Lower Bounds of Decay Rates for Solution to the Single-Layer Quasi-Geostrophic Model

In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies .

Dynamic Event-Triggered Quadratic Nonfragile Filtering for Non-Gaussian Systems:Tackling Multiplicative Noises and Missing Measurements

This paper focuses on the quadratic nonfragile filtering problem for linear non-Gaussian systems under multiplicative noises,multiple missing measurements as well as the dynamic event-triggered transmission scheme.The multiple missing measurements are characterized through random variables that obey some given probability distributions,and thresholds of the dynamic event-triggered scheme can be adjusted dynamically via an auxiliary variable.Our attention is concentrated on designing a dynamic event-triggered quadratic nonfragile filter in the well-known minimum-variance sense.To this end,the original system is first augmented by stacking its state/measurement vectors together with second-order Kronecker powers,thus the original design issue is reformulated as that of the augmented system.Subsequently,we analyze statistical properties of augmented noises as well as high-order moments of certain random parameters.With the aid of two well-defined matrix difference equations,we not only obtain upper bounds on filtering error covariances,but also minimize those bounds via carefully designing gain parameters.Finally,an example is presented to explain the effectiveness of this newly established quadratic filtering algorithm.

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.

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.

Experimental investigation into the salinity effect on the physicomechanical properties of carbonate saline soil

For engineering structures with saline soil as a filling material,such as channel slope,road subgrade,etc.,the rich soluble salt in the soil is an important potential factor affecting their safety performance.This study examines the Atterberg limits,shear strength,and compressibility of carbonate saline soil samples with different NaHCO3 contents in Northeast China.The mechanism underlying the influence of salt content on soil macroscopic properties was investigated based on a volumetric flask test,a mercury intrusion porosimetry(MIP)test,and a scanning electron microscopic(SEM)test.The results demonstrated that when NaHCO3 contents were lower than the threshold value of 1.5%,the bound water film adsorbed on the surface of clay particles thickened continuously,and correspondingly,the Atterberg limits and plasticity index increased rapidly as the increase of sodium ion content.Meanwhile,the bonding force between particles was weakened,the dispersion of large aggregates was enhanced,and the soil structure became looser.Macroscopically,the compressibility increased and the shear strength(mainly cohesion)decreased by 28.64%.However,when the NaHCO3 content exceeded the threshold value of 1.5%,the salt gradually approached solubility and filled the pores between particles in the form of crystals,resulting in a decrease in soil porosity.The cementation effect generated by salt crystals increased the bonding force between soil particles,leading to a decrease in plasticity index and an improvement in soil mechanical properties.Moreover,this work provides valuable suggestions and theoretical guidance for the scientific utilization of carbonate saline soil in backfill engineering projects.

Nonlinear Seebeck and Peltier effects in a Majorana nanowire coupled to leads

We theoretically study nonlinear thermoelectric transport through a topological superconductor nanowire hosting Majorana bound states(MBSs) at its two ends, a system named as Majorana nanowire(MNW). We consider that the MNW is coupled to the left and right normal metallic leads subjected to either bias voltage or temperature gradient. We focus our attention on the sign change of nonlinear Seebeck and Peltier coefficients induced by mechanisms related to the MBSs, by which the possible existence of MBSs might be proved. Our results show that for a fixed temperature difference between the two leads, the sign of the nonlinear Seebeck coefficient(thermopower) can be reversed by changing the overlap amplitude between the MBSs or the system equilibrium temperature, which are similar to the cases in linear response regime. By optimizing the MBS–MBS interaction amplitude and system equilibrium temperature, we find that the temperature difference may also induce sign change of the nonlinear thermopower. For zero temperature difference and finite bias voltage, both the sign and magnitude of nonlinear Peltier coefficient can be adjusted by changing the bias voltage or overlap amplitude between the MBSs. In the presence of both bias voltage and temperature difference, we show that the electrical current at zero Fermi level and the states induced by overlap between the MBSs keep unchanged, regardless of the amplitude of temperature difference. We also find that the direction of the heat current driven by bias voltage may be changed by weak temperature difference.

