the fluxes (generalized velocities), hold for arbitrary magnitude forces (i.e., far from the linear regime) for the net probabilities for stepping and for chemical reaction.

Time-domain studies of very-large-angle magnetization dynamics excited by spin transfer torques

We describe time-domain measurements which provide information about the large-angle nonlinear dynamics of nanomagnets excited by spin-transfer torque from a spin-polarized current. Sampling-oscilloscope measurements, which average over thousands of experimental time traces, show that the mean reversal time for spin-transfer-driven magnetic switching has a steplike dependence on magnetic field, consistent with simulations which predict that the reversal trajectories differ by integer numbers of precession cycles. Storage-oscilloscope measurements of individual experimental traces reveal nonperiodic large-amplitude resistance variations at values of magnetic field and current in a crossover region between the regimes of spin-transfer-driven switching and steady-state precession. We also observe directly the existence of time-dependent switching, on the nanosecond scale, between different precessional modes and between a precessional mode and a static state, at particular values of magnetic field and current bias.

Measurements of dynamic forces between drops with the AFM: novel considerations in comparisons between experiment and theory.

Dynamic forces between a deformable tetradecane oil drop (radius of curvature ≈ 25 μm) anchored on the cantilever of the Atomic Force Microscope (AFM) and similar oil drops (radii of curvature 80 to 500 μm) on the substrate in aqueous electrolyte with added sodium dodecyl sulfate surfactant have been studied. Measurements were made over a range of scan rates that span the range of Brownian velocities of such emulsion drops. The adsorbed anionic surfactants impart a stabilising electrical double layer repulsion between the drops so coalescence was not observed under present conditions. Force-displacement data follow reversible trajectories at low scan rates (<0.5 μm s-1) but exhibit increasingly large hysteric effects for scan rates up to 30 μm s-1. The coupling between deformations of the interacting drops and deflections of the AFM cantilever at high scan rates facilitates a self-consistent and independent estimate of the cantilever spring constant if one models variations of cantilever deflection with piezo displacement. In addition to giving excellent agreement between predicted and measured dynamic forces, our model also furnishes quantitative information about: variations of the force with interfacial separation, deformations and velocities of interfaces, pressure distributions in the aqueous film between the drops as well as the absolute separation between the interacting drops. A new dimpling phenomenon is inferred to occur when interacting drops are being separated after the formation of a flattened aqueous film. These new capabilities in the evaluation and interpretation of AFM force measurements overcome a major limitation in the use of the AFM for the absolute quantification of force-separation data.

Influence of the k‐space trajectory on the dynamic T1‐weighted signal in quantitative first‐pass cardiac perfusion MRI at 3T

The dynamic T(1)-weighted signal in first-pass myocardial perfusion MRI can vary as a function of k-space trajectory. The purpose of this study, therefore, was to compare the relative T(1)-weighted signal produced by the linear, centric, and reverse centric k-space trajectories at 3T. The centric k-space trajectory yielded higher arterial input function (AIF) than the linear and reverse centric k-space trajectories (6.21 +/- 0.84 vs. 4.75 +/- 0.75 vs. 4.39 +/- 0.85 mM, respectively; N = 9; P < 0.01), and the reverse centric k-space trajectory yielded higher myocardial signal contrast (as a fraction of equilibrium magnetization) than the linear and centric k-space trajectories (0.17 +/- 0.02 vs. 0.12 +/- 0.02 vs. 0.05 +/- 0.01, respectively; N = 9; P < 0.001). Compared to the linear k-space trajectory, the centric k-space trajectory is relatively optimal for the quantification of AIF, whereas the reverse centric k-space trajectory is relatively optimal for high contrast of myocardial wall enhancement.

