Off-axis Region Research Articles

THE COMPARISON OF 2D DOSE PATIENT-SPECIFIC QUALITY ASSURANCE BETWEEN MONTE CARLO-CONVOLUTION AND MODIFIED CLARKSON INTEGRATION ALGORITHM

A sophisticated machine of radiotherapy treatment process follows the complexity of the quality assurance (QA) measurement. Non-measurement QA becomes one of the solutions to reduce the medical physicists’ workload. However, this method has not been clinically established. This study compared two non-measurement methods of patient-specific quality assurance (PSQA) to find the feasible algorithm for the adaptive radiotherapy process. Monte Carlo-based (MC) PSQA used a phase space file of the medical linear accelerator (Linac) to obtain the photon energy fluence and forward projected to the isoplane. In contrast, Modified Clarkson Integration-based (MCI) used a non-uniform fluence map in the isoplane. For the modulated intensity, we used a pair of the dynamic log files of the multileaf-collimator (MLC) and then employed them in the algorithms. The dose distributions of MC and MCI methods were compared to the treatment planning system (TPS) using gamma index analysis. We found that the gamma pass rates (GPR) for MC-TPS and MCI-TPS were 99.54% and 99.57%, respectively. Further, the dose distribution in the off-axis region for the MCI method showed lesser accuracy due to the higher secondary dose contribution. The linac log file information can be used and calculated into a 2D dose distribution using both MC and MCI methods, providing high-accuracy results.

Abundant off-axis hydrothermal activity in the 29–30 ridge segment of the Southwest Indian Ridge: evidence from ferromanganese crusts

In the ultra-slow spreading mid-ocean ridge, seafloor hydrothermal ventings mostly occur in the off-axis region. The plume of hydrothermal venting provides Fe, Mn and other metal materials for the growth of ferromanganese crust in the surrounding seamounts, showing unique geochemical characteristics that are different from that of hydrogenetic crust. Based on five samples of ferromanganese crusts, major, trace and rare earth element analysis was carried out to identify their material sources. Combined with the investigation data of water column and seafloor camera photos by deep towed hydrothermal detection system, the potential of hydrothermal activity in the 29–30 ridge segment of the Southwest Indian ridge was evaluated. The results showed that the ferromanganese crust in the study area had significantly higher Fe/Mn value (average 1.9), relatively higher Si and Al contents, and significantly higher Ca/P value (average 9.3),without significant phosphorylation. ferromanganese crust in the study area have significantly lower Co and Ni contents (about 1600 mg/kg on average), and relatively lower Sr, Ba, Pb, Cu, Zr and Mo contents (between 100-1000 mg/kg on average). The contents of W, Th and Te are also relatively low (average content between 10–50 mg/kg); The total rare earth element content of the crust in the study area is relatively low (about 928 mg/kg on average), and the light rare earth is relatively enriched. The standardized rare earth curve of the shale shows a left-leaning pattern as a whole, showing the enrichment of heavy rare earth relative to the shale. The Co content and rare earth element content of the ferromanganese crusts in this area are significantly lower than those of hydrogenetic crusts. The discrimination diagrams of ternary and bivariate material sources reveal that they have mixed hydrothermal and hydrogenetic origins. The three crust samples of S1, S2, and S5 are located within 2 km of the known hydrothermal fields, indicating a correlation between ferromanganese crust and the location of hydrothermal activity. There is no known hydrothermal field near the S3 and S4 stations. Altered rocks and water column turbidity anomalies were found near S3 station, and large areas of altered rocks and suspected hydrothermal biological remains were also found near S4 station, indicating that hydrothermal activity may exist in both areas. In addition to the two new hydrothermal fields identified in this article, the spatial frequency of hydrothermal activity in the study area reaches 15 sites/100 km, which is significantly higher than other well investigated oceanic ridges. Out of the eight hydrothermal fields in the study area, seven are located in the off axis region, mainly because the hydrothermal activity in this area is controlled by high angle and large offset normal faults and one-way detachment faults. This also indicates that the off-axis region of the Southwest Indian Ridge has high potential for hydrothermal activity.

