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In this work, an absolute method to calibrate an α-spectrometer is proposed taking into account the Source-to-Detector, and lateral distances due to eccentric source distribution. An analytical formula to calibrate an α-spectrometer is derived and the Simpson's integration method was utilized to solve these equations in its integral form numerically using a written C computer code. The general Monte Carlo N-particle code, MCNP as well as experimental measurements for some standard α-emitters are used to benchmark the proposed method. An agreement was found between the efficiency results calculated by MC and the proposed method with a maximum relative difference of about 0.5%. While, experimental measurement of α-emitters activity employing the proposed method differs by about 1.65% from the certified values. Accounting for the man made error allows to accurately quantify the assayed sample. Therefore, the inaccuracy in the efficiency results due to non-accurate inputs pertained to the source, and detector radii, Source–Detector distances, and eccentric source distribution are investigated in the Source-to-Detector distance range of (4 to 44 mm). The results show that a difference of ±1% in the detector radius, and Source-to-Detector distance than the normal values yields a relative difference of about ±2%, while a difference of ±50% in the source radius or source lateral distance from detector symmetry axis could only yields inaccuracy of less than ±3% in the efficiency results.

Intracardiac electrograms (iEGMs) are time traces of the electrical potential recorded close to the heart muscle. We calculate unipolar and bipolar iEGMs analytically for a myocardial slab with parallel myofibers and validate them against numerical bidomain simulations. The analytical solution obtained via the method of mirrors is an infinite series of arctangents. It goes beyond the solid angle theory and is in good agreement with the simulations, even though bath loading effects were not accounted for in the analytical calculation. At a large distance from the myocardium, iEGMs decay as 1/R (unipolar), 1/R² (bipolar and parallel), and 1/R³ (bipolar and perpendicular to the endocardium). At the endocardial surface, there is a mathematical branch cut. Here, we show how a thicker myocardium generates iEGMs with larger amplitudes and how anisotropy affects the iEGM width and amplitude. If only the leading-order term of our expansion is retained, it can be determined how the conductivities of the bath, torso, myocardium, and myofiber direction together determine the iEGM amplitude. Our results will be useful in the quantitative interpretation of iEGMs, the selection of thresholds to characterize viable tissues, and for future inferences of tissue parameters. [ABSTRACT FROM AUTHOR]

Crystal structure prediction is demanding in two senses: this is a difficult problem, both experimentally and computationally, yet we want to find new materials with new properties that take unknown crystal structures. Using statistical information on the local environment of already reported stable crystal structures would be helpful when, for instance, finding new crystal structures through visually adding atoms sequentially to a cluster of atoms, which is an intuitive procedure that does not require substantial computational resources. This study conducted hierarchical classification of frequently appearing structure types in the ICSD database by comparing the occurrence ratios of H, B, C, N, O, F, and transition metals (TM) in binary, ternary, and quaternary crystals. The bond angle and solid angle distributions of Delaunay polyhedra with atoms as vertices were considered as descriptors of the local environment for each structure type. Hierarchical clustering of structure types based on bond angle or solid angle distributions revealed that the structure types can be broadly categorized into those favoring TM oxides, having low TM occurrence, and having high TM occurrence. Our results indicate that the anion, or lack of, plays a key role in determining the crystal structure type, and structure types strongly preferred by TM oxides can accommodate a broad range of angles.

Future automotive interior lighting might have the potential to go beyond decorative purposes by influencing alertness, circadian physiology, and sleep. As the available space in the interior of an automobile for lighting applications is limited, understanding the impact of various luminous surface sizes on non-image-forming effects is fundamental in this field. In a laboratory study using a within-subject design, 18 participants were exposed to two bright light conditions with different solid angles and one dim light condition in a balanced, randomized order during the course of the evening. Our results demonstrate that both light conditions significantly increased subjective alertness and reduced salivary melatonin concentration but not cognitive performance compared to dim light. The solid angle of light exposure at constant corneal illuminance only affected visual comfort. While subjective alertness can be increased and melatonin can be attenuated with rather small luminaires, larger solid angles should be considered if visual comfort is a priority.