Using Reverse Air Trajectory (HYSPLIT) to Identify Potential Sources of Hg and Jurisdictional Rule

Using Reverse Air Trajectory (HYSPLIT) to Identify Potential Sources of Hg and Jurisdictional Rule

TH‐D‐L100J‐02: Exact Image Reconstruction in Reverse Helical Cone‐Beam CT for Radiation Therapy

Purpose: To propose an exact image reconstruction algorithm based on Pack‐Noo formula for a reverse helical cone‐beam CT (CBCT) which is potentially a useful scanning geometry for image‐acquisition in image‐guided radiation therapy. Method and Materials: Last year, we proposed a novel scanning geometry named reverse helical trajectory for a CBCT imager mounted on a linear accelerator (LINAC) treatment system, and applied a chord‐based backprojection filtration (BPF) algorithm for exact image reconstruction. It was shown that there is a middle gap in the reconstructed image which is due to lack of chords passing through the gap. The gap was removed when we used an additional long line segment connecting the end points of the revere helices. However, larger patient dose and longer scan time due to additional line scan were pointed out as drawbacks of the proposed method. In this work, we applied Pack‐Noo formula, which does not depend on the existence of chords for reconstructing the exact image, to propose an exact image reconstruction algorithm for a reverse helical trajectory. Cone‐beam data requirement for the proposed algorithm was exploited to address the concept of reduced cone‐beam scan. A numerical study using 3D Shepp‐Logan phantom was performed. Results: We showed the proposed algorithm can reconstruct the image without any gap in the middle from the cone‐beam data acquired by a reverse helical scan. Additional line scan, which is necessary for chord‐based BPF algorithms to remove the middle gap, is not needed for exact image reconstruction with the proposed algorithm. Conclusion: A new algorithm based on Pack‐Noo formula for exact image reconstruction in reverse helical cone‐beam CT was proposed. Without any additional line scan which is necessary for chord‐based BPF algorithms to reconstruct the complete image, the proposed algorithm successfully reconstructed the image.

Performance assessment of hanging funnel‐and‐gate structures designed by reverse particle tracking for capturing polluted groundwater

AbstractThe objective of this study was to evaluate the capability of partially penetrating (hanging) funnel‐and‐gate structures, designed using reverse flow trajectories, for capturing plumes of contaminated groundwater. Linear capture structures, comprised of two slurry cutoff walls on either side of a permeable gate, were positioned perpendicular to regional groundwater flow in a hypothetical unconfined aquifer. A four‐step approach was used for each of two simulated settings: (1) a numerical mass transport model generated a contaminant plume originating from a source area; (2) a particle‐tracking model projected groundwater flow paths upstream from a treatment gate; (3) the structure was widened and deepened until bounding path lines contained the plume; and (4) mass transport simulation tested the ability of the structure to capture the plume. Results of this study suggest that designing funnel‐and‐gate structures using reverse particle tracking may result in too small a structure to capture a contaminant plume. This practice generally ignores effects of hydrodynamic dispersion, which may enlarge plumes such that contaminants move beneath or around a capture structure. This bypassing effect may be considerable even for low values of dispersivity. Particle‐tracking approaches may also underestimate the amount of time required to reduce contaminant concentrations to acceptable levels. © 2007 Wiley Periodicals, Inc.

Generating a geometric mode for clarifying differences between an operator method and SU(2) wave representation

We study both numerically and experimentally a specific geometric mode, named VW mode, in an end-pumped Nd:YVO4 laser with a plano-concave cavity near the 1/3-degeneracy. Three theoretical methods are used to analyze the transverse profiles, the operator method [J. Opt. Soc. Am. A 22, 1559 (2005)], the SU(2) wave representation [Phys. Rev. A 69, 053807 (2004)], and the Fox-Li approach. Some differences among them are addressed and clarified. Moreover, the generating conditions for VW mode are found peculiar and its propagation character is demonstrated. By comparing the experimental mode patterns with the three numerical results, we conclude that the field of a geometric mode in the operator method should be extended to include those of the reverse directional trajectories and the SU(2) coherent state representation is found too specific to produce the fringes within some transverse patterns.

On the sampling requirements for exponential-work free-energy calculations

Calculation of free-energy differences using exponential-work averaging methods is examined, focusing on the amount of sampling required to converge to an accurate result. Prior research that has demonstrated that the necessary amount of sampling scales exponentially with the dissipated work associated with the reverse trajectory is reviewed. The result is demonstrated through a pedagogical application to a model process involving adiabatic compression and expansion of a gas.