Comprehensive clinical evaluation of TomoEQA for patient-specific pre-treatment quality assurance in helical tomotherapy

BackgroundBased on a previous study on the feasibility of TomoEQA, an exit detector-based patient-specific pre-treatment quality assurance (QA) method for helical tomotherapy, an in-depth clinical evaluation was conducted.MethodsData of one hundred patients were analyzed to evaluate the clinical usefulness of TomoEQA for patient-specific pre-treatment QA in comparison with the conventional phantom-based method. Additional investigations were also performed under unusual measurement conditions to validate the off-axis region. In addition to the clinical evaluation of TomoEQA, a statistical analysis was conducted to determine the plan parameters that affect the pass/failure results of pre-treatment QA.ResultsThe average and standard deviations of the gamma passing rate and point dose error for TomoEQA were comparable to those of the conventional QA method. For TomoEQA, the average values of the gamma passing rate and point dose error were 96.32% (standard deviation (1 sigma) = 3.94; 95% confidence interval (CI), 95.55 to 97.09) and − 1.12% (standard deviation (1 sigma) = 1.04; CI, − 1.32 to − 0.92), respectively. For the conventional QA method, the average values of the gamma passing rate and point dose error were 95.95% (standard deviation (1 sigma) = 4.35; 95% confidence interval (CI), 95.10 to 96.80) and − 1.20% (standard deviation (1 sigma) = 1.61; CI, − 1.52 to − 0.88), respectively. Further experiments on the off-axis region demonstrated that TomoEQA can provide accurate results for 3D dose analysis, which is inherently difficult in the conventional QA method. Through a statistical analysis based on the results of TomoEQA, it was validated that the total fraction (Total Fx), monitor units, beam-on-time, leaf-of-time below 100 ms, and planning target volume diameter were statistically significant for the pass/failure of the pre-treatment QA results.ConclusionsTomoEQA is a clinically beneficial alternative to the conventional phantom-based QA method.

Development and dosimetric evaluation of the IMRT prostate at outside-the-irradiated field in a heterogeneity male pelvis phantom

Abstract Background: Intensity-modulated radiation therapy (IMRT) treatment delivery requires pre-treatment patient-specific quality assurance (QA) for the dosimetry verification due to its complex multileaf-collimator movement. The prostate target close position between the bladder and rectum requires a tight margin during planning, and mistreatment would have a huge impact on the patient. A commercially available QA tool consists of a homogeneous medium and does not represent an exact photon interaction on the tumour and also on the nearby healthy organ. Objective: A heterogeneous male pelvis phantom was developed and investigated the efficiency of the treatment planning system (TPS) calculation on the off-axis region. Methods: Polymethyl methacrylate was used for the phantom housing, and the material closed to the bladder, rectum and prostate density was chosen to construct the organ models. The phantom was scanned and validated by the computed tomography number and density. An IMRT treatment was planned in the Monaco TPS, and a thermoluminescent dosimeter (TLD-100) was used to validate the point dosimetry. In addition, an EGSnrc Monte Carlo simulation was carried out to validate the phantom dosimetry. Results & Discussion: The dose measurement between TLD-100, TPS, and EGSnrc was compared and validated in the pelvis phantom. In the prostate region, the dose difference was within ± 5%, and the maximum dose difference outside-the-irradiated field was up to 20·07 % and 47·31 % in TPS and TLD-100, respectively. Meanwhile, the measured dose was lower than the calculated dose, and it was apparent for the dose outside-the-irradiated field. Conclusion: The developed heterogeneity male pelvis phantom was validated and verified to be an important QA device for validating radiation dosimetry in the pelvis region. The dose outside-the-irradiated field was underestimated by both TPS and TLD, respectively.

