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Membrane distillation (MD) is widely used in the field of seawater desalination. Among its various sub-categories, air gap membrane distillation (AGMD) stands out due to its high thermal efficiency and compatibility with low-grade heat sources. This study delves into the impact of varying operating conditions on AGMD performance, employing numerical simulations which are grounded in experimental validation. The objective was to enhance the performance of AGMD, mitigate polarization phenomena, and provide a reference for optimizing membrane component design. The results show that the agreements between the simulated and the experimental values were high. When increasing the feed temperature and decreasing the coolant temperature, the impact of polarization phenomena on the performance of AGMD was reduced. The mass flux, Total Permeate Concentration (TPC), and heat flux increased by 81.69%, 36.89%, and 118.01%, respectively, when the feed temperature was increased from 50 °C to 75 °C. When the coolant temperature decreased from 22 °C to 7 °C, the mass flux increased by 37.06%. The response surface analysis revealed that the feed temperature has significant influence on AGMD performance, and there is a noticeable interaction between the feed temperature and coolant temperature. These findings will play key roles in practical applications.

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The study investigates the efficiency of air-gap membrane distillation (AGMD) in water recovery and antibiotics removal from wastewater, focusing on high-concentration scenarios. Experimental findings reveal enhanced membrane performance with increasing the feed temperature, resulting in vapor permeate fluxes of up to 5 kg/m2.h at higher temperatures. Despite experiencing flux reduction caused by fouling from humic acid (HA) in the feed antibiotics solution, the antibiotics consistently maintain near-complete rejection rates (>99%) over 48 h. The foulant on the membrane surface was illustrated by SEM imaging. To know the temperature polarization and the fouling resistance, mathematical modeling was used, and it validates experimental results, elucidating temperature polarization effects and mass transfer coefficients. An increase in feed flow rates reduced thermal boundary layers, enhancing heat flux. Higher temperatures reduced HA fouling resistance. Therefore, AGMD proves effective in water recovery and antibiotics removal, with mathematical models aiding fouling understanding for future research and detailed computational fluid dynamics (CFD) models.

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In underground coal mining, machine operators put themselves at risk when getting close to the machine or cutting face to observe the process. To improve the safety and efficiency of machine operators, a cutting force sensor is proposed. A linear cutting machine is used to cut two separate coal samples cast in concrete with conical pick cutters to simulate mining with a continuous miner. Linear and neural network regression models are fit using 100 random 70:30 test/train splits. The normal force exceeds 60 kN during the rock-cutting tests, and it is averaged using a low pass filter with a 10 Hertz cutoff frequency. The sensor uses measurements of the resonant frequency of capacitive cells in a steel case to determine cutting forces. When used in the rock-cutting experiments, the sensor conforms to the tooling and the stiffness and sensitivity are increased compared to the initial configuration. The sensor is able to track the normal force on the conical picks with a mean absolute error less than 6 kN and an R2 score greater than 0.60 using linear regression. A small neural network with a second-order polynomial expansion is able to improve this to a mean absolute error of less than 4 kN and an R2 score of around 0.80. Filtering measurements before regression fitting is explored. This type of sensor could allow operators to assess tool wear and material type using objective force measurements while maintaining a greater distance from the cutting interface.

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BACKGROUND AND PURPOSE: This study aimed to investigate the reproducibility of a novel approach using 3D printed brachytherapy applicators for the treatment of skin cancer. Specifically, we aimed to assess the accuracy of applicator placement and to minimize the existence of air gap pockets between the applicator and the patient's skin. MATERIALS AND METHODS: A total of 20 patients plans diagnosed with skin cancer were enrolled in this study. All patients underwent high dose rate (HDR) brachytherapy. To ensure precise applicator placement, patient-specific 3D printed applicators were designed based on individual body and tumor topography, utilizing data obtained from computer tomography (CT) scans. All applicators were fabricated using fused deposition modeling technology. RESULTS: The error in applicator placement was measured and found to be less than 1.0 mm on average, with a standard deviation of 0.9 mm. Additionally, the average error in air gap pockets between the applicator and the patient's skin was 0.4 mm (standard deviation was 0.5 mm). The study demonstrated that the personalized approach of 3D printed brachytherapy applicator placement in skin cancer treatment yielded highly accurate results. The average error of less than 1.0 mm in applicator positioning and the minimal air gap pockets demonstrated the reproducibility and precision of this technique. CONCLUSION: Our study establishes the reproducibility and accuracy of 3D-printed brachytherapy applicator placement in the treatment of skin cancer. This personalized treatment approach offers a highly precise method for delivering radiation therapy, minimizing the risk to adjacent healthy tissues, and enhancing overall patient outcomes.

