Curvature Correction Method Research Articles

Riemannian geometric modeling of underwater acoustic ray propagation ·application——Riemannian geometric model of convergence zone in deep ocean remote sound propagation

Convergence-zone (CZ) sound propagation is one of the most important hydro-acoustic phenomena in the deep ocean, which allows the acoustic signals with high intensity and low distortion to realize the long-range transmission. Accurate prediction and identification of CZ is of great significance in implementing remote detection or communication, but there is still no standard definition in the sense of mathematical physics for convergence zone. Especially for the issue of systematic error of computation introduced by the earth curvature, there is no exact propagation model. The curvature-correction methods always lead to the imprecision of the ray phase. In previous research work, we realized that the Riemannian geometric meaning of the caustics phenomena caused by ray convergence is that the caustic points are equivalent to the conjugate points, which form on geodesics with positive section curvature. In this work, we present a spherical layered acoustic ray propagation model for CZ based on the Riemannian geometric theory. With direct computation in the curved manifolds of the earth , a Riemannian geometric description of CZ is provided for the first time, on the basis of comprehensive analysis about its characteristics. And it shows that the mathematical expression of section curvature adds an additional item <inline-formula><tex-math id="M1">\begin{document}${{\hat c(l){{\hat c}^\prime }(l)}}/{l}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221495_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20221495_M1.png"/></alternatives></inline-formula> after considering the earth curvature, which reflects the influence of the earth curvature on the ray topology and CZ. By means of Jacobi field theory of Riemannian geometry, computational rule and method of the location and distance of CZ in deep water are proposed. Taking the typical Munk sound velocity profile for example, the new Riemannian geometric model of CZ is compared with the normal mode and curvature-correction method. Simulation and analysis show that the Riemannian geometric model of CZ given in this paper is a mathematical form naturally considering the earth curvature with theoretical accuracy, which lays more solid scientific foundations for the study of convergence zone. Moreover, we find that the location of CZ moves towards sound source when the earth curvature is considered, and the width of CZ near the sea surface first increases and then decreases with sound propagation proceeding. The maximum width is about 20 km and the minimum is about 4 km.

Curvature Correction of a Notched Continuum Robot Based on a Static Model Considering Large Deformation and Friction Effect

Continuum robots are often used as wrist joints in medical robots because of their high dexterity and flexibility. Especially, the notched continuum robot (NCR) is used in the miniaturized wristed surgical robot. The Piecewise Constant Curvature (PCC) assumption is often used in the design of NCR. However, due to the friction effect, ideal PCC is difficult to achieve. Static analysis is a necessary means to correct the curvature of NCR. The static modeling of NCR is often based on the theory of small deformation. However, this cannot obtain accurate solutions at large bending angles. In this paper, a static model of a triangular-notched continuum robot is proposed. It presents a curvature correction method of NCR, considering large deformation. In addition, the friction effect is considered in the correction of PCC. The static model is derived from the end notch. Based on the Coulomb friction model, the recurrence relationship of the force on the cable is obtained. Then the elliptic integral solution corresponding to the large deformation assumption is calculated. The deformation parameters of the NCR are obtained by numerical iteration. Finally, the capability and validity of the static model proposed in this paper are verified in the experiment. This paper is of great significance for establishing an accurate static model for curvature correction and design of the notched continuum robot.

Highly Accurate, Fully Digital Temperature Sensor With Curvature Correction

In this paper, a highly accurate, fully digital temperature sensor with a curvature correction scheme is proposed. Conventional analog temperature sensors are complex and require a large area. Digital temperature sensors are simple with small area, but they have large inaccuracies due to process variations and curvature errors. In particular, curvature errors become more severe as the technology scales down. Thus, a highly accurate curvature correction method is proposed that can be used even in the latest technology nodes. The proposed curvature correction method achieves lower temperature errors with a smaller area than the conventional curvature correction method by using a simple correction. A temperature error that occurs up to 17 °C before the curvature correction is reduced to a range of −0.6 °C to +0.8 °C after the curvature correction. In addition, the measurement results indicate that the resolution is 0.09 °C /bit in the temperature range from 0 °C to 100 °C. The implementation in 14 nm technology node Xilinx ZCU102 field-programmable gate arrays proves that the proposed temperature sensor is very cost effective, while using only 85 slices. Compared with previous digital temperature sensors, the proposed temperature sensor achieves the smallest error and uses the smallest number of hardware resources while being implemented in a state-of-the-art technology node.