Intracardiac electrograms (iEGMs) are time traces of the electrical potential recorded close to the heart muscle. We calculate unipolar and bipolar iEGMs analytically for a myocardial slab with parallel myofibers and validate them against numerical bidomain simulations. The analytical solution obtained via the method of mirrors is an infinite series of arctangents. It goes beyond the solid angle theory and is in good agreement with the simulations, even though bath loading effects were not accounted for in the analytical calculation. At a large distance from the myocardium, iEGMs decay as 1/R (unipolar), 1/R2 (bipolar and parallel), and 1/R3 (bipolar and perpendicular to the endocardium). At the endocardial surface, there is a mathematical branch cut. Here, we show how a thicker myocardium generates iEGMs with larger amplitudes and how anisotropy affects the iEGM width and amplitude. If only the leading-order term of our expansion is retained, it can be determined how the conductivities of the bath, torso, myocardium, and myofiber direction together determine the iEGM amplitude. Our results will be useful in the quantitative interpretation of iEGMs, the selection of thresholds to characterize viable tissues, and for future inferences of tissue parameters.

This paper presents the design of an arc-shaped near-isotropic self-complementary antenna for spectrum sensing application. An arc-shaped dipole with horizontal and vertical arms is used to achieve a near isotropic radiation pattern. The radiation pattern improved by adjusting the horizontal and vertical arm lengths. Simulated and experimental results show that the proposed antenna has an impedance bandwidth of 146% (2.4–18.4 GHz) for VSWR ≤ 2 with a good radiation pattern. In order to quantify the antenna performance, antenna gain variation, bandwidth, efficiency, and size have been compared with previously reported designs. It is shown that the proposed arc-shaped antenna can achieve nearly isotropic radiation patterns with a maximum radiation efficiency of 92%. The isotropic performance of the antenna has been characterized by observing the radiation pattern and solid angle. The FR4 substrate is used as a dielectric with relative permittivity 4.4 and loss tangent of 0.02. ( ε r = 4.4, h = 1.6 mm) The simulated and measured results are in good comparison, and the proposed design is a suitable candidate for spectrum sensing. [ABSTRACT FROM AUTHOR]

Future automotive interior lighting might have the potential to go beyond decorative purposes by influencing alertness, circadian physiology, and sleep. As the available space in the interior of an automobile for lighting applications is limited, understanding the impact of various luminous surface sizes on non-image-forming effects is fundamental in this field. In a laboratory study using a within-subject design, 18 participants were exposed to two bright light conditions with different solid angles and one dim light condition in a balanced, randomized order during the course of the evening. Our results demonstrate that both light conditions significantly increased subjective alertness and reduced salivary melatonin concentration but not cognitive performance compared to dim light. The solid angle of light exposure at constant corneal illuminance only affected visual comfort. While subjective alertness can be increased and melatonin can be attenuated with rather small luminaires, larger solid angles should be considered if visual comfort is a priority. [ABSTRACT FROM AUTHOR]

