Strong Stability Preserving IMEX Methods for Partitioned Systems of Differential Equations

We investigate strong stability preserving(SSP)implicit-explicit(IMEX)methods for partitioned systems of differential equations with stiff and nonstiff subsystems.Conditions for order p and stage order q=p are derived,and characterization of SSP IMEX methods is provided following the recent work by Spijker.Stability properties of these methods with respect to the decoupled linear system with a complex parameter,and a coupled linear system with real parameters are also investigated.Examples of methods up to the order p=4 and stage order q—p are provided.Numerical examples on six partitioned test systems confirm that the derived methods achieve the expected order of convergence for large range of stepsizes of integration,and they are also suitable for preserving the accuracy in the stiff limit or preserving the positivity of the numerical solution for large stepsizes.

Hybrid Strategy of Partitioned and Monolithic Methods for Solving Strongly Coupled Analysis of Inverse and Direct Piezoelectric and Circuit Coupling

The inverse and direct piezoelectric and circuit coupling are widely observed in advanced electro-mechanical systems such as piezoelectric energy harvesters.Existing strongly coupled analysis methods based on direct numerical modeling for this phenomenon can be classified into partitioned or monolithic formulations.Each formulation has its advantages and disadvantages,and the choice depends on the characteristics of each coupled problem.This study proposes a new option:a coupled analysis strategy that combines the best features of the existing formulations,namely,the hybrid partitioned-monolithic method.The analysis of inverse piezoelectricity and the monolithic analysis of direct piezoelectric and circuit interaction are strongly coupled using a partitioned iterative hierarchical algorithm.In a typical benchmark problem of a piezoelectric energy harvester,this research compares the results from the proposed method to those from the conventional strongly coupled partitioned iterative method,discussing the accuracy,stability,and computational cost.The proposed hybrid concept is effective for coupled multi-physics problems,including various coupling conditions.

Algorithm Selection Method Based on Coupling Strength for Partitioned Analysis of Structure-Piezoelectric-Circuit Coupling

In this study, we propose an algorithm selection method based on coupling strength for the partitioned analysis ofstructure-piezoelectric-circuit coupling, which includes two types of coupling or inverse and direct piezoelectriccoupling and direct piezoelectric and circuit coupling. In the proposed method, implicit and explicit formulationsare used for strong and weak coupling, respectively. Three feasible partitioned algorithms are generated, namely(1) a strongly coupled algorithm that uses a fully implicit formulation for both types of coupling, (2) a weaklycoupled algorithm that uses a fully explicit formulation for both types of coupling, and (3) a partially stronglycoupled and partially weakly coupled algorithm that uses an implicit formulation and an explicit formulation forthe two types of coupling, respectively.Numerical examples using a piezoelectric energy harvester,which is a typicalstructure-piezoelectric-circuit coupling problem, demonstrate that the proposed method selects the most costeffectivealgorithm.

Experimental Investigation of Lee–Yang Criticality Using Non-Hermitian Quantum System

Lee–Yang theory clearly demonstrates where the phase transition of many-body systems occurs and the asymptotic behavior near the phase transition using the partition function under complex parameters. The complex parameters make the direct investigation of Lee–Yang theory in practical systems challenging. Here we construct a non-Hermitian quantum system that can correspond to the one-dimensional Ising model with imaginary parameters through the equality of partition functions. By adjusting the non-Hermitian parameter,we successfully obtain the partition function under different imaginary magnetic fields and observe the Lee–Yang zeros. We also observe the critical behavior of free energy in vicinity of Lee–Yang zero that is consistent with theoretical prediction. Our work provides a protocol to study Lee–Yang zeros of the one-dimensional Ising model using a single-qubit non-Hermitian system.

