Mirror Method Research Articles

Analytical Model of Magnetic Field Generated by Racetrack Superconducting Excitation Winding Within Cylindrical Ferromagnetic Boundary Based on Mirror Method

Analytical Model of Magnetic Field Generated by Racetrack Superconducting Excitation Winding Within Cylindrical Ferromagnetic Boundary Based on Mirror Method

A Study of High Transient Response Low Dropout Linear Regulator Chips

Abstract. With the rapid development of the microelectronics industry in the world, electronic products are being updated more and more quickly. This has created a growing large market demand for power management chips. Low drop-out linear regulators have become one of the most widely used types of power management chips due to their advantages of high stability, low drop-out voltage, and fast response. This paper is a data collection study and comparison of improvement methods based on high transient response low drop-out linear regulators. It describes the basic principles of LDOs as well as the principles, advantages and disadvantages of different improvement methods. It was found that the method of shortening the overshoot and undershoot durations by constructing transient enhancement circuits was the best in terms of performance among the following research methods. The stability of capacitor-less LDO is harder to control. Using compensation circuits to improve stability will increase circuit complexity. The capacitor-coupled current mirror method has a longer startup time, because it takes some time for it to reach homeostasis. The high complexity and energy consumption of the dual feedback loop structure makes the circuit costly.

Virtual surgical planning in tripod zygomatico-maxillary complex fractures: A prospective comparison between two different strategies

Multifragmentary and displaced zygomaticomaxillary complex (ZMC) fractures are often a challenge for the maxillofacial surgeon. The aim of this study was to evaluate the improved performance in the management of patients with tripod fracture of the orbito-zygomaticomaxillary complex, using two different methods of virtual surgical planning — virtual reduction and mirroring — compared with traditional management. A cohort of 60 patients was selected and divided into three groups, each consisting of 20 individuals. Patients in the first group were managed using the virtual reduction method, those in the second group using the mirroring method, and those in the third group using a traditional surgical approach. Having achieved virtual fracture reduction, a stereolithographic model was printed, on which preplating of the plates was performed. The results showed that virtual reduction was the most accurate in absolute terms, with a mean discrepancy in juxtaposition of the preoperative and postoperative CT images of 0.175 mm (SD ± 0.147), compared with 0.403 (SD ± 0.166) for the mirror method (and traditional method (0.875, SD ± 0.112; p > 0.0001). The average surgical time for virtual reduction (89.5 min) was faster than for mirroring (94.25 min) and for the traditional approach (96.75 min). In conclusion, the use of virtual surgical planning allows greater intraoperative accuracy, reduced surgical time, and reduced postoperative complications compared with traditional surgery. Of the two methods, virtual reduction performed best for the outcomes decribed.

Universal methods for variational inequalities: Deterministic and stochastic cases

In this paper, we propose universal proximal mirror methods to solve the variational inequality problem with Hölder-continuous operators in both deterministic and stochastic settings. The proposed methods automatically adapt not only to the oracle’s noise (in the stochastic setting of the problem) but also to the Hölder continuity of the operator without having prior knowledge of either the problem class or the nature of the operator information. We analyzed the proposed algorithms in both deterministic and stochastic settings and obtained estimates for the required number of iterations to achieve a given quality of a solution to the variational inequality. We showed that, without knowing the Hölder exponent and Hölder constant of the operators, the proposed algorithms have the least possible in the worst-case sense complexity for the considered class of variational inequalities. We also compared the resulting stochastic algorithm with other popular optimizers for the task of image classification.

Mathematical modelling for strata deformation caused by rectangular pipe jacking construction in composite layered ground

In this study, analytical solutions of vertical deformation of ground surface and horizontal displacement of strata are derived combining the Mindlin solution and the mirror method due to rectangular pipe jacking tunneling in composite strata, which considers the combined effect of five factors of additional excavation pressure, friction of rectangular pipe jacking and soils, segment-soil friction, grouting filling and strata loss, respectively. The theoretical calculation results were verified against the measured data in two project cases. Moreover, effect factors of rectangular jacking pipe cross-sectional dimensions, embedment of tunnel axial depth, elasticity modulus on the interlayer and the Poisson's ratio of the interlayer on strata deformation is investigated. The results imply that the theoretical calculation values obtained using this method are more closely correlated with the observed values compared to those computed using the single stratum model. The primary cause of terrene upheaval in front of the working surface is the increased excavation pressure on the working face and the horizontal displacement of the deep soils and the surface subsidence behind the excavation face is resulting from the soil loss as the main influencing factor. The varying cross-section size of pipe jacking is able to impact on the vertical deformation of the soil, but it has a limited impact on the lateral displacement of the strata. The affection of the buried depth of the tunnel axis on strata deformation is more notable in the rectangular pipe jacking construction. As the axial tunnel depth growth, the ground surface maximum subsidence value gradually decreases, while the crest value of horizontal distortion mildly increases. When the rise of the interlayered modulus of elasticity, the maximum earth surface subsidence enlarged gradually while the subsidence trough slight diminution. Moreover, the greatest horizontal displacement exhibits a relatively minor fluctuation, but there is a trend of upward movement in the position. The influence of Poisson's ratio of the interlayer on the strata deformation is comparatively weak.