Three structurally diverse 5-phenyltetrazolato (Tz) Ti, Zr, and Ta complexes, namely, (C 2 H 8 N)[Ti 2 (C 7 H 5 N 4 ) 5 (C 2 H 6 N) 4 ]·1.45C 6 H 6 or (Me 2 NH 2 )[Ti 2 (NMe 2 ) 4 (2,3-μ-Tz) 3 (2-η 1 -Tz) 2 ]·1.45C 6 H 6 , (1·1.45C 6 H 6 ), [Zr 2 (C 7 H 5 N 4 ) 6 (C 2 H 6 N) 2 (C 2 H 7 N) 2 ]·1.12C 6 H 6 ·0.382CH 2 Cl 2 or [Zr 2 (Me 2 NH) 2 (NMe 2 ) 2 (2,3-μ-Tz) 3 (2-η 1 -Tz) 2 (1,2-η 2 -Tz)]·1.12C 6 H 6 ·0.38CH 2 Cl 2 (2·1.12C 6 H 6 ·0.38CH 2 Cl 2 ), and (C 2 H 8 N) 2 [Ta 2 (C 7 H 5 N 4 ) 8 (C 2 H 6 N) 2 O]·0.25C 7 H 8 or (Me 2 NH 2 ) 2 [Ta 2 (NMe 2 ) 2 (2,3-μ-Tz) 2 (2-η 1 -Tz) 6 O]·0.25C 7 H 8 (3·0.25C 7 H 8 ), where TzH is 5-phenyl-1H-tetrazole, have been synthesized and structurally characterized. All three complexes are dinuclear; the Ti center in 1 is six-coordinate, whereas the Zr and Ta atoms in 2 and 3 are seven-coordinate. The coordination environments of the Ti centers in 1 are similar, and so are the ligations of the Ta centers in 3. In contrast, the two Zr centers in 2 bear a different number of ligands, one of which is a bidentate η 2 -5-phenyltetrazolato ligand that has not been observed previously for d-block elements. The dimethylamido ligand, present in the starting materials, remained unchanged, or was converted to dimethylamine and dimethylammonium during the synthesis. Dimethylamine coordinates as a neutral ligand, whereas dimethylammonium is retained as a hydrogen-bonded entity bridging Tz ligands., (open access.)

In this paper we compared two different solid angle formulations to determine the amount of cavitation potential energy that is transfer from a source to a surface. The first formulation used an analytical expression for the solid angle of a planar triangle while the second formulation used a fully continuous form of the solid angle projection approach which represents the surface specific impact power at a point location. The comparison was conducted on a NACA 0018-45 hydrofoil. A block-structured computational mesh was created in ICEM CFD. Transient simulations were performed in Ansys CFX where the SST turbulence model with Reboud's correction was used. For the cavitation modelling the Schnerr-Sauer cavitation model with the recommended values was used. Result from Ansys CFX were imported into Matlab where the potential power applied to the surface was calculated for both formulations. The results of the study show that both formulations work well and predict similar locations where erosion occurred, the difference is in the absolute values which are significantly higher in the formulation that used the fully continuous form of the solid angle. [ABSTRACT FROM AUTHOR]

Virtual reality is increasingly used in medicine for diagnostics, for visualisation of complex structures and for preoperative planning. In interventional radiology, minimally invasive approach could be described with a target point representing the desired needle tip position and an array of all possible trajectories leading to it resembling irregular “cone” or “pyramid”. We present a pilot study of planning a minimally invasive posterior infrazygomatic and suprazygomatic approaches into the pterygopalatine fossa using a solid angle as a measure of size of the approach in five virtually reconstructed heads. The minimally invasive approaches were planned by manually drawing the edges of “pyramids” that described each approach in 3D using virtual reality program Tracer. For each head, a transverse diameter was measured and for each approach a solid angle size, average edge length and estimated area on the skin from where the target point could be reached were calculated. We found that, the solid angle of posterior infrazygomatic approach was significantly larger than suprazygomatic approach (p0.001). Furthermore, the transverse head diameter and solid angle in posterior infrazygomatic approach were negatively correlated (ρ=-0.55, p=0.0002), while transverse head diameter and the estimated area on the skin from where the target point could be reached in the suprazygomatic approach were positively correlated (ρ=0.37, p=0.0206). In conclusion, our findings provide important preliminary evidence on the feasibility of evaluating and comparing different minimally invasive approaches using virtual reality systems, and affirm the validity of solid angle as a measure of the size of the approach.