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.

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.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS

This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.

THE LIMITING PROFILE OF SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS WITH A SHRINKING SELF-FOCUSING CORE

In this paper,we consider the semilinear elliptic equation systems{△u+u=αQ_(n)(x)|u|^(α-2)|v|^(β)u in R^(N),-△v+v=βQ(x)|u|^(α)|v|^(β-2)v in R^(N),where N≥3,α,β>1,α+β<2^(*),2^(*)=2N/N-2 and Q_(n) are bounded given functions whose self-focusing cores{x∈R^(N)|Q_(n)(x)>0} shrink to a set with finitely many points as n→∞.Motivated by the work of Fang and Wang[13],we use variational methods to study the limiting profile of ground state solutions which are concentrated at one point of the set with finitely many points,and we build the localized concentrated bound state solutions for the above equation systems.

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.

Localization for mixed near-field and far-field sources under impulsive noise

In order to solve the problem that the performance of traditional localization methods for mixed near-field sources(NFSs)and far-field sources(FFSs)degrades under impulsive noise,a robust and novel localization method is proposed.After eliminating the impacts of impulsive noise by the weighted out-lier filter,the direction of arrivals(DOAs)of FFSs can be estimated by multiple signal classification(MUSIC)spectral peaks search.Based on the DOAs information of FFSs,the separation of mixed sources can be performed.Finally,the estimation of localizing parameters of NFSs can avoid two-dimension spectral peaks search by decomposing steering vectors.The Cramer-Rao bounds(CRB)for the unbiased estimations of DOA and range under impulsive noise have been drawn.Simulation experiments verify that the proposed method has advantages in probability of successful estimation(PSE)and root mean square error(RMSE)compared with existing localization methods.It can be concluded that the proposed method is effective and reliable in the environment with low generalized signal to noise ratio(GSNR),few snapshots,and strong impulse.

Shape Analysis of Agricultural Parcels for Land Consolidation Priorities in Tekirdag Province,Turkey

Shape irregularity,a sub-factor of parcel fragmentation is a problem that hinders sustainable agriculture and is solved using land consolidation projects.Determination of the parcel shape degree contributes significantly to spatial prioritization where there is also a high probability of achieving positive effects of consolidation projects.This study aims to determine the shape degree of the agricultural parcels both at singular and rural county scales in Tekirdag Province,Turkey in 2020 by combining the parcel shape index(PSI) with the minimum bounding geometry index(MBG) to improve parcel scores.Hot-spot zones of the highly irregular and near optimum parcels were also determined using Getis-Ord G_(i)^(*) statistic.The parcel degrees were classified into four categories,namely highly irregular,irregular,regular and near optimum.The obtained unweighted scores of the parameters exhibit deviations from the expected values.After weighting by pairwise comparison,the values approached ideal scores.Among 346 740 parcels,53% were highly irregular and irregular and 47% were regular and near optimum shapes after weighting whereas these were 70% and 30%,respectively before weighting.The average parcel degree of 63 rural counties was regular while the average parcel degree of the remaining 264 rural counties was irregular.The combined use of PSI and MBG index improved the correctness of the parcel shape score.It could be suggested to use as a tool in land consolidation prioritization.

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.

非正则赋权有向图A_(α)谱半径的上界

Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w_(1)^(+),w_(2)^(+),...,w_(n)^(+)).In this paper,we study the matrix A_(α)(D),which is defined as Aα(D)=αW(D)+(1−α)A(D),0≤α≤1.The spectral radius of A_(α)(D)is called the Aαspectral radius of D,denoted byλα(D).We obtain some upper bounds on the Aαspectral radius of strongly connected irregular weighted digraphs.

Optimization of Generator Based on Gaussian Process Regression Model with Conditional Likelihood Lower Bound Search

The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems.