A Maple Package on Symbolic Computation of Conserved Densities for （1＋l）-Dimensional Nonlinear Evolution Systems

A new algorithm for symbolic computation of polynomial-type conserved densities for nonlinear evolution systems is presented. The algorithm is implemented in Maple. The improved algorithm is more efficient not only in removing the redundant terms of the genera/form of the conserved densities but also in solving the conserved densities with the associated flux synchronously without using Euler operator. Furthermore, the program conslaw.mpl can be used to determine the preferences for a given parameterized nonlinear evolution systems. The code is tested on several well-known nonlinear evolution equations from the soliton theory.

EXACT NULL CONTROLLABILITY OF NON-AUTONOMOUS FUNCTIONAL EVOLUTION SYSTEMS WITH NONLOCAL CONDITIONS

In this article, by using theory of linear evolution system and Schauder fixed point theorem, we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonlocal conditions. In particular, the compactness condition or Lipschitz condition for the function g in the nonlocal conditions appearing in various literatures is not required here. An example is also provided to show an application of the obtained result.

Stability in Probability and Inverse Optimal Control of Evolution Systems Driven by Levy Processes

This paper first develops a Lyapunov-type theorem to study global well-posedness(existence and uniqueness of the strong variational solution)and asymptotic stability in probability of nonlinear stochastic evolution systems(SESs)driven by a special class of Levy processes,which consist of Wiener and compensated Poisson processes.This theorem is then utilized to develop an approach to solve an inverse optimal stabilization problem for SESs driven by Levy processes.The inverse optimal control design achieves global well-posedness and global asymptotic stability of the closed-loop system,and minimizes a meaningful cost functional that penalizes both states and control.The approach does not require to solve a Hamilton-Jacobi-Bellman equation(HJBE).An optimal stabilization of the evolution of the frequency of a certain genetic character from the population is included to illustrate the theoretical developments.

ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM

This paper is concerned with the existence and the nonlinear asymptotic stabil- ity of traveling wave solutions to the Cauchy problem for a system of dissipative evolution equations {θt=vζx＋（ζθ）x＋aθxx,ζt=-θx＋βζxx;with initial data and end states （ζθ）（x,0）=（ζ0,θ0）（x）→（ζ±,θ±）as x→∞.We obtain the existence of traveling wave solutions by phase plane analysis and show the asymptotic nonlinear stability of traveling wave solutions without restrictions on the coeffi- cients a and v by the method of energy estimates.

Inverse Optimal Control of Evolution Systems and Its Application to Extensible and Shearable Slender Beams

An optimal(practical) stabilization problem is formulated in an inverse approach and solved for nonlinear evolution systems in Hilbert spaces. The optimal control design ensures global well-posedness and global practical K∞-exponential stability of the closed-loop system, minimizes a cost functional,which appropriately penalizes both state and control in the sense that it is positive definite(and radially unbounded) in the state and control, without having to solve a Hamilton-Jacobi-Belman equation(HJBE). The Lyapunov functional used in the control design explicitly solves a family of HJBEs. The results are applied to design inverse optimal boundary stabilization control laws for extensible and shearable slender beams governed by fully nonlinear partial differential equations.

Phanerozoic Tectonic Evolution,Metallogenesis and Formation of Mineral Systems in China

The continental Asia is mainly composed of three major tectonic regimes,the Tethys,Paleo Asian Ocean,and West Pacific.It underwent multi-stage plate convergences,ocean-continent transformations,and subductions,collisions and/or collages,and post collisional(orogenic)extensions in Phanerozoic.Tectonic evolution of the Asia brings up a unique fault system and tectonic geomorphological features in the China's Mainland.Also,it provides a geodynamic background for the formation and evolution of metallogeneses and mineral systems,resulting in nonuniform distribution of tectono-metallogenic systems and metallogenic belts.The spatiotemporal distribution of mineral deposits in China and adjacent areas exhibits periodic variation under controlling of the full life Wilson cycle and tectonic evolution,forming the plate convergence-related mineral system in East Asia.Porphyry Cu deposits are mainly related to compressional systems in Paleozoic and early Mesozoic,and more closely related to post-collision extensional settings in late Mesozoic and Cenozoic.Orogenic Au deposits mainly formed in post-orogeny extensional setting.Alkaline rock related rare earth element deposits formed mainly at margins of the North China and Yangtze cratons.Granite-pegmatite Li and other rare metal deposits formed mainly in early Mesozoic,related to Indosinian post-orogeny extension.Tectono-metallogenic systems provide important basis for the prospecting of mineral resources.