Airgap-harmonic-oriented Partitioned Design Method of PMV Motor with Improved Torque Performances

Here,we introduce a partitioned design method that is oriented toward airgap harmonic for permanent magnet vernier(PMV)motors.The method proposes the utilization of airgap flux harmonics as an effective bridge between the torque design region and the torque performances.To illustrate the efficacy of this method,a partitioned design PMV motor is presented and compared with the initial design.Firstly,the torque design region of the rotor is artfully divided into the torque enhancement region and ripple reduction region.Meanwhile,the main harmonics that generate output torque are chosen and enhanced,optimization.Moreover,the harmonics that generate torque ripple are selected and reduced based on torque harmonics optimization.Finally,the functions of the partitioned PMV motor torque are assessed based on the finite element method.By the purposeful design of these two regions,the output torque is strengthened while torque ripple is inhibited effectively,verifying the effectiveness and reasonability of the proposed design method.

Strong coupling between height of gaps and thickness of thermal boundary layer in partitioned convection system

A direct numerical simulation(DNS) method is used to calculate the partitioned convection system with Ra number ranging from 10^7 to 2×10^9.Using the boundary layer thickness to normalize the height of gaps d, we find a strong consistency between the variation of the TD number(the average value of the temperature in each heat transfer channel is averaged after taking the absolute values) with the change of the height of gaps and the variation of the TD number with the change of Ra number in partitioned convection.For a given thickness of partition, heights of gaps are approximately equal to 0.5 or 1 time of the thermal boundary layer thickness λθ at different Ra numbers.TD number representing temperature characteristics is almost the constant value, which means that TD number is a function of d/λθ only.Analysis of local temperature field of area in gaps shows that the temperature distribution in the gaps are basically the same when d/λθ is certain.The heat transfer Nu number of the system at d/λθ≈ 0.5 is larger than that of d/λθ≈ 1, both of them have the same scaling law with Ra number and Nu^Ra^0.25.

System Vulnerability Analysis Using Graph Pathfinding Strategies in Partitioned Networks

In this paper, a new method has been introduced to find the most vulnerable lines in the system dynamically in an interconnected power system to help with the security and load flow analysis in these networks. Using the localization of power networks, the power grid can be divided into several divisions of sub-networks in which, the connection of the elements is stronger than the elements outside of that division. By using our proposed method, the probable important lines in the network can be identified to do the placement of the protection apparatus and planning for the extra extensions in the system. In this paper, we have studied the pathfinding strategies in most vulnerable line detection in a partitioned network. The method has been tested on IEEE39-bus system which is partitioned using hierarchical spectral clustering to show the feasibility of the proposed method.

Symplectic partitioned Runge-Kutta method based onthe eighth-order nearly analytic discrete operator and its wavefield simulations

We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.

Alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of AuCu_3-type sublattice system

Taking AuCu3-type sublattice system as an example, three discoveries have been presented: First, the third barrier hindering the progress in metal materials science is that researchers have got used to recognizing experimental phenomena of alloy phase transitions during extremely slow variation in temperature by equilibrium thinking mode and then taking erroneous knowledge of experimental phenomena as selected information for establishing Gibbs energy function and so-called equilibrium phase diagram. Second, the equilibrium holographic network phase diagrams of AuCu3-type sublattice system may be used to describe systematic correlativity of the composition?temperature-dependent alloy gene arranging structures and complete thermodynamic properties, and to be a standard for studying experimental subequilibrium order-disorder transition. Third, the equilibrium transition of each alloy is a homogeneous single-phase rather than a heterogeneous two-phase, and there exists a single-phase boundary curve without two-phase region of the ordered and disordered phases; the composition and temperature of the top point on the phase-boundary curve are far away from the ones of the critical point of the AuCu3 compound.

Alloy gene Gibbs energy partition function and equilibrium holographic network phase diagrams of Au_3Cu-type sublattice system

Taking Au3Cu-type sublattice system as an example, three discoveries have been presented. First, the fourth barrier to hinder the progress of metal materials science is that today’s researchers do not understand that the Gibbs energy function of an alloy phase should be derived from Gibbs energy partition function constructed of alloy gene sequence and their Gibbs energy sequence. Second, the six rules for establishing alloy gene Gibbs energy partition function have been discovered, and it has been specially proved that the probabilities of structure units occupied at the Gibbs energy levels in the degeneracy factor for calculating configuration entropy should be degenerated as ones of component atoms occupied at the lattice points. Third, the main characteristics unexpected by today’s researchers are as follows. There exists a single-phase boundary curve without two-phase region coexisting by the ordered and disordered phases. The composition and temperature of the top point on the phase-boundary curve are far away from those of the critical point of the Au3Cu compound; At 0 K, the composition of the lowest point on the composition-dependent Gibbs energy curve is notably deviated from that of the Au3Cu compounds. The theoretical limit composition range of long range ordered Au3Cu-type alloys is determined by the first jumping order degree.

Effects of projectile parameters on the momentum transfer and projectile melting during hypervelocity impact

The effects of projectile/target impedance matching and projectile shape on energy,momentum transfer and projectile melting during collisions are investigated by numerical simulation.By comparing the computation results with the experimental results,the correctness of the calculation and the statistical method of momentum transfer coefficient is verified.Different shapes of aluminum,copper and heavy tungsten alloy projectiles striking aluminum,basalt,and pumice target for impacts up to 10 km/s are simulated.The influence mechanism of the shape of the projectile and projectile/target density on the momentum transfer was obtained.With an increase in projectile density and length-diameter ratio,the energy transfer time between the projectile and targets is prolonged.The projectile decelerates slowly,resulting in a larger cratering depth.The energy consumed by the projectile in the excavation stage increased,resulting in lower mass-velocity of ejecta and momentum transfer coefficient.The numerical simulation results demonstrated that for different projectile/target combinations,the higher the wave impedance of the projectile,the higher the initial phase transition velocity and the smaller the mass of phase transition.The results can provide theoretical guidance for kinetic impactor design and material selection.

ADVANCED FREQUENCY-DIRECTED RUN-LENTH BASED CODING SCHEME ON TEST DATA COMPRESSION FOR SYSTEM-ON-CHIP

Test data compression and test resource partitioning （TRP） are essential to reduce the amount of test data in system-on-chip testing. A novel variable-to-variable-length compression codes is designed as advanced fre- quency-directed run-length （AFDR） codes. Different [rom frequency-directed run-length （FDR） codes, AFDR encodes both 0- and 1-runs and uses the same codes to the equal length runs. It also modifies the codes for 00 and 11 to improve the compression performance. Experimental results for ISCAS 89 benchmark circuits show that AFDR codes achieve higher compression ratio than FDR and other compression codes.

Long Duration Coverage Control of Multiple Robotic Surface Vehicles Under Battery Energy Constraints

Dear Editor,This letter addresses long duration coverage problem of multiple robotic surface vehicles(RSVs) subject to battery energy constraints,in addition to uncertainties and disturbances. An anti-disturbance energy-aware control method is proposed for performing coverage task of RSVs. Firstly, a centroidal Voronoi tessellation(CVT) is used to optimize the partition of the given coverage area.

Restraint effect of partition wall on the tunnel floor heave in layered rock mass

The presence of horizontal layered rocks in tunnel engineering significantly impacts the stability and strength of the surrounding rock mass,leading to floor heave in the tunnel.This study focused on preparing layered specimens of rock-like material with varying thickness to investigate the failure behaviors of tunnel floors.The results indicate that thin-layered rock mass exhibits weak interlayer bonding,causing rock layers near the surface to buckle and break upwards when subjected to horizontal squeezing.With an increase in the layer thickness,a transition in failure mode occurs from upward buckling to shear failure along the plane,leading to a noticeable reduction in floor heave deformation.The primary cause of significant deformation in floor heave is upward buckling failure.To address this issue,the study proposes the installation of a partition wall in the middle of the floor to mitigate heave deformation of the rock layers.The results demonstrate that the partition wall has a considerable stabilizing effect on the floor,reducing the zone of buckling failure and minimizing floor heave deformation.It is crucial for the partition wall to be sufficiently high to prevent buckling failure and ensure stability.Through simulation calculations on an engineering example,it is confirmed that implementing a partition wall can effectively reduce floor heave and enhance the stability of tunnel floor.

