A Provable Positivity-Preserving Local Discontinuous Galerkin Method for the Viscous and Resistive MHD Equations

In this paper,we construct a high-order discontinuous Galerkin(DG)method which can preserve the positivity of the density and the pressure for the viscous and resistive magnetohydrodynamics(VRMHD).To control the divergence error in the magnetic field,both the local divergence-free basis and the Godunov source term would be employed for the multi-dimensional VRMHD.Rigorous theoretical analyses are presented for one-dimensional and multi-dimensional DG schemes,respectively,showing that the scheme can maintain the positivity-preserving(PP)property under some CFL conditions when combined with the strong-stability-preserving time discretization.Then,general frameworks are established to construct the PP limiter for arbitrary order of accuracy DG schemes.Numerical tests demonstrate the effectiveness of the proposed schemes.

Neural Network-Based Limiter with Transfer Learning

Recent works have shown that neural networks are promising parameter-free limiters for a variety of numerical schemes(Morgan et al.in A machine learning approach for detect-ing shocks with high-order hydrodynamic methods.et al.in J Comput Phys 367:166-191.,2018;Veiga et al.in European Conference on Computational Mechanics andⅦEuropean Conference on Computational Fluid Dynamics,vol.1,pp.2525-2550.ECCM.,2018).Following this trend,we train a neural network to serve as a shock-indicator function using simulation data from a Runge-Kutta discontinuous Galer-kin(RKDG)method and a modal high-order limiter(Krivodonova in J Comput Phys 226:879-896.,2007).With this methodology,we obtain one-and two-dimensional black-box shock-indicators which are then coupled to a standard limiter.Furthermore,we describe a strategy to transfer the shock-indicator to a residual distribution(RD)scheme without the need for a full training cycle and large data-set,by finding a mapping between the solution feature spaces from an RD scheme to an RKDG scheme,both in one-and two-dimensional problems,and on Cartesian and unstruc-tured meshes.We report on the quality of the numerical solutions when using the neural network shock-indicator coupled to a limiter,comparing its performance to traditional lim-iters,for both RKDG and RD schemes.

Lateral earth pressure of granular backfills on retaining walls with expanded polystyrene geofoam inclusions under limited surcharge loading

Existing studies have focused on the behavior of the retaining wall equipped with expanded polystyrene(EPS)geofoam inclusions under semi-infinite surcharge loading rather than limited surcharge loading.In this paper,the failure mode and the earth pressure acting on the rigid retaining wall with EPS geofoam inclusions and granular backfills(henceforth referred to as EPS-wall),under limited surcharge loading are investigated through two-and three-dimensional model tests.The testing results show that different from the sliding of almost all the backfill in the EPS-wall under semi-infinite surcharge loading,only an approximately triangular backfill slides in the wall under limited surcharge loading.The distribution of the lateral earth pressure on the EPS-wall under limited surcharge loading is non-linear,and the distribution changes from the increase of the wall depth to the decrease with the increase of the limited surcharge loading.An approach based on the force equilibrium of a differential element is developed to predict the lateral earth pressure behind the EPS-wall subjected to limited surcharge loading,and its performance was fully validated by the three-dimensional model tests.

Study on the formation of arc plasma on the resistive wall liquid metal current limiter

Due to its significant attributes,the liquid metal current limiter(LMCL)is considered a new strategy for limiting short-circuit current in the power grid.A resistive wall liquid metal current limiter(RWLMCL)is designed to advance the starting current-limiting time.Experiments are performed to investigate the dynamic behaviors of liquid metal,and the influence of different currents on the liquid metal self-shrinkage effect is compared and analyzed.Furthermore,the liquid metal self-shrinkage effect is mathematically modeled,and the reason for the formation of arc plasma is obtained by simulation.The laws of arc plasma formation and the current transfer in the cavity are revealed,and the motion mechanisms are explained by physical principles.The simulations are in accordance with the test data.It is demonstrated that the sudden change of the current density at both ends of the wall causes the liquid metal to shrink and depress under the electromagnetic force,and the current starts to transfer from the liquid metal path to the wall resistance path.The RWLMCL can effectively advance the starting current-limiting time.