Synergy effect of the Ohkawa current drive of electron cyclotron waves and the lower hybrid current drive: a new mechanism

A new synergy mechanism between the Ohkawa current drive (OKCD) of electron cyclotron (EC) waves and the lower hybrid current drive (LHCD) is discovered and discussed. The methodology to achieve this synergy effect is also introduced. Improvement of OKCD efficiency can be achieved by up to a factor of ~2.5 in the far off-axis radial region (ρ > 0.6) of tokamak plasma. By making EC wave heating of electrons have a parallel velocity in the co-Ip direction and the lower hybrid wave heating of electrons have a parallel velocity in the counter-Ip direction, the mechanism of this new synergy effect comes from the results of the electron trapping and detrapping processes. The OKCD makes the low-speed, barely-passing electrons be trapped (trapping process), the LHCD pulls some of the high-speed barely-trapped electrons out of the trapped region in velocity space (detrapping process) and accelerates the detrapped electrons to a higher speed.

Theoretical analysis of key factors achieving reversed magnetic shear q-profiles sustained with lower hybrid waves on EAST

The phase space analysis technique is applied to provide new insights into the fully non-inductive lower hybrid current driven (LHCD) discharges on EAST (Garofalo et al 2017 Nucl. Fusion 57 076037). The analysis shows that there are bounded and unbounded topologies of lower hybrid (LH) waves in phase space. For typical parameters on EAST, the propagation domain for 4.6 GHz LH waves is bounded, while unbounded for 2.45 GHz LH waves and one of the conditions is recognized to be good for achieving an off-axis current profile driven by 4.6 GHz LH waves on EAST. The parametric analysis on the potential power deposition (PPD) region for those experiments demonstrates that the reversed magnetic shear dominates the wave behavior, and confines the LH power absorption to the far off-axis region as long as it occurs in the 4.6 GHz dominated LHCD discharge. GENRAY/CQL3D simulations also confirm this effect of reversed shear on the power absorption of 4.6 GHz waves. A bounded propagation domain and a positive feedback loop between magnetic shear reversal and off-axis LHCD profile could explain the LH-only-sustained strong reversed magnetic shear observed in experiments on multiple machines. In contrast, there is no such effect for 2.45 GHz waves on EAST since the PPD region is less sensitive to the change of reversed shear due to the unbounded propagation domain.

Spatial distribution of Ti vapor admixture ratio in Ar induction thermal plasma torch during Ti feedstock injection

The spatial distribution of the Ti vapor admixture ratio (XTi) was determined together with Ti excitation temperature () from two-dimensional (2D) optical emission spectroscopy (OES) during Ti feedstock injection into an Ar induction thermal plasma (ICTP) torch for Ti nanoparticle synthesis. The XTi is one important parameter affecting ICTP properties such as its electrical conductivity. The value of XTi was estimated from the radiation intensity ratio of the Ar atomic line to the Ti atomic line, and obtained from 2D OES observation. Furthermore the electron density (ne) was also determined from the estimated results of and XTi through the equilibrium composition. These 2D OES results revealed as 2500–4000 K at around the central axis of the ICTP torch, although it was higher than 4000 K in the off-axis region. In the off-axis region, XTi and ne were much higher than in the on-axis region.

On current drive by Ohkawa mechanism of electron cyclotron wave in large inverse aspect ratio tokamaks

A localized and efficient current drive method in the outer-half region of the tokamak with a large inverse aspect ratio is proposed via the Ohkawa mechanism of electron cyclotron (EC) waves. Further off-axis Ohkawa current drive (OKCD) via EC waves was investigated in high electron beta βe HL-2M-like tokamaks with a large inverse aspect ratio, and in EAST-like tokamaks with a low inverse aspect ratio. OKCD can be driven efficiently, and the driven current profile is spatially localized in the radial region, ranging from 0.62 to 0.85, where the large fraction of trapped electrons provides an excellent advantage for OKCD. Furthermore, the current drive efficiency increases with an increase in minor radius, and then drops when the minor radius beyond a certain value. The effect of trapped electrons greatly enhances the current driving capability of the OKCD mechanism. The highest current drive efficiency can reach 0.183 by adjusting the steering mirror to change the toroidal and poloidal incident angle, and the total driven current by OKCD can reach 20–32 kA MW−1 in HL-2M-like tokamaks. The current drive is less efficient for the EAST-like scenario due to the lower inverse aspect ratio. The results show that OKCD may be a valuable alternative current drive method in large inverse aspect ratio tokamaks, and the potential capabilities of OKCD can be used to suppress some important magnetohydrodynamics instabilities in the far off-axis region.