Control of Earth system evolution on the formation and enrichment of marine ultra-deep petroleum in China

Taking the Paleozoic of the Sichuan and Tarim basins in China as example,the controlling effects of the Earth system evolution and multi-spherical interactions on the formation and enrichment of marine ultra-deep petroleum in China have been elaborated.By discussing the development of“source-reservoir-seal”controlled by the breakup and assembly of supercontinents and regional tectonic movements,and the mechanisms of petroleum generation and accumulation controlled by temperature-pressure system and fault conduit system,Both the South China and Tarim blocks passed through the intertropical convergence zone(ITCZ)of the low-latitude Hadley Cell twice during their drifts,and formed hydrocarbon source rocks with high quality.It is proposed that deep tectonic activities and surface climate evolution jointly controlled the types and stratigraphic positions of ultra-deep hydrocarbon source rocks,reservoirs,and seals in the Sichuan and Tarim basins,forming multiple petroleum systems in the Ediacaran-Cambrian,Cambrian-Ordovician,Cambrian-Permian and Permian-Triassic strata.The matching degree of source-reservoir-seal,the type of organic matter in source rocks,the deep thermal regime of basin,and the burial-uplift process across tectonic periods collectively control the entire process from the generation to the accumulation of oil and gas.Three types of oil and gas enrichment models are formed,including near-source accumulation in platform marginal zones,distant-source accumulation in high-energy beaches through faults,and three-dimensional accumulation in strike-slip fault zones,which ultimately result in the multi-layered natural gas enrichment in ultra-deep layers of the Sichuan Basin and co-enrichment of oil and gas in the ultra-deep layers of the Tarim Basin.

Prediction and Output Estimation of Pattern Moving in Non-Newtonian Mechanical Systems Based on Probability Density Evolution

A prediction framework based on the evolution of pattern motion probability density is proposed for the output prediction and estimation problem of non-Newtonian mechanical systems,assuming that the system satisfies the generalized Lipschitz condition.As a complex nonlinear system primarily governed by statistical laws rather than Newtonian mechanics,the output of non-Newtonian mechanics systems is difficult to describe through deterministic variables such as state variables,which poses difficulties in predicting and estimating the system’s output.In this article,the temporal variation of the system is described by constructing pattern category variables,which are non-deterministic variables.Since pattern category variables have statistical attributes but not operational attributes,operational attributes are assigned to them by posterior probability density,and a method for analyzing their motion laws using probability density evolution is proposed.Furthermore,a data-driven form of pattern motion probabilistic density evolution prediction method is designed by combining pseudo partial derivative(PPD),achieving prediction of the probability density satisfying the system’s output uncertainty.Based on this,the final prediction estimation of the system’s output value is realized by minimum variance unbiased estimation.Finally,a corresponding PPD estimation algorithm is designed using an extended state observer(ESO)to estimate the parameters to be estimated in the proposed prediction method.The effectiveness of the parameter estimation algorithm and prediction method is demonstrated through theoretical analysis,and the accuracy of the algorithm is verified by two numerical simulation examples.

Deep Structure Optimization for Incremental Hierarchical Fuzzy Systems Using Improved Differential Evolution Algorithm

The optimization of the rule base of a fuzzy logic system (FLS) based on evolutionary algorithm has achievednotable results. However, due to the diversity of the deep structure in the hierarchical fuzzy system (HFS) and thecorrelation of each sub fuzzy system, the uncertainty of the HFS’s deep structure increases. For the HFS, a largenumber of studies mainly use fixed structures, which cannot be selected automatically. To solve this problem, thispaper proposes a novel approach for constructing the incremental HFS. During system design, the deep structureand the rule base of the HFS are encoded separately. Subsequently, the deep structure is adaptively mutated basedon the fitness value, so as to realize the diversity of deep structures while ensuring reasonable competition amongthe structures. Finally, the differential evolution (DE) is used to optimize the deep structure of HFS and theparameters of antecedent and consequent simultaneously. The simulation results confirm the effectiveness of themodel. Specifically, the root mean square errors in the Laser dataset and Friedman dataset are 0.0395 and 0.0725,respectively with rule counts of rules is 8 and 12, respectively.When compared to alternative methods, the resultsindicate that the proposed method offers improvements in accuracy and rule counts.

