Distributed Nash Equilibrium Seeking Strategies Under Quantized Communication

This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.

Magnetopause properties at the dusk magnetospheric flank from global magnetohydrodynamic simulations,the kinetic Vlasov equilibrium,and in situ observations--Potential implications for SMILE

We derived the properties of the terrestrial magnetopause(MP)from two modeling approaches,one global–fluid,the other local–kinetic,and compared the results with data collected in situ by the Magnetospheric Multiscale 2(MMS2)spacecraft.We used global magnetohydrodynamic(MHD)simulations of the Earth’s magnetosphere(publicly available from the NASA-CCMC[National Aeronautics and Space Administration–Community Coordinated Modeling Center])and local Vlasov equilibrium models(based on kinetic models for tangential discontinuities)to extract spatial profiles of the plasma and field variables at the Earth’s MP.The global MHD simulations used initial solar wind conditions extracted from the OMNI database at the time epoch when the MMS2 observes the MP.The kinetic Vlasov model used asymptotic boundary conditions derived from the same in situ MMS measurements upstream or downstream of the MP.The global MHD simulations provide a three-dimensional image of the magnetosphere at the time when the MMS2 crosses the MP.The Vlasov model provides a one-dimensional local view of the MP derived from first principles of kinetic theory.The MMS2 experimental data also serve as a reference for comparing and validating the numerical simulations and modeling.We found that the MP transition layer formed in global MHD simulations was generally localized closer to the Earth(roughly by one Earth radius)from the position of the real MP observed by the MMS.We also found that the global MHD simulations overestimated the thickness of the MP transition by one order of magnitude for three analyzed variables:magnetic field,density,and tangential speed.The MP thickness derived from the local Vlasov equilibrium was consistent with observations for all three of these variables.The overestimation of density in the Vlasov equilibrium was reduced compared with the global MHD solutions.We discuss our results in the context of future SMILE(Solar wind Magnetosphere Ionosphere Link Explorer)campaigns for observing the Earth’s MP.

Kinetic equilibrium reconstruction with internal safety factor profile constraints on EAST tokamak

Reconstruction of plasma equilibrium plays an important role in the analysis and simulation of plasma experiments. The kinetic equilibrium reconstruction with pressure and edge current constraints has been employed on EAST tokamak. However, the internal safety factor(q) profile is not accurate. This paper proposes a new way of incorporating q profile constraints into kinetic equilibrium reconstruction. The q profile is yielded from the Polarimeter Interferometer(POINT)reconstruction. Virtual probes containing information on q profile constraints are added to inputs of the kinetic equilibrium reconstruction program to obtain the final equilibrium. The new equilibrium produces a more accurate internal q profile. This improved method would help analyze EAST experiments.

Numerical analysis for the free-boundary current reversal equilibrium in the AC plasma current operation in a tokamak

In recent decades, tokamak discharges with zero total toroidal current have been reported in tokamak experiments, and this is one of the key problems in alternating current(AC) operations.An efficient free-boundary equilibrium code is developed to investigate such advanced tokamak discharges with current reversal equilibrium configuration. The calculation results show that the reversal current equilibrium can maintain finite pressure and also has considerable effects on the position of the X-point and the magnetic separatrix shape, and hence also on the position of the strike point on the divertor plates, which is extremely useful for magnetic design, MHD stability analysis, and experimental data analysis etc. for the AC plasma current operation on tokamaks.

Deciphering the linear relationship in the activity of the oxygen reduction reaction on Pt electrodes:A decisive role of adsorbates

