Error Analysis of A New Higher Order Boundary Element Method for A Uniform Flow Passing Cylinders

A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.

Error reachable set based stabilization of switched linear systems with bounded peak disturbances

This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results.

Geometric Error Identification of Gantry-Type CNC Machine Tool Based on Multi-Station Synchronization Laser Tracers

Laser tracers are a three-dimensional coordinate measurement system that are widely used in industrial measurement.We propose a geometric error identification method based on multi-station synchronization laser tracers to enable the rapid and high-precision measurement of geometric errors for gantry-type computer numerical control(CNC)machine tools.This method also improves on the existing measurement efficiency issues in the single-base station measurement method and multi-base station time-sharing measurement method.We consider a three-axis gantry-type CNC machine tool,and the geometric error mathematical model is derived and established based on the combination of screw theory and a topological analysis of the machine kinematic chain.The four-station laser tracers position and measurement points are realized based on the multi-point positioning principle.A self-calibration algorithm is proposed for the coordinate calibration process of a laser tracer using the Levenberg-Marquardt nonlinear least squares method,and the geometric error is solved using Taylor’s first-order linearization iteration.The experimental results show that the geometric error calculated based on this modeling method is comparable to the results from the Etalon laser tracer.For a volume of 800 mm×1000 mm×350 mm,the maximum differences of the linear,angular,and spatial position errors were 2.0μm,2.7μrad,and 12.0μm,respectively,which verifies the accuracy of the proposed algorithm.This research proposes a modeling method for the precise measurement of errors in machine tools,and the applied nature of this study also makes it relevant both to researchers and those in the industrial sector.

Bayesian Filtering for High-Dimensional State-Space Models With State Partition and Error Compensation

In the era of exponential growth of data availability,the architecture of systems has a trend toward high dimensionality,and directly exploiting holistic information for state inference is not always computationally affordable.This paper proposes a novel Bayesian filtering algorithm that considers algorithmic computational cost and estimation accuracy for high-dimensional linear systems.The high-dimensional state vector is divided into several blocks to save computation resources by avoiding the calculation of error covariance with immense dimensions.After that,two sequential states are estimated simultaneously by introducing an auxiliary variable in the new probability space,mitigating the performance degradation caused by state segmentation.Moreover,the computational cost and error covariance of the proposed algorithm are analyzed analytically to show its distinct features compared with several existing methods.Simulation results illustrate that the proposed Bayesian filtering can maintain a higher estimation accuracy with reasonable computational cost when applied to high-dimensional linear systems.

A Combined Antenna Array Deployment with High Positioning Accuracy and Low Angular Measurement Error

In this paper,an antenna array composed of circular array and orthogonal linear array is proposed by using the design of long and short baseline“orthogonal linear array”and the circular array ambiguity resolution design of multi-group baseline clustering.The effectiveness of the antenna array in this paper is verified by sufficient simulation and experiment.After the system deviation correction work,it is found that in the L/S/C/X frequency bands,the ambiguity resolution probability is high,and the phase difference system error between each channel is basically the same.The angle measurement error is less than 0.5°,and the positioning error is less than 2.5 km.Notably,as the center frequency increases,calibration consistency improves,and the calibration frequency points become applicable over a wider frequency range.At a center frequency of 11.5 GHz,the calibration frequency point bandwidth extends to 1200 MHz.This combined antenna array deployment holds significant promise for a wide range of applications in contemporary wireless communication systems.

Chiral bound states in a staggered array of coupled resonators

We study the chiral bound states in a coupled-resonator array with staggered hopping strengths,which interacts with a two-level small atom through a single coupling point or two adjacent ones.In addition to the two typical bound states found above and below the energy bands,this system presents an extraordinary chiral bound state located within the energy gap.We use the chirality to quantify the breaking of the mirror symmetry.We find that the chirality value undergoes continuous changes by tuning the coupling strengths.The preferred direction of the chirality is controlled not only by the competition between the intracell and the intercell hoppings in the coupled-resonator array,but also by the coherence between the two coupling points.In the case with one coupling point,the chirality values varies monotonously with difference between the intracell hopping and the intercell hoppings.While in the case with two coupling points,due to the coherence between the two coupling points the perfect chiral states can be obtained.