Novel Adaptive Memory Event-Triggered-Based Fuzzy Robust Control for Nonlinear Networked Systems via the Differential Evolution Algorithm

This article mainly investigates the fuzzy optimization robust control issue for nonlinear networked systems characterized by the interval type-2(IT2)fuzzy technique under a differential evolution algorithm.To provide a more reasonable utilization of the constrained communication channel,a novel adaptive memory event-triggered(AMET)mechanism is developed,where two event-triggered thresholds can be dynamically adjusted in the light of the current system information and the transmitted historical data.Sufficient conditions with less conservative design of the fuzzy imperfect premise matching(IPM)controller are presented by introducing the Wirtinger-based integral inequality,the information of membership functions(MFs)and slack matrices.Subsequently,under the IPM policy,a new MFs intelligent optimization technique that takes advantage of the differential evolution algorithm is first provided for IT2 TakagiSugeno(T-S)fuzzy systems to update the fuzzy controller MFs in real-time and achieve a better system control effect.Finally,simulation results demonstrate that the proposed control scheme can obtain better system performance in the case of using fewer communication resources.

Analysis of System Value Evolution Trends of Energy Storage in Decarbonization Process

With the continuous expansion of the scale of renewable energy installation,the demand for energy storage has increased significantly.However,there are significant differences in the value of energy storage in different scenarios,and the phenomenon of diminishing marginal benefits of energy storage is becoming more apparent.Therefore,themulti-dimensional value evolution trend of energy storage has become a key issue.This study selects indicators from three dimensions of energy storage:low-carbon emission reduction,smoothing wind and solar power fluctuations,and saving generation costs,quantifying the economic,environmental,and technical values of energy storage.This forms a quantitative evaluation system for energy storage value.By comparing the calculated system values under different energy storage capacities,the marginal value evolution trend of energy storage is obtained.Meanwhile,considering factors such as the utilization rate of renewable energy,the change in energy storage value under different scenarios is analyzed.The results show that the value of long-duration energy storage is significantly affected by the energy storage capacity.Specifically,when the charge-discharge efficiency of longduration energy storage reaches 0.6 or above,the system value increases significantly.Additionally,appropriately reducing the cost of energy storage capacity also helps to improve its system value.

Numerical modeling on strain energy evolution in rock system interaction with energy-absorbing prop and rock bolt

The interaction mechanism between coal and rock masses with supporting materials is significant in roadway control, especially in deep underground mining situations where dynamic hazards frequently happened due to high geo-stress and strong disturbed effects. This paper is to investigate the strain energy evolution in the interaction between coal and rock masses with self-designed energy-absorbing props and rock bolts by numerical modeling with the finite difference method. The interaction between rock and rock bolt/prop is accomplished by the cables element and the interface between the inner and outer props. Roadway excavation and coal extraction conditions in deep mining are numerically employed to investigate deformation, plastic zone ranges, strain energy input, accumulation, dissipation,and release. The effect on strain energy input, accumulation, dissipation, and release with rock deformation, and the plastic zone is addressed. A ratio of strain energy accumulation, dissipation, and release with energy input a, β, γ is to assess the dynamic hazards. The effects on roadway excavation and coal extraction steps of a, β, γ are discussed. The results show that:(1) In deep high geo-stress roadways, the energyabsorbing support system plays a dual role in resisting deformation and reducing the scope of plastic zones in surrounding rock, as well as absorbing energy release in the surrounding rock, especially in the coal extraction state to mitigate disturbed effects.(2) The strain energy input, accumulation is dependent on roadway deformation, the strain energy dissipation is relied on plastic zone area and disturbed effects, and strain energy release density is the difference among the three. The function of energyabsorbing rock bolts and props play a key role to mitigate strain energy release density and amount, especially in coal extraction condition, with a peak density value from 4×10^(4) to 1×10^(4)J/m^(3), and amount value from 3.57×10^(8) to 1.90×10^(6)J.(3) When mining is advanced in small steps, the strain energy accumulation is dominated. While in a large step, the released energy is dominant, thus a more dynamic hazards proneness. The energy-absorbing rock bolt and prop can reduce three times strain energy release amount, thus reducing the dynamic hazards. The results suggest that energy-absorbing props and rock bolts can effectively reduce the strain energy in the coal and rock masses, and prevent rock bursts and other hazards.The numerical model developed in this study can also be used to optimize the design of energyabsorbing props and rock bolts for specific mining conditions.

Spatiotemporal evolution of ecosystem service value and topographic gradient effect in the Da-Xiao Liangshan Mountains in Sichuan Province,China

The Da-Xiao Liangshan mountains are critical ecological function areas and essential ecological barriers in the upper reaches of the Yangtze River in China.This study selected a total of six periods of land use land cover(LULC)data from 1995 to 2020,to estimate the ecosystem service value(ESV)and analyzed its spatiotemporal evolution and topographic gradient divergence.The results showed that:(1)The ESV increased by 1.1 billion yuan,with an increase rate of 1.47%from 1995 to 2020.Two time periods,2005–2010 and 2015–2020,showed more significant increases than other periods.(2)The elevation and slope of mountainous areas determine the type of land use and further influence the spatial pattern of ESV.(3)Although woodland and grassland are the main land use types of the study area(more than 90%),the hydrological regulation function of the water area partially compensated for the impact of the encroachment of the built-up area on the ESV of grassland.(4)The spatial distribution of ESVs showed an inverted V-shaped characteristic as the topographic gradient increased,with the dominant position being the 5th topographic gradient zone.Finally,this study provided relevant recommendations for ecosystem protection and optimization.The findings of this study clarified the influence of topographical factors on the spatial differentiation of ESV and provided novel insights into ecosystem protection.

