Nonlinear perturbation of a high-order exceptional point:Skin discrete breathers and the hierarchical power-law scaling

We study the nonlinear perturbation of a high-order exceptional point(EP)of the order equal to the system site number L in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity.Notably,we find a class of discrete breathers that aggregate to one boundary,here named as skin discrete breathers(SDBs).The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP.Specifically,the response of nonlinear energy to the perturbation is given by E_(m)∝Γ~(α_(m)),whereα_(m)=3^(m-1)is the power with m=1,...,L labeling the nonlinear energy bands.This is in sharp contrast to the L-th root of a linear perturbation in general.These SDBs decay in a double-exponential manner,unlike the edge states or skin modes in linear systems,which decay exponentially.Furthermore,these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity.They are also stable,as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis.As nonreciprocal nonlinear models may be experimentally realized in various platforms,such as the classical platform of optical waveguides,where Kerr nonlinearity is naturally present,and the quantum platform of optical lattices with Bose-Einstein condensates,our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity,particularly on high-order EPs,and benchmark the relevant simulations.

Wavelet inverse scale space for image restoration

This paper proposes a model for image restoration by combining the wavelet shrinkage and inverse scale space （ISS） method. The ISS is applied to the wavelet representation to modify the retained wavelet coefficients, and the coefficients smaller than the threshold are set to zero. The curvature term of the ISS can remove the edge artifacts and preserve sharp edges. For the multiscale interpretation of the ISS and the multiscale property of the wavelet representation, small details are preserved. This paper illustrates that the wavelet ISS model can be deduced from the wavelet based on a total variation minimization problem. A stopping criterion is obtained from this minimization in the sense of the Bregman distance in the wavelet domain. Numerical examples show the improvement for the image denoising with the proposed method in the sense of the signal to noise ratio and with fewer details remained in the residue.

Bayesian seismic multi-scale inversion in complex Laplace mixed domains

Seismic inversion performed in the time or frequency domain cannot always recover the long-wavelength background of subsurface parameters due to the lack of low-frequency seismic records. Since the low-frequency response becomes much richer in the Laplace mixed domains, one novel Bayesian impedance inversion approach in the complex Laplace mixed domains is established in this study to solve the model dependency problem. The derivation of a Laplace mixed-domain formula of the Robinson convolution is the first step in our work. With this formula, the Laplace seismic spectrum, the wavelet spectrum and time-domain reflectivity are joined together. Next, to improve inversion stability, the object inversion function accompanied by the initial constraint of the linear increment model is launched under a Bayesian framework. The likelihood function and prior probability distribution can be combined together by Bayesian formula to calculate the posterior probability distribution of subsurface parameters. By achieving the optimal solution corresponding to maximum posterior probability distribution, the low-frequency background of subsurface parameters can be obtained successfully. Then, with the regularization constraint of estimated low frequency in the Laplace mixed domains, multi-scale Bayesian inversion inthe pure frequency domain is exploited to obtain the absolute model parameters. The effectiveness, anti-noise capability and lateral continuity of Laplace mixed-domain inversion are illustrated by synthetic tests. Furthermore,one field case in the east of China is discussed carefully with different input frequency components and different inversion algorithms. This provides adequate proof to illustrate the reliability improvement in low-frequency estimation and resolution enhancement of subsurface parameters, in comparison with conventional Bayesian inversion in the frequency domain.

Low-Level Temperature Inversions and Their Effect on Aerosol Condensation Nuclei Concentrations under Different Large-Scale Synoptic Circulations

Knowledge of the statistical characteristics of inversions and their effects on aerosols under different large-scale synoptic circulations is important for studying and modeling the diffusion of pollutants in the boundary layer. Based on results gen- erated using the self-organizing map （SOM） weather classification method, this study compares the statistical characteristics of surface-based inversions （SBIs） and elevated inversions （EIs）, and quantitatively evaluates the effect of SBIs on aerosol condensation nuclei （CN） concentrations and the relationship between temperature gradients and aerosols for six prevailing synoptic patterns over the the Southern Great Plains （SGP） site during 2001-10. Large-scale synoptic patterns strongly influ- ence the statistical characteristics of inversions and the accumulation of aerosols in the low-level atmosphere. The activity, frequency, intensity, and vertical distribution of inversions are significantly different among these synoptic patterns. The verti- cal distribution of inversions varies diurnally and is significantly different among the different synoptic patterns. Anticyclonic patterns affect the accumulation of aerosols near the ground more strongly than cyclonic patterns. Mean aerosol CN con- centrations increase during SBIs compared to no inversion cases by 16.1%, 22.6%, 24.5%, 58.7%, 29.8% and 23.7% for the six synoptic patterns. This study confirms that there is a positive correlation between temperature gradients and aerosol CN concentrations near the ground at night under similar large-scale synoptic patterns. The relationship is different for different synoptic patterns and can be described by linear functions. These findings suggest that large-scale synoptic patterns change the static stability of the atmosphere and inversions in the lower atmosphere, thereby influencing the diffusion of aerosols near the ground.