Reverse Trajectory Approach to Computing Ionospheric Currents to the Special Sensor Ultraviolet Limb Imager on DMSP

The special sensor ultraviolet limb imager was developed by the U.S. Naval Research Laboratory and is deployed on the Defense Meteorological Satellite Program (DMSP) F16 polar-orbiting spacecraft. The instrument is experiencing a level of noise that is, at times, interfering with its proper operation. The noise is correlated with the spacecraft chassis potential. The potentials about DMSP and the resulting ionospheric current entering the instrument were computed to determine if the noise could be due to this current. In order to obtain results of sufficient accuracy, it is necessary to use a reverse trajectory technique that effectively integrates over the thermal distribution of incident ions. The reverse trajectory technique is described in detail. Once the resistance between the mirror surface and the chassis is taken into account, the current computed using this approach shows the same dependence on the chassis potential as the observed noise, which supports the conjecture that ionospheric ions are responsible for the noise

The influence of polar vortex ozone depletion on NH mid-latitude ozone trends in spring

Abstract. Reverse domain-filling trajectory calculations have been performed for the years 1993, 1995, 1996, 1997, and 2000 to calculate the spreading of ozone depleted air from the polar vortex to midlatitudes in spring. We find that for these years with massive Arctic ozone depletion the zonal mean total ozone column at midlatitudes is reduced with between 7 and 12 DU in the April-May period. The polar vortex and remnants have preferred locations which leads to longitudinal differences in the midlatitude ozone trends. Together with decadal variations in circulation the dilution of ozone depleted air may explain the major fraction of longitudinal differences in midlatitude ozone trends. For the period 1979–1997 the dilution may explain 50% of the longitudinal differences in ozone trends and for the period 1979–2002 it may explain 45%. The dilution also has a significant impact on the zonal mean ozone trends in the April-May period. Although uncertainties are large due to uncertainties in the ozone depletion values and neglect of ozone depletion in other years than 1993, 1995, 1996, 1997, and 2000 we have tried to calculate the size of this effect. We estimate that dilution may explain 29% of the trend in the period 1979–1997 and 33% of the trend in the period 1979–2002 as a lower limit.

SU‐CC‐ValA‐10: Cone‐Beam CT for Radiation Therapy with Reverse Helical Trajectory

Purpose: To propose and study a novel scanning trajectory, named reverse helical trajectory, for a cone‐beam CT (CBCT) imager mounted on a linear accelerator (LINAC) treatment system by applying an exact 3D backprojection filtration (BPF) algorithm. Method and Materials: A numerical study using 3D Shepp‐Logan phantom was performed. We applied the PI‐line‐based BPF algorithm to reconstruct exact 3D image from data acquired numerically for a reverse helical trajectory. It was revealed that there is a middle gap in the reconstructed image which is due to lack of PI‐lines passing through the gap. Application of a chord‐based BPF algorithm showed a reduction in the middle gap. Two kinds of line plus reverse helical trajectories were proposed and tested to reduce the middle gap further. One of them is a reverse helical trajectory with a short line segment between two helices separated apart. The other one is a reverse helical trajectory with a long line segment connecting the end points of the revere helices. Results: The middle gap in the reconstructed image was reduced by employing a chord‐based BPF algorithm. The gap was reduced further when we modified the scanning trajectory by inserting a line segment between two helices. The gap was removed completely when we used a reverse helical trajectory with a long line segment connecting the end points of the revere helices. Conclusion: A novel scanning geometry for a LINAC‐mounted CBCT imager was proposed, and a preliminary numerical study was performed. The middle gap in the reconstructed image obtained by PI‐line‐based BPF algorithm was effectively eliminated by using a chord‐based BPF algorithm with a line plus reverse helical trajectory.

Design and analysis of output feedback force control in parallel turning

AbstractParallel machine tools (i.e. machine tools capable of cutting a part with multiple tools simultaneously but independently) are being utilized more and more to increase operation productivity, decrease set-ups and reduce floor space. Process control is the utilization of real-time process sensor information to adjust process parameters (e.g. feed, spindle speed) automatically in order to increase operation productivity and quality. To date, however, these two technologies have not been combined. This paper describes the design of an output feedback controller for a parallel turning operation that accounts for the inherent non-linearities in the force process. An analysis of the process equilibriums explains the system's stability behaviour for different design specifications and the reverse trajectory method is used to numerically determine the exact stability boundary. Effects of saturation on stability are also analysed, and from this sufficient conditions for global stability are obtained. Final...