Spatio-temporal Evolution of the Rural Regional System and Its Evolution Mechanism in Huang-Huai-Hai Area of China

The problem of rural development arises from the evolution of rural regional system.It is urgent to deepen the research on the evolution process and mechanism of rural regional system.However,there are relatively few studies on rural development from the perspective of the evolution process,driving mechanism and evolution mechanism of rural regional system.Therefore,this study took Huang-Huai-Hai Area for example,started with the systematicness of the rural regional system,the spatio-temporal pattern and driving mechanism of rural regional system evolution,and further summarized and refined the evolution mechanism of the rural regional system.The methods of spatial pattern analysis,gray correlation degree and geographical detection were adopted.The results showed that the problems in rural areas were often dominated by one factor and produced by the joint action of many factors.Factors such as county urbanization,county economy,county public service,agricultural mechanization,surrounding cities and convenient transportation will affect the evolution of rural regional systems.Based on the evolution of the elements in the rural regional system,the evolution types of rural regional system can be divided into decline type,equilibrium type and growth type.This study can provide a reference for understanding the process of rural rise and fall and can also guide rural revitalization and rural sustainable development.

Insight into the ammonia torrefaction and pyrolysis system of cellulose:Unraveling the evolution of chemical structure and nitrogen migration mechanism

This study aimed to investigate the mechanism of nitrogen doping,migration,and conversion during ammonia torrefaction and also explore the evolution law of the chemical structure of cellulose.The results showed that the ammonia torrefaction pretreatment could significantly optimize the distribution of nitrogen and oxygen elements in cellulose.The carbon skeleton first captured the active nitrogenous radicals to form-NHn-N,and pyridine-N and pyrrole-N originated from the conversion of-NHn-N.The existence of C=O played a major role in the immobilization of nitrogen.The nitrogen in bio-oil exists mainly in the form of five-and six-membered heterocycles.The correlation analysis showed that the main precursors for the formation of nitrogenous heterocyclic compounds were five-membered Oheterocyclic compounds.Finally,the product distribution characteristics in the torrefaction-pyrolysis systems were summarized,and the nitrogen doping and conversion mechanisms were proposed.This study expanded the boundaries of cellulose pretreatment and the production of high-value chemicals.

Design of high-performance ion-doped CoP systems for hydrogen evolution:From multi-level screening calculations to experiment

Rational design of high-performance electrocatalysts for hydrogen evolution reaction(HER)is vital for future renewable energy systems.The incorporation of foreign metal ions into catalysts can be an effective approach to optimize its performance.However,there is a lack of systematic theoretical studies to reveal the quantitative relationships at the electronic level.Here,we develop a multi-level screening methodology to search for highly stable and active dopants for CoP catalysts.The density functional theory(DFT)calculations and symbolic regression(SR)were performed to investigate the relationship between the adsorption free energy(ΔG_(H^(*)))and 10 electronic parameters.The mathematic formulas derived from SR indicate that the difference of work function(ΔΦ)between doped metal and the acceptor plays the most important role in regulatingΔG_(H^(*)),followed by the d-band center(d-BC)of doped system.The descriptor of HER can be expressed asΔG_(H^(*))=1.59×√|0.188ΔΦ+d BC+0.120|1/2-0.166 with a high determination coefficient(R^(2)=0.807).Consistent with the theoretical prediction,experimental results show that the Al-CoP delivers superior electrocatalytic HER activity with a low overpotential of75 m V to drive a current density of 10 mA cm^(-2),while the overpotentials for undoped CoP,Mo-CoP,and V-CoP are 206,134,and 83 m V,respectively.The current work proves that theΔΦis the most significant regulatory parameter ofΔG_(H^(*))for ion-doped electrocatalysts.This finding can drive the discovery of high-performance ion-doped electrocatalysts,which is crucial for electrocatalytic water splitting.