Spatiotemporal distribution of thermal plasma temperature and precursor formation in a torch during TiO2 nanopowder synthesis

The spatiotemporal distribution of Ti excitation temperature () was determined from two-dimensional optical emission spectroscopy (2D OES) during TiO2 nanopowder synthesis using an inductively coupled thermal plasma (ICTP) torch. The Ti feedstock powder was injected intermittently into the ICTP torch to elucidate the evaporation of the feedstock and the formation of atomic vapour, precursor molecules, and particle nuclei dynamically. The spectroscopic observation results revealed that was estimated as 2500–4000 K around the central axis of the ICTP torch, and more than 4500 K in the off-axis region. In the on-axis region, TiO was detected with a high radiation intensity in the lower temperature region. These results showed that TiO molecules are formed only in the low temperature region around the central axis of the ICTP torch. In addition, TiO molecular density could be high, especially in the downstream region at the central axis of the ICTP torch.

Large-charge quasimonoenergetic electron beams produced by off-axis colliding laser pulses in underdense plasma.

Electrons can be efficiently injected into a plasma wave by colliding two counterpropagating laser pulses in a laser wakefield acceleration. However, the generation of a high-quality electron beam with a large charge is difficult in the traditional on-axis colliding scheme due to the growth of the electron beam duration coming from the increase of the beam charge. To solve this problem, we propose an off-axis colliding scheme, in which the collision point is away from the axis of the driver pulse. We show that the electrons injected from the off-axis region are highly concentered on the tail of the bubble even for a large trapped charge, thus feeling almost the same accelerating field. As a result, quasimonoenergetic electron beams with a large charge can be produced. The validity of this scheme is confirmed by both the particle-in-cell simulations and the Hamiltonian model. Furthermore, it is shown that a Laguerre-Gauss (LG) laser can be adopted as the injection pulse to realize the off-axis colliding injection in three dimensions symmetrically, which may be useful in simplifying the technical layout of the real experiment setup.

A current drive by using the fast wave in frequency range higher than two timeslower hybrid resonance frequency on tokamaks

An efficient current drive scheme in central or off-axis region is required for the steady state operation of tokamak fusion reactors. The current drive by using the fast wave in frequency range higher than two times lower hybrid resonance (w>2wlh) could be such a scheme in high density, high temperature reactor-grade tokamak plasmas. First, it has relatively higher parallel electric field to the magnetic field favorable to the current generation, compared to fast waves in other frequency range. Second, it can deeply penetrate into high density plasmas compared to the slow wave in the same frequency range. Third, parasitic coupling to the slow wave can contribute also to the current drive avoiding parametric instability, thermal mode conversion and ion heating occured in the frequency range w<2wlh. In this study, the propagation boundary, accessibility, and the energy flow of the fast wave are given via cold dispersion relation and group velocity. The power absorption and current drive efficiency are discussed qualitatively through the hot dispersion relation and the polarization. Finally, those characteristics are confirmed with ray tracing code GENRAY for the KSTAR plasmas.