Design and analysis of output feedback force control in parallel turning

Parallel machine tools (i.e. machine tools capable of cutting a part with multiple tools simultaneously but independently) are being utilized more and more to increase operation productivity, decrease set-ups and reduce floor space. Process control is the utilization of real-time process sensor information to adjust process parameters (e.g. feed, spindle speed) automatically in order to increase operation productivity and quality. To date, however, these two technologies have not been combined. This paper describes the design of an output feedback controller for a parallel turning operation that accounts for the inherent non-linearities in the force process. An analysis of the process equilibriums explains the system's stability behaviour for different design specifications and the reverse trajectory method is used to numerically determine the exact stability boundary. Effects of saturation on stability are also analysed, and from this sufficient conditions for global stability are obtained. Finally, the system is analysed for robustness to parameter uncertainties. Simulations and phase portraits are used to verify the developed theory.

Dynamic modeling of geomagnetic cutoff for the 23–24 November 2001 solar energetic particle event

We investigate numerically the time variations of geomagnetic cutoffs of solar energetic particles. As a test case, the geomagnetic cutoff of 25 MeV protons is modeled for the 23–24 November 2001 solar energetic particle (SEP) event. Following Smart and Shea [2001], solar energetic particle access is determined by computing the reverse particle trajectories. Magnetospheric fields are obtained from the Lyon‐Feder‐Mobarry (LFM) global MHD model, which is driven by measured solar wind parameters at the sunward boundary. We find well‐defined surfaces of constant cutoff that exhibit dynamic behavior in response to solar wind conditions. We show that dynamic modeling of cutoff surfaces may be used as a tool to investigate SEP access to the inner magnetosphere. The numerical results are compared with proton observations from a highly elliptical orbit (HEO) satellite. The results suggest that an enhancement in the solar wind dynamic pressure plays a role in the observed ion injection.

Development of Oil Spill Scenarios for Contingency Planning Along the Brazilian Coast

ABSTRACT After an oil spill in Guanabara Bay due to the collapse of a marine fuel pipeline in January 2000, PETROBRAS (a Brazilian company among the 15 largest oil companies in the world) is facing important challenges regarding its environmental commitment to Brazilian society. To face these new challenges, PETROBRAS launched a program for excellence in environmental, health and safety management that includes the development of oil spill contingency plans for its facilities. The present paper describes an oil spill modeling project for 25 facilities along the Brazilian coast. The implementation of the project involved a detailed meteorological and oceanographic characterization of each study area with a review of existing data, data collection, and hydrodynamic modeling covering more than 9,000 km of coastline. Based on the requirement of scenarios for both typical and critical conditions, the oil fates and trajectory modeling system OILMAP was applied to simulate oil spill incidents in all 25 sites, most of them oil terminals from TRANSPETRO, a PETROBRAS subsidiary. Due to Brazil's continental dimensions, the environmental conditions simulated ranged from the subtropical Patos Lagoon in the southernmost part of the country to the equatorial Solimoes River, including estuaries, coastal zones, and offshore sites. The developed modeling system allows oil spill contingency specialists to develop response plans for typical spills in the selected locations. By performing reverse trajectory calculations from sensitive sites such as water intakes or fragile wetlands, it is also be possible to identify probable release locations of spills and principal avenues of vulnerability for these important resources. This paper presents a description of the implementation of the system and the results of this modeling approach for a typical oil terminal located in the city of Vitoria, eastern Brazilian coast.

High-Resolution Stratospheric Tracer Fields Reconstructed with Lagrangian Techniques: A Comparative Analysis of Predictive Skill

Numerical experiments and statistical analyses are conducted to determine the skill of different Lagrangian techniques for the construction of tracer distributions. High-resolution potential vorticity (PV) maps are calculated from simulations of the 1996/97 arctic winter stratospheric dynamics using two different numerical schemes—reverse domain filling trajectories (RDF) and contour advection with surgery (CAS)—and data from three meteorological agencies (NCEP, the Met Office, and ECMWF). The PV values are then converted into ozone (O3) concentrations and statistically compared to in situ O3 data measured by the electro chemical ozone cell (ECOC) instrument during the Airborne Polar Experiment (APE) using cross correlation, rms differences, and the Kolmogorov–Smirnov (KS) test. Results indicate that while Lagrangian techniques are successful in increasing the presence of lower-scale tracer structures with respect to the plain meteorological analyses, they significantly improve the statistical agreement between the simulated and the measured tracer profiles only when there is clear evidence of filaments in the measured data. This better fit is most clearly seen by using the KS test, rather than cross correlation. It is argued that this difference in the performance of Lagrangian techniques can be partly related to the treatment of mixing processes in the framework of the Lagrangian schemes. Statistical analyses also show that the temporal rather than the spatial resolution of the input meteorological fields, used to advect tracers, enhances the predictive skill of the Lagrangian products. The best overall performance is obtained with the Lagrangian product (not gridded) based on high-resolution reverse trajectories calculated along a flight track, in particular when the simulation is initialized with ECMWF data. Other products, such as CAS initialized with ECMWF and 3D-gridded RDF initialized with the Met Office data, show fairly good performances, thus with lower statistical confidence.