Surface geometry plays a central role in the design of bridges, vaults and shells, using various techniques for generating a geometry which aims to balance structural, spatial, aesthetic and construction requirements. In this paper we propose the use of surfaces defined such that given closed curves subtend a constant solid angle at all points on the surface and form its boundary. Constant solid angle surfaces enable one to control the boundary slope and hence achieve an approximately constant span-to-height ratio as the span varies, making them structurally viable for shell structures. In addition, when the entire surface boundary is in the same plane, the slope of the surface around the boundary is constant and thus follows a principal curvature direction. Such surfaces are suitable for surface grids where planar quadrilaterals meet the surface boundaries. They can also be used as the Airy stress function in the form finding of shells having forces concentrated at the corners. Our technique employs the Gauss-Bonnet theorem to calculate the solid angle of a point in space and Newton's method to move the point onto the constant solid angle surface. We use the Biot-Savart law to find the gradient of the solid angle. The technique can be applied in parallel to each surface point without an initial mesh, opening up for future studies and other applications when boundary curves are known but the initial topology is unknown. We show the geometrical properties, possibilities and limitations of surfaces of constant solid angle using examples in three dimensions. • Constant solid angle surfaces enable the control of the slope at the boundary. • Points on a constant solid angle surfaces can be found without a mesh. • The solid angle is dimensionless and therefore useful with varying spans. • Enables surface grids in which planar quadrilaterals meet the surface boundaries. • Can be used as Airy stress functions in form finding to direct forces towards corners. [ABSTRACT FROM AUTHOR]

The geometrical efficiency of a source-to-detector configuration is considered to be necessary in the calculation of the full energy peak efficiency, especially for NaI(Tl) and HPGe gamma-ray spectroscopy detectors. The geometrical efficiency depends on the solid angle subtended by the radioactive sources and the detector surfaces. The present work is basically concerned to establish a new mathematical approach for calculating the solid angle and geometrical efficiency, based on conversion of the geometrical solid angle of a non-axial radioactive point source with respect to a circular surface of the detector to a new equivalent geometry. The equivalent geometry consists of an axial radioactive point source with respect to an arbitrary elliptical surface that lies between the radioactive point source and the circular surface of the detector. This expression was extended to include coaxial radioactive circular disk source. The results were compared with a number of published data to explain how significant this work is in the efficiency calibration procedure for the γ-ray detection systems, especially in case of using isotropic radiating γ-ray sources in the form of point and disk shapes.

In this paper, we present a straightforward analytical method for calculating the efficiencies of an ovoid shape (elliptical cylindrical) detector by using a randomly located point source. To determine the activity of an unknown radioactive source, absolute efficiency is required and we should take into account the attenuation of the gamma-ray photons by the source container and the detector housing materials. The soundness of the resultant straightforward analytical method was successfully confirmed by comparison with some published data.

This paper presents the design of an arc-shaped near-isotropic self-complementary antenna for spectrum sensing application. An arc-shaped dipole with horizontal and vertical arms is used to achieve a near isotropic radiation pattern. The radiation pattern improved by adjusting the horizontal and vertical arm lengths. Simulated and experimental results show that the proposed antenna has an impedance bandwidth of 146% (2.4–18.4 GHz) for VSWR ≤ 2 with a good radiation pattern. In order to quantify the antenna performance, antenna gain variation, bandwidth, efficiency, and size have been compared with previously reported designs. It is shown that the proposed arc-shaped antenna can achieve nearly isotropic radiation patterns with a maximum radiation efficiency of 92%. The isotropic performance of the antenna has been characterized by observing the radiation pattern and solid angle. The FR4 substrate is used as a dielectric with relative permittivity 4.4 and loss tangent of 0.02. (εr = 4.4, h = 1.6 mm) The simulated and measured results are in good comparison, and the proposed design is a suitable candidate for spectrum sensing.

Virtual reality is increasingly used in medicine for diagnostics, for visualisation of complex structures and for preoperative planning. In interventional radiology, minimally invasive approach could be described with a target point representing the desired needle tip position and an array of all possible trajectories leading to it resembling irregular "cone" or "pyramid". We present a pilot study of planning a minimally invasive posterior infrazygomatic and suprazygomatic approaches into the pterygopalatine fossa using a solid angle as a measure of size of the approach in five virtually reconstructed heads. The minimally invasive approaches were planned by manually drawing the edges of "pyramids" that described each approach in 3D using virtual reality program Tracer. For each head, a transverse diameter was measured and for each approach a solid angle size, average edge length and estimated area on the skin from where the target point could be reached were calculated. We found that, the solid angle of posterior infrazygomatic approach was significantly larger than suprazygomatic approach (p<0.001). Furthermore, the transverse head diameter and solid angle in posterior infrazygomatic approach were negatively correlated (p=-0.55, p=0.0002), while transverse head diameter and the estimated area on the skin from where the target point could be reached in the suprazygomatic approach were positively correlated (p=0.37, p=0.0206). In conclusion, our findings provide important preliminary evidence on the feasibility of evaluating and comparing different minimally invasive approaches using virtual reality systems, and affirm the validity of solid angle as a measure of the size of the approach. [ABSTRACT FROM AUTHOR]