Investigation of flow separation in a centrifugal pump impeller based on improved delayed detached eddy simulation method

The mechanism of flow separation in the impeller of a centrifugal pump with a low specific speed was explored by experimental, numerical, and theoretical methods. A novel delayed Reynolds-averaged Navier–Stokes/large eddy simulation hybrid algorithm combined with a rotation and curvature correction method was developed to calculate the inner flow field of the original pump for the large friction loss in the centrifugal impeller, high adverse pressure gradient, and large blade curvature. Boundary vorticity flux theory was introduced for internal flow diagnosis, and the relative velocity vector near the surface of the blade and the distribution of the dimensionless pressure coefficient was analyzed. The validity of the numerical method was verified, and the location of the backflow area and its flow features were determined. Finally, based on flow diagnosis, the geometric parameters influencing the flow state of the impeller were specifically adjusted to obtain a new design impeller. The results showed that the distribution of the boundary vorticity flux peak values, the skin friction streamline, and near-wall relative velocities improved significantly after the design change. In addition, the flow separation was delayed, the force applied on the blade was improved, the head under the part-load condition was improved, and the hydraulic efficiency was improved over the global flow ranges. It was demonstrated that the delayed Reynolds-averaged Navier–Stokes/large eddy simulation hybrid algorithm was capable to capture the separation flow in a centrifugal pump, and the boundary vorticity flux theory was suitable for the internal flow diagnosis of centrifugal pump.

A Resistorless High-Precision Compensated CMOS Bandgap Voltage Reference

A resistorless high-precision compensated CMOS bandgap voltage reference (BGR), which is compatible with a standard CMOS process, is presented in this paper. A higher-order curvature correction method called base-emitter voltage linearization is adapted to directly compensate the thermal nonlinearity of base–emitter voltage. With proper mathematical operations of high-order temperature currents, most of the nonlinear temperature terms in $V_{\mathrm {BE}}$ can be greatly eliminated. The proposed BGR, which is implemented in 0.35- $\mu \text{m}$ CMOS technology, is capable of working down to 2 V supply voltages with 1.14055 V mean output voltage. A minimum temperature coefficient of 1.01 ppm/°C with a temperature range from −40 °C to 125 °C is realized, and a power-supply noise attenuation of 61 dB is achieved without any filter capacitors. The line regulation is better than 2 mV/V from 2 V to 5 V supply voltage while dissipating a maximum supply current of $33~\mu \text{A}$ . The active area of the presented BGR is 180 $\mu \text {m}\times 220\,\,\mu \text{m}$ .

Prediction of Flame Burning Velocity at Early Flame Development Time With High Exhaust Gas Recirculation and Spark Advance

Diluting spark-ignited (SI) stoichiometric combustion engines with excess residual gas improves thermal efficiency and allows the spark to be advanced toward maximum brake torque (MBT) timing. However, flame propagation rates decrease and misfires can occur at high exhaust gas recirculation (EGR) conditions and advanced spark, limiting the maximum level of charge dilution and its benefits. The misfire limits are often determined for a specific engine from extensive experiments covering a large range of speed, torque, and actuator settings. To extend the benefits of dilute combustion while at the misfire limit, it is essential to define a parameterizable, physics-based model capable of predicting the misfire limits, with cycle to cycle varied flame burning velocity as operating conditions change based on the driver demand. A cycle-averaged model is the first step in this process. The current work describes a model of cycle-averaged laminar flame burning velocity within the early flame development period of 0–3% mass fraction burned. A flame curvature correction method is used to account for both the effect of flame stretch and ignition characteristics, in a variable volume engine system. Comparison of the predicted and the measured flame velocity was performed using a spark plug with fiber optical access. The comparison at a small set of spark and EGR settings at fixed load and speed, shows an agreement within 30% of uncertainty, while 20% uncertainty equals ± one standard deviation over 2000 cycles.

Evaluation of accuracy of a novel elastic fusion algorithm — a prospective clinical study

Background: Although rigid fusion is generally accepted as gold-standard method, it often stands for time consuming and manual registration procedure. A novel elastic fusion algorithm is introduced to overcome these drawbacks. Objectives: To investigate image registration accuracy of bony structures and adjacent soft tissues provided by novel elastic fusion algorithm. Methods: Five patients (3 male, 2 female, mean of 57 years) with outboard obtained computed tomography (CT) imaging of the head and neck were included in the study. For each, a 3-Tesla (3 T) magnetic resonance imaging (MRI; Philips Healthcare, Best, The Netherlands) of the same region was conducted. The MRI protocol included three-dimensional (3D), axial and sagittal two-dimensional scans showing different contrasts and was repeated three times with the patient in neutral, flexed and rotated head position. To verify accuracy of novel spine curvature correction method (embedded in the ImageFusion Element, Brainlab AG, Feldkirchen, Germany), 80–120 bony landmarks were defined in the CT image, transferred via rigid fusion and used as starting value for elastic fusion algorithm. Finally, Euclidian distances between rigidly and elastically transferred landmarks were determined. Findings: Although the image data revealed strong translational and rotational displacements of vertebrae in both modalities (due to varying head positions), 95% of the landmarks showed an error below 3 mm. However, using 3D MRI data provides highest registration accuracy and co-registration of axial MRI acquisitions is superior than compared to sagittal MR images. Conclusion: Generally, it can be stated that elastic fusion provides high MR-to-CT image registration accuracy and represents a considerable step towards soft tissue registration and navigation.

A curvature correction turbulent model for computations of cloud cavitating flows

Purpose– The purpose of this paper is to assess the predictive capability of the streamline curvature correction model (CCM) and investigate the unsteady vortex behavior of the cloud cavitating flows around a hydrofoil.Design/methodology/approach– The design of the paper is based on introducing the curvature correction method to the originalk-εmodel. Calculations of unsteady cloud cavitating flows around a Clark-Y hydrofoil are performed using both the CCM and the baseline model.Findings– Compared with the baseline model, better agreements are observed between the predictions of the CCM model and experimental data, especially the cavity shedding process. Based on the computations, it is demonstrated that streamline curvature correction of the CCM model can effectively decrease predicted turbulence kinetic energy and eddy viscosity in cavity shedding region. This leads to the better prediction for the recirculation zone located downstream of the attached cavity, and dynamics of this recirculation zone contribute to the formation and development of the re-entrant jet.Originality/value– The authors apply streamline curvature correction to the calculations of unsteady cloud cavitating flows and discuss the interactions between the cavitation unsteadiness and vortex structures to get an insight of the correction mechanics.

Field curvature correction method for ultrashort throw ratio projection optics design using an odd polynomial mirror surface.