Despite substantial efforts in developing high-performance catalysts for the oxygen reduction reaction(ORR),the persistent challenge lies in the high onset overpotential of the ORR,and the effect of the elec-trolyte solution cannot be ignored.Consequently,we have systematically investigated the impact of adsorbate species and concentration,as well as solution pH,on the ORR activity on Pt(111)and Pt(poly)electrodes.The results all tend to establish a linear quantitative relationship between the onset potential for ORR and the adsorption equilibrium potential of the adsorbate.This finding indicates the decisive role of adsorbates in the onset potential for ORR,suggesting that the adsorption potential of adsorbates can serve as an intuitive criterion for ORR activity.Additional support for this conclusion is derived from experimental results obtained from the oxygen evolution reaction on Pt(poly)with different adsorbate species and from the hydrogen evolution reaction on Pt(111)with iodine adsorption.We further propose both an empirical equation for the onset potential for ORR and the concept of a potential-regulated adsor-bate shielding effect to elucidate the influence of adsorbates on ORR activity.This study provides new insights into the high onset overpotential of the ORR and offers potential strategies for predicting and enhancingORRactivity inthefuture.

Phase equilibrium data prediction and process optimizationin butadiene extraction process

In response to the lack of reliable physical parameters in the process simulation of the butadiene extraction,a large amount of phase equilibrium data were collected in the context of the actual process of butadiene production by acetonitrile.The accuracy of five prediction methods,UNIFAC(UNIQUAC Functional-group Activity Coefficients),UNIFAC-LL,UNIFAC-LBY,UNIFAC-DMD and COSMO-RS,applied to the butadiene extraction process was verified using partial phase equilibrium data.The results showed that the UNIFAC-DMD method had the highest accuracy in predicting phase equilibrium data for the missing system.COSMO-RS-predicted multiple systems showed good accuracy,and a large number of missing phase equilibrium data were estimated using the UNIFAC-DMD method and COSMO-RS method.The predicted phase equilibrium data were checked for consistency.The NRTL-RK(non-Random Two Liquid-Redlich-Kwong Equation of State)and UNIQUAC thermodynamic models were used to correlate the phase equilibrium data.Industrial device simulations were used to verify the accuracy of the thermodynamic model applied to the butadiene extraction process.The simulation results showed that the average deviations of the simulated results using the correlated thermodynamic model from the actual values were less than 2%compared to that using the commercial simulation software,Aspen Plus and its database.The average deviation was much smaller than that of the simulations using the Aspen Plus database(>10%),indicating that the obtained phase equilibrium data are highly accurate and reliable.The best phase equilibrium data and thermodynamic model parameters for butadiene extraction are provided.This improves the accuracy and reliability of the design,optimization and control of the process,and provides a basis and guarantee for developing a more environmentally friendly and economical butadiene extraction process.

Stability analysis of tunnel face reinforced with face bolts

Face bolting has been widely utilized to enhance the stability of tunnel face,particularly in soft soil tunnels.However,the influence of bolt reinforcement and its layout on tunnel face stability has not been systematically studied.Based on the theory of linear elastic mechanics,this study delved into the specific mechanisms of bolt reinforcement on the tunnel face in both horizontal and vertical dimensions.It also identified the primary failure types of bolts.Additionally,a design approach for tunnel face bolts that incorporates spatial layout was established using the limit equilibrium method to enhance the conventional wedge-prism model.The proposed model was subsequently validated through various means,and the specific influence of relevant bolt design parameters on tunnel face stability was analyzed.Furthermore,design principles for tunnel face bolts under different geological conditions were presented.The findings indicate that bolt failure can be categorized into three stages:tensile failure,pullout failure,and comprehensive failure.Increasing cohesion,internal friction angle,bolt density,and overlap length can effectively enhance tunnel face stability.Due to significant variations in stratum conditions,tailored design approaches based on specific failure stages are necessary for bolt design.

Multi-Objective Equilibrium Optimizer for Feature Selection in High-Dimensional English Speech Emotion Recognition

Speech emotion recognition(SER)uses acoustic analysis to find features for emotion recognition and examines variations in voice that are caused by emotions.The number of features acquired with acoustic analysis is extremely high,so we introduce a hybrid filter-wrapper feature selection algorithm based on an improved equilibrium optimizer for constructing an emotion recognition system.The proposed algorithm implements multi-objective emotion recognition with the minimum number of selected features and maximum accuracy.First,we use the information gain and Fisher Score to sort the features extracted from signals.Then,we employ a multi-objective ranking method to evaluate these features and assign different importance to them.Features with high rankings have a large probability of being selected.Finally,we propose a repair strategy to address the problem of duplicate solutions in multi-objective feature selection,which can improve the diversity of solutions and avoid falling into local traps.Using random forest and K-nearest neighbor classifiers,four English speech emotion datasets are employed to test the proposed algorithm(MBEO)as well as other multi-objective emotion identification techniques.The results illustrate that it performs well in inverted generational distance,hypervolume,Pareto solutions,and execution time,and MBEO is appropriate for high-dimensional English SER.

