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Author(s):  
Tuba Tekin ◽  
Isabel Blum ◽  
Bjoern Delfs ◽  
Ann-Britt Schönfeld ◽  
Bjoern Poppe ◽  
...  

Abstract Objective This study investigates the perturbation correction factors of air-filled ionization chambers regarding their depth and magnetic field dependence. Focus has been placed on the displacement or gradient correction factor Pgr. Besides, the shift of the effective point of measurement Peff that can be applied to account for the gradient effect has been compared between the cases with and without magnetic field. Approach The perturbation correction factors have been simulated by stepwise modifications of the models of three ionization chambers (Farmer 30013, Semiflex 3D 31021 and PinPoint 3D 31022, all from PTW Freiburg). A 10 cm x 10 cm 6 MV photon beam perpendicular to the chamber’s axis was used. A 1.5 T magnetic field was aligned parallel to the chamber’s axis. The correction factors were determined between 0.4 and 20 cm depth. The shift of Peff from the chamber's reference point Pref, ∆z, was determined by minimizing the variation of the ratio between dose-to-water Dw(zref+∆z) and the dose-to-air Dair(zref) along the depth. Main Results The perturbation correction factors with and without magnetic field are depth dependent in the build-up region but can be considered as constant beyond the depth of dose maximum. Additionally, the correction factors are modified by the magnetic field. Pgr at the reference depth is found to be larger in 1.5 T magnetic field than in the magnetic field free case, where an increase of up to 1% is obserbed for the largest chamber (Farmer 30013). The magnitude of ∆z for all chambers decreases by 40% in a 1.5 T magnetic field with the sign of ∆z remains negative. Significance In reference dosimetry, the change of Pgr in a magnetic field can be corrected by applying the magnetic field correction factor kB Qmsr when the chamber is positioned with its Pref at the depth of measurement. However, due to the depth dependence of the perturbation factors, it is more convenient to apply the ∆z-shift during chamber positioning in relative dosimetry.


Author(s):  
H. Merad ◽  
F. Merghadi ◽  
A. Merad

In this paper, we present an exact solution of the Klein–Gordon equation in the framework of the fractional-dimensional space, in which the momentum and position operators satisfying the R-deformed Heisenberg algebras. Accordingly, three essential problems have been solved such as: the free Klein–Gordon equation, the Klein–Gordon equation with mixed scalar and vector linear potentials and with mixed scalar and vector inversely linear potentials of Coulomb-type. For all these considered cases, the expressions of the eigenfunctions are determined and expressed in terms of the special functions: the Bessel functions of the first kind for the free case, the biconfluent Heun functions for the second case and the confluent hypergeometric functions for the end case, and the corresponding eigenvalues are exactly obtained.


2021 ◽  
Vol 5 (4) ◽  
pp. 271
Author(s):  
Yu Gu ◽  
Muhammad Altaf Khan ◽  
Y. S. Hamed ◽  
Bassem F. Felemban

In the present work, we study the COVID-19 infection through a new mathematical model using the Caputo derivative. The model has all the possible interactions that are responsible for the spread of disease in the community. We first formulate the model in classical differential equations and then extend it into fractional differential equations using the definition of the Caputo derivative. We explore in detail the stability results for the model of the disease-free case when R0<1. We show that the model is stable locally when R0<1. We give the result that the model is globally asymptotically stable whenever R0≤1. Further, to estimate the model parameters, we consider the real data of the fourth wave from Pakistan and provide a reasonable fitting to the data. We estimate the basic reproduction number for the proposed data to be R0=1.0779. Moreover, using the real parameters, we present the numerical solution by first giving a reliable scheme that can numerically handle the solution of the model. In our simulation, we give the graphical results for some sensitive parameters that have a large impact on disease elimination. Our results show that taking into consideration all the possible interactions can describe COVID-19 infection.


2021 ◽  
Vol 7 (10) ◽  
pp. 135
Author(s):  
Guanhua Hao ◽  
Alpha T. N’Diaye ◽  
Thilini K. Ekanayaka ◽  
Ashley S. Dale ◽  
Xuanyuan Jiang ◽  
...  

The X-ray-induced spin crossover transition of an Fe (II) molecular thin film in the presence and absence of a magnetic field has been investigated. The thermal activation energy barrier in the soft X-ray activation of the spin crossover transition for [Fe{H2B(pz)2}2(bipy)] molecular thin films is reduced in the presence of an applied magnetic field, as measured through X-ray absorption spectroscopy at various temperatures. The influence of a 1.8 T magnetic field is sufficient to cause deviations from the expected exponential spin state transition behavior which is measured in the field free case. We find that orbital moment diminishes with increasing temperature, relative to the spin moment in the vicinity of room temperature.


2021 ◽  
Vol 925 ◽  
Author(s):  
C.R. Constante-Amores ◽  
A. Batchvarov ◽  
L. Kahouadji ◽  
S. Shin ◽  
J. Chergui ◽  
...  

We study the effect of surfactants on the dynamics of a drop-interface coalescence using full three-dimensional direct numerical simulations. We employ a hybrid interface-tracking/level-set method, which takes into account Marangoni stresses that arise from surface-tension gradients, interfacial and bulk diffusion and sorption kinetic effects. We validate our predictions against the experimental data of Blanchette and Bigioni (Nat. Phys., vol. 2, issue 4, 2006, pp. 254–257) and perform a parametric study that demonstrates the delicate interplay between the flow fields and those associated with the surfactant bulk and interfacial concentrations. The results of this work unravel the crucial role of the Marangoni stresses in the flow physics of coalescence, with particular attention paid to their influence on the neck reopening dynamics in terms of stagnation-point inhibition, and near-neck vorticity generation. We demonstrate that surfactant-laden cases feature a rigidifying effect on the interface compared with the surfactant-free case, a mechanism that underpins the observed surfactant-induced phenomena.