Quasiclassical Trajectory and Transition State Theory Studies of the N(4S) + H2 ↔ NH(X3Σ-) + H Reaction

Detailed forward and reverse quasiclassical trajectory and variational transition state theory studies of the title reaction are presented. The potential energy surface (PES) has been calculated at the MCQDPT2// FORS-MCSCF(7,6)/6-311++G * * level of theory using GAMESS. Selection of points and analytical interpolation of the surface was done using the GROW program of Collins, Thompson, Jordan, and Bettens. Broad ranges of translational energies, and ground and excited rovibrational energy levels (v,j) are chosen as initial conditions of the reactant molecules. All three reactions considered in this study (e.g., N + H 2 and NH + H abstraction and exchange) show angular distributions that are backward peaked. Both the forward ion and the exchange reactions show product vibrational distributions that are dominated by the ground state, whereas the reverse reaction prefers v' = 1 for trajectories initiated at low E T . The rate constants for the forward and reverse reactions were found to be in good accord with available experimental and theoretical data and can be expressed in the Arrhenius form as k(T) = 6.85 x 10 - 1 0 exp(-25.9(kcal/mol)/RT) and k(T) = 1.85 x 10 - 1 4 T 1 . 0 7 exp(-2.2(kcal/mol)/RT) cm 3 molecule - 1 s - 1 , respectively. For ICVT results, these rate constants can be similarly expressed as k(T) = 5.52 x 10 - 1 0 exp(-32.4(kcal/mol)/RT) and k(T) = 1.56 x 10 - 1 6 T 1 . 6 4 exp(-0.7(kcal/mol)/RT) cm 3 molecule - 1 s - 1 , respectively. The reasonable agreement with the available data substantiates the sufficiency of the computational methods employed in this study.

Comparison of cross‐tropopause transport and ozone in the upper troposphere and lower stratosphere region

Wintertime tracer transport in the atmospheric “middle world” is analyzed for five winters using three different advection methods, namely Eulerian advection, reverse domain‐filling trajectory calculations, and contour advection with a diagnosis of filaments. In all approaches, isentropic motion is assumed. The results are compared to synopses of ozone derived from the Measurement of Ozone and Water Vapor by Airbus In‐Service Aircraft (MOZAIC) airborne ozone measurement program. Tracer and ozone data are cast into the “reduced” space spanned by equivalent latitude, potential temperature, and time. In this representation some anomalies of MOZAIC ozone are mirrored in corresponding features of stratospheric tracer mass mixing ratios. Eulerian and reverse domain‐filling trajectory studies give similar results, suggesting that numerical diffusion only plays a minor role. Tracer transport out of the stratosphere minimizes in the height range of 340 to 350 K. The trajectory studies reveal preferred regions of isentropic stratosphere‐troposphere exchange associated with the positions of storm tracks. These asymmetries are similar to asymmetries in the correlation of potential vorticity (PV) and ozone found in the MOZAIC data. Zonal asymmetries are also found in the occurrence of filamentary structure in the contour advection simulations with filamentation maximizing downstream of the North Atlantic storm track. Hemispheric‐ and seasonal‐mean filamentation activity is strongly correlated with stratosphere‐troposphere exchange discerned from the Lagrangian transport experiments. In both signals the winter of 1997/1998 shows the lowest activity of the five winters analyzed here. A drop in activity in the winter of 1995/1996 may, however, be related to the introduction of a more advanced data assimilation scheme to the European Centre for Medium‐Range Weather Forecasts (ECMWF) analysis cycle. This change may also be partly responsible for a somewhat improved correlation of PV and MOZAIC ozone at high equivalent latitudes after the winter of 1994/1995.