This paper presents a field curvature correction method of designing an ultrashort throw ratio (TR) projection lens for an imaging system. The projection lens is composed of several refractive optical elements and an odd polynomial mirror surface. A curved image is formed in a direction away from the odd polynomial mirror surface by the refractive optical elements from the image formed on the digital micromirror device (DMD) panel, and the curved image formed is its virtual image. Then the odd polynomial mirror surface enlarges the curved image and a plane image is formed on the screen. Based on the relationship between the chief ray from the exit pupil of each field of view (FOV) and the corresponding predescribed position on the screen, the initial profile of the freeform mirror surface is calculated by using segments of the hyperbolic according to the laws of reflection. For further optimization, the value of the high-order odd polynomial surface is used to express the freeform mirror surface through a least-squares fitting method. As an example, an ultrashort TR projection lens that realizes projection onto a large 50 in. screen at a distance of only 510 mm is presented. The optical performance for the designed projection lens is analyzed by ray tracing method. Results show that an ultrashort TR projection lens modulation transfer function of over 60% at 0.5 cycles/mm for all optimization fields is achievable with f-number of 2.0, 126° full FOV, <1% distortion, and 0.46 TR. Moreover, in comparing the proposed projection lens' optical specifications to that of traditional projection lenses, aspheric mirror projection lenses, and conventional short TR projection lenses, results indicate that this projection lens has the advantages of ultrashort TR, low f-number, wide full FOV, and small distortion.

A High-Precision Compensated CMOS Bandgap Voltage Reference Without Resistors

A high-precision compensated CMOS bandgap reference without resistors, which is fabricated in 0.5- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula> CMOS technology, is presented in this brief. The circuit uses ratioed transistors together with the inverse-function technique to produce a first-order temperature-insensitive voltage reference. More importantly, a higher-order curvature correction method called <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$V_{BE}$</tex></formula> linearization is presented to directly compensate for the thermal nonlinearity of the base–emitter voltage. The power consumption of the proposed reference is 0.648 mW at 3.6 V. A temperature coefficient of 11.8 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\hbox{ppm}/^{\circ}\hbox{C}$</tex> </formula> and power supply rejection ratio (PSRR) of more than 31 dB at low frequencies are easily achieved.

Direct curvature correction for noncontact imaging modalities applied to multispectral imaging

Noncontact optical imaging of curved objects can result in strong artifacts due to the object's shape, leading to curvature biased intensity distributions. This artifact can mask variations due to the object's optical properties, and makes reconstruction of optical/physiological properties difficult. In this work we demonstrate a curvature correction method that removes this artifact and recovers the underlying data, without the necessity of measuring the object's shape. This method is applicable to many optical imaging modalities that suffer from shape-based intensity biases. By separating the spatially varying data (e.g., physiological changes) from the background signal (dc component), we show that the curvature can be extracted by either averaging or fitting the rows and columns of the images. Numerical simulations show that our method is equivalent to directly removing the curvature, when the object's shape is known, and accurately recovers the underlying data. Experiments on phantoms validate the numerical results and show that for a given image with 16.5% error due to curvature, the method reduces that error to 1.2%. Finally, diffuse multispectral images are acquired on forearms in vivo. We demonstrate the enhancement in image quality on intensity images, and consequently on reconstruction results of blood volume and oxygenation distributions.

Low cost curvature correction of bandgap references for integrated sensors

Due to increasing demands on the accuracy of integrated sensors, it is very important to improve the accuracy of bandgap voltage references. Since the second order non linearity of the function V BE( T) is generally the main limit to the accuracy of calibrated bandgap voltage references, several methods for the curvature-correction of V BE( T) have been reported in literature; unfortunately these methods require quite complex circuitry. In this paper we investigate a low cost curvature correction method, consisting in taking advantage of the temperature dependence of integrated resistors and in using PTAT/ R collector currents; furthermore we introduce two new circuit topologies which permit to take full advantage of this approach in spite of technological limitations.

Series Resistance Compensation in PTAT Temperature Sensors and Bandgap Reference Circuits

A general compensation technique for the extrinsic series resistor in the pn diode has been proposed in this paper. Proportional-to-absolute-temperature (PTAT) temperature sensors and bandgap reference circuits using diodes have been also proposed. In the design of bandgap reference circuits, the most common method used to produce an output voltage that is independent of temperature variations is the curvature correction method. The series resistance compensation technique represents part of this curvature. Several designs of PTAT temperature and bandgap circuits have been proposed in this work. For illustration, the PTAT sensor and bandgap circuits are numerically simulated, using the proposed algorithm.