Angular Moments Research Articles

2. Entropic closure for MRI-guided radiotherapy

Introduction The majority of patients affected by cancer are nowadays treated by radiotherapy, which consists in delivering a homogeneous dose with energetic particles. Magnetic Resonance Imaging (MRI)-guided radiotherapy shows precisely the tumor position in real time and allows to direct the photon beams to the tumor while sparing organs at risks. Our work consists in the validation of a new model developped to simulate the energy deposition of the particles used in radiotherapy (electrons, photons and protons) in the presence of strong magnetic field, within human tissues, and its adaptation to this new technology. Material and methods This model is based on a kinetic entropic closure of the linearized Boltzmann equation [1] , which describes the transport of energetic particles in the matter. This equation takes a lot of computation time to be solved due to the high number of variables. To simplify this, we replace fluences by angular moments, which allows getting rid of the angular variables and improve the calculation time. We obtain a set of angular moments equations, and we close this set using the Boltzmann’s principle of entropy maximization on the two first equations of the set. This model has an accuracy comparable to references Monte-Carlo (MC) codes [2] (Geant4, MCNPx, Penelope), and is less time-consuming than these ones. We added the Lorentz force into our code to study the influence of a magnetic field on the dose deposition, and compared it to the reference full MC code FLUKA. To further validate our model, we have carried out an experimental campaign in which we irradiated a composition of materials of different mass densities, with 6 and 18 MV photon beams of a Varian Clinac 21Ex accelerator, without and with the influence of a 0.87 T magnetic field of amplitude induced by a permanent magnet. Results We show a good agreement between our model and the FLUKA code ( Fig. 1 ). We highlight the effects that occur on the propagation of particles in the matter in presence of a magnetic field of a few Tesla. Indeed, it modifies the dose deposition by shifting the deposition of energy, leading to an increased diffusion depending on the orientation of the magnetic field. Moreover, it also leads to an increase or decrease of the dose deposited at the interfaces between materials depending on their difference between mass densities. The results of our experiments lead to the same conclusions. These effects have to be taken into account in order to prevent creation of hot spots or a spread of energy distribution in a human body, within computation times compatible with the clinical environment. Conclusion Our model is a good candidate for future Treatment Planning Systems since it allows a faster and efficient way to plan a viable treatment for a patient in presence of strong magnetic fields. A magnetic field modifies the profile of the dose deposition such as it has to be taken into account in calculations to prevent the dramatic changes which occur at interfaces between media of different density. This work takes place in the framework of POPRA (Programme Optique Physique et Radiotherapie en Aquitaine), which involves several laboratories around problematics on the topic of cancer treatment.

Dihadron fragmentation functions in the quark-jet model: Longitudinally polarized quarks

We study the dihadron fragmentation functions (DiFF) of longitudinally polarized quarks into pion pairs. The quark-jet framework is used to model the sequential hadronization of a polarized quark into hadrons, where the polarization transfer to the remnant quark in each hadron emission step is calculated using the spin density matrix formalism. Using Monte Carlo (MC) simulations of the hadronization process, we find a nonvanishing helicity dependent DiFF, $G_1^\perp$ , which is also related to the longitudinal jet handedness. A method is developed for extracting the angular moments of this DiFF, which enter the expressions for the azimuthal asymmetries for an electron-positron annihilation process into two pairs of hadrons from back-to-back jets and the dihadron production in semi-inclusive deep inelastic scattering. Finally, we derive explicit integral expressions for DiFFs where only two hadrons are emitted by a quark and use them to validate our MC results for both unpolarized and helicity dependent DiFFs.

A Detailed Comparison of Multidimensional Boltzmann Neutrino Transport Methods in Core-collapse Supernovae

Abstract The mechanism driving core-collapse supernovae is sensitive to the interplay between matter and neutrino radiation. However, neutrino radiation transport is very difficult to simulate, and several radiation transport methods of varying levels of approximation are available. We carefully compare for the first time in multiple spatial dimensions the discrete ordinates (DO) code of Nagakura, Yamada, and Sumiyoshi and the Monte Carlo (MC) code Sedonu, under the assumptions of a static fluid background, flat spacetime, elastic scattering, and full special relativity. We find remarkably good agreement in all spectral, angular, and fluid interaction quantities, lending confidence to both methods. The DO method excels in determining the heating and cooling rates in the optically thick region. The MC method predicts sharper angular features due to the effectively infinite angular resolution, but struggles to drive down noise in quantities where subtractive cancellation is prevalent, such as the net gain in the protoneutron star and off-diagonal components of the Eddington tensor. We also find that errors in the angular moments of the distribution functions induced by neglecting velocity dependence are subdominant to those from limited momentum-space resolution. We briefly compare directly computed second angular moments to those predicted by popular algebraic two-moment closures, and we find that the errors from the approximate closures are comparable to the difference between the DO and MC methods. Included in this work is an improved Sedonu code, which now implements a fully special relativistic, time-independent version of the grid-agnostic MC random walk approximation.

A new approach to three-dimensional neutron transport solution based on the method of characteristics and linear axial approximation

A new approach based on the method of characteristics (MOC) is proposed to solve the neutron transport equation. A new three-dimensional (3D) spatial discretization is applied to avoid the instability issue of the transverse leakage iteration of the traditional 2D/1D approach. In this new approach, the axial and radial variables are discretized in two different ways: the linear expansion is performed in the axial direction, then, the 3D solution of the angular flux is transformed to be the planar solution of 2D angular expansion moments, which are solved by the planar MOC sweeping. Based on the boundary and interface continuity conditions, the 2D expansion moment solution is equivalently transformed to be the solution of the axially averaged angular flux. Using the piecewise averaged angular flux at the top and bottom surfaces of 3D meshes, the planes are coupled to give the 3D angular flux distribution. The 3D CMFD linear system is established from the surface net current of every 3D pin-mesh to accelerate the convergence of power iteration. The STREAM code is extended to be capable of handling 3D problems based on the new approach. Several benchmarks are tested to verify its feasibility and accuracy, including the 3D homogeneous benchmarks and heterogeneous benchmarks. The computational sensitivity is discussed. The results show good accuracy in all tests. With the CMFD acceleration, the convergence is stable. In addition, a pin-cell problem with void gap is calculated. This shows the advantage compared to the traditional 2D/1D MOC methods.

Spin angular momentum induced by optical quasi-phonons activated in birefringent uniaxial crystals

The present report formally establishes the expression of the angular momentum of the quasi-phonons induced by linearly polarized light. The transferred mechanical torque due to phonons is then determined from the spin angular momentum and is shown to be measurable from Raman scattering experiments. To investigate this, the electric field due the excited dipoles and the associated macroscopic dielectric polarization vectors were first calculated using a lattice dynamical model in order to derive in a second step the analytical expression of the angular momentum density arising from the inelastic light scattering by quasi-phonons. The numerical results of the calculated angle dependent mode electric fields and the induced spin angular moments as well as the transferred torques were analyzed with regard to some typical behaviors of the interacting modes and it is shown that the fluctuations of the effective charges is their main origin.

Pair-correlated stereodynamics for diatom-diatom rotational energy transfer: NO(A2Σ+) + N2.

We have performed a crossed molecular beam velocity-map ion imaging study of state-to-state rotational energy transfer of NO(A2Σ+, v = 0, N = 0, j = 0.5) in collisions with N2 and have measured rotational angular momentum polarization dependent images of product NO(A) rotational levels N' = 3 and 5-11 for collisions at an average energy of 797 cm-1. We present an extension of our previously published [T. F. M. Luxford et al., J. Chem. Phys. 145, 174 304 (2016)] image analysis which includes the effect of rotational excitation of the unobserved collision partner and critically evaluate this methodology. We report differential cross sections and angle-resolved angular momentum alignment moments for NO(A) levels N' = 3 and 5-11 as a function of the rotational excitation of the coincident N2 partner. The scattering dynamics of NO(A) + N2 share similarities with those previously reported for NO(A) + Ne and Ar, although with detailed differences. We use comparison of the measurements reported here to the scattering of NO(A) with Ne, and the known NO(A)-Ne potential energy surface, to draw conclusions about the previously unknown NO(A)-N2 potential.