On High-Resolution Entropy-Consistent Flux with Slope Limiter for Hyperbolic Conservation Laws

This paper proposes a new version of the high-resolution entropy-consistent(EC-Limited)flux for hyperbolic conservation laws based on a new minmod-type slope limiter.Firstly,we identify the numerical entropy production,a third-order differential term deduced from the previous work of Ismail and Roe[11].The corresponding dissipation term is added to the original Roe flux to achieve entropy consistency.The new,resultant entropy-consistent(EC)flux has a general and explicit analytical form without any corrective factor,making it easy to compute and a less-expensive method.The inequality constraints are imposed on the standard piece-wise quadratic reconstruction to enforce the pointwise values of bounded-type numerical solutions.We design the new minmod slope limiter as combining two separate limiters for left and right states.We propose the EC-Limited flux by adding this reconstruction data method to the primitive variables rather than to the conservative variables of the EC flux to preserve the equilibrium of the primitive variables.These resulting fluxes are easily applied to general hyperbolic conservation laws while having attractive features:entropy-stable,robust,and non-oscillatory.To illustrate the potential of these proposed fluxes,we show the applications to the Burgers equation and the Euler equations.

A Stroke-Limitation AMD Control System with Variable Gain and Limited Area for High-Rise Buildings

Collisions between a moving mass and an anti-collision device increase structural responses and threaten structural safety.An active mass damper(AMD)with stroke limitations is often used to avoid collisions.However,a strokelimited AMD control system with a fixed limited area shortens the available AMD stroke and leads to significant control power.To solve this problem,the design approach with variable gain and limited area(VGLA)is proposed in this study.First,the boundary of variable-limited areas is calculated based on the real-time status of the moving mass.The variable gain(VG)expression at the variable limited area is deduced by considering the saturation of AMD stroke.Then,numerical simulations of a stroke-limited AMD control system with VGLA are conducted on a high-rise building structure.These numerical simulations show that the proposed approach has superior strokelimitation performance compared with a stroke-limited AMD control system with a fixed limited area.Finally,the proposed approach is validated through experiments on a four-story steel frame.

Supplementary Information to“Balancing the quantum speed limit and instantaneous energy cost in adiabatic quantum evolution”

I.SUPPLEMENTARY NOTE 1:THEORETICAL MATERIALS.The quantum speed limit(QSL)is essential for quantum computing and quantum communication,referring to the minimum time required for a quantum system to evolve from one state to another.Two well-known forms of the QSL are the Mandelstam-Tamm(MT)relation TqsL≥πh/2△E[S1]and the Margolus-Levitin(ML)relation TqsL≥πh/2(E)[S2]where Tqst is denoted as the QSL time,h is the reduced Planck's constant,△E is the energy uncertainty(standard deviation)of the system,and(E)is the average energy of the system above its ground state.Both of relations provide a lower bound on the evolution time.

Cosmology-Independent Photon Mass Limits from Localized Fast Radio Bursts by Using Artificial Neural Networks

A hypothetical photon mass m_(γ) can produce a frequency-dependent vacuum dispersion of light, which leads to an additional time delay between photons with different frequencies when they propagate through a fixed distance. The dispersion measure and redshift measurements of fast radio bursts(FRBs) have been widely used to constrain the rest mass of the photon. However, all current studies analyzed the effect of the frequency-dependent dispersion for massive photons in the standard ΛCDM cosmological context. In order to alleviate the circularity problem induced by the presumption of a specific cosmological model based on the fundamental postulate of the masslessness of photons, here we employ a new model-independent smoothing technique, artificial neural network(ANN), to reconstruct the Hubble parameter H(z) function from 34 cosmic-chronometer measurements.By combining observations of 32 well-localized FRBs and the H(z) function reconstructed by ANN, we obtain an upper limit of m_(γ) ≤ 3.5 × 10^(-51)kg, or equivalently m_(γ) ≤ 2.0 × 10^(-15)eV/c^(2)(m_(γ) ≤ 6.5 × 10^(-51)kg, or equivalently m_(γ) ≤ 3.6 × 10^(-15)eV/c_(2)) at the 1σ(2σ) confidence level. This is the first cosmology-independent photon mass limit derived from extragalactic sources.