Influence of correlation scale errors on aquifer hydraulic conductivity inversion precision

In order to investigate the influence of correlation scale error on the inversion precision of the hydraulic conductivity of the aquifer,the successive linear estimator(SLE)was used to invert the hydraulic conductivity field of a heterogeneous aquifer based on synthetic experiments.By increasing the numbers of observation wells and pumping tests,we analyzed the difference between the estimated and true values of hydraulic conductivity with different correlation scale errors.The relationships between the observation well number and the error in inversion results,and between the pumping test number and the error in inversion results were investigated.The results show that,if the amount of observed head data is insufficient,there will be errors in inversion results with changing correlation scale.Due to the existence of correlation scale error,the improvement of inversion precision gradually slows down with the increase of the amount of observed head data,which indicates that too much observed head data causes data redundancy.Therefore,for the synthetic experiments described in this paper,the observation well number should be less than 41,the pumping test number should be less than 17,and a more suitable method should be selected according to the precision requirements of specific situations in practical engineering.

The Inverse Gravity Inflationary Theory of Cosmology

Cosmological expansion or inflation is mathematically described by the theoretical notion of inverse gravity whose variations are parameterized by a factor that is a function of the distance to which cosmological expansion takes prominence over gravity. This assertion is referred to as the inverse gravity inflationary assertion. Thus, a correction to Newtonian gravitational force is introduced where a parameterized inverse gravity force term is incorporated into the classical Newtonian gravitational force equation where the inverse force term is negligible for distances less than the distance to which cosmological expansion takes prominence over gravity. Conversely, at distances greater than the distance to which cosmological expansion takes prominence over gravity. The inverse gravity term is shown to be dominant generating universal inflation. Gravitational potential energy is thence defined by the integral of the difference (or subtraction) between the conventional Newtonian gravitational force term and the inverse gravity term with respect to radius (r) which allows the formulation, incorporation, and mathematical description to and of gravitational redshift, the Walker-Robertson scale factor, the Robinson-Walker metric, the Klein-Gordon lagrangian, and dark energy and its relationship to the energy of the big bang in terms of the Inverse gravity inflationary assertion. Moreover, the dynamic pressure of the expansion of a cosmological fluid in a homogeneous isotropic universe is mathematically described in terms of the inverse gravity inflationary assertion using the stress-energy tensor for a perfect fluid. Lastly, Einstein’s field equations for the description of an isotropic and homogeneous universe are derived incorporating the mathematics of the inverse gravity inflationary assertion to fully show that the theoretical concept is potentially interwoven into the cosmological structure of the universe.

Coastal bathymetry inversion using SAR-based altimetric gravity data:A case study over the South Sandwich Island

The global bathymetry models are usually of low accuracy over the coastline of polar areas due to the harsh climatic environment and the complex topography.Satellite altimetric gravity data can be a supplement and plays a key role in bathymetry modeling over these regions.The Synthetic Aperture Radar(SAR)altimeters in the missions like CryoSat-2 and Sentinel-3A/3B can relieve waveform contamination that existed in conventional altimeters and provide data with improved accuracy and spatial resolution.In this study,we investigate the potential application of SAR altimetric gravity data in enhancing coastal bathymetry,where the effects on local bathymetry modeling introduced from SAR altimetry data are quantified and evaluated.Furthermore,we study the effects on bathymetry modeling by using different scale factor calculation approaches,where a partition-wise scheme is implemented.The numerical experiment over the South Sandwich Islands near Antarctica suggests that using SARbased altimetric gravity data improves local coastal bathymetry modeling,compared with the model calculated without SAR altimetry data by a magnitude of 3:55 m within 10 km of offshore areas.Moreover,by using the partition-wise scheme for scale factor calculation,the quality of the coastal bathymetry model is improved by 7.34 m compared with the result derived from the traditional method.These results indicate the superiority of using SAR altimetry data in coastal bathymetry inversion.