Element specific electronic states and spin-flip-like behavior of Ce in (Ce0.2Gd0.8)Ni composed of heavy fermion CeNi and ferri-magnet GdNi through XMCD method

The electronic states of the three constituent elements in the crystal mixed system between CeNi and GdNi, Ce0.2Gd0.8Ni, were investigated by soft X-ray magnetic circular dichroism (XMCD) with the aid of sum rule analysis. Not only Gd 4f but also Ni 3d and Ce 4f electrons were magnetic and both magnetic moments of Ni and Ce were coupled anti-parallel to the direction of the Gd magnetic moment, which is in accordance with the general rule in rare earth (RE)-transition metal (TM) systems. After saturation, Ce magnetic moment decreased over 2T and this behavior was explained by a spin-flip behavior of the Ce magnetic moment with keeping their electronic states unchanged. Furthermore, the magnetic field dependence on a part of the XAS at Ce M4,5 absorption edges, which had been observed in the Gd=0.5 disappeared in the present sample in Gd-rich content of 0.8 and this could be explained by the increase of molecular field from Gd on Ce 4f electrons. In addition, sum rule analysis has revealed that the magnetic moments of Gd 4f and Ni 3d electrons could retain small values of angular (orbital) magnetic moments µL and this was explained consistently.

Angular analyses of exclusive B¯→XJℓ1ℓ2 decays for spin J≤4

As an update to our previous calculation for spin $J\leq2$, we present the angular moments for exclusive $\overline{B} \to X_J \ell_1 \ell_2$, where $\ell_1$ is a charged massless lepton and $\ell_2$ is a charged or neutral massless lepton, and $X_J$ is a mesonic system with spin $J\leq4$. The expected applications include higher resonances in the $[K\pi]$ system in $\overline{B}^0 \to K^- \pi^+ \mu^- \mu^+$ at LHCb in Run~II, and in the $[\pi \pi]$ system for $ \overline{B} \to \pi \pi \ell^- \bar{\nu}_\ell$ at Belle~II. For the $J\leq2$ case, we also provide a set of consistency relations among the measured moments observables and validate them against the latest measurements from LHCb.

Monitoring geomagnetic disturbance predictors using data of ground measurements of cosmic rays

Results from investigating the behavior of zonal components of the first two angular moments of the distribution of cosmic rays observed in 2015 are presented. The global survey approach developed at the Institute of Cosmophysical Research and Aeronomy, Siberian Branch, Russian Academy of Sciences, is used to determine the zonal harmonics. In this technique, the worldwide network of neutron monitors acts as a single multidirectional detector of cosmic rays. It is shown that sharp increases in the positive amplitudes of zonal harmonics, considered to be predictors of geomagnetic field disturbances with a probability of ~0.75, precede geomagnetic storms with Dst < −50 nT. A geomagnetic storm predictor becomes apparent in periods of time from several hours to 1.5 days. Geomagnetic disturbances are currently monitored in real time using the global survey approach based on data from the worldwide neutron monitor database (http://www.nmdb.eu). The initial results from forecasting can be found on the Internet (http://www.ysn.ru/~starodub/SpaceWeather/global_survey_real_time.html).