Dependence of impact regime boundaries on the initial temperatures of projectiles and targets

Towards higher impact velocities,ballistic events are increasingly determined by the material temperatures.Related effects might range from moderate thermal softening to full phase transition.In particular,it is of great interest to quantify the conditions for incipient or full melting of metals during impact interactions,which result in a transition from still strength-affected to hydrodynamic material behavior.In this work,we investigate to which extent the respective melting thresholds are also dependent on the initial,and generally elevated,temperatures of projectiles and targets before impact.This is studied through the application of a model developed recently by the authors to characterize the transition regime between high-velocity and hypervelocity impact,for which the melting thresholds of materials were used as the defining quantities.The obtained results are expected to be of general interest for ballistic application cases where projectiles or targets are preheated.Such conditions might result,for example,from aerodynamic forces acting onto a projectile during atmospheric flight,explosive shapedcharge-jet formation or armor exposure to environmental conditions.The performed analyses also broaden the scientific understanding of the relevance of temperature in penetration events,generally known since the 1960s,but often not considered thoroughly in impact studies.

A simple route for preparation of TRIP-assisted Si-Mn steel with excellent performance using direct strip casting

The complex producing procedures and high energy-consuming limit the large-scale production and application of advanced high-strength steels(AHSSs).In this study,the direct strip casting(DSC)technology with unique sub-rapid solidification characteristics and cost advantages was applied to the production of low-alloy Si-Mn steel with the help of quenching&partitioning(Q&P)concept to address these issues.Compared this method with the conventional compact strip production(CSP)process,the initial microstructure formed under different solidification conditions and the influence of heat treatment processes on the final mechanical properties were in-vestigated.The results show that the initial structure of the DSC sample is a dual-phase structure composed of fine lath martensite and bainite,while the initial structure of the CSP sample consists of pearlite and ferrite.The volume fraction and carbon content of retained austenite(RA)in DSC samples are usually higher than those in CSP samples after the same Q&P treatment.DSC samples typically demonstrate better comprehensive mechanical properties than the CSP sample.The DSC sample partitioned at 300℃ for 300 s(DSC-Pt300)achieves the best comprehensive mechanical properties,with yield strength(YS)of 1282 MPa,ultimate tensile strength(UTS)of 1501 MPa,total elongation(TE)of 21.5%,and product of strength and elongation(PSE)as high as 32.3 GPa·%.These results indicate that the excellent mechanical properties in low-alloy Si-Mn steel can be obtained through a simple process(DSC-Q&P),which also demonstrates the superiority of DSC technology in manufacturing AHSSs.

The Weighted Basis for PHT-Splines

PHT-splines are defined as polynomial splines over hierarchical T-meshes with very efficient local refinement properties.The original PHT-spline basis functions constructed by the truncation mechanism have a decay phenomenon,resulting in numerical instability.The non-decay basis functions are constructed as the B-splines that are defined on the 2×2 tensor product meshes associated with basis vertices in Kang et al.,but at the cost of losing the partition of unity.In the field of finite element analysis and topology optimization,forming the partition of unity is the default ingredient for constructing basis functions of approximate spaces.In this paper,we will show that the non-decay PHT-spline basis functions proposed by Kang et al.can be appropriately modified to form a partition of unity.Each non-decay basis function is multiplied by a positive weight to form the weighted basis.The weights are solved such that the sum of weighted bases is equal to 1 on the domain.We provide two methods for calculatingweights,based on geometric information of basis functions and the subdivision of PHT-splines.Weights are given in the form of explicit formulas and can be efficiently calculated.We also prove that the weights on the admissible hierarchical T-meshes are positive.