Dynamic inverse control of feedback linearization in ballistic correction based on nose cone swinging

It is a complicated nonlinear controlling problem to conduct a two-dimensional trajectory correction of rockets.By establishing the aerodynamic correction force mathematical model of rockets on nose cone swinging,the linear control is realized by the dynamic inverse nonlinear controlling theory and the three-time-scale separation method.The control ability and the simulation results are also tested and verified.The results show that the output responses of system track the expected curve well and the error is controlled in a given margin.The maximum correction is about±314 m in the lengthwise direction and±1 212 m in the crosswise direction from the moment of 5 s to the drop-point time when the angle of fire is 55°.Thus,based on the dynamic inverse control of feedback linearization,the trajectory correction capability of nose cone swinging can satisfy the requirements of two-dimensional ballistic correction,and the validity and effectiveness of the method are proved.

Regularized focusing inversion for large-scale gravity data based on GPU parallel computing

Processing large-scale 3-D gravity data is an important topic in geophysics field. Many existing inversion methods lack the competence of processing massive data and practical application capacity. This study proposes the application of GPU parallel processing technology to the focusing inversion method, aiming at improving the inversion accuracy while speeding up calculation and reducing the memory consumption, thus obtaining the fast and reliable inversion results for large complex model. In this paper, equivalent storage of geometric trellis is used to calculate the sensitivity matrix, and the inversion is based on GPU parallel computing technology. The parallel computing program that is optimized by reducing data transfer, access restrictions and instruction restrictions as well as latency hiding greatly reduces the memory usage, speeds up the calculation, and makes the fast inversion of large models possible. By comparing and analyzing the computing speed of traditional single thread CPU method and CUDA-based GPU parallel technology, the excellent acceleration performance of GPU parallel computing is verified, which provides ideas for practical application of some theoretical inversion methods restricted by computing speed and computer memory. The model test verifies that the focusing inversion method can overcome the problem of severe skin effect and ambiguity of geological body boundary. Moreover, the increase of the model cells and inversion data can more clearly depict the boundary position of the abnormal body and delineate its specific shape.

基于遗传-模式搜索算法的微尺度管控区域大气污染物PM2.5溯源

针对微尺度管控区域可能发生的大气污染提出有效的靶向诊断方法-结合高斯烟羽模型和遗传-模式搜索算法的大气污染物分布式溯源方法.将污染源反算模型得到的污染物理论质量浓度与传感器网络观测值的数据对应关系作为目标函数,使用模式搜索算法嵌入遗传算法加快反算模型的搜索过程,反算得到污染源强度和位置.依托杭州市亚运板球场馆大气感知器网络进行实验验证,监测2021年10月PM2.5质量浓度、气象数据,对所提出的混合式大气污染溯源方法进行实验验证.实验结果表明:改进遗传-模式搜索算法对于多维变量的搜索效果较好,能快速精准地反算污染源的位置和强度,可以为微尺度管控区域突发性气体污染防治提供应急决策参考.

电化学除碳酸钙垢阴极表面脱垢工艺优化研究

电化学除碳酸钙垢过程中,大量的沉积物覆盖在阴极表面,导致除垢效率降低,应及时对阴极表面进行脱垢处理。本文首先搭建了超声波清洗装置,研究了超声波频率、功率、时间对带垢极板脱垢效果的影响规律。其次,将阴阳极反接,实验研究了不同电流密度、时间下带垢极板的脱垢效果。最后从除垢率和除垢时间综合对比分析了阴阳极反接和超声波除垢的效果,提出了电化学除碳酸钙垢阴极表面脱垢工艺技术,为电化学沉积法去除油田采出液碳酸钙垢的技术推广提供支持。