Speed limit effect during lane change in a two-lane lattice model under V2X environment

Speed limit measures are ubiquitous due to the complexity of the road environment,which can be supplied with the help of vehicle to everything(V2X)communication technology.Therefore,the influence of speed limit on traffic system will be investigated to construct a two-lane lattice model accounting for the speed limit effect during the lane change process under V2X environment.Accordingly,the stability condition and the mKdV equation are closely associated with the speed limit effect through theory analysis.Moreover,the evolution of density and hysteresis loop is simulated to demonstrate the positive role of the speed limit effect on traffic stability in the cases of strong reaction intensity and high limited speed.

Proteomic response of Phaeocystis globosa to nitrogen limitation

Phaeocystis globosa is an important unicellular eukaryotic alga that can also form colonies.P.globosa can cause massive harmful algal blooms and plays an important role in the global carbon or sulfur cycling.Thus far,the ecophysiology of P.globosa has been investigated by numerous studies.However,the proteomic response of P.globosa to nitrogen depletion remains largely unknown.We compared four protein preparation methods of P.globosa for two-dimensional electrophoresis(2-DE)(Urea/Triton X-100 with trichloroacetic acid(TCA)/acetone precipitation;TCA/acetone precipitation;Radio Immuno Precipitation Assay(RIPA)with TCA/acetone precipitation;and Tris buffer).Results show that the combination of RIPA with TCA/acetone precipitation had a clear gel background and showed the best protein spot separation effect,based on which the proteomic response to nitrogen depletion was studied using 2-DE.In addition,we identified six differentially expressed proteins whose relative abundance increased or decreased more than 1.5-fold(P<0.05).Most proteins could not be identified,which might be attributed to the lack of genomic sequences of P.globosa.Under nitrogen limitation,replication protein-like,RNA ligase,and sn-glycerol-3-phosphate dehydrogenase were reduced,which may decrease the DNA replication level and ATP production in P.globosa cells.The increase of endonucleaseⅢand transcriptional regulator enzyme may affect the metabolic and antioxidant function of P.globosa cells and induce cell apoptosis.These findings provide a basis for further proteomic study of P.globosa and the optimization of protein preparation methods of marine microalgae.

THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH

This paper deals with the problem of limit cycles for the whirling pendulum equation x=y,y=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=0.The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions satisfy.Furthermore,the exact bound of a special case is given using the Chebyshev system.At the end,some numerical simulations are given to illustrate the existence of limit cycles.

An approach for determination of lateral limit angle in kinematic planar sliding analysis for rock slopes

Planar sliding is one of the frequently observed types of failure in rock slopes.Kinematic analysis is a classic and widely used method to examine the potential failure modes in rock masses.The accuracy of planar sliding kinematic analysis is significantly influenced by the value assigned to the lateral limit angleγlim.However,the assignment ofγlim is currently used generally based on an empirical criterion.This study aims to propose an approach for determining the value ofγlim in deterministic and probabilistic kinematic planar sliding analysis.A new perspective is presented to reveal thatγlim essentially influences the probability of forming a potential planar sliding block.The procedure to calculate this probability is introduced using the block theory method.It is found that the probability is correlated with the number of discontinuity sets presented in rock masses.Thus,different values ofγlim for rock masses with different sets of discontinuities are recommended in both probabilistic and deterministic planar sliding kinematic analyses;whereas a fixed value ofγlim is commonly assigned to different types of rock masses in traditional method.Finally,an engineering case was used to compare the proposed and traditional kinematic analysis methods.The error rates of the traditional method vary from 45%to 119%,while that of the proposed method ranges between 1%and 17%.Therefore,it is likely that the proposed method is superior to the traditional one.