Equilibrium Strategy of the Pursuit-Evasion Game in Three-Dimensional Space

The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.

Deep learning approaches to recover the plasma current density profile from the safety factor based on Grad–Shafranov solutions across multiple tokamaks

Many magnetohydrodynamic stability analyses require generation of a set of equilibria with a fixed safety factor q-profile while varying other plasma parameters.A neural network(NN)-based approach is investigated that facilitates such a process.Both multilayer perceptron(MLP)-based NN and convolutional neural network(CNN)models are trained to map the q-profile to the plasma current density J-profile,and vice versa,while satisfying the Grad–Shafranov radial force balance constraint.When the initial target models are trained,using a database of semianalytically constructed numerical equilibria,an initial CNN with one convolutional layer is found to perform better than an initial MLP model.In particular,a trained initial CNN model can also predict the q-or J-profile for experimental tokamak equilibria.The performance of both initial target models is further improved by fine-tuning the training database,i.e.by adding realistic experimental equilibria with Gaussian noise.The fine-tuned target models,referred to as fine-tuned MLP and fine-tuned CNN,well reproduce the target q-or J-profile across multiple tokamak devices.As an important application,these NN-based equilibrium profile convertors can be utilized to provide a good initial guess for iterative equilibrium solvers,where the desired input quantity is the safety factor instead of the plasma current density.

Intrinsic correlation between the generalized phase equilibrium condition and mechanical behaviors in hydrate-bearing sediments

The phase equilibrium and mechanical behaviors of natural gas hydrate-bearing sediment are essential for gas recovery from hydrate reservoirs.In heating closed systems,the temperature-pressure path of hydrate-bearing sediment deviates from that of pure bulk hydrate,reflecting the porous media effect in phase equilibrium.A generalized phase equilibrium equation was established for hydrate-bearing sediments,which indicates that both capillary and osmotic pressures cause the phase equilibrium curve to shift leftward on the temperature-pressure plane.In contrast to bulk hydrate,hydrate-bearing sediment always contains a certain amount of unhydrated water,which keeps phase equilibrium with the hydrate within the hydrate stability field.With changes in temperature and pressure,a portion of pore hydrate and unhydrated water may transform into each other,affecting the shear strength of hydrate-bearing sediment.A shear strength model is proposed to consider not only hydrate saturation but also the change in temperature and pressure of hydrate-bearing sediment.The model is validated by experimental data with various hydrate saturation,temperature and pressure conditions.The deformation induced by partial dissociation was studied through depressurization tests under constant effective stress.The reduction in gas pressure within the hydrate stability field indeed caused sediment deformation.The dissociation-induced deformation can be reasonably estimated as the difference in volume between hydrate-bearing and hydrate-free sediments from the compression curves.

A Mean-Field Game for a Forward-Backward Stochastic System With Partial Observation and Common Noise

This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.

Magnetic diagnostics layout design for CFETR plasma equilibrium reconstruction

Plasma equilibrium reconstruction provides essential information for tokamak operation and physical analysis.An extensive and reliable set of magnetic diagnostics is required to obtain accurate plasma equilibrium.This study designs and optimizes the magnetic diagnostics layout for the reconstruction of the equilibrium of the plasma according to the scientific objectives,engineering design parameters,and limitations of the Chinese Fusion Engineering Test Reactor(CFETR).Based on the CFETR discharge simulation,magnetic measurement data are employed to reconstruct consistent plasma equilibrium parameters,and magnetic diagnostics'number and position are optimized by truncated Singular value decomposition,verifying the redundancy reliability of the magnetic diagnostics layout design.This provides a design solution for the layout of the magnetic diagnostics system required to control the plasma equilibrium of CFETR,and the developed design and optimization method can provide effective support to design magnetic diagnostics systems for future magnetic confinement fusion devices.