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Purpose: Determining the impact of air gap errors on the skin dose in postoperative breast cancer radiotherapy under dynamic intensity-modulated radiation therapy (IMRT) techniques. Methods: This was a retrospective study that involved 55 patients who underwent postoperative radiotherapy following modified radical mastectomy. All plans employed tangential IMRT, with a prescription dose of 50 Gy, and bolus added solely to the chest wall. Simulated air gap depth errors of 2 mm, 3 mm, and 5 mm were introduced at depression or inframammary fold areas on the skin, resulting in the creation of air gaps named Air2, Air3, and Air5. Utilizing a multivariable GEE, the average dose (Dmean) of the local skin was determined to evaluate its relationship with air gap volume and the lateral beam's average angle (AALB). Additionally, an analysis was conducted on the impact of gaps on local skin. Results: When simulating an air gap depth error of 2 mm, the average Dmean in plan2 increased by 0.46 Gy compared to the initial plan (planO) (p < .001). For the 3-mm air gap, the average Dmean of plan3 was 0.51 Gy higher than that of planO (p < .001). When simulating the air gap as 5 mm, the average Dmean of plan5 significantly increased by 0.59 Gy compared to planO (p < .001). The TCP results showed a similar trend to those of Dmean. As the depth of air gap error increases, NTCP values also gradually rise. The linear regression of the multivariable GEE equation indicates that the volume of air gaps and the AALB are strong predictors of Dmean. Conclusion: With small irregular air gap errors simulated in 55 patients, the values of skin's Dmean, TCP, and NTCP increased. A multivariable linear GEE regression model may effectively explain the impact of air gap volume and AALB on the local skin.

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Objectives. The purpose of this study was to calculate the dynamic air gap thickness between the human body and the turnout gear. Relationships between the air gap thickness and joint range of motion (ROM) were also explored. Methods. The air gap thickness and joint ROM of 12 male firefighters walking in a control condition with no self-contained breathing apparatus (SCBA) and three varying-strapped SCBAs were measured using three-dimensional (3D) body scanning and 3D inertial motion capture. The interpolation technique was employed to predict the air gap thickness curve during walking. The dynamic air gap thickness was compared with the joint ROM to see how they relate to the location and percentage of movement restriction. Results. During the walking, the air gap fluctuated as a sine curve. Carrying SCBA reduced the air gap thickness at the trunk most (F = 11.17, p < 0.001, η2 = 0.63), and adjusting the shoulder strap length altered the air gap distribution at the trunk. The reduced air gap at the pelvis caused an incremental restriction on pelvis rotation. Conclusions. A compatibility design of the shoulder strap and hip belt in SCBA with the turnout jacket is suggested.

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In the automotive industry, there has been considerable focus on developing various sensors for engine oil monitoring. However, when it comes to monitoring the condition of brake fluid, which is crucial for ensuring safety, there has been a lack of a secure online method for this monitoring. This study addresses this gap by developing a hybrid silica nanofiber mat, or an aerogel integrated with an optical fiber sensor, to monitor brake fluid condition. The incorporation of silica nanofibers in this hybrid enhances the sensitivity of the optical fiber glass surface by at least 3.75 times. Furthermore, creating an air gap between the glass surface of the optical fiber and the nanofibers boosts sensitivity by at least 5 times, achieving a better correlation coefficient (R2 = 0.98). In the case of silica aerogel, the sensitivity is enhanced by 10 times, but this enhancement relies on the presence of the established air gap. The air gap was adjusted to range from 0.5 mm to 1 mm, without any significant change in the measurement within this range. The response time of the developed sensor is a minimum of 15 min. The sensing material is irreversible and has a diameter of 2.5 mm, making it easily replaceable. Overall, the sensor demonstrates strong repeatability, with approximately 90% consistency, and maintains uncertainty levels below 5% across specific ranges: from 3% to 6% for silica aerogel and from 5% to 6% for silica nanofibers in the presence of an air gap. These findings hold promise for integrating such an optical fiber sensor into a car's electronic system, enabling the direct online monitoring of brake fluid quality. Additionally, the study elucidates the effect of water absorption on the refractive index of brake fluid, as well as on the silica nanomaterials.