횡풍이 작용하는 속도로의 회전구간에서 도로의 편경사각이 주행차량의 전복사고에 미치는 영향에 관한 분석연구

최근 경기도의 혼잡한 시간에 교통 문제를 해결하기 위해 2층 버스 서비스가 검토되고 있다. 2층 버스의 경우 높이와 폭의 비율이 일반 고속버스 보다 1.16배 이상 크며, 2층 버스의 C.G 점이 일반 버스보다 높다. 2층 버스가 고속 주행 시 강한 측면 바람 상태에서 차선 이탈과 같은 주행 안정성 문제가 특히 심각할 수 있다. 본 수치 해석 연구에서는 고속 주행 중 측면 바람 조건 및 편경사 조건에서 2층 버스의 주행 특성을 검토 하였다. 주어진 주행 조건에서 버스의 동적 안정성을 평가하기 위하여, CFD 수치 시뮬레이션을 이용하여 모델 버스의 롤링, 피칭 및 요잉모멘트를 계산하고, 도로 위 주어진 주행 조건하에서 모델 버스의 복구 각 모멘트 결과와 비교 하였다. 이 연구에서 모델 버스는 직선 도로를 따라 이동할 때 어떤 측면 바람 상태에서도 안정된 상태에 있다는 것을 알게 되었다. 그러나 버스가 측면 바람 상태에서 곡선 도로를 따라 이동 중에 측면 바람 (15m/s)에서 선회 반경이 100m 미만인 곡선 도로를 통과할 때 버스는 불안정한 조건에 동적으로 도달 할 수 있고 버스가 뒤집힐 가능성이 있다. 그러나 어떤 주행 조건에서도 모델 버스가 차선 이탈 가능성은 낮았다. Kyeonggi Provincial Government is considering double decker bus service to solve the problem of heavy rush hour traffic. However, the height-to-width ratio is more than 1.16 times larger than that of a general high-speed single decker bus, and the center of gravity is higher. This could cause driving stability problems, such as turnover and breakaway from the lane, especially under strong side-wind conditions at high speed. In this numerical study, the driving characteristics of a model double decker bus were reviewed under side-wind and superelevation conditions at high driving speed. The rolling, pitching, and yawing moment of the model bus were calculated with CFD numerical simulation, and the results were compared to the recovery angular moments of the model bus to evaluate the dynamic stability under given driving conditions. As the model vehicle moves on a straight level road, it is stable under any side-wind conditions. However, on a curved road under side-wind conditions, it could reach unstable conditions dynamically. There is a chance that the bus will turn over when it moves on a curved road with a radius of gyration less than 100 m under side-wind (15 m/s). However, there is a very small chance of breakaway from the lane under any driving conditions.

A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer

We have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used to compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. We compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.

The $M_1$ Angular Moments Model in a Velocity-Adaptive Frame for Rarefied Gas Dynamics Applications

In the present work the $M_1$ angular moments model in a velocity-adaptive frame is presented for rarefied gas dynamics applications. First of all, the derivation of the angular $M_1$ moments model in the particle mean velocity frame is introduced. The choice of the mean velocity framework in order to enforce the Galilean invariance property of the model is highlighted. In addition, it is shown that the model rewritten in terms of the entropic variables is Friedrichs-symmetric. Also, the derivation of the associated conservation laws and the zero mean velocity condition are detailed. Second, a suitable numerical scheme, preserving the realizable requirement of the numerical solution for the angular $M_1$ moments model in the mean velocity frame, is proposed. Third, some numerical results obtained considering several test cases in different collisional regimes are displayed.

Fatigue injury risk in anterior cruciate ligament of target side knee during golf swing

A golf-related ACL injury can be linked with excessive golf play or practice because such over-use by repetitive golf swing motions can increase damage accumulation to the ACL bundles. In this study, joint angular rotations, forces, and moments, as well as the forces and strains on the ACL of the target-side knee joint, were investigated for ten professional golfers using the multi-body lower extremity model. The fatigue life of the ACL was also predicted by assuming the estimated ACL force as a cyclic load. The ACL force and strain reached their maximum values within a short time just after ball-impact in the follow-through phase. The smaller knee flexion, higher internal tibial rotation, increase of the joint compressive force and knee abduction moment in the follow-through phase were shown as to lead an increased ACL loading. The number of cycles to fatigue failure (fatigue life) in the ACL might be several thousands. It is suggested that the excessive training or practice of swing motion without enough rest may be one of factors to lead to damage or injury in the ACL by the fatigue failure. The present technology can provide fundamental information to understand and prevent the ACL injury for golf players.