Response of semicircular canyons and movable cylindrical cavities to SH waves in anisotropic half-space geology

The development of tunnels or the laying of underground pipelines are essential engineering projects in modern society, and in canyon tunnels and underground pipeline projects, the surface motion and cavity edge motion have been topics of concern in ground vibration problems. We investigate the wave scattering problem in an elastic half-space anisotropic medium containing a semicircular canyon and a subsurface movable cylindrical cavity by using the wave function expansion method, the complex function method, and the mirror method. By deriving the governing equation and transforming it into the standard form of the Helmholtz equation satisfying the zero-stress boundary condition, we solve the corresponding displacement functions. Introducing a position correction coefficient, the scattered wavefield in a half-space anisotropic medium is constructed by the mirror method, which improves the problem of scattered wave source singularity in anisotropic half-space media. Then, combining the free boundary conditions with a Fourier series expansion method, we solve the unknown coefficients in the equations. The correctness of the method is verified by degenerating it to a classical analytic solution. Finally, using frequency- and time-domain analysis, we investigate the effects of the relevant parameters on the surface motion [Formula: see text], the dynamic stress concentration factor, and the displacement amplitude [Formula: see text]. The results indicate that rock anisotropy and the presence of semicircular canyons have a significant effect on the dynamic response of subsurface structures. This not only provides a theoretical basis for practical unlined tunnels or pipeline projects but also can provide a basis for seismic design of underground structures.

An Underwater Passive Electric Field Positioning Method Based on Scalar Potential

In order to fulfill the practical application demands of precisely localizing underwater vehicles using passive electric field localization technology, we propose a scalar-potential-based method for the passive electric field localization of underwater vehicles. This method is grounded on an intelligent differential evolution algorithm and is particularly suited for use in three-layer and stratified oceanic environments. Firstly, based on the potential distribution law of constant current elements in a three-layer parallel stratified ocean environment, the mathematical positioning model is established using the mirror method. Secondly, the differential evolution (DE) algorithm is enhanced with a parameter-adaptive strategy and a boundary mutation processing mechanism to optimize the key objective function in the positioning problem. Additionally, the simulation experiments of the current element in the layered model prove the effectiveness of the proposed positioning method and show that it has no special requirements for the sensor measurement array, but the large range and moderate number of sensors are beneficial to improve the positioning effect. Finally, the laboratory experiments on the positioning method proposed in this paper, involving underwater simulated current elements and underwater vehicle tracks, were carried out successfully. The results indicate that the positioning method proposed in this paper can achieve the performance requirements of independent initial value, strong anti-noise capabilities, rapid positioning speed, easy implementation, and suitability in shallow sea environments. These findings suggest a promising practical application potential for the proposed method.

Systematic error calibration of vertical dynamic interferometer with sloshing liquid plane.

Liquid mirror can calibrate the interferometer system error by measuring the surface of a steady-state, high-viscosity liquid; however, strict environmental safeguards are typically required. To address this problem, we propose a new liquid mirror method based on liquid micro-amplitude sloshing to calibrate dynamic interferometer system error. According to the multimodal analysis method of fluid finite amplitude sloshing, the liquid surface sloshing surface was modeled and analyzed, a time dimensional mean model was established, and the minimum sampling time was calculated. Finally, the error of the liquid surface sloshing was reduced by time averaging to realize the absolute calibration of the dynamic interferometer's systematic error. According to the proposed minimum sampling time theory, when the mean processing time is greater than the minimum sampling time, the error in the sloshing liquid surface can be controlled to within λ/100. The method's correctness is proven through an experimental comparison of different calibration methods.

Approaches to Measuring Language Lateralisation: An Exploratory Study Comparing Two fMRI Methods and Functional Transcranial Doppler Ultrasound.

In this exploratory study we compare and contrast two methods for deriving a laterality index (LI) from functional magnetic resonance imaging (fMRI) data: the weighted bootstrapped mean from the LI Toolbox (toolbox method), and a novel method that uses subtraction of activations from homologous regions in left and right hemispheres to give an array of difference scores (mirror method). Data came from 31 individuals who had been selected to include a high proportion of people with atypical laterality when tested with functional transcranial Doppler ultrasound (fTCD). On two tasks, word generation and semantic matching, the mirror method generally gave better agreement with fTCD laterality than the toolbox method, both for individual regions of interest, and for a large region corresponding to the middle cerebral artery. LI estimates from this method had much smaller confidence intervals (CIs) than those from the toolbox method; with the mirror method, most participants were reliably lateralised to left or right, whereas with the toolbox method, a higher proportion were categorised as bilateral (i.e., the CI for the LI spanned zero). Reasons for discrepancies between fMRI methods are discussed: one issue is that the toolbox method averages the LI across a wide range of thresholds. Furthermore, examination of task-related t-statistic maps from the two hemispheres showed that language lateralisation is evident in regions characterised by deactivation, and so key information may be lost by ignoring voxel activations below zero, as is done with conventional estimates of the LI.

Surround Sensing Technique for Trucks Based on Multi-Features and Improved Yolov5 Algorithm.

The traditional rearview mirror method cannot fully guarantee safety when driving trucks. RGB and infrared images collected by cameras are used for registration and recognition, so as to achieve the perception of surroundings and ensure safe driving. The traditional scale-invariant feature transform (SIFT) algorithm has a mismatching rate, and the YOLO algorithm has an optimization space in feature extraction. To address these issues, this paper proposes a truck surround sensing technique based on multi-features and an improved YOLOv5 algorithm. Firstly, the edge corner points and infrared features of the preset target region are extracted, and then a feature point set containing the improved SIFT algorithm is generated for registration. Finally, the YOLOv5 algorithm is improved by fusing infrared features and introducing a composite prediction mechanism at the prediction end. The simulation results show that, on average, the image stitching accuracy is improved by 17%, the time is reduced by 89%, and the target recognition accuracy is improved by 2.86%. The experimental results show that this method can effectively perceive the surroundings of trucks, accurately identify targets, and reduce the missed alarm rate and false alarm rate.

Dynamic response of semi-cylindrical depression, cylindrical cavity and type-III crack to SH wave in half-space anisotropic media

In this study, the anti-plane dynamic response of an elastic half-space anisotropic medium containing surface semi-cylindrical depressions and internal cylindrical cavity and type-III crack is solved analytically. The wave function expansion method, the complex function method and the Green's function method can be used to effectively construct the free wave field equation and the scattered wave field equation in the case of SH wave incidence, in which the scattered wave field generated by the crack is constructed by the Green's function method and the "crack cut" method. For the scattered wave field generated by a circular cavity is constructed using the mirror method, where the positional offset coefficient in the mirror method of a half-space anisotropic medium is introduced, which well solves the problem of the asymmetry of the scattered wave field. Finally, the effects of anisotropic strength of the medium, SH wave incidence angle and dimensionless incident wave number on the surface displacement amplitude (|W|), dynamic stress concentration factor (DSCF) at the boundary of the circular cavity and dynamic stress intensity factor (DSIF) at the crack tip are investigated in both frequency and time domains under different working conditions, and conclusions different from those of isotropic medium are obtained, which provide some theoretical references for the earthquake-resistant design of the underground structure with canyon topography and the surface building.

Dynamic anti-planar characteristics of circular holes in laminated structures under the action of line source

Based on the complex variable function method and the wave function expansion method, the dynamic anti-plane characteristics of the circular hole in the laminated structure under line source excitation were studied. To deal with the interface problem within the laminated structure, the idea of “fit” is adopted to construct continuity conditions that satisfy displacement and stress. The circular hole boundary stress-free condition is used, the wave field is constructed using the mirror method, and the unknown coefficients of the scattered wave field are solved through Fourier series expansion, and finally the total wave field in the laminated structure is obtained. Taking the dynamic stress distribution of a circular hole in a laminated structure as a specific calculation example, the effects of changes in line source position, layer thickness, and medium hard-soft ratio on the dynamic stress concentration coefficient around the circular hole are discussed. The results show that when the line source load is applied directly above the circular hole and the lower layer is narrow, the dynamic stress concentration coefficient will have a sudden change compared with other situations. When other conditions are the same, under low, medium, and high-frequency wave fields, the dynamic stress concentration caused by different soft-to-hard ratios shows completely different rules. These rules can be used to better detect defects in laminated structures.

Validation of the dew point chilled mirror method for the measurement of water activity on solid pharmaceutical products, testing the effect of different temperatures, sample preparations, and environment exposure times

AbstractObjectiveThe objective of this investigation is to validate the dew point chilled mirror method for quantifying water activity in tablets and capsules, evaluating the effects of different temperatures, sample preparations, and local environmental exposure times.Key findingsThe validation of an acute and precise water activity measurement method has become an important goal in the pharmaceutical industry, because it may help to predict the microbiological bioburden on solid products, since most xerophilic and osmophilic microorganisms are unable to grow at water activity levels below 0.60, to safely reduce the frequency of routine microbiological analysis using conventional methods. For all the solid samples tested, a suitability of method was carried out, considering the sample preparation, environmental exposure times, and different measuring temperatures. Following USP guidelines, essential parameters such as precision (SD < 0.5), accuracy (% recovery in the 95%–105% range), linearity (R2 > 0.99), ruggedness (ANOVA, P < .05), robustness, operative range (aw 0.17–1), limits of detection (aw = 0.17), and limit of quantification (aw = 0.25) were met by the dew point methodology.ConclusionThe dew point chilled mirror method was proven to yield accurate, precise, and robust data, making it an outstanding methodology to be implemented in the pharmaceutical industry for measuring the water activity status in tablets and capsules as a direct assessment of the microbial burden.

Effect of Shock-Wave-Mediated Collapse on Nanobubble Characteristics.

To enhance the comprehension of the cavitation mechanism and explore its practical use in industrial production, this study developed models involving oxygen, varying bubble radii, and bubble quantities. This study uses molecular dynamics simulations coupled with the momentum mirror method to examine the collapse characteristics of bubbles during ultrasonic cavitation. The investigation uncovers patterns in the fluctuation of the maximum local density of water molecules, released pressure, and temperature. The findings demonstrate that, when oxygen-containing bubbles collapse at identical radii, the local density is notably higher and diminishes more rapidly. Moreover, the changes in the shape exhibit greater regularity. During the bubble collapse, a depression forms on the bubble's surface, coinciding with a notable surge in local density around the depression. As bubble radii and quantities increase, so does the local density along with a concurrent rise in the maximum pressure. Intriguingly, the model demonstrates the lowest pressure at Z = 35 Å accompanied by the emergence of a small crescent-shaped region with a reduced density. Throughout the pressure ascension phase, the rate of the maximum pressure change escalates with an increase in the number of bubbles. Conversely, during the pressure descent phase, the rate of the maximum pressure change diminishes with a growing number of bubbles. However, it is important to note that the maximum pressure does not exhibit a direct correlation with the number of bubbles. Ultimately, this study provides valuable technical guidance and a theoretical foundation for the integration of ultrasonic cavitation in industrial production processes.

Tunnel Geohazard Evaluation Using Improved Seismic Time-Reversal Mirror

Tunnel geohazard evaluation method is an important method for evaluating the geo-hazard during tunnel construction. The seismic method has become the most widely used approach for understanding the geological conditions ahead of the tunnel face. Limited by the small aperture in the tunnel and the little offset of the observation system, migration methods for imaging geological structures are mainly based on Ray theory without using the dynamic information of reflected waves, resulting in less accurate imaging results. To improve the detection accuracy, the time reversal mirror method was studied and improved for better imaging geological conditions ahead of the tunnel face. Specifically, for the positioning error caused by the traditional time reversal mirror method (based on constant velocity), the parameter of variable velocity was added and optimized for the calculation process. By calculating each velocity value in different propagation paths, the reflected waves can focus on the scattering point with a more accurate location. Based on several typical adverse geology numerical simulations proved that the improved time reverse mirror method can get more accurate imaging results than the traditional method, achieving the position and imaging of fault, fractured zone, etc. Then the improved method has been applied in a water supply project and successfully predicted the distribution of adverse geologies ahead of the tunnel face, which further verified the applicability and effectiveness of the improved time reversal mirror method. This paper provides reference and guidance for similar water diversion projects and tunnel engineering geological detection.

Impact of electrode orientation, myocardial wall thickness, and myofiber direction on intracardiac electrograms: numerical modeling and analytical solutions.

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/R 2 (bipolar and parallel), and 1/R 3 (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.