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PURPOSE: To assess a large panel of MR compatible detectors on the full range of measurements required for a 0.35 T MR-linac commissioning by using a specific statistical method represented as a continuum of comparison with the Monte Carlo (MC) TPS calculations. This study also describes the commissioning tests and the secondary MC dose calculation validation. MATERIAL AND METHODS: Plans were created on the Viewray TPS to generate MC reference data. Absolute dose points, PDD, profiles and output factors were extracted and compared to measurements performed with ten different detectors: PTW 31010, 31021, 31022, Markus 34045 and Exradin A28 MR ionization chambers, SN Edge shielded diode, PTW 60019 microdiamond, PTW 60023 unshielded diode, EBT3 radiochromic films and LiF µcubes. Three commissioning steps consisted in comparison between calculated and measured dose: the beam model validation, the output calibration verification in four different phantoms and the commissioning tests recommended by the IAEA-TECDOC-1583. MAIN RESULTS: The symmetry for the high resolution detectors was higher than the TPS data of about 1%. The angular responses of the PTW 60023 and the SN Edge were - 6.6 and - 11.9% compared to the PTW 31010 at 60°. The X/Y-left and the Y-right penumbras measured by the high resolution detectors were in good agreement with the TPS values except for the PTW 60023 for large field sizes. For the 0.84 × 0.83 cm2 field size, the mean deviation to the TPS of the uncorrected OF was - 1.7 ± 1.6% against - 4.0 ± 0.6% for the corrected OF whereas we found - 4.8 ± 0.8% for passive dosimeters. The mean absolute dose deviations to the TPS in different phantoms were 0 ± 0.4%, - 1.2 ± 0.6% and 0.5 ± 1.1% for the PTW 31010, PTW 31021 and Exradin A28 MR respectively. CONCLUSIONS: The magnetic field effects on the measurements are considerably reduced at low magnetic field. The PTW 31010 ionization chamber can be used with confidence in different phantoms for commissioning and QA tests requiring absolute dose verifications. For relative measurements, the PTW 60019 presented the best agreement for the full range of field size. For the profile assessment, shielded diodes had a behaviour similar to the PTW 60019 and 60023 while the ionization chambers were the most suitable detectors for the symmetry. The output correction factors published by the IAEA TRS 483 seem to be applicable at low magnetic field pending the publication of new MR specific values.

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In present study a cylindrical module is studied based on air gap membrane distillation configuration and studied for desalination purpose. A complete theoretical model was developed with consideration of design and operating parameters that enabled a Cylindrical Air Gap Membrane Distillation (CAGMD) module specific performance analysis. Theoretical model was verified with the literature as well as with the experimental results carried out on a lab scale CAGMD module. The effect of support nets which supports the membrane on the air gap side is also discussed on the performance. Support nets made up of four different thermal conductivities material- copper, aluminum, brass and polypropylene (PP) are considered for this study. The effect of feed temperature and flow rate, air gap width, cold flow rate, effect of thermal conductivities of support nets and height of the module was studied on the performance of CAGMD module. Permeate flux, Specific Thermal Energy Consumption (STEC) and the Gained output ratio (GOR) was selected as the performance indicators and the results for all the resulted parameters obtained from experimental and theoretical model falls in good agreement with only 6% deviation, that suggests that the proposed model is best suitable for predicting the behavior of any cylindrical AGMD module with great effectiveness. It is suggested that for better performance of the system feed flow rate, temperature and cold flow rate should be maintained at higher level. Maximum permeate flux achieved from the CAGMD module is 9.22 kg/m2h.

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Due to their geometry and thermal physiology, hands are most vulnerable to cold weather injuries and loss of dexterity. Gloves are the most common for hand protection during exposure to extreme thermal and hazardous environments. Although glove microclimate properties such as area factor, air gap thickness, and contact area play a significant role in thermal protection, identifying local (at individual hand segments) glove microclimate properties is still a research gap. For the first time, the glove-microclimate properties for 16 hand segments at high spatial resolution were analyzed by employing state-of-the-art hand-held 3D scanner and post-processing techniques for different glove types. Our results clearly indicate that the glove area factor for distal phalanges is significantly higher (by 49.8 %) than that for other hand segments, which increases the heat transfer from distal phalanges. In contrast, average air gap thickness was relatively uniform across all hand segments. The glove type had a pronounced effect on glove microclimate properties, e.g., bulky and heavy cold weather protective gloves had a larger average air gap thickness and glove area factor. Regression models are also developed to estimate the glove microclimate properties from simple measurement (i.e., ease allowance). Overall, this study provides essential information for the design and development of protective gloves that can help improve safety, comfort, and dexterity. Methods and mathematical models developed in this study also contribute to facilitating extremity (e.g., hand) focused thermoregulation modeling, hazard simulation, injury prediction, ergonomic design, optimum performance (dexterity and tactility) along with thermal protection.

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Finned tubular air gap membrane distillation is a new membrane distillation method, and its functional performance, characterization parameters, finned tube structures, and other studies have clear academic and practical application value. Therefore, the tubular air gap membrane distillation experiment modules composed of PTFE membrane and finned tubes were constructed in this work, and three representative air gap structures, including tapered finned tube, flat finned tube, and expanded finned tube, were designed. Membrane distillation experiments were carried out in the form of water cooling and air cooling, and the influences of air gap structures, temperature, concentration, and flow rate on the transmembrane flux were analyzed. The good water-treatment ability of the finned tubular air gap membrane distillation model and the applicability of air cooling for the finned tubular air gap membrane distillation structure were verified. The membrane distillation test results show that with the tapered finned tubular air gap structure, the finned tubular air gap membrane distillation has the best performance. The maximum transmembrane flux of the finned tubular air gap membrane distillation could reach 16.3 kg/m2/h. Strengthening the convection heat transfer between air and fin tube could increase the transmembrane flux and improve the efficiency coefficient. The efficiency coefficient (σ) could reach 0.19 under the condition of air cooling. Compared with the conventional air gap membrane distillation configuration, air cooling configuration for air gap membrane distillation is an effective way to simplify the system design and offers a potential way for the practical applications of membrane distillation on an industrial scale.

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Major public institutions and organizations that handle sensitive data frequently enforce strong security policies by implementing network separation policies that segregates their internal work networks and internet network using air gaps to prevent the leakage of confidential information. Such closed networks have long been considered the most secure technique for protecting data; however, studies have shown that they are no longer effective in providing a safe data protection environment. Research on air-gap attacks remains in its infancy stage. Studies have been conducted to check the method and demonstrate the possibility of transmitting data using various transmission media available within the closed network. These transmission media include optical signals such as HDD LEDs, acoustic signals such as speakers, and the electrical signals of power lines. This paper examines various media used for air-gap attacks by analyzing different techniques and their essential functions, strengths, and limitations. The findings of this survey and the follow-up analysis aim to assist companies and organizations in protecting their information by providing an understanding of air-gap attacks and their current trends.

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The thermal protection performance of fire suit is vital to the safety of firefighters. Using certain physical properties of fabrics to evaluate their thermal protection performance speeds up the process. This work aims to develop a TPP value prediction model that can be easily applied. Five properties of three types of Aramid 1414 made of the same material were tested, and the relationships between the physical properties of Aramid 1414 and its thermal protection performance (TPP value) were investigated. The results showed that the TPP value of the fabric had a positive correlation with grammage and air gap, and a negative correlation with the underfill factor. A stepwise regression analysis was used to solve the collinearity issue between the independent variables. Finally, a model for predicting TPP value by air gap and underfill factor was developed. The method adopted in this work reduced the number of independent variables in the prediction model, which is conducive to the application of the model.

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Reconfigurable logic circuits implemented by two-dimensional (2D) ambipolar semiconductors provide a prospective solution for the post-Moore era. It is still a challenge for ambipolar nanomaterials to realize reconfigurable polarity control and rectification with a simplified device structure. Here, an air-gap barristor based on an asymmetric stacking sequence of the electrode contacts was developed to resolve these issues. For the 2D ambipolar channel of WSe2, the barristor can not only be reconfigured as an n- or p-type unipolar transistor but also work as a switchable diode. The air gap around the bottom electrode dominates the reconfigurable behaviors by widening the Schottky barrier here, thus blocking the injection of both electrons and holes. The electrical performances can be improved by optimizing the electrode materials, which achieve an on/off ratio of 104 for the transistor and a rectifying ratio of 105 for the diode. A complementary inverter and a switchable AND/OR logic gate were constructed by using the air-gap barristors as building blocks. This work provides an efficient approach with great potential for low-dimensional reconfigurable electronics.

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A novel design of an air gap membrane distillation (AGMD) module was proposed to enhance the permeate flux improvement for the desalination of pure water productivity. The modeling equations for predicting permeate flux in the AGMD module by inserting Λ-ribs carbon-fiber open slots under various hydrodynamic angles were developed theoretically and experimentally. The temperature distributions of both hot and cold feed streams were represented graphically with the hot saline flow rate, inlet saline temperature, and carbon-fiber hydrodynamic angles as parameters. The results showed a good agreement between the experimental results and theoretical predictions. Designed by inserting Λ-ribs carbon-fiber open slots into the flow channel, the membrane distillation module was implemented to act as an eddy promoter and yield an augmented turbulence flow. The effect of Λ-ribs carbon-fiber open slots not only assured the membrane stability by preventing vibration but also increased the permeate flux by diminishing the temperature polarization of the thermal boundary layer. The permeate flux improvement by inserting Λ-ribs carbon-fiber open slots in the AGMD module provided the maximum relative increment of up to 15.6% due to the diminution of the concentration polarization effect. The experimental data was incorporated with the hydrodynamic angle of Λ-ribs carbon-fiber open slots to correlate the enhancement factor with the Nusselt numbers to confirm the theoretical predictions. The accuracy derivation between the experimental results and theoretical predictions was pretty good, within 9.95≤E≤1.85. The effects of operating and designing parameters of hot saline flow rate, inlet saline temperature, and hydrodynamic angle on the permeate flux were also delineated by considering both the power consumption increment and permeate flux enhancement.

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Based on the wire-tube DBD reactor, this paper studied the effects of different discharge lengths, discharge air gaps, and electrical parameters on the discharge characteristics of the DBD discharge module. The results show that under the condition of increasing applied voltage, different discharge lengths, discharge air gaps, thicknesses of the insulating medium, and equivalent capacitance of insulating medium all show an increasing trend, while the equivalent capacitance of air-gap medium fluctuated within a certain range. When the discharge length was 30 cm, the discharge air gap was 2 mm, and the thickness of the insulating medium was 1 mm, the discharge effect was the best. In terms of electrical parameters, with the increase of the applied voltage, the "burr" of the current waveform increased, the load voltage and discharge power also increased, the discharge air gap voltage remained almost unchanged, and the equivalent capacitance value of the insulating medium continued to increase while the equivalent capacitance of the air gap medium remained almost unchanged. The optimized DBD discharge module was used for the treatment of exhaust gas containing H2S. The results show that when the gas flow rate was 80 L·h-1, the initial concentration was 50 mg·m-3, and the applied voltage was 65 V, the removal efficiency could reach 100% in 4 s. The energy efficiency analysis of the DBD discharge module shows that the energy efficiency of the discharge module varies by changing the different parameters; in the case of H2S degradation, the end products were mainly SO2 and SO3.

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An air gap is a technique that increases the security of information systems. The use of unconventional communication channels allows for obtaining communication that is of interest to the attacker as well as to cybersecurity engineers. One of the very dangerous forms of attack is the use of computer screen brightness modulation, which is not visible to the user but can be observed from a distance by the attacker. Once infected, the computer can transmit data over long distances. Even in the absence of direct screen visibility, transmission can be realized by analyzing the modulated reflection of the monitor's afterglow. The paper presents a new method for the automatic segmentation of video sequences to retrieve the transmitted data that does not have the drawbacks of the heretofore known method of growth (filling) based on an analysis of adjacent pixels. A fast camera operating at 380 fps was used for image acquisition. The method uses the characteristics of the amplitude spectrum for individual pixels, which is specific to the light sources in the room, and clustering with the k-means algorithm to group pixels into larger areas. Then, using the averaging of values for individual areas, it is possible to recover the 2-PAM (pulse-amplitude modulation) signal even at a 1000 times greater level of interference in the area to the transmitted signal, as shown in the experiments. The method does not require high-quality lenses.

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Both the physical properties of the fabric materials used in clothing and the effective design of the clothing, primarily in terms of the air gap thickness, restrict the transmission of the thermal energy from the heat source to the firefighter's body. The air gap distribution over the body in real deployment conditions of firefighters will vary, and is likely to be different from the air gap distribution in standardised manikin tests in standing upright posture. In this study, we investigated differences in the distribution of air layers in firefighters' clothing in three postures reflecting realistic on-duty exposure conditions (crawling, hose-holding, and standing upright used in laboratory tests) using 3D body scanning technology. The body posture induced substantial changes in the air gap thickness on the upper body (chest and back) and lower body. These changes were reflected in both the thermal and evaporative resistance of the ensemble, and consequently, in their potential thermal performance in the field. Therefore, it is recommended to consider body postures during the evaluation of clothing protective performance. Secondly, the knowledge of local clothing properties in real-life exposure provides a true protection mapping and gives design inputs to improve the local protective properties of firefighters' clothing.