Differential branching fraction and angular moments analysis of the decay B 0 → K +π− μ + μ − in the K 0,2 ∗ (1430)0 region

Measurements of the differential branching fraction and angular moments of the decay $B^0 \to K^+ \pi^- \mu^+ \mu^-$ in the $K^+\pi^-$ invariant mass range $1330<m(K^+ \pi^-)<1530~MeV/c^2$ are presented. Proton-proton collision data are used, corresponding to an integrated luminosity of 3 $fb^{-1}$ collected by the LHCb experiment. Differential branching fraction measurements are reported in five bins of the invariant mass squared of the dimuon system, $q^2$, between 0.1 and 8.0 $GeV^2/c^4$. For the first time, an angular analysis sensitive to the S-, P- and D-wave contributions of this rare decay is performed. The set of 40 normalised angular moments describing the decay is presented for the $q^2$ range 1.1--6.0 $GeV^2/c^4$.

Refinement of the Pseudosource Method of Calculating RBMK Cluster Cells

The KLARA option is now being used to perform multigroup calculations of VVER and RBMK cluster cells and to prepare few-group characteristics of cells in the WIMS-SH-2.0 and SVL systems. The transition to 69-group calculations of RBMK cluster cells has revealed instability. Analysis has shown that the instability is associated with a discrepancy in the type of pole in several integrals arising in the calculation of the angular moments of the sinusoidal components of the Greens function. The removal of this singularity by adding two lines of the angular moments of the sinusoidal components eliminated this instability. The difference of K∞ calculated using the KLARA and PIJ options was less than 0.2% for cluster cells with and without fuel.

Experimental testing of ab initio potential energy surfaces: Stereodynamics of NO(A2Σ+) + Ne inelastic scattering at multiple collision energies.

We present a crossed molecular beam velocity-map ion imaging study of state-to-state rotational energy transfer of NO(A2Σ+, v = 0, N = 0, j = 0.5) in collisions with Ne atoms. From these measurements, we report differential cross sections and angle-resolved rotational angular momentum alignment moments for product states N' = 3 and 5-10 for collisions at an average energy of 523 cm-1, and N' = 3 and 5-14 for collisions at an average energy of 1309 cm-1, respectively. The experimental results are compared to the results of close-coupled quantum scattering calculations on two literature ab initio potential energy surfaces (PESs) [Pajón-Suárez et al., Chem. Phys. Lett. 429, 389 (2006) and Cybulski and Fernández, J. Phys. Chem. A 116, 7319 (2012)]. The differential cross sections from both experiment and theory show clear rotational rainbow structures at both collision energies, and comparison of the angles observed for the rainbow peaks leads to the conclusion that Cybulski and Fernández PES better represents the NO(A2Σ+)-Ne interaction at the collision energies used here. Sharp, forward scattered (<10°), peaks are observed in the experimental differential cross sections for a wide range of N' at both collision energies, which are not reproduced by theory on either PES. We identify these as L-type rainbows, characteristic of attractive interactions, and consistent with a shallow well in the collinear Ne-N-O geometry, similar to that calculated for the NO(A2Σ+)-Ar surface [Kłos et al., J. Chem. Phys. 129, 244303 (2008)], but absent from both of the NO(A2Σ+)-Ne surfaces tested here. The angle-resolved alignment moments calculated by quantum scattering theory are generally in good agreement with the experimental results, but both experiment and quantum scattering theories are dramatically different to the predictions of a classical rigid-shell, kinematic-apse conservation model. Strong oscillations are resolved in the experimental alignment moments as a function of scattering angle, confirming and extending the preliminary report of this behavior [Steill et al., J. Phys. Chem. A 117, 8163 (2013)]. These oscillations are correlated with structure in the differential cross section, suggesting an interference effect is responsible for their appearance.