Theoretical investigation of excited dipole bound states of alkali-containing diatomic anions

Information about electronic excited states of molecular anions plays an important role in investigating electron attachment and detachment processes.Here we present a high-level theoretical study of the electronic structures of 12 alkali-metal-containing diatomic anions MX-(MX = LiH,LiF,LiCl,NaF,NaCl,NaBr,RbCl,KCl,KBr,RbI,KI and CsI).The equation-of-motion electron-attachment coupled-cluster singles and doubles(EOM-EA-CCSD) method is used to calculate the electron binding energies(EBEs) of 10 electronic excited states of each of the 12 molecule anions.With addition of different s-/p-/d-type diffusion functions in the basis set,we have identified possible excited dipole bound states(DBSs) of each anion.With the investigation of EBEs on the 12 MXs with dipole moment(DM) up to 12.1 D,we evaluate the dependence of the number of anionic excited DBSs on molecular DM.The results indicate that there are at least two or three DBSs of anions with a molecular DM larger than 7 D and a molecule with DM > 10 D can sustain a π-DBS of the anion.Our study has some implications for the excited DBS electronic states of alkali-metal-containing diatomic molecules.

Comparison of the Minimum Bounding Rectangle and Minimum Circumscribed Ellipse of Rain Cells from TRMM

Based on the TRMM dataset, this paper compares the applicability of the improved MCE(minimum circumscribed ellipse), MBR(minimum bounding rectangle), and DIA(direct indexing area) methods for rain cell fitting. These three methods can reflect the geometric characteristics of clouds and apply geometric parameters to estimate the real dimensions of rain cells. The MCE method shows a major advantage in identifying the circumference of rain cells. The circumference of rain cells identified by MCE in most samples is smaller than that identified by DIA and MBR, and more similar to the observed rain cells. The area of rain cells identified by MBR is relatively robust. For rain cells composed of many pixels(N> 20), the overall performance is better than that of MCE, but the contribution of MBR to the best identification results,which have the shortest circumference and the smallest area, is less than that of MCE. The DIA method is best suited to small rain cells with a circumference of less than 100 km and an area of less than 120 km^(2), but the overall performance is mediocre. The MCE method tends to achieve the highest success at any angle, whereas there are fewer “best identification”results from DIA or MBR and more of the worst ones in the along-track direction and cross-track direction. Through this comprehensive comparison, we conclude that MCE can obtain the best fitting results with the shortest circumference and the smallest area on behalf of the high filling effect for all sizes of rain cells.

Coulomb-assisted nonlocal electron transport between two pairs of Majorana bound states in a superconducting island

We investigate the nonlocal transport modulated by Coulomb interactions in devices comprising two interacting Majorana wires,where both nanowires are in proximity to a mesoscopic superconducting(SC)island.Each Majorana bound state(MBS)is coupled to one lead via a quantum dot with resonant levels.In this device,the nonlocal correlations can be induced in the absence of Majorana energy splitting.We find that the negative differential conductance and giant current noise cross correlation could be induced,due to the interplay between nonlocality of MBSs and dynamical Coulomb blockade effect.This feature may provide a signature for the existence of the MBSs.

MINIMIZERS OF L^(2)-SUBCRITICAL VARIATIONAL PROBLEMS WITH SPATIALLY DECAYING NONLINEARITIES IN BOUNDED DOMAINS

This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.

Holevo bound independent of weight matrices for estimating two parameters of a qubit

Holevo bound plays an important role in quantum metrology as it sets the ultimate limit for multi-parameter estimations,which can be asymptotically achieved.Except for some trivial cases,the Holevo bound is implicitly defined and formulated with the help of weight matrices.Here we report the first instance of an intrinsic Holevo bound,namely,without any reference to weight matrices,in a nontrivial case.Specifically,we prove that the Holevo bound for estimating two parameters of a qubit is equivalent to the joint constraint imposed by two quantum Cramér–Rao bounds corresponding to symmetric and right logarithmic derivatives.This weightless form of Holevo bound enables us to determine the precise range of independent entries of the mean-square error matrix,i.e.,two variances and one covariance that quantify the precisions of the estimation,as illustrated by different estimation models.Our result sheds some new light on the relations between the Holevo bound and quantum Cramer–Rao bounds.Possible generalizations are discussed.

Error field penetration in J-TEXT tokamak based on two-fluid drift-MHD model

An externally generated resonant magnetic perturbation can induce complex non-ideal MHD responses in their resonant surfaces.We have studied the plasma responses using Fitzpatrick's improved two-fluid model and program LAYER.We calculated the error field penetration threshold for J-TEXT.In addition,we find that the island width increases slightly as the error field amplitude increases when the error field amplitude is below the critical penetration value.However,the island width suddenly jumps to a large value because the shielding effect of the plasma against the error field disappears after the penetration.By scanning the natural mode frequency,we find that the shielding effect of the plasma decreases as the natural mode frequency decreases.Finally,we obtain the m/n=2/1 penetration threshold scaling on density and temperature.