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BACKGROUND: In Magnetic Resonance-Linac (MR-Linac) dosimetry formalisms, a new correction factor, kB,Q , has been introduced to account for corresponding changes to detector readings under the beam quality, Q, and the presence of magnetic field, B. PURPOSE: This study aims to develop and implement a Monte Carlo (MC)-based framework for the determination of kB,Q correction factors for a series of ionization chambers utilized for dosimetry protocols and dosimetric quality assurance checks in clinical 1.5 T MR-Linacs. Their dependencies on irradiation setup conditions are also investigated. Moreover, to evaluate the suitability of solid phantoms for dosimetry checks and end-to-end tests, changes to the detector readings due to the presence of small asymmetrical air gaps around the detector's tip are quantified. METHODS: Phase space files for three irradiation fields of the ELEKTA Unity 1.5 T/7 MV flattening-filter-free MR-Linac were provided by the manufacturer and used as source models throughout this study. Twelve ionization chambers (three farmer-type and nine small-cavity detectors, from three manufacturers) were modeled (including their dead volume) using the EGSnrc MC code package. kB,Q values were calculated for the 10 × 10 cm2 irradiation field and for four cardinal orientations of the detectors' axes with respect to the 1.5 T magnetic field. Potential dependencies of kB,Q values with respect to field size, depth, and phantom material were investigated by performing additional simulations. Changes to the detectors' readings due to the presence of small asymmetrical air gaps (0.1 up to 1 mm) around the chambers' sensitive volume in an RW3 solid phantom were quantified for three small-cavity chambers and two orientations. RESULTS: For both parallel (to the magnetic field) orientations, kB,Q values were found close to unity. The maximum correction needed was 1.1%. For each detector studied, the kB,Q values calculated for the two parallel orientations agreed within uncertainties. Larger corrections (up to 5%) were calculated when the detectors were oriented perpendicularly to the magnetic field. Results were compared with corresponding ones found in the literature, wherever available. No considerable dependence of kB,Q with respect to field size (down to 3 × 3 cm2 ), depth, or phantom material was noticed, for the detectors investigated. As compared to the perpendicular one, in the parallel to the magnetic field orientation, the air gap effect is minimized but is still considerable even for the smallest air gap considered (0.1 mm). CONCLUSION: For the 10 × 10 cm2 field, magnetic field correction factors for 12 ionization chambers and four orientations were determined. For each detector, the kB,Q value may be also applied for dosimetry procedures under different irradiation parameters provided that the orientation is taken into account. Moreover, if solid phantoms are used, even the smallest asymmetrical air gap may still bias small-cavity chamber response. This work substantially expands the availability and applicability of kB,Q correction factors that are detector- and orientation-specific, enabling more options in MR-Linac dosimetry checks, end-to-end tests, and quality assurance protocols.

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This paper presents a fast design optimization using an effective characteristic analysis for linear permanent magnet motors (LPMMs) with techniques for improving motor performance such as using an auxiliary tooth, permanent magnet (PM) skew, and overhang structures. These techniques have different effects on the characteristics of the LPMM depending on the combinations of each other, resulting in complexity in the design optimization process. In particular, the three-dimensional (3-D) effect of the PM skew and overhang structure takes a lot of time to be analyzed. To deal with this problem, an effective magnetic field analysis method and a novel optimization algorithm are proposed. Preferentially, the field reconstruction method is used for a fast and accurate evaluation of the magnetic field of the LPMM. In the proposed magnetic field analysis method, the change of magnetic field distribution due to the addition of an auxiliary tooth is predicted, and the 3-D magnetic field effect of PM skew and overhang structure is considered. By reducing the computational burden in the magnetic field analysis, the electromagnetic characteristics of LPMMs can be calculated quickly, such as detent force, end force, thrust force, and back-EMF. The effect of the auxiliary tooth and overhang structure on the optimal PM skew length is investigated with comparative study results. Subsequently, the proposed optimization algorithm has the advantage of reducing time cost by providing multimodal optimization and robustness evaluation of local peaks at the same time. The proposed method is verified via comparison with finite element analysis and experimental results.

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