观测信息不足条件下TanDEM-X InSAR的大范围林下地形反演

TerraSAR/TanDEM-X InSAR双站卫星系统是目前最主要的全球测图卫星系统之一,但该系统主要获取单基线、单极化InSAR数据。受观测信息不足的限制,无法直接分离植被体散射与地表散射信息,难以获取高精度的森林高度和林下地形。鉴于此,本文提出了联合单/双基线的大范围林下地形反演方法,其核心思想为:在InSAR干涉对重叠区,每个干涉对有不同的基线,两个干涉对重叠相当于双基线观测,可以采用RVoG模型估计森林高度。然后,利用简化的RVoG模型(C-SINC模型),以重叠区反演的树高结果为已知值,通过假定不同树高的散射过程具有相似性,对C-SINC模型进行求解进而获取林下地形。最后,以西班牙Teruel试验区对本文方法进行验证,与LiDAR DEM进行精度对比,InSAR DEM的RMSE为7.43 m,本文方法获取的林下地形RMSE为5.98 m,精度提高了20%。本文方法为利用TanDEM-X实现大范围林下地形测绘提供了参考。

Mass-Based Environmental Factor and Energy Assessment of Microwave-Assisted Synthesized Transition Metal Nanostructures

This paper describes mass-based energy phase-space projection of microwave-assisted synthesis of transition metals (zinc oxide, palladium, silver, platinum, and gold) nanostructures. The projection uses process energy budget (measured in kJ) on the horizontal axes and process density (measured in kJg−1) on the vertical axes. These two axes allow both mass usage efficiency (Environmental-Factor) and energy efficiency to be evaluated for a range of microwave applicator and metal synthesis. The metrics are allied to the: second, sixth and eleventh principle of the twelve principle of Green Chemistry. This analytical approach to microwave synthesis (widely considered as a useful Green Chemistry energy source) allows a quantified dynamic environmental quotient to be given to renewable plant-based biomass associated with the reduction of the metal precursors. Thus allowing a degree of quantification of claimed “eco-friendly” and “sustainable” synthesis with regard to waste production and energy usage.

基于声发射的不同粒径花岗岩细观破裂机理研究

为了研究粒径对岩石细观破裂机制的影响,本文开展了直剪条件下不同粒径花岗岩的声发射试验,结合矩张量反演理论分析岩石微破裂机制。研究结果表明:1在相同应力水平下,随着粒径的增加,微破裂的扩展范围及贯通程度均有增加趋势;2不同粒径花岗岩的微观破裂机制均以剪切型为主比,随着粒径的增大,剪切型占比逐渐升高。以上研究成果有利于增进人们对岩石微观破裂机制及其影响因素的认识,可应用于预测及解释岩石宏观断裂过程及模式。

Predictors of short-term outcome in patients with acute middle cerebral artery occlusion: unsuitability of fluid-attenuated inversion recovery vascular hyperintensity scores

Fluid-attenuated inversion recovery （FLAIR） vascular hyperintensity （FVH） is used to assess leptomeningeal collateral circulation, but clinical outcomes of patients with FVH can be very different. The aim of the present study was to assess a FVH score and explore its relationship with clinical outcomes. Patients with acute ischemic stroke due to middle cerebral artery M1 occlusion underwent magnetic resonance imaging and were followed up at 10 days （National Institutes of Health Stroke Scale） and 90 days （modified Rankin Scale） to determine short-term clinical outcomes. Effective collateral circulation indirectly improved recovery of neurological function and short-term clinical outcome by extending the size of the pial penumbra and reducing infarct lesions. FVH score showed no correlation with 90-day functional clinical outcome and was not sufficient as an independent predictor of short-term clinical outcome.

Exploring landslide erosion volume-area scaling relationships by slip depth using changes in DTMs for basin sediment volume estimation

Landslides produce large quantities of sediment deposits and reduce reservoir life. This study investigated landslides at the Shihmen Reservoir basin in Taiwan that were induced by Typhoon Sinlaku and Typhoon Jangmi in 2008. We formulate scaling relationships between landslide erosion volume and area and conclude that sediment budget can be estimated based on the easier-todetermine landslide erosion area. The methodologies applied for the investigation were geomorphological analysis through 5 m × 5 m digital terrain models(DTMs) of the basin created before and after the landslide events and spatial analysis through a geographic information system. The erosion area and volume of landslides were measured through the subtraction of DTMs produced before and after the events. Statistical analysis revealed that the landslide erosion frequency–magnitude distribution exhibited power-law behaviors with a scaling exponent of 2.15 for the frequency–area distribution and 1.66 for the frequency–volume distribution. This paper proposes different scaling relationships for different moving depths, and landslide erosion volumes were estimated on the basis of depth; thus, landslides of different scales can be distinguished to avoid errors in volume estimation. Two different scaling exponents are proposed: 1.21 for landslide erosions with depths of less than 2 m and 1.01 for landslide erosions with depths of more than 2 m. The proposed scaling relationships are practical for landslide erosion volume estimation by different depths according to the landslide area, and they can provide preliminary results for sediment budget planning in a reservoir basin.