Author(s):  
Guanhua Hao ◽  
Alpha T. N'Diaye ◽  
Thilini K. Ekanayaka ◽  
Ashley S. Dale ◽  
Xuanyuan Jiang ◽  
...  

The X-ray induced spin crossover transition of an Fe(II) molecular thin film in the presence and absence of a magnetic field has been investigated. The thermal activation energy barrier in the soft X-ray activation of the spin crossover transition for [Fe{H2B(pz)2}2(bipy)] molecular thin films is reduced in the presence of an applied magnetic field, as measured through X-ray absorption spectroscopy at various temperatures. The influence of a 1.8 T magnetic field is sufficient to cause deviations from the expected exponential spin state transition behavior that is measured in the field free case. We find that orbital moment diminishes with increasing temperature, relative to the spin moment in the vicinity of room temperature.


Author(s):  
Parvin Chahardah-Cherik ◽  
Manoochehr Fathi-Moghadam ◽  
Sadegh Haghighipour

Abstract In this study, transient flow and partial blockage in polyethylene (PE) pipe network are investigated experimentally and numerically using the method of characteristics in the time domain considering pipe-wall viscoelasticity. The experiments were conducted on a PE pipe network with and without partial blockage. The experimental pressure signals were damped during a short period of time in the blockage-free case. The numerical model was calibrated by the inverse transient analysis (ITA). The hydraulic transient solver calibrated with one Kelvin–Voigt element showed good consistency with the experimental results. Partial blockages with different lengths and sizes were examined at different locations of the pipe network. Results reveal an increase in head loss, pressure signal damping, and phase shift with increase in blockage. In addition, the location and characteristics of blockages with different sizes were determined using the ITA in the pipe network.


Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 897
Author(s):  
Michele Delvecchio ◽  
Francesco Petiziol ◽  
Sandro Wimberger

We study the robustness of different sweep protocols for accelerated adiabaticity following in the presence of static errors and of dissipative and dephasing phenomena. While in the noise-free case, counterdiabatic driving is, by definition, insensitive to the form of the original sweep function, this property may be lost when the quantum system is open. We indeed observe that, according to the decay and dephasing channels investigated here, the performance of the system becomes highly dependent on the sweep function. Our findings are relevant for the experimental implementation of robust shortcuts-to-adiabaticity techniques for the control of quantum systems.


2021 ◽  
Vol 7 ◽  
Author(s):  
Gerold Huber ◽  
Dirk Wollherr ◽  
Martin Buss

The potential of large elastic deformations in control applications, e.g., robotic manipulation, is not yet fully exploited, especially in dynamic contexts. Mainly because essential geometrically exact continuum models are necessary to express these arbitrarily large deformation dynamics, they typically result in a set of nonlinear, coupled, partial differential equations that are unsuited for control applications. Due to this lack of appropriate models, current approaches that try to exploit elastic properties are limited to either small deflection assumptions or quasistatic considerations only. To promote further exploration of this exciting research field of large elastic deflection control, we propose a geometrically exact, but yet concise a beam model for a planar, shear-, and torsion-free case without elongation. The model is derived by reducing the general geometrically exact the 3D Simo–Reissner beam model to this special case, where the assumption of inextensibility allows expressing the couple of planar Cartesian parameters in terms of the curve tangent angle of the beam center line alone. We further elaborate on how the necessary coupling between position-related boundary conditions (i.e., clamped and hinged ends) and the tangent angle parametrization of the beam model can be incorporated in a finite element method formulation and verify all derived expressions by comparison to analytic initial value solutions and an energy analysis of a dynamic simulation result. The presented beam model opens the possibility of designing online feedback control structures for accessing the full potential that elasticity in planar beam dynamics has to offer.


2021 ◽  
Vol 1 ◽  
pp. 1-8
Author(s):  
Oleksandr Samoilenko ◽  
Yurii Kuzmenko

The method for processing of the measurement results obtained from Comite International des Poids et Measures (CIPM) Key, Regional Metrology Organizations (RMO) or supplementary comparisons, from the proficiency testing by interlaboratory comparisons and the calibrations is proposed. It is named by authors as adjustment by least square method (LSM). Additive and multiplicative parameters for each measuring standard of every particular laboratory will be the results of this adjustment. As well as the parameters for each artifact. The parameters of the measurements standards are their additive and multiplicative degrees of equivalence from the comparison and the estimations of the systematic errors (biases) from calibrations. The parameters of the artifacts are the key comparisons reference value from the comparison and the assigned quantity values from the calibrations. The adjustment is considered as a way to solving a problem of processing the great amount of homogeneous measurements with many measuring standards at a different comparison levels (CIPM, RMO or supplementary), including connected problems. Four different cases of the adjustments are considered. The first one is a free case of adjustment. It was named so because of the fact that none of participants has any advantage except their uncertainties of measurements. The second one is a fixed case of adjustment. Measuring results of RMO and supplementary comparisons are rigidly linked to additive and multiplicative parameters of measuring standards of particular laboratories participated in CIPM key comparisons. The third one is a case of adjustment with dependent equations. This one is not so rigidly linked of the new comparisons results to previous or to some other comparisons as for fixed case. It means that the new results of comparisons are influenced by the known additive and multiplicative parameters and vice versa. The fourth one is a free case of adjustment with additional summary equations. In that case certain checking equations are added to the system of equations. So, the sum of parameters multiplied by their weights of all measurement standards for particular laboratories participated in comparisons should be equal to zero.


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