Determination of Timer Error and Evaluation of Its Effect on Dose for OB6, GammaBeam X200 and X-Ray Irradiators at the Secondary Standard Dosimetry Laboratory in Nigeria

Timer error as well as its convention is very important for dose accuracy during irradiation. This paper determines the timer error of irradiators at Secondary Standard Dosimetry Laboratory (SSDL) in Nigeria. The irradiators are Cs-137 OB6 irradiator and X-ray irradiators at the Protection level SSDL;and Co-60 irradiator at the Therapy Level SSDL. PTW UNIDOS electrometer and LS01 Ionization chamber were used at the Protection Level to obtain doses for both Cs-137 OB6 and X-ray irradiators while an IBA farmer type ionization chamber and an IBA DOSE 1 electrometer were used at the Protection Level SSDL. Single/multiple exposure method and graphical method were used in the determination of the timer error for the three irradiators. The timer error obtained for Cs-137 OB6 irradiator was 0.48 ± 0.01 s, the timer error for the X-ray irradiator was 0.09 ± 0.01 s while the timer error obtained for GammaBeam X200 was 1.21 ± 0.04 s. It was observed that the timer error is not affected by source to detector distance. It was also observed that the timer error of Co-60 Gamma X200 irradiator is increasing with the age of the machine. Source to detector distance and field size do not contribute towards the timer error of the irradiators. The timer error of the Co-60 Gamma X200 irradiator (the only irradiator among the irradiators with a pneumatic system) increases with the age of the irradiator.

An Insight Survey on Sensor Errors and Fault Detection Techniques in Smart Spaces

The widespread adoption of the Internet of Things (IoT) has transformed various sectors globally, making themmore intelligent and connected. However, this advancement comes with challenges related to the effectiveness ofIoT devices. These devices, present in offices, homes, industries, and more, need constant monitoring to ensuretheir proper functionality. The success of smart systems relies on their seamless operation and ability to handlefaults. Sensors, crucial components of these systems, gather data and contribute to their functionality. Therefore,sensor faults can compromise the system’s reliability and undermine the trustworthiness of smart environments.To address these concerns, various techniques and algorithms can be employed to enhance the performance ofIoT devices through effective fault detection. This paper conducted a thorough review of the existing literature andconducted a detailed analysis.This analysis effectively links sensor errors with a prominent fault detection techniquecapable of addressing them. This study is innovative because it paves theway for future researchers to explore errorsthat have not yet been tackled by existing fault detection methods. Significant, the paper, also highlights essentialfactors for selecting and adopting fault detection techniques, as well as the characteristics of datasets and theircorresponding recommended techniques. Additionally, the paper presents amethodical overview of fault detectiontechniques employed in smart devices, including themetrics used for evaluation. Furthermore, the paper examinesthe body of academic work related to sensor faults and fault detection techniques within the domain. This reflectsthe growing inclination and scholarly attention of researchers and academicians toward strategies for fault detectionwithin the realm of the Internet of Things.

Prevalence of visual impairment and estimation of refractive errors among school children in Kakamega,Kenya

AIM:To investigate the prevalence of visual impairment(VI)and provide an estimation of uncorrected refractive errors in school-aged children,conducted by optometry students as a community service.METHODS:The study was cross-sectional.Totally 3343 participants were included in the study.The initial examination involved assessing the uncorrected distance visual acuity(UDVA)and visual acuity(VA)while using a+2.00 D lens.The inclusion criteria for a subsequent comprehensive cycloplegic eye examination,performed by an optometrist,were as follows:a UDVA<0.6 decimal(0.20 logMAR)and/or a VA with+2.00 D≥0.8 decimal(0.96 logMAR).RESULTS:The sample had a mean age of 10.92±2.13y(range 4 to 17y),and 51.3%of the children were female(n=1715).The majority of the children(89.7%)fell within the age range of 8 to 14y.Among the ethnic groups,the highest representation was from the Luhya group(60.6%)followed by Luo(20.4%).Mean logMAR UDVA choosing the best eye for each student was 0.29±0.17(range 1.70 to 0.22).Out of the total,246 participants(7.4%)had a full eye examination.The estimated prevalence of myopia(defined as spherical equivalent≤-0.5 D)was found to be 1.45%of the total sample.While around 0.18%of the total sample had hyperopia value exceeding+1.75 D.Refractive astigmatism(cil<-0.75 D)was found in 0.21%(7/3343)of the children.The VI prevalence was 1.26%of the total sample.Among our cases of VI,76.2%could be attributed to uncorrected refractive error.Amblyopia was detected in 0.66%(22/3343)of the screened children.There was no statistically significant correlation observed between age or gender and refractive values.CONCLUSION:The primary cause of VI is determined to be uncorrected refractive errors,with myopia being the most prevalent refractive error observed.These findings underscore the significance of early identification and correction of refractive errors in school-aged children as a means to alleviate the impact of VI.