High adsorption selectivity of activated carbon and carbon molecular sieve boosting CO_(2)/N_(2) and CH_(4)/N_(2) separation

Flue gas and coal bed methane are two important sources of greenhouse gases.Pressure swing adsorption process has a wide range of application in the field of gas separation,and the selection of adsorbent is crucial.In this regard,in order to assess the better adsorbent for separating CO_(2) from flue gas and CH_(4) from coal bed methane,adsorption isotherms of CO_(2),CH_(4) and N_(2) on activated carbon and carbon molecular sieve are measured at 303.15,318.15 and 333.15 K,and up to 250 kPa.The experimental data fit better with Langmuir 2 compared to Langmuir 3 and Langmuir-Freundlich models,and Clausius-Clapeyron equation was used to calculate the isosteric heat.Both the order of the adsorbed amount and the adsorption heat on the two adsorbents are CO_(2)>CH_(4)>N_(2).The adsorption kinetics are calculated by the pseudo-first kinetic model,and the order of adsorption rates on activated carbon is N_(2)-CH_(4)>CO_(2),while on carbon molecular sieve,it is CO_(2)-N_(2)>CH_(4).It is shown that relative molecular mass and adsorption heat are the primary effect on kinetics for activated carbon,while kinetic diameter is the main resistance factor for carbon molecular sieve.Moreover,the adsorption selectivity of CH_(4)/N_(2) and CO_(2)/N_(2) were estimated with the ideal adsorption solution theory,and carbon molecular sieve performed best at 318.15 K for both CO_(2) and CH_(4) separation.The study suggested that activated carbon is a better choice for separating flue gas and carbon molecular sieve can be a strong candidate for separating coal bed methane.

Metamorphic P-T conditions and ages of garnet-biotite schists in the Dahongshan Group from the southwestern Yangtze Block

The Dahongshan Group,situated at the southwestern margin of the Yangtze Block,represents a geological unit characterized by relatively high-grade metamorphism in the region.This paper investigates the garnet-biotite schist from the Laochanghe Formation of the Dahongshan Group,employing an integrated approach that includes petrological analysis,phase equilibrium modeling,and zircon U-Pb dating.The schist is mainly composed of garnet,biotite,plagioclase,quartz,rutile,and ilmenite.Phase equilibrium modeling revealed the peak metamorphic conditions of 8-9 kbar and 635-675°C.By further integrating the prograde metamorphic profile of garnet and geothermobarometric results,a clockwise P-T metamorphic evolution path is constructed,which includes an increase in temperature and pressure during the prograde stage.LA-ICP-MS zircon U-Pb dating and zircon Ti thermometry constrains the post-peak metamorphic age of 831.2±7.2 Ma.Integrated with previously reported results,it is revealed that the southwestern margin of the Yangtze Block experienced a large-scale regional metamorphism during the Neoproterozoic(890-750 Ma),which is related to the collisional orogenic process.This may be associated with the late-stage assembly of the Rodinia supercontinent or with local compression and subduction processes during the breakup of the Rodinia supercontinent.

Shear strength degradation of gas hydrate-bearing sediment due to partial hydrate dissociation