Hybrid optimal design method for magnetic field coils under magnetic shielding boundary

A novel strategy for designing uniform magnetic field and gradient magnetic field coils considering the boundary effect of magnetic shielding is proposed in this study. This strategy uses intelligent optimization algorithm to skillfully transform the complex coil design problem into the spatial optimization problem of individual population. The mirror method is combined with Green’s function to accurately calculate the magnetic field, and the target field method (TFM) is combined with the whale optimization algorithm to optimize the stream functions using adaptive ridge regression. The minimum fitness function is defined as the real-time magnetic field relative error, and the optimal ridge coefficient is continuously obtained by determining the current density coefficient. The proposed method significantly reduces the magnetic field deviation in the target area compared to the conventional TFM, with reductions ranging from 12.2% to 0.11% (Bx coil), 0.3% to 0.02% (Bz coil), 20% to 10% (dBx/dz coil) and 2.9% to 2.4% (dBz/dz coil). The strategy has been effectively validated by analytical simulations and experimental results, and is expected to be applied to the design of uniform field coils and gradient coils for ultra-high precision atomic sensors.

Anti-plane dynamics of right-angle rare earth giant magnetostrictive medium with cylindrical conducting inclusion

In this paper, the anti-plane dynamics of rare earth giant magnetostrictive material with a cylindrical magnetically conducting inclusion in right-angle domain under the incidence of SH waves are studied. The governing equation and constitutive equation of magneto-elastic coupling are established. The outward scattered wave and internal standing wave caused by the inclusion are given by combining the complex function method, the wave function expansion method and mirror method. At the same time, the magnetic potential caused by wave is given by solving the Laplace equation. On the basis of boundary conditions, the Fourier series expansion method and effective truncated series are introduced to establish and solve infinite linear algebraic integral equations. Finally, based on numerical calculation, the analysis of dynamic stress concentration factor and magnetic field intensity concentration factor under different parameter combinations is given. The purpose of this paper is to provide an effective analytical method for the research of fracture dynamics of giant magnetostrictive materials under multi-magnetic field coupling.

Fuzzy response to SH guided-wave scattering by semicircular depressions on the boundary of a ribbon-shaped elastic plate

In this paper, the fuzzy scattering problem with semicircular depressions on the boundary of a band-shaped elastic plate with steady SH guided wave incident is studied and an analytical solution is given. First, the SH guided wave is constructed by the guided wave expansion method, and then the scattered wave satisfying the free condition of the boundary stress of the strip domain is constructed by the cumulative mirror method. Finally, a definite solution equation is obtained based on the fact that the shear stress at the edge of the semi-circular recessed hole is zero. In this paper, the ambiguity of the number of waves and the width of the bands is taken into account. In order to avoid the irreversibility of interval algorithm and the difficulty of solving non-linear equations, the membership function of fuzzy quantity is segmented to make the membership degree and fuzzy quantity correspond respectively. A deterministic problem that translates into piecewise processing. Two numerical examples are given to examine the changes in fuzzy response of different numbers of fuzzy waves and fuzzy thicknesses to the dynamic stress concentration factor of the hoop at the collapse limit.

The systematic comparison between Gaussian mirror and Model-X knockoff models

While the high-dimensional biological data have provided unprecedented data resources for the identification of biomarkers, consensus is still lacking on how to best analyze them. The recently developed Gaussian mirror (GM) and Model-X (MX) knockoff-based methods have much related model assumptions, which makes them appealing for the detection of new biomarkers. However, there are no guidelines for their practical use. In this research, we systematically compared the performance of MX-based and GM methods, where the impacts of the distribution of explanatory variables, their relatedness and the signal-to-noise ratio were evaluated. MX with knockoff generated using the second-order approximates (MX-SO) has the best performance as compared to other MX-based methods. MX-SO and GM have similar levels of power and computational speed under most of the simulations, but GM is more robust in the control of false discovery rate (FDR). In particular, MX-SO can only control the FDR well when there are weak correlations among explanatory variables and the sample size is at least moderate. On the contrary, GM can have the desired FDR as long as explanatory variables are not highly correlated. We further used GM and MX-based methods to detect biomarkers that are associated with the Alzheimer’s disease-related PET-imaging trait and the Parkinson’s disease-related T-tau of cerebrospinal fluid. We found that MX-based and GM methods are both powerful for the analysis of big biological data. Although genes selected from MX-based methods are more similar as compared to those from the GM method, both MX-based and GM methods can identify the well-known disease-associated genes for each disease. While MX-based methods can have a slightly higher power than that of the GM method, it is less robust, especially for data with small sample sizes, unknown distributions, and high correlations.