RKDG Methods with Multi-resolution WENO Limiters for Solving Steady-State Problems on Triangular Meshes

In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.

Revisting High-Resolution Schemes with van Albada Slope Limiter

Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws.The family of minmod limiters serves as the prototype example.Here,we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et al.(Astron Astrophys 108:76–84,1982).The van Albada(vA)limiter is smoother near extrema,and consequently,in many cases,it outperforms the results obtained using the standard minmod limiter.In particular,we prove that the vA limiter ensures the one-dimensional Total-Variation Diminishing(TVD)stability and demonstrate that it yields noticeable improvement in computation of one-and two-dimensional systems.

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.

Performance Limits and Advancements in Single 2D Transition Metal Dichalcogenide Transistor

Two-dimensional(2D)transition metal dichalcogenides(TMDs)allow for atomic-scale manipulation,challenging the conventional limitations of semiconductor materials.This capability may overcome the short-channel effect,sparking significant advancements in electronic devices that utilize 2D TMDs.Exploring the dimension and performance limits of transistors based on 2D TMDs has gained substantial importance.This review provides a comprehensive investigation into these limits of the single 2D-TMD transistor.It delves into the impacts of miniaturization,including the reduction of channel length,gate length,source/drain contact length,and dielectric thickness on transistor operation and performance.In addition,this review provides a detailed analysis of performance parameters such as source/drain contact resistance,subthreshold swing,hysteresis loop,carrier mobility,on/off ratio,and the development of p-type and single logic transistors.This review details the two logical expressions of the single 2D-TMD logic transistor,including current and voltage.It also emphasizes the role of 2D TMD-based transistors as memory devices,focusing on enhancing memory operation speed,endurance,data retention,and extinction ratio,as well as reducing energy consumption in memory devices functioning as artificial synapses.This review demonstrates the two calculating methods for dynamic energy consumption of 2D synaptic devices.This review not only summarizes the current state of the art in this field but also highlights potential future research directions and applications.It underscores the anticipated challenges,opportunities,and potential solutions in navigating the dimension and performance boundaries of 2D transistors.

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.

Seismic-induced surficial failure of cohesive slopes using three-dimensional limit analysis:A case study of the Wangjiayan landslide in Beichuan, China

A seismic-induced landslide is a common geological catastrophe that occurs in nature.The Wangjiayan landslide,which was triggered by the Wenchuan earthquake,is a typical case in point.The Wanjiayan landslide caused many casualties and resulted in enormous property loss.This study constructs a simple surficial failure model based on the upper bound approach of three-dimensional(3D)limit analysis to evaluate the slope stability of the Wangjiayan case,while a traditional two-dimensional(2D)analysis is also conducted as a reference for comparison with the results of the 3D analysis.A quasi-static calculation is used to study the effect of the earthquake in terms of horizontal ground acceleration,while a parametric study is conducted to evaluate the critical cohesion of slopes.Rather than employing a 3D analysis,using the 2D analysis yields an underestimation regarding the safety factor.In the Wangjiayan landslide,the difference in the factors of safety between the 3D and 2D analyses can reach 20%.The sliding surface morphology as determined by the 3D method is similar to actual morphology,and the parameters of both are also compared to analyze the reliability of the proposed 3D method.

THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS

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.

Effects of nutrient limitations on the sinking velocity of Thalassiosira weissflogii

The sinking of diatoms is critic al to the formation of oceanic biological pumps and coastal hypoxic zones.However,little is known about the effects of different nutrient restrictions on diatom sinking.In this study,we measured the sinking velocity(SV) of Thalassiosira weissflogii using a new phytoplankton video observation instrument and analyzed major biochemical components under varying nutrient conditions.Our results showed that the SV of T.weissflogii under different nutrient limitation conditions varied substantially.The highest SV of(1.77±0.02) m/d was obtained under nitrate limitation,signific antly surpassing that under phosphate limitation at(0.98±0.13) m/d.As the nutrient limitation was released,the SV steadily decreased to(0.32±0.03) m/d and(0.15±0.05) m/d,respectively.Notably;under conditions with limited nitrate and phosphate concentrations,the SV values of T.weissflogii significantly positively correlated with the lipid content(P <0.001),with R^(2) values of 0.86 and 0.69,respectively.The change of the phytoplankton SV was primarily related to the intracellular compo sition,which is controlled by nutrient conditions but did not significantly correlate with transparent extracellular polymer and biosilica contents.The results of this study help to understand the regulation of the vertical sinking process of diatoms by nutrient restriction and provide new insights into phytoplankton dynamics and their relationship with the marine nutrient structure.

Monolithic Convex Limiting for Legendre-Gauss-Lobatto Discontinuous Galerkin Spectral-Element Methods

We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.