Extraction of methane hydrate from subseafloor reservoir may potentially trigger seabed slides and induce subsidence.To address the problems,it is crucial to properly characterize the phase equilibrium condition of pore hydrate and the shear strength of the soil.As one of the key constitutive components,the phase equilibrium condition enforces a constraint over pore gas pressure,temperature and unhydrated water content.Such a constraint,however,has been traditionally ignored in analyzing the mechanical behavior of hydrate-bearing soil.In this paper,a series of stepwise hydrate dissociation tests was performed,and the phase equilibrium condition of pore hydrate was determined,providing an effective way to evaluate the unhydrated water content during hydrate dissociation.Meanwhile,a series of direct shear tests was also conducted to explore the shear strength characteristics of the soil.It is shown that the shear strength of the hydrate-bearing soil can be significantly influenced by pore gas pressure,unhydrated water content,hydrate saturation and several other factors.In particular,the measured shear strength depends upon the initial water content of the sample,pointing to a potential problem that the shear strength could be wrongly determined if not properly interpreted.A shear strength criterion,which enforces the equilibrium condition of pore hydrate,is developed for hydrate-bearing soil,establishing a link between the equilibrium condition and the shear strength.The proposed equation describes well the shear strength characteristics of hydrate-bearing soils,remarkably unifying the effects of pore pressure,temperature,water content and hydrate saturation.

Experimental confirmation of the linear relation between plasma current and external vertical magnetic field in EXL-50 spherical torus energetic electron plasmas

A three-fluid equilibrium plasma with bulk plasma and energetic electrons has been observed on the Xuanlong-50(EXL-50) spherical torus, where the energetic electrons play a crucial role in sustaining the plasma current and pressure. In this study, the equilibrium of a multi-fluid plasma was investigated by analyzing the relationship between the external vertical magnetic field(B_(V)),plasma current(I_(p)), the poloidal ratio(β_(p)) and the Shafranov formula. Remarkably, our research demonstrates some validity of the Shafranov formula in the presence of multi-fluid plasma in EXL-50 spherical torus. This finding holds significant importance for future reactors as it allows for differentiation between alpha particles and background plasma. The study of multi-fluid plasma provides a significant reference value for the equilibrium reconstruction of burning plasma involving alpha particles.

Measurement and Correlation of Liquid-liquid Equilibria for 1-Hexene-n-Hexane-3-Methysulfolane

Utilizing solvent extraction to separate alkanes and olefins from catalytic light gasoline is an effective method for maximizing the utility of gasoline fractions.This study presents the determination of liquid-liquid equilibrium data for the ternary system of 1-hexene-n-hexane-3-methylsulfolane at 30℃,40℃,and 50℃under atmospheric pressure.The obtained data facilitated the construction of a ternary phase diagram for the system.The results showed that the extraction selectivity of 1-hexene/n-hexane exceeded 1.5 when using 3-methylsulfolane as the extraction solvent.Furthermore,the thermodynamic consistency of the experimental data was examined using Hand’s equation and the Othmer-Tobias method.The correlation coefficient,R^(2)≥0.9578,indicated the acceptable reliability of the phase equilibrium data.Subsequently,the NRTL(non-random two liquid)model was used to correlate the liquid-liquid phase equilibrium data and derive the binary interaction parameter.Notably,the results demonstrated that the root mean square deviation of the NRTL model correlation values from the experimental values did not exceed 2.5%.

Dynamics of Low-Viscosity Liquids Interface in an Unevenly Rotating Vertical Layer

The behavior of two immiscible low-viscosity liquids differing in density and viscosity in a vertical flat layer undergoing modulated rotation is experimentally studied.The layer has a circular axisymmetric boundary.In the absence of modulation of the rotation speed,the interphase boundary has the shape of a short axisymmetric cylinder.A new effect has been discovered,under the influence of rotation speed modulation,the interface takes on a new dynamic equilibrium state.A more viscous liquid covers the end boundaries of the layer in the form of thin films,which have the shape of round spots of almost constant radius;with increasing amplitude of the velocity modulation,the wetting boundary expands.It is found that upon reaching the critical amplitude of oscillations,the film of a viscous liquid loses stability,and the outer edge of the wetting spot collapses and takes on a feathery structure.It is shown that this threshold is caused by the development of the Kelvin-Helmholtz oscillatory instability of the film.The spreading radius of a spot of light viscous liquid and its stability are studied depending on the rotation rate,amplitude,and frequency of rotation speed modulation.The discovered averaged effects are determined by different oscillatory interaction of fluids with