Deformable Catalytic Material Derived from Mechanical Flexibility for Hydrogen Evolution Reaction

Deformable catalytic material with excellent flexible structure is a new type of catalyst that has been applied in various chemical reactions,especially electrocatalytic hydrogen evolution reaction(HER).In recent years,deformable catalysts for HER have made great progress and would become a research hotspot.The catalytic activities of deformable catalysts could be adjustable by the strain engineering and surface reconfiguration.The surface curvature of flexible catalytic materials is closely related to the electrocatalytic HER properties.Here,firstly,we systematically summarized self-adaptive catalytic performance of deformable catalysts and various micro–nanostructures evolution in catalytic HER process.Secondly,a series of strategies to design highly active catalysts based on the mechanical flexibility of lowdimensional nanomaterials were summarized.Last but not least,we presented the challenges and prospects of the study of flexible and deformable micro–nanostructures of electrocatalysts,which would further deepen the understanding of catalytic mechanisms of deformable HER catalyst.

Precisely Control Relationship between Sulfur Vacancy and H Absorption for Boosting Hydrogen Evolution Reaction

Ef fective and robust catalyst is the core of water splitting to produce hydrogen.Here, we report an anionic etching method to tailor the sulfur vacancy(VS) of NiS_(2) to further enhance the electrocatalytic performance for hydrogen evolution reaction(HER). With the VS concentration change from 2.4% to 8.5%, the H* adsorption strength on S sites changed and NiS_(2)-VS 5.9% shows the most optimized H* adsorption for HER with an ultralow onset potential(68 m V) and has long-term stability for 100 h in 1 M KOH media. In situ attenuated-total-reflection Fourier transform infrared spectroscopy(ATR-FTIRS) measurements are usually used to monitor the adsorption of intermediates. The S-H* peak of the Ni S_(2)-VS 5.9% appears at a very low voltage, which is favorable for the HER in alkaline media. Density functional theory calculations also demonstrate the Ni S_(2)-VS 5.9% has the optimal |ΔG^(H*)| of 0.17 e V. This work offers a simple and promising pathway to enhance catalytic activity via precise vacancies strategy.

Valence electronic engineering of superhydrophilic Dy-evoked Ni-MOF outperforming RuO_(2) for highly efficient electrocatalytic oxygen evolution

Tackling the problem of poor conductivity and catalytic stability of pristine metal-organic frameworks(MOFs) is crucial to improve their oxygen evolution reaction(OER) performance.Herein,we introduce a novel strategy of dysprosium(Dy) doping,using the unique 4f orbitals of this rare earth element to enhance electrocatalytic activity of MOFs.Our method involves constructing Dy-doped Ni-MOF(Dy@Ni-MOF) nanoneedles on carbon cloth via a Dy-induced valence electronic perturbation approach.Experiments and density functional theory(DFT) calculations reveal that Dy doping can effectively modify the electronic structure of the Ni active centers and foster a strong electronic interaction between Ni and Dy.The resulting benefits include a reduced work function and a closer proximity of the d-band center to the Fermi level,which is conducive to improving electrical conductivity and promoting the adsorption of oxygen-containing intermediates.Furthermore,the Dy@Ni-MOF achieves superhydrophilicity,ensuring effective electrolyte contact and thus accelerating reaction kinetics,Ex-situ and in-situ analysis results manifest Dy_(2)O_(3)/NiOOH as the actual active species.Therefore,Dy@Ni-MOF shows impressive OER performance,significantly surpassing Ni-MOF.Besides,the overall water splitting device with Dy@NiMOF as an anode delivers a low cell voltage of 1.51 V at 10 mA cm^(-2) and demonstrates long-term stability for 100 h,positioning it as a promising substitute for precious metal catalysts.

Mg/MgO interfaces as efficient hydrogen evolution cathodes causing accelerated corrosion of additive manufactured Mg alloys:A DFT analysis

The corrosion rates of additive-manufactured Mg alloys are higher than their as-cast counterparts,possibly due to increased kinetics for the hydrogen evolution reaction on secondary phases,which may include oxide inclusions.Scanning Kelvin Probe Force Microscopy demonstrated that MgO inclusions could act as cathodes for Mg corrosion,but their low conductivity likely precludes this.However,the density of state calculations through density functional theory using hybrid HSE06 functional revealed overlapping electronic states at the Mg/MgO interface,which facilitates electron transfers and participates in redox reactions.Subsequent determination of the hydrogen absorption energy at the Mg/MgO interface reveals it to be an excellent catalytic site,with HER being found to be a factor of 23x more efficient at the interface than on metallic Mg.The results not only support the plausibility of the Mg/MgO interface being an effective cathode to the adjacent anodic Mg matrix during corrosion but also contribute to the understanding of the enhanced cathodic activities observed during the anodic dissolution of magnesium.