The concentration of energy from Edge Lasers by Diffractive Optical Component

The aim of this paper is to design a diffractive optical element based on the laser junction numerical model. We assumed a ?long? laser junction emitting quasi-monochromatic, spatially incoherent light that corresponds to the high power laser. Diffractive optics approach can be used due to the narrowband illumination. The especially designed numerical junction model was experimentally verified. Then a numerically designed diffractive focusing element was manufactured and tested in the experimental setup. This paper includes theoretical investigations, numerical modeling as well as experimental data. Full Text: PDF ReferencesE. Wolf, "New theory of partial coherence in the space?frequency domain. Part I: spectra and cross spectra of steady-state sources", J. Opt. Soc. Am. 72, 343 (1982). CrossRef E. Wolf, "Coherence theory of laser resonator modes", J. Opt. Soc. Am. A 1, 541 (1984). CrossRef A. Naqwi and F. Durst, "Focusing of diode laser beams: a simple mathematical model", Appl. Opt. 29, 1780 (1990) CrossRef J. Yang, T. Chen, G. Ding and X. Yuan, "Focusing of diode laser beams: a partially coherent Lorentz model", Proc. SPIE 6824, 68240A (2007); CrossRef X. Zeng and A. Naqwi, "Far-field distribution of double-heterostructure diode laser beams", Appl. Opt. 32, 4491 (1993). CrossRef Y. Li and J. Katz, "Nonparaxial analysis of the far-field radiation patterns of double-heterostructure lasers", Appl. Opt. 35, 1442 (1996). CrossRef X. Zeng, Z. Feng, and Y. An, "Far-field expression of a high-power laser diode", Appl. Opt. 43, 5168 (2004) CrossRef J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, "Shifted-elementary-mode representation for partially coherent vectorial fields", J. Opt. Soc. Am. A 27, 2004 (2010). CrossRef J. Turunen, "Elementary-field representations in partially coherent optics", J. Mod. Opt. 58, 509 (2011). CrossRef H. Partanen, J. Tervo, and J. Turunen, "Spatial coherence of broad-area laser diodes", Appl. Opt. 52, 3221 (2013) CrossRef M. Sypek, "Light propagation in the Fresnel region. New numerical approach", Opt. Commun., 116, 43 (1995) CrossRef Z. Jaroszewicz, A. Kolodziejczyk, M. Sypek, C. Gomez-Reino, "Non-paraxial analytical solution for the generation of focal curves", J. Mod. Opt., 43, 617 (1996) CrossRef M. Sypek, C. Prokopowicz, M. Gorecki, "Image multiplying and high-frequency oscillations effects in the Fresnel region light propagation simulation", Opt. Eng., 42, 3158 (2003) CrossRef C. Prokopowicz, "Numerical calculation of light propagation in off-axis region", Proc. SPIE, 5484, 482 (2004). CrossRef A. Sobczyk, Z. Jaroszewicz, A. Kolodziejczyk, A. Kowalik, Cz. Prokopowicz, M. Sypek, "Nonparaxial anamorphic diffractive lenses", J. Opt., 15, 025702 (1-5) (2013) CrossRef

Heating and current drive by fast wave in lower hybrid range of frequency on Versatile Experiment Spherical Torus

An efficient heating and current drive scheme in central or off-axis region is required to realize steady state operation of tokamak fusion reactor. And the fast wave in lower hybrid resonance range of frequency could be a candidate for such an efficient scheme in high density and high temperature plasmas. Its propagation and absorption characteristics including current drive and coupling efficiency are analyzed for Versatile Experiment Spherical Torus and it is shown that it is possible to drive current with considerable current drive efficiency in central region. The RF system for the fast wave experiment including klystron, transmission systems, inter-digital antenna, and RF diagnostics are given as well in this paper.

Intermittent bursts induced by double tearing mode reconnection

Reversed magnetic shear (RMS) configuration is assumed to be the steady-state operation scenario for the future advanced tokamaks like International Thermonuclear Experimental Reactor. In this work, we numerically discover a phenomenon of violent intermittent bursts induced by self-organized double tearing mode (DTM) reconnection in the RMS configuration during the very long evolution, which may continuously lead to annular sawtooth crashes and thus badly impact the desired steady-state operation of the future advanced RMS tokamaks. The key process of the intermittent bursts in the off-axis region is similar to that of the typical sawtooth relaxation oscillation in the positive magnetic shear configuration. It is interestingly found that in the decay phase of the DTM reconnection, the zonal field significantly counteracts equilibrium field to make the magnetic shear between the two rational surfaces so weak that the residual self-generated vortices of the previous DTM burst are able to trigger a reverse DTM reconnection by curling the field lines.