Probabilistic Analysis of Slope Using Finite Element Approach and Limit Equilibrium Approach around Amalpata Landslide of West Central, Nepal

The stability study of the ongoing and recurring Amalpata landslide in Baglung in Nepal’s Gandaki Province is presented in this research. The impacted slope is around 200 meters high, with two terraces that have different slope inclinations. The lower bench, located above the basement, consistently fails and sets others up for failure. The fluctuating water level of the slope, which travels down the slope masses, exacerbates the slide problem. The majority of these rocks are Amalpata landslide area experiences several structural disruptions. The area’s stability must be evaluated in order to prevent and control more harm from occurring to the nearby agricultural land and people living along the slope. The slopes’ failures increase the damages of house existing in nearby area and the erosion of the slope. Two modeling techniques the finite element approach and the limit equilibrium method were used to simulate the slope. The findings show that, in every case, the terrace above the basement is where the majority of the stress is concentrated, with a safety factor of near unity. Using probabilistic slope stability analysis, the failure probability was predicted to be between 98.90% and 100%.

Quantitative prediction model for the depth limit of oil accumulation in the deep carbonate rocks:A case study of Lower Ordovician in Tazhong area of Tarim Basin

With continuous hydrocarbon exploration extending to deeper basins,the deepest industrial oil accumulation was discovered below 8,200 m,revealing a new exploration field.Hence,the extent to which oil exploration can be extended,and the prediction of the depth limit of oil accumulation(DLOA),are issues that have attracted significant attention in petroleum geology.Since it is difficult to characterize the evolution of the physical properties of the marine carbonate reservoir with burial depth,and the deepest drilling still cannot reach the DLOA.Hence,the DLOA cannot be predicted by directly establishing the relationship between the ratio of drilling to the dry layer and the depth.In this study,by establishing the relationships between the porosity and the depth and dry layer ratio of the carbonate reservoir,the relationships between the depth and dry layer ratio were obtained collectively.The depth corresponding to a dry layer ratio of 100%is the DLOA.Based on this,a quantitative prediction model for the DLOA was finally built.The results indicate that the porosity of the carbonate reservoir,Lower Ordovician in Tazhong area of Tarim Basin,tends to decrease with burial depth,and manifests as an overall low porosity reservoir in deep layer.The critical porosity of the DLOA was 1.8%,which is the critical geological condition corresponding to a 100%dry layer ratio encountered in the reservoir.The depth of the DLOA was 9,000 m.This study provides a new method for DLOA prediction that is beneficial for a deeper understanding of oil accumulation,and is of great importance for scientific guidance on deep oil drilling.

Limit load and failure mechanisms of a vertical Hoek-Brown rock slope

The problem considered in this short note is the limit load determination of a vertical rock slope.The classical limit theorem is employed with the use of adaptive finite elements and nonlinear programming to determine upper and lower bound limit loads of a Hoek-Brown vertical rock slope.The objective function of the mathematical programming problem is such as to optimize a boundary load,which is known as the limit load,resembling the ultimate bearing capacity of a strip footing.While focusing on the vertical slope,parametric studies are carried out for several dimensionless ratios such as the dimensionless footing distance ratio,the dimensionless height ratio,and the dimensionless rock strength ratio.A comprehensive set of design charts is presented,and failure envelopes shown with the results explained in terms of three identified failure mechanisms,i.e.the face,the toe,and the Prandtl-type failures.These novel results can be used with great confidence in design practice,in particularly noting that the current industry-based design procedures for the presented problem are rarely found.

Internal limiting membrane peeling combined with silicone oil or air tamponade for highly myopic foveoschisis

AIM:To compare the efficacy of pars plana vitrectomy(PPV)combined with internal limiting membrane(ILM)and silicone oil or sterile air tamponade for the treatment of myopic foveoschisis(MF)in highly myopic eyes.METHODS:This retrospective study included 48 myopic eyes of 40 patients with MF and axial lengths(ALs)ranging from 26-32 mm treated between January 2020 and January 2022.All patients were underwent PPV combined with ILM peeling followed by sterile air or silicone oil tamponade and followed up at least 12mo.Based on the features on spectral-domain optical coherence tomography(SD-OCT),the eyes were divided into the MF-only group(Group A,n=15 eyes),MF with central foveal detachment group(Group B,n=20 eyes),and MF with lamellar macular hole group(Group C,n=13 eyes).According to AL,eyes were further divided into three groups:Group D(26.01-28.00 mm,n=12 eyes),Group E(28.01-30.00 mm,n=26 eyes),and Group F(30.01-32.00 mm,n=10 eyes).The best-corrected visual acuity(BCVA),central foveal thickness(CFT),and complications were recorded.RESULTS:The patients included 16 males and 24 females with the mean age of 56±9.82y.The BCVA and CFT improved in all groups after surgery(P<0.01),while there was no significant difference of the CFT in Group A,B,and C postoperatively(P>0.05).The intergroup differences of BCVA and CFT postoperatively were statistically significant in Group D,E,and F.Twenty eyes were injected with sterile air,and 28 eyes were injected with silicone oil for tamponade based on the AL.However,there was no statistically significant difference among Groups D,E,and F in terms of the results of sterile air or silicone oil tamponade.The mean recovery time was 5.9mo for MF patients subjected to silicone oil tamponade and 7.7mo for patients subjected to sterile air tamponade,and the difference was not statistically significant.CONCLUSION:PPV and ILM peeling combined with silicone oil or sterile air tamponade can achieve good results for MF in highly myopic eyes with ALs≤32 mm.