A Sharding Scheme Based on Graph Partitioning Algorithm for Public Blockchain

Blockchain technology,with its attributes of decentralization,immutability,and traceability,has emerged as a powerful catalyst for enhancing traditional industries in terms of optimizing business processes.However,transaction performance and scalability has become the main challenges hindering the widespread adoption of blockchain.Due to its inability to meet the demands of high-frequency trading,blockchain cannot be adopted in many scenarios.To improve the transaction capacity,researchers have proposed some on-chain scaling technologies,including lightning networks,directed acyclic graph technology,state channels,and shardingmechanisms,inwhich sharding emerges as a potential scaling technology.Nevertheless,excessive cross-shard transactions and uneven shard workloads prevent the sharding mechanism from achieving the expected aim.This paper proposes a graphbased sharding scheme for public blockchain to efficiently balance the transaction distribution.Bymitigating crossshard transactions and evening-out workloads among shards,the scheme reduces transaction confirmation latency and enhances the transaction capacity of the blockchain.Therefore,the scheme can achieve a high-frequency transaction as well as a better blockchain scalability.Experiments results show that the scheme effectively reduces the cross-shard transaction ratio to a range of 35%-56%and significantly decreases the transaction confirmation latency to 6 s in a blockchain with no more than 25 shards.

Improved simulation of winter wheat yield in North China Plain by using PRYM-Wheat integrated dry matter distribution coefficient

The accurate simulation of regional-scale winter wheat yield is important for national food security and the balance of grain supply and demand in China.Presently,most remote sensing process models use the“biomass×harvest index(HI)”method to simulate regional-scale winter wheat yield.However,spatiotemporal differences in HI contribute to inaccuracies in yield simulation at the regional scale.Time-series dry matter partition coefficients(Fr)can dynamically reflect the dry matter partition of winter wheat.In this study,Fr equations were fitted for each organ of winter wheat using site-scale data.These equations were then coupled into a process-based and remote sensingdriven crop yield model for wheat(PRYM-Wheat)to improve the regional simulation of winter wheat yield over the North China Plain(NCP).The improved PRYM-Wheat model integrated with the fitted Fr equations(PRYM-Wheat-Fr)was validated using data obtained from provincial yearbooks.A 3-year(2000-2002)averaged validation showed that PRYM-Wheat-Fr had a higher coefficient of determination(R^(2)=0.55)and lower root mean square error(RMSE=0.94 t ha^(-1))than PRYM-Wheat with a stable HI(abbreviated as PRYM-Wheat-HI),which had R^(2) and RMSE values of 0.30 and 1.62 t ha^(-1),respectively.The PRYM-Wheat-Fr model also performed better than PRYM-Wheat-HI for simulating yield in verification years(2013-2015).In conclusion,the PRYM-Wheat-Fr model exhibited a better accuracy than the original PRYM-Wheat model,making it a useful tool for the simulation of regional winter wheat yield.

Evaluating the relative importance of predictors in Generalized Additive Models using the gam.hp R package

Generalized Additive Models(GAMs)are widely employed in ecological research,serving as a powerful tool for ecologists to explore complex nonlinear relationships between a response variable and predictors.Nevertheless,evaluating the relative importance of predictors with concurvity(analogous to collinearity)on response variables in GAMs remains a challenge.To address this challenge,we developed an R package named gam.hp.gam.hp calculates individual R^(2) values for predictors,based on the concept of'average shared variance',a method previously introduced for multiple regression and canonical analyses.Through these individual R^(2)s,which add up to the overall R^(2),researchers can evaluate the relative importance of each predictor within GAMs.We illustrate the utility of the gam.hp package by evaluating the relative importance of emission sources and meteorological factors in explaining ozone concentration variability in air quality data from London,UK.We believe that the gam.hp package will improve the interpretation of results obtained from GAMs.