Purpose
To introduce a new analytical methodology to calculate quantities of interest in particle radiotherapy inside the treatment planning system. Models are proposed to calculate dose‐averaged LET ...(LETd) in proton radiotherapy.
Material and methods
A kernel‐based approach for the spectral fluence of particles is developed by means of analytical functions depending on depth and lateral position. These functions are obtained by fitting them to data calculated with Monte Carlo (MC) simulations using Geant4 in liquid water for energies from 50 to 250 MeV. Contributions of primary, secondary protons and alpha particles are modeled separately. Lateral profiles and spectra are modeled as Gaussian functions to be convolved with the fluence coming from the nozzle. LETd is obtained by integrating the stopping power curves from the PSTAR and ASTAR databases weighted by the spectrum at each position. The fast MC code MCsquare is employed to benchmark the results.
Results
Considering the nine energies simulated, fits for the functions modeling the fluence in‐depth provide an average
R2
equal to 0.998, 0.995 and 0.986 for each one of the particles considered. Fits for the Gaussian lateral functions yield average
R2
of 0.997, 0.982 and 0.993, respectively. Similarly, the Gaussian functions fitted to the computed spectra lead to average
R2
of 0.995, 0.938 and 0.902. LETd calculation in water shows mean differences of −0.007 ± 0.008 keV/μm with respect to MCsquare if only protons are considered and 0.022 ± 0.007 keV/μm including alpha particles. In a prostate case, mean difference for all voxels with dose >5% of prescribed dose is 0.28 ± 0.23 keV/μm.
Conclusion
This new spectral fluence‐based methodology allows for simultaneous calculations of quantities of interest in proton radiotherapy such as dose, LETd or microdosimetric quantities. The method also enables the inclusion of more particles by following an analogous process.
The paper presents the results of an on-site survey on several historic brick masonries with different heritage values, historical ages, and internal functions. The experimental data have been ...compared with the results of the standard procedures normally used in Italy for assessing the thermo-physical behavior of traditional walls, in order to provide a guidance for energy audit, simulation, and labelling of historic buildings. The research methodology is based on the following steps: (i) selection of traditional building masonries; (ii) interdisciplinary assessment for materials characterization; (iii) thermal performance evaluation using different standard procedures suggested by the Italian legislation framework; (iv) comparison between the results; and (v) final performances assessment. Compared with the experimental measurements, standard and analytical procedures tend to overestimate the thermal performance of historic brick masonries. There is a correspondence between the historical ages and the λ-value of bricks. The bricks manufactured by pre-industrial techniques have lower densities than the industrial ones. This is due to the artisanship of clay, which caused the presence of sand, raw materials, and air, improving their thermal performance.
Accurate prediction of the magnetic field is an essential guideline for permanent magnetic gear design and optimization. The existing magnetic field calculation methods are divided into 2-D and 3-D ...calculation methods. For coaxial magnetic gears, the calculation of a 2-D magnetic field can be employed to meet the design requirements. However, as a new spatial transmission mechanism, nutation magnetic gear relies on a 3-D magnetic field to transmit force and torque. Therefore, the 2-D magnetic field cannot meet the design requirements. Hence, it is necessary to accurately predict the 3-D magnetic field. In this article, an analytical mathematical model of the 3-D magnetic field of magnetic gears is established. To verify the accuracy of the model, the magnetic field generated by the same magnetic gear is predicted by the proposed model, finite element method, and equivalent current method. The results indicate that the 3-D magnetic field mathematical model proposed in this article can accurately predict a 3-D magnetic field, which is an essential guide for the research and optimization of magnetic gears.
•A model of the elastic–viscoelastic double-layer composite beam is established.•The reliability of the double-layer composite beam model is verified by test data.•The mechanical response of ACWSS ...under temperature load is analyzed.•The leading cause of passive tensile damage of ACWSS is a strain mutation.•ACWSS at the expansion joint mainly bears axial tensile/compression deformation.