Research on the Upper Limit of Accuracy for Predicting Theoretical Tandem Mass Spectrometry

In recent years, numerous theoretical tandem mass spectrometry prediction methods have been proposed, yet a systematic study and evaluation of their theoretical accuracy limits have not been conducted. If the accuracy of current methods approaches this limit, further exploration of new prediction techniques may become redundant. Conversely, a need for more precise prediction methods or models may be indicated. In this study, we have experimentally analyzed the limits of accuracy at different numbers of ions and parameters using repeated spectral pairs and integrating various similarity metrics. Results show significant achievements in accuracy for backbone ion methods with room for improvement. In contrast, full-spectrum prediction methods exhibit greater potential relative to the theoretical accuracy limit. Additionally, findings highlight the significant impact of normalized collision energy and instrument type on prediction accuracy, underscoring the importance of considering these factors in future theoretical tandem mass spectrometry predictions.

Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids

A novel class of weighted essentially nonoscillatory （WENO） schemes based on Hermite polynomi- als, termed as HWENO schemes, is developed and applied as limiters for high order discontinuous Galerkin （DG） method on triangular grids. The developed HWENO methodology utilizes high-order derivative information to keep WENO re- construction stencils in the von Neumann neighborhood. A simple and efficient technique is also proposed to enhance the smoothness of the existing stencils, making higher-order scheme stable and simplifying the reconstruction process at the same time. The resulting HWENO-based limiters are as compact as the underlying DG schemes and therefore easy to implement. Numerical results for a wide range of flow conditions demonstrate that for DG schemes of up to fourth order of accuracy, the designed HWENO limiters can simul- taneously obtain uniform high order accuracy and sharp, es- sentially non-oscillatory shock transition.

Investigation on the Arc Ignition Characteristics and Energy Absorption of Liquid Metal Current Limiter Based on Self-Pinch Effect

The GaInSn liquid metal current limiter based on the fluid pinch effect has broad application prospects due to its particular properties. However, the limited rated current and abil- ity of power dissipation are the critical problems for its wide application. Firstly, the temperature distribution of the liquid metal current limiter （LMCL） was obtained by experiments with a rated current of 1 kA and the arc ignition phenomenon was observed with 1.5 kA, which indicates that the rated current is mainly limited by the arc rather than the high temperature compared to the traditional switchgears. Furthermore, an improved method is proposed by adding the paralleled pure resistance, impedance or another LMCL element to protect the setup from the fault energy concentration in the setup. The problem of a slower arc voltage increasing rate can be solved by adding a paralleled impedance with suitable parameters. Finally, the current limiting properties based on the improved method were investigated and the alternating oscillating current was found between two paralleled LMCL elements owing to their deviation of arc ignition in reality.

Plasma Limiter Based on Surface Wave Plasma Excited by Microwave

A novel plasma limiter, in which the plasma is excited by surface wave, is presented. The breakdown time of some gases filled in the limiter were calculated as a function of gas pres- sure, ionization degree and density of seed electrons under low pressure （0.01 -1 Torr） and high pressure （10 -1000 Torr） cases. The results show that the limiter filled with Xe with a pressure of 0.9 Torr, seed electron density of 10^16 m^-3, and ionization degree of 10^-4, has a breakdown time of approximate 19.6 ns.