INCOMPRESSIBLE LIMIT OF IDEAL MAGNETOHYDRODYNAMICS IN A DOMAIN WITH BOUNDARIES

We study the incompressible limit of classical solutions to compressible ideal magneto-hydrodynamics in a domain with a flat boundary.The boundary condition is characteristic and the initial data is general.We first establish the uniform existence of classical solutions with respect to the Mach number.Then,we prove that the solutions converge to the solution of the incompressible MHD system.In particular,we obtain a stronger convergence result by using the dispersion of acoustic waves in the half space.

Exploring device physics of perovskite solar cell via machine learning with limited samples

Perovskite solar cells(PsCs)have developed tremendously over the past decade.However,the key factors influencing the power conversion efficiency(PCE)of PSCs remain incompletely understood,due to the complexity and coupling of these structural and compositional parameters.In this research,we demon-strate an effective approach to optimize PSCs performance via machine learning(ML).To address chal-lenges posed by limited samples,we propose a feature mask(FM)method,which augments training samples through feature transformation rather than synthetic data.Using this approach,squeeze-and-excitation residual network(SEResNet)model achieves an accuracy with a root-mean-square-error(RMSE)of 0.833%and a Pearson's correlation coefficient(r)of 0.980.Furthermore,we employ the permu-tation importance(PI)algorithm to investigate key features for PCE.Subsequently,we predict PCE through high-throughput screenings,in which we study the relationship between PCE and chemical com-positions.After that,we conduct experiments to validate the consistency between predicted results by ML and experimental results.In this work,ML demonstrates the capability to predict device performance,extract key parameters from complex systems,and accelerate the transition from laboratory findings to commercialapplications.

Effects of phosphorus limitation on sinking velocities of phytoplankton during summer in the Changjiang River Estuary

The sinking of phytoplankton is critical to organic matter transportation in the ocean and it is an essential process for the formation of coastal hypoxic zones.This study was based on a field investigation conducted during the summer of 2022 in the Changjiang River(Yangtze River) Estuary(CJE) and its adjacent waters.The settling column method was employed to measure the sinking velocity(SV) of different size fractions of phytoplankton at the surface of the sea and to analyze their environmental control mechanisms.The findings reveal significant spatial variation in phytoplankton SV(-0.55-2.41 m/d) within the CJE.High-speed sinking was predominantly observed in phosphate-depleted regions beyond the CJE front.At the same time,an upward trend was more commonly observed in the phosphate-rich regions near the CJE mouth.The SV ranges for different sizefractionated phytoplankton,including micro-(>20 μm),nano-(2-20 μm),and picophytoplankton(0.7-2 μm),were-0.50-4.74 m/d,-1.04-1.59 m/d,and-1.24-1.65 m/d,respectively.Correlation analysis revealed a significant negative correlation between SV and dissolved inorganic phosphorus(DIP),implying that the influence of DIP contributes to SV.The variations in phytoplankton alkaline phosphatase activity suggested a significant increase in SV across all size fractions in the event of phosphorus limitation.Phytoplankton communities with limited photo synthetic capacity(maximum photochemical efficience,Fv/Fm <0.3) were found to have higher SV than that of communities with strong capacity,suggesting a link between sinking and alterations in physiological conditions due to phosphate depletion.The findings from the in situ phosphate enrichment experiments confirmed a marked decrease in SV following phosphate supplementation.These findings suggest that phosphorus limitation is the primary driver of elevated SV in the CJE.This study enhances the comprehension of the potential mechanisms underlying hypoxic zone formation in the CJE,providing novel insights into how nearshore eutrophication influences organic carbon migration.

Influence of joint spacing and rock characteristics on the toppling stability of cut rock slope through a simplified limit equilibrium method

Toppling failure of rock mass/soil slope is an important geological and environmental problem.Clarifying its failure mechanism under different conditions has great significance in engineering.The toppling failure of a cutting slope occurred in a hydropower station in Kyushu,Japan illustrates that the joint characteristic played a significant role in the occurrence of rock slope tipping failure.Thus,in order to consider the mechanical properties of jointed rock mass and the influence of geometric conditions,a simplified analytical approach based on the limit equilibrium method for modeling the flexural toppling of cut rock slopes is proposed to consider the influence of the mechanical properties and geometry condition of jointed rock mass.The theoretical solution is compared with the numerical solution taking Kyushu Hydropower Station in Japan as one case,and it is found that the theoretical solution obtained by the simplified analysis method is consistent with the numerical analytical solution,thus verifying the accuracy of the simplified method.Meanwhile,the Goodman-Bray approach conventionally used in engineering practice is improved according to the analytical results.The results show that the allowable slope angle may be obtained by the improved Goodman-Bray approach considering the joint spacing,the joint frictional angle and the tensile strength of rock mass together.