ISAR cross-range scaling based on the MUSIC technique

Cross-range scaling plays an important role in the inverse synthetic aperture radar(ISAR) imaging. Many of the published cross-range scaling algorithms are based on the fast Fourier transformation(FFT). However, the FFT technique is resolution limited, so that the FFT-based algorithms will fail in the rotation velocity(RV) estimation of the slow rotation target. In this paper,we propose an accurate cross-range scaling algorithm based on the multiple signal classification(MUSIC) method. We first select some range bins with the mono-component linear frequency modulated(LFM) signal model. Then, we dechirp the signal of each selected range bin into the form of sinusoidal signal, and utilize the super-resolution MUSIC technique to accurately estimate the frequency. After processing all the range bins, a linear relationship related to the RV can be obtained. Eventually, the ISAR image can be scaled. The proposal can precisely estimate the small RV of the slow rotation target with low computational complexity. Furthermore, the proposal can also be used in the case of cross-range scaling for the sparse aperture data. Experimental results with the simulated and raw data validate the superiority of the novel method.

IMAGE-BASED SCALING FOR SHIP TOP VIEW ISAR IMAGES

A high quality top view or side view ship ISAR image with proper cross-range scale is very useful for target recognition. A technique aiming at solving the ship top view image scaling is developed, in which the cross-range scale information is obtained by measuring the slopes of the two feature lines of the ship, the centerline and the stern line. Neither the prior knowledge about the ship nor the tracking data is required. The proposed technique is fully based on the image. It is used with ease and high efficiency. Examples are provided to demonstrate its effectiveness with both simulated and real data. The scaled results are in accordance with the real shape of the ship.

Uniqueness, scale, and resolution issues in groundwater model parameter identification

This paper first visits uniqueness, scale, and resolution issues in groundwater flow forward modeling problems. It then makes the point that non-unique solutions to groundwater flow inverse problems arise from a lack of information necessary to make the problems well defined. Subsequently, it presents the necessary conditions for a well-defined inverse problem. They are full specifications of （1） flux boundaries and sources/sinks, and （2） heads everywhere in the domain at at least three times （one of which is t = 0）, with head change everywhere at those times being nonzero for transient flow. Numerical experiments are presented to corroborate the fact that, once the necessary conditions are met, the inverse problem has a unique solution. We also demonstrate that measurement noise, instability, and sensitivity are issues related to solution techniques rather than the inverse problems themselves. In addition, we show that a mathematically well-defined inverse problem, based on an equivalent homogeneous or a layered conceptual model, may yield physically incorrect and scenario-dependent parameter values. These issues are attributed to inconsistency between the scale of the head observed and that implied by these models. Such issues can be reduced only if a sufficiently large number of observation wells are used in the equivalent homogeneous domain or each layer. With a large number of wells, we then show that increase in parameterization can lead to a higher-resolution depiction of heterogeneity if an appropriate inverse methodology is used. Furthermore, we illustrate that, using the same number of wells, a highly parameterized model in conjunction with hydraulic tomography can yield better characterization of the aquifer and minimize the scale and scenario-dependent problems. Lastly, benefits of the highly parameterized model and hydraulic tomography are tested according to their ability to improve predictions of aquifer responses induced by independent stresses not used in the inverse modeling efforts.

ISAR Imaging and Cross-Range Scaling Based on Image Rotation Correlation

With the rapid advancement of technology,not only do we need to acquire a clear in-verse synthetic aperture radar(ISAR)image,but also the real size of the target on the imaging plane,so it’s particularly important for the ISAR to rescale the images.That is,the ISAR image which is in the range-Doppler domain is converted into the range-azimuth domain.Actually,the key point to solving the problem is to estimate the rotation parameters.In this paper,a new scheme to rescale the images is proposed.For the sake of solving the problem of two-dimensional image blur and target high-speed,the instantaneous range instantaneous Doppler(IRID)method is used to obtain ISAR images,and the rotation parameters are estimated by comparing the rotation correlation of the two images.Using this method,the error of the estimated rotation parameters is greatly reduced,so that the target can be rescaled accurately.The simulation results verify the ef-fectiveness of the proposed algorithm.