Nonlinear evolution of double tearing modes in tokamak plasmas via multiple helicity simulation

Nonlinear evolution of multiple double tearing modes (multi-DTMs) with different helicities (DHs) in several reversed magnetic shear configurations is investigated by employing a reduced magnetohydrodynamic model in cylindrical geometry. It is found that the basic characterizations of the nonlinear evolution process of the system depend on the linear unstable spectrum of multi-DTMs with DHs. In the case that the linear growth rates of multi-DTMs with DHs are comparable to each other, continuous bursts occur one after another due to a sequence of magnetic energy release induced by multi-DTMs reconnections on different pairs of resonant surfaces with DHs. Moreover, the overlapping of the magnetic island chains of multi-DTMs during the continuous bursts process results in the strong magnetic stochasticity in the off-axis region. Such unique nonlinear evolution of multi-DTMs with DHs cannot be reproduced by the single helicity simulation. However, in the case that the linear growth rates of DTMs with the dominant helicity are much larger than the counterparts of DTMs with the other helicities, the main nonlinear physical process obtained by the multiple helicity simulation can be reproduced by the single helicity simulation.

A Light-Field-Based Method to Adjust On-Axis Rounded Leaf End MLC Position to Predict Off-Axis MLC Penumbra Region Dosimetric Performance in a Radiation Therapy Planning System

Purpose. An analytical and experimental study of split shape dose calculation correction by adjusting the position of the on-axis round leaf end position is presented. We use on-axis corrected results to predict off-axis penumbra region dosimetric performance in an intensity-modulated radiation therapy treatment planning system. Materials and Methods. The precise light-field edge position (X tang.p) was derived from the on-axis 50% dose position created by using the nominal light field for geometric and mathematical manipulation. Leaf position (X mlc.p) could be derived from X tang.p by defining in the treatment planning system for monitor unit calculation. On-axis offset (correction) could be obtained from the position corresponding to 50% of the central axis dose minus the Xmlc.p position. The off-axis 50% dose position can then be derived from the on-axis 50% dose position. Results. The monitor unit calculation of the split shape using the on-axis rounded leaf end MLC penumbra region could provide an under-or overdose of 7.5% per millimeter without an offset correction. When using the on-axis rounded leaf end offset correction to predict the off-axis dose, the difference between the off- and on-axis 50% dose position is within ±1.5 mm. Conclusions. It is possible to achieve a dose calculation within 0.5% error for an adjusted MLC leaf edge location in the treatment planning system with careful measurement and an accurate on-axis offset correction. Dose calculations located at an off-axis spilt shape region should be used carefully due to noncorrectable errors which were found to be up to 10%.

Quantum path interferences of high-order harmonic generation in two-color Gaussian beams

The phase matching of the quantum paths in high-order harmonic generation is investigated in two-color laser fields. The results show that the spatial distribution of the laser field is optimized by adjusting the laser beam waist, the phase-matching properties of the long trajectories can be modulated effectively, and then good phase matching for both the two paths can be achieved from on-axis region to off-axis region. A radial clear interference fringe induced by the well phase-matching of two paths can be observed by placing a near-field filter, which has great potential for distinguishing clearly different interference effects and observing higher order trajectories with improved detection sensitivity.

Petrological geodynamic modeling of mid-ocean ridges

Mid-ocean ridges are the primary location where the Earth’s oceanic crust is formed. Beneath spreading ridges several processes such as dynamic melting and partial crystallization modify the petrology of the upper mantle and affect the Earth’s global geochemical evolution. A unified picture of the temporal and spatial evolution of melt and residual mantle, as well as crustal production and melt dynamics requires a comprehensive model that takes into account simultaneously the complexity of the physical processes involved and the petrological variations of the ridge system. Here we present the first results of a 2-D numerical approach applied to a spreading ridge that fully couples a two-phase flow model for melt and solid mantle and a chemical thermodynamic model which provides a spatial and temporal description of the minerals and melt abundance and composition. The most significant features found by this study are the following. (1) Accumulation of melt is observed at the base of the lithosphere in the off-axis region (<∼50 km from the ridge axis). (2) Crustal production (thickness) shows temporal variations which are mainly induced by periodic discharge of the melt accumulated underplate. (3) Magma waves develop between 10 and 30 km depth in proximity of the ridge axis. However to accurately resolve melt fluctuations, the grid size must be smaller than the compaction length for porous flow. Since in this study the compaction length decreases with depth, we have used a simplified 1-D melt model incorporating the two-phase flow dynamics and the thermodynamic formulation to show that the depth at which magma waves start to form increases by increasing the numerical resolution. Despite the limitation of the numerical grid resolution, we have observed that variations of the melt content do not appear to have significant influence on major elements composition of the residual solid and melt. (4) In the initial stage of the ridge evolution, a melting area detaches from the main melting region around the ridge axis. It is possible that this type of development may repeat over time beyond the duration of the simulation model of this study (∼15 Ma). Sluggish coupling between the dynamics of the lithosphere and the asthenospheric mantle flow suggests that accretion of the lithosphere by conductive cooling away from the ridge center involves portions of the upper mantle that not necessarily passed through the spreading ridge. (5) During the development of the spreading ridge, the asthenosphere affected by the melting process deflects downwards, creating in this way a chemical heterogeneity in the large mantle circulation. (6) Composition of major elements in the residual solid after partial melting is in agreement with the chemical pattern observed in abyssal peridotites. However, in order to explain the large variation of major elements content found in abyssal peridotite, a consistent petrological and geodynamic model of the evolution of the mid-ocean ridge, requires that partial crystallization of small amount of melt refertilizes the depleted mantle. The petrological model presented in this study accounts for the complexity of polybaric dynamic melting and the continuous reactions between the residual solid and melt, but it is limited by the assumption of local thermodynamic equilibrium within a domain defined by the numerical grid size. The interpretation of the petrological results needs to be carefully evaluated to ensure that the time and space scale of the numerical model complies with the constraints provided by solid–melt reactive experiments and the spatial scale of the petrological structures observed in mid-ocean ridges. (7) Melt distribution and thermal structure are revealed by the seismic shear wave map computed from the numerical model. Certain observations, such as the extent of the melting region, overall agree quite well with the evidences from seismic studies from various ridge settings.

Effect of low-density heterogeneities in telecobalt therapy and validation of dose calculation algorithm of a treatment planning system.

Telecobalt machines are still prominently used for the treatment of a variety of cancer cases in developing countries. The human body is a heterogeneous composition of variety of tissues and cavities which vary widely in their physical and radiological properties. The presence of heterogeneities in the path of telecobalt beam presents an altered dose distribution in the region of clinical interests. A computerized treatment planning system (TPS) is generally used for calculating the dose distribution in the patient. Experimental measurements were carried out in a telecobalt beam with the objectives to study the effects of low-density heterogeneities and to verify the ability of the ASHA radiotherapy TPS in predicting the altered dose distribution along the central axis and off-axis of the beam. Locally available kailwood was tested for its lung equivalence and measurements were carried out in a polymethyl methacrylate phantom by introducing lung equivalent and air gap heterogeneities. A comparison of experimentally measured and TPS calculated dose values indicates that the TPS overestimates the dose by 11.6% in lung equivalent (kailwood) heterogeneity along the central axis. Similarly, it was found that the TPS overestimates the dose by 3.9% and 5.9%, respectively, with air heterogeneity of 1.0 and 2.0 cm. While testing the adequacy of TPS in off-axis region, it was found that the TPS calculation does not indicate the widening of the beam profile in the low-density heterogeneity region. This study suggests that the effective path length based algorithm of the ASHA radiotherapy TPS is unable to achieve the recommended 3% accuracy of clinical dose calculation in heterogeneous media.

Exact and approximate symmetries for light propagation equations with higher order nonlinearity

For the first time exact analytical solutions to the eikonal equations in (1+1) dimensions with a refractive index being a saturated function of intensity are constructed. It is demonstrated that the solutions exhibit collapse; an explicit analytical expression for the self-focusing position, where the intensity tends to infinity, is found. Based on an approximated Lie symmetry group, solutions to the eikonal equations with arbitrary nonlinear refractive index are constructed. Comparison between exact and approximate solutions is presented. Approximate solutions to the nonlinear Schrödinger equation in (1 + 2) dimensions with arbitrary refractive index and initial intensity distribution are obtained. A particular case of refractive index consisting of Kerr refraction and multiphoton ionization is considered. It is demonstrated that the beam collapse can take place not only at the beam axis but also in an off-axis ring region around it. An analytical condition distinguishing these two cases is obtained and explicit formula for the self-focusing position is presented.