Amplitude analysis ofB−→D+π−π−decays

The Dalitz plot analysis technique is used to study the resonant substructures of $B^{-} \to D^{+} \pi^{-} \pi^{-}$ decays in a data sample corresponding to 3.0 ${\rm fb}^{-1}$ of $pp$ collision data recorded by the LHCb experiment during 2011 and 2012. A model-independent analysis of the angular moments demonstrates the presence of resonances with spins 1, 2 and 3 at high $D^{+}\pi^{-}$ mass. The data are fitted with an amplitude model composed of a quasi-model-independent function to describe the $D^{+}\pi^{-}$ S-wave together with virtual contributions from the $D^{*}(2007)^{0}$ and $B^{*0}$ states, and components corresponding to the $D^{*}_{2}(2460)^{0}$, $D^{*}_{1}(2680)^{0}$, $D^{*}_{3}(2760)^{0}$ and $D^{*}_{2}(3000)^{0}$ resonances. The masses and widths of these resonances are determined together with the branching fractions for their production in $B^{-} \to D^{+} \pi^{-} \pi^{-}$ decays. The $D^{+}\pi^{-}$ S-wave has phase motion consistent with that expected due to the presence of the $D^{*}_{0}(2400)^{0}$ state. These results constitute the first observations of the $D^{*}_{3}(2760)^{0}$ and $D^{*}_{2}(3000)^{0}$ resonances.

Comparative stereodynamics in molecule-atom and molecule-molecule rotational energy transfer: NO(A(2)Σ(+)) + He and D2.

We present a crossed molecular beam scattering study, using velocity-map ion-imaging detection, of state-to-state rotational energy transfer for NO(A(2)Σ(+)) in collisions with the kinematically identical colliders He and D2. We report differential cross sections and angle-resolved rotational angular momentum polarization moments for transfer of NO(A, v = 0, N = 0, j = 0.5) to NO(A, v = 0, N' = 3, 5-12) in collisions with He and D2 at respective average collision energies of 670 cm(-1) and 663 cm(-1). Quantum scattering calculations on a literature ab initio potential energy surface for NO(A)-He [J. Kłos et al., J. Chem. Phys. 129, 244303 (2008)] yield near-quantitative agreement with the experimental differential scattering cross sections and good agreement with the rotational polarization moments. This confirms that the Kłos et al. potential is accurate within the experimental collisional energy range. Comparison of the experimental results for NO(A) + D2 and He collisions provides information on the hitherto unknown NO(A)-D2 potential energy surface. The similarities in the measured scattering dynamics of NO(A) imply that the general form of the NO(A)-D2 potential must be similar to that calculated for NO(A)-He. A consistent trend for the rotational rainbow maximum in the differential cross sections for NO(A) + D2 to peak at more forward angles than those for NO(A) + He is consistent with the NO(A)-D2 potential being more anisotropic with respect to NO(A) orientation. No evidence is found in the experimental measurements for coincident rotational excitation of the D2, consistent with the potential having low anisotropy with respect to D2. The NO(A) + He polarization moments deviate systematically from the predictions of a hard-shell, kinematic-apse scattering model, with larger deviations as N' increases, which we attribute to the shallow gradient of the anisotropic repulsive NO(A)-He potential energy surface.

Study of signal demultiplexing in beam Laguerre-Gaussian after passing low mode fibers

In the experimental study demonstrated the possibility of demultiplexing complex signal in the optical low mode fiber, feed beams of different wavelengths, with different polarization states with different orbital angular moments. We get a picture of the distribution of polarization possible to identify each of the beams with different wavelengths on the type of mode. Thus, analyzing the superposition of the beams on the mode composition, we can distinguish between the input signal to carry out his final demultiplexing.

INFLUENCE OF GONARTHROSIS ON KINEMATICS INDICATORS OF THE KNEE JOINT

Aim. To establish peculiarity of the influence of gonarthrosis on kinematics indices of the knee joint at people at the age of 45–60 with the help of markless motion method. Materials and methods. In the research 81 people took part. In the group of the control entered 42 people without symptomatic evidences of gonarthrosis, in the experimental group – 39 people with gonarthrosis of the 1 and 2 degrees at the age of 40 to 65. With the help of the markless motion method and software Brekel Pro Body» was made biomechanical analysis of the kinematics of knee joints. Results. It is established that people at the age of 40 to 65, suffering with gonarthrosis have authentically more angular moments of lateral mode of motions and rotations in knee joints. Conclusion. Under analysis of the kinematics of knee joints, between the control and the experimental groups were fixed significant differences (t-test, p &lt; 0,01). Besides there were fixed differences between dominant and non-dominant limbs, which mean that the force of muscles of lower limbs can also be a modificative factor, which influences on the strain in joints that potentially can lead to the development and/or advance of degenerative damage in the knee joint.