Iterative physical optics method based on efficient occlusion judgment with bounding volume hierarchy technology

This paper builds a binary tree for the target based on the bounding volume hierarchy technology,thereby achieving strict acceleration of the shadow judgment process and reducing the computational complexity from the original O(N^(3))to O(N^(2)logN).Numerical results show that the proposed method is more efficient than the traditional method.It is verified in multiple examples that the proposed method can complete the convergence of the current.Moreover,the proposed method avoids the error of judging the lit-shadow relationship based on the normal vector,which is beneficial to current iteration and convergence.Compared with the brute force method,the current method can improve the simulation efficiency by 2 orders of magnitude.The proposed method is more suitable for scattering problems in electrically large cavities and complex scenarios.

Higher-order expansions of powered extremes of logarithmic general error distribution

In this paper,Let M_(n)denote the maximum of logarithmic general error distribution with parameter v≥1.Higher-order expansions for distributions of powered extremes M_(n)^(p)are derived under an optimal choice of normalizing constants.It is shown that M_(n)^(p),when v=1,converges to the Frechet extreme value distribution at the rate of 1/n,and if v>1 then M_(n)^(p)converges to the Gumbel extreme value distribution at the rate of(loglogn)^(2)=(log n)^(1-1/v).

Relationships between Terrain Features and Forecasting Errors of Surface Wind Speeds in a Mesoscale Numerical Weather Prediction Model

Numerical weather prediction(NWP)models have always presented large forecasting errors of surface wind speeds over regions with complex terrain.In this study,surface wind forecasts from an operational NWP model,the SMS-WARR(Shanghai Meteorological Service-WRF ADAS Rapid Refresh System),are analyzed to quantitatively reveal the relationships between the forecasted surface wind speed errors and terrain features,with the intent of providing clues to better apply the NWP model to complex terrain regions.The terrain features are described by three parameters:the standard deviation of the model grid-scale orography,terrain height error of the model,and slope angle.The results show that the forecast bias has a unimodal distribution with a change in the standard deviation of orography.The minimum ME(the mean value of bias)is 1.2 m s^(-1) when the standard deviation is between 60 and 70 m.A positive correlation exists between bias and terrain height error,with the ME increasing by 10%−30%for every 200 m increase in terrain height error.The ME decreases by 65.6%when slope angle increases from(0.5°−1.5°)to larger than 3.5°for uphill winds but increases by 35.4%when the absolute value of slope angle increases from(0.5°−1.5°)to(2.5°−3.5°)for downhill winds.Several sensitivity experiments are carried out with a model output statistical(MOS)calibration model for surface wind speeds and ME(RMSE)has been reduced by 90%(30%)by introducing terrain parameters,demonstrating the value of this study.

Enhancing the Goos-Hänchen shift based on quasi-bound states in the continuum through material asymmetric dielectric compound gratings

Quasi-bound state in the continuum(QBIC)resonance is gradually attracting attention and being applied in Goos-Hänchen(GH)shift enhancement due to its high quality(Q)factor and superior optical confinement.Currently,symmetry-protected QBIC resonance is often achieved by breaking the geometric symmetry,but few cases are achieved by breaking the material symmetry.This paper proposes a dielectric compound grating to achieve a high Q factor and high-reflection symmetry-protectede QBIC resonance based on material asymmetry.Theoretical calculations show that the symmetry-protected QBIC resonance achieved by material asymmetry can significantly increase the GH shift up to-980 times the resonance wavelength,and the maximum GH shift is located at the reflection peak with unity reflectance.This paper provides a theoretical basis for designing and fabricating high-performance GH shift tunable metasurfaces/dielectric gratings in the future.

A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Two-Dimensional Incompressible Flow

For solving two-dimensional incompressible flow in the vorticity form by the fourth-order compact finite difference scheme and explicit strong stability preserving temporal discretizations,we show that the simple bound-preserving limiter in Li et al.(SIAM J Numer Anal 56:3308–3345,2018)can enforce the strict bounds of the vorticity,if the velocity field satisfies a discrete divergence free constraint.For reducing oscillations,a modified TVB limiter adapted from Cockburn and Shu(SIAM J Numer Anal 31:607–627,1994)is constructed without affecting the bound-preserving property.This bound-preserving finite difference method can be used for any passive convection equation with a divergence free velocity field.