Purpose: The concept of 4πc radiotherapy is a radiotherapy planning technique receiving much attention in recent times. The aim of this article is to disprove the feasibility of the 4π radiotherapy using a cantilever-type linear accelerator or any other external-beam delivery machines. Materials and Methods: A surface integral-based mathematical derivation for the maximum achievable solid angle for a linear accelerator was carried out respecting the rotational boundary conditions for gantry and couch in three-dimensional Euclidean space. The allowed movements include a gantry rotation of 0–2πc and a table rotation of πc/2 - 0 - 3πc/2) . Results: Total achievable solid angle by cantilever-type linear accelerator (or any teletherapy machine employing a cantilever design) is 1/r2 π ∫ - θ=0 π ∫ φ=0 (rSinθdφ). (rdθ) = 2πc, which is applicable only for the foot and brain radiotherapy where the allowed table rotation is 90°–0°–270°. For other sites such as pelvis, thorax, or abdomen, achievable solid angle as the couch rotation comes down significantly. Practically, only suitable couch angle is 0° by avoiding gantry–couch–patient collision. Conclusions: Present cantilever design of linear accelerator prevents achieving a 4π radian solid angle at any point in the patient. Even the most modern therapy machines like CyberKnife which has a robotic arm also cannot achieve 4π geometry. Maximum achievable solid angle under the highest allowable boundary condition(s) cannot exceed 2πc, which is restricted for only extremities such as foot and brain radiotherapy. For other parts of the body such as pelvis, thorax, and abdomen, the solid angle is reduced to 1/5th (maximum value) of the 4πc. To obtain a 4πc solid angle in a three-dimensional Euclidean space, the patient has to be a zero-dimensional point and X-ray head of the linear accelerator has a freedom to rotate in every point of a hypothetical sphere of radius 1 m. This article establishes geometrically why it is not possible to achieve a 4πc solid angle.

In this work, an absolute method to calibrate an α -spectrometer is proposed taking into account the Source-to-Detector, and lateral distances due to eccentric source distribution. An analytical formula to calibrate an α -spectrometer is derived and the Simpson's integration method was utilized to solve these equations in its integral form numerically using a written C computer code. The general Monte Carlo N-particle code, MCNP as well as experimental measurements for some standard α -emitters are used to benchmark the proposed method. An agreement was found between the efficiency results calculated by MC and the proposed method with a maximum relative difference of about 0.5%. While, experimental measurement of α -emitters activity employing the proposed method differs by about 1.65% from the certified values. Accounting for the man made error allows to accurately quantify the assayed sample. Therefore, the inaccuracy in the efficiency results due to non-accurate inputs pertained to the source, and detector radii, Source-Detector distances, and eccentric source distribution are investigated in the Source-to-Detector distance range of (4 to 44 mm). The results show that a difference of ± 1 % in the detector radius, and Source-to-Detector distance than the normal values yields a relative difference of about ± 2 % , while a difference of ± 50 % in the source radius or source lateral distance from detector symmetry axis could only yields inaccuracy of less than ± 3 % in the efficiency results., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Author(s).)

Ultra-widefield fluorescein angiography (UWFA) is an emerging imaging modality used to characterise pathologies in the retinal vasculature, such as microaneurysms (MAs) and vascular leakages. Despite its potential value for diagnosis and disease screening, objective quantitative assessment of retinal pathologies by UWFA is currently limited because laborious manual processing is required. In this report, we describe a geometrical method for uneven brightness compensation inherent to UWFA imaging technique. The correction function is based on the geometrical eyeball shape, therefore it is fully automated and depends only on pixel distance from the center of the imaged retina. The method’s performance was assessed on a database containing 256 UWFA images with the use of several image quality measures that show the correction method improves image quality. The method is also compared to the commonly used CLAHE approach and was also employed in a pilot study for vascular segmentation, giving a noticeable improvement in segmentation results. Therefore, the method can be used as an image preprocessing step in retinal UWFA image analysis.