The theoretical development of the temperature effect of the full-section asphalt concrete waterproof sealing structure (ACWSS) of the ballastless track subgrade lags the engineering practice. In order to reveal the passive tensile damage behavior of ACWSS from the perspective of theoretical analysis, in this paper, the base plate of the ballastless track and the ACWSS is simplified into an elastic–viscoelastic double layer composite beam model. The analytical calculation method for passive tensile damage of ACWSS under temperature load is derived theoretically. The change of surface stress and strain of ACWSS with time is calculated and analyzed. The theoretical analysis and calculation results show that the variation of the surface strain, the maximum strain, and the time corresponding to the strain peak of ACWSS are consistent with the measured results. The model of the double-layer composite beam has high reliability, and the analytical calculation method of passive tensile damage is reasonable and practical. The temperature stress of ACWSS at the expansion joint of the base plate is synchronized with the temperature change, indicating that the asphalt concrete at this location is mainly subjected to axial tension (or compression). It is suggested that the structural design should be judged by comparing the number of periodic temperature loads and the allowable fatigue number of asphalt concrete, which further improves the design method and technical system of the ACWSS in China's high-speed railway. It has important theoretical and practical significance.
Due to the large size and thin wall characteristics, the large-scale ring is prone to plastic instability, resulting in loss of ring roundness. An analytical calculation model of roundness error is ...proposed to design the feeding process. This model is established by analytically deriving the relationships between feeding process, ring geometry, contact arc length, rolling force, ring vibration angle, ring bending angle, contact arc length increment and ring roundness error at different rolling stages. Compared with numerical calculation and production trial, the analytical model can predict the roundness error with reasonable accuracy and high efficiency and guide feeding process design.
•The analytical calculation model of the roundness error in radial–axial ring rolling process is presented.•The criteria for the switching of different roll stages is determined analytically, which is the premise to calculate the ring bending angle accurately.•The construction of the analytical calculation model related to ring rolling process is based on geometry, kinematics and dynamics.
This paper proposes a computation model for efficiency map in a low-speed and high-torque permanent-magnet synchronous machine without magnetic bridge. According to the magnetic field distribution, ...the whole machine topology is then divided into seven types of subdomains. By means of the magnetic field prediction and classic loss model, different losses and electromagnetic torques of motor under different working conditions are obtained, and finally the full analytical calculation of the motor efficiency in the all working domain is realized. The impact of rotor saturation is analyzed by establishing a local polar coordinate system. Then a program is used to build efficiency map. Results from Finite Elements Analysis (FEA) are used to verify the proposed method.
An analytical calculation of the winding flux linkages and torque is proposed for fully pitched mutual coupled switched reluctance motors to develop a machine model without using numerical methods. ...The proposed technique is not empirical and does not require any finite-element analysis (FEA). The design parameters and the material properties of the machine are the only inputs to the model, which can predict the winding flux linkages and torque at any phase currents and rotor positions. The model is applicable for the rotor positions where the stator and rotor poles overlap. Initial assumptions and then the step-by-step procedure for flux linkage, co-energy, and torque calculations are provided. The flux linkages and torque predicted through the proposed modeling technique are compared with the FEA results. Finally, experimental results of flux linkage and torque are provided to verify the accuracy of the proposed modeling technique.
This paper presents an analytical approach to determine the air-gap magnetic field and the winding inductance in the brushless doubly-fed reluctance machine (BDFRM) with flux barriers. By dividing ...one flux guide layer into several segments, a calculus method based on magnetic circuit analysis is developed and specific analytical expression of the air-gap flux density is rigorously derived. Then, the included angle between fundamental components with the same pole pairs is also discussed. Based on the air-gap flux density distribution, the inductance expressions between different windings are also presented. Three kinds of finite element analysis models are established and studied. As a result, the accuracy of the analytical model can be verified by simulations and experimental data from an existing BDFRM prototype.
Grid forming (GFM) control strategy has been increasingly used in grid-connected converters to regulate system frequency and mimic the inertia of synchronous generator. However, the description of ...its power angle dynamics under large disturbances is still lacking up to date, which may pose great challenges to stable operation and economic configuration of grid-connected converters in the future power system. To overcome the aforementioned obstacle, a Krylov-Bogoliubov-Mitropolsky (KBM) asymptotic method with the perturbation theory is presented first in this article to derive an analytical solution for power angle trajectory under large disturbances. Considering that the antiderivative problem is usually unsolvable due to the complicated perturbation function, a tailored integral method is further proposed to address this problem and simplify the final result, which facilitates the KBM asymptotic method to the analysis and calculation of power angle trajectory. As a result, an explicit and accurate time-domain expression is obtained, and it reveals the quantitative relationships between control parameters and dynamic characteristics, which may provide a good potential for system transient stability analysis and GFM converter design. In the end, the effectiveness and accuracy of the proposed method are verified by both simulations and control-hardware-in-loop experiments.