• Two new theorems in attitude kinematics were developed using the slewing motion of a single axis and rotation about the axis. • Derived Ishlinskii's theorem and the Goodman-Roberson theorem based on the newly developed kinematic theorems. • Found that a general attitude transformation consists of a slewing transformation of an axis followed by a rotational transformation about the axis, where the two transformations commute. Attitude kinematics using a single axis was developed to establish the relationships among the axis trajectory, enclosed solid angle and the associated attitude transformation. An arbitrary transformation due to a sequence of finite rotations or due to propagation consisting of an infinite number of infinitesimal rotations is equivalent to the product of a slewing transformation along a great circle arc linking the initial and final orientations of the axis followed by a rotational transformation about the axis. A key finding of this work is that the slewing transformation commutes with the rotational transformation, if the trajectory of the slewing transformation is fixed in space and the axis orientation is accounted for in the rotational transformation. The results were used to establish two new kinematic theorems. The new theorems provided simple derivations of Ishlinskii's theorem, the Goodman-Roberson theorem and a result found by Montgomery. The findings in this work were applied to attitude propagation by separating attitude rotational increments that are normal to the axis with those that are parallel to the axis. The normal and parallel angular increments were integrated separately to form the slewing transformation and rotational transformation, respectively. The product of the two commuting transformations formed the total propagation transformation. The findings were validated by using them to create and implement a propagation algorithm. Numerical testing showed that the new algorithm has accuracy comparable to traditional attitude propagation algorithms when stress tested with pure coning motion. [ABSTRACT FROM AUTHOR]

A new Rococo 2 X‐ray fluorescence detector was implemented into the cryogenic sample environment at the Hard X‐ray Micro/Nano‐Probe beamline P06 at PETRA III, DESY, Hamburg, Germany. A four sensor‐field cloverleaf design is optimized for the investigation of planar samples and operates in a backscattering geometry resulting in a large solid angle of up to 1.1 steradian. The detector, coupled with the Xspress 3 pulse processor, enables measurements at high count rates of up to 106 counts per second per sensor. The measured energy resolution of ∼129 eV (Mn Kα at 10000 counts s−1) is only minimally impaired at the highest count rates. The resulting high detection sensitivity allows for an accurate determination of trace element distributions such as in thin frozen hydrated biological specimens. First proof‐of‐principle measurements using continuous‐movement 2D scans of frozen hydrated HeLa cells as a model system are reported to demonstrate the potential of the new detection system. [ABSTRACT FROM AUTHOR]

ST elevation on an electrocardiogram is a hallmark of acute transmural ischemia. However, the underlying mechanism remains unclear. We hypothesized that high ischemic sensitivities of epicardial adenosine triphosphate-sensitive potassium (IKATP) and sodium (INa) currents play key roles in the genesis of ST elevation. Using a multi-scale heart simulation under moderately ischemic conditions, transmural heterogeneities of IKATP and INa created a transmural gradient, opposite to that observed in subendocardial injury, leading to ST elevation. These heterogeneities also contributed to the genesis of hyper-acute T waves under mildly ischemic conditions. By contrast, under severely ischemic conditions, although action potentials were suppressed transmurally, the potential gradient at the boundary between the ischemic and normal regions caused ST elevation without a contribution from transmural heterogeneity. Thus, transmural heterogeneities of ion channel properties may contribute to the genesis of ST-T changes during mild or moderate transmural ischemia, while ST elevation may be induced without the contribution of heterogeneity under severe ischemic conditions. [ABSTRACT FROM AUTHOR]

A Monte Carlo procedure is presented to calculate the solid angle subtended between a HPGe collimated detector and a PWR 17 x 17 fuel assembly. Self-shielding within the assembly is assessed in the case of gamma rays encountered in gamma spectroscopy of spent nuclear fuel. Self-shielding renders a non-uniform 3-D distribution of the radioactivity within the assembly whose extend depends on gamma ray energies of interest. Hence, the solid angle is reduced to an effective one for each of the different energies of interest.

Purpose: The concept of 4πc radiotherapy is a radiotherapy planning technique receiving much attention in recent times. The aim of this article is to disprove the feasibility of the 4π radiotherapy using a cantilever-type linear accelerator or any other external-beam delivery machines. Materials and Methods: A surface integral-based mathematical derivation for the maximum achievable solid angle for a linear accelerator was carried out respecting the rotational boundary conditions for gantry and couch in three-dimensional Euclidean space. The allowed... the foot and brain radiotherapy where the allowed table rotation is 90°-0°-270°. For other sites such as pelvis, thorax, or abdomen, achievable solid angle as the couch rotation comes down significantly. Practically, only suitable couch angle is 0° by avoiding gantry-couch-patient collision. Conclusions: Present cantilever design of linear accelerator prevents achieving a 4π radian solid angle at any point in the patient. Even the most modern therapy machines like CyberKnife which has a robotic arm also cannot achieve 4π geometry. Maximum achievable solid angle under the highest allowable boundary condition(s) cannot exceed 2πc, which is restricted for only extremities such as foot and brain radiotherapy. For other parts of the body such as pelvis, thorax, and abdomen, the solid angle is reduced to 1/5th (maximum value) of the 4πc. To obtain a 4πc solid angle in a three-dimensional Euclidean space, the patient has to be a zero-dimensional point and X-ray head of the linear accelerator has a freedom to rotate in every point of a hypothetical sphere of radius 1 m. This article establishes geometrically why it is not possible to achieve a 4πc solid angle. [ABSTRACT FROM AUTHOR]

Ambient electromagnetic and RF energy is an ubiquitous energy resource that is found everywhere but difficult to harvest because of the time-varying orientation of incoming radiations and the low efficiency of RF rectifiers resulting from a low input power density operation. In response to these two challenges that come with the design of rectennas for ambient energy harvesting, this paper discusses a figure of merit to evaluate the rectenna performance that combines the rectification efficiency, the radiation efficiency, and the spherical coverage of the antenna. To illustrate this proposed figure of merit, a rectenna with a strengthen RF-to-dc efficiency and also a full spatial coverage is designed using beam-forming networks. The resulting system is demonstrated for a wireless sensor mounted on a pole. To maintain a reasonable size of the prototype, a miniaturization technique of a $4 \times 4$ Butler matrix (BM) is investigated, which allows for the reduction of the footprint of the BM by 2 compared to its classical microstrip design counterpart at 2.4 GHz. The overall rectification efficiency and dc power patterns are reported for the elevation plane of one multidirectional rectenna at 2.4 GHz for an incident power density of $0.45\,\,\mu \text {W}\cdot \text {cm}^{-2}$. It is shown that the system can triple the dc output power compared to a three-dipole counterpart occupying the same area. Furthermore, while the maximum harvesting capability at $1 \,\,\mu \text {W}\cdot \text {cm}-^{2}$ does not exceed $28\pi $ %.steradian in the literature, it reaches $43.6\pi $ %.steradian with the proposed demonstrator. [ABSTRACT FROM AUTHOR]

Collective motion is one of the most ubiquitous behaviours displayed by social organisms and has led to the development of numerous models. Recent advances in the understanding of sensory system and information processing by animals impels one to revise classical assumptions made in decisional algorithms. In this context, we present a model describing the three-dimensional visual sensory system of fish that adjust their trajectory according to their perception field. Furthermore, we introduce a stochastic process based on a probability distribution function to move in targeted directions rather than on a summation of influential vectors as is classically assumed by most models. In parallel, we present experimental results of zebrafish (alone or in group of 10) swimming in both homogeneous and heterogeneous environments. We use these experimental data to set the parameter values of our model and show that this perception-based approach can simulate the collective motion of species showing cohesive behaviour in heterogeneous environments. Finally, we discuss the advances of this multilayer model and its possible outcomes in biological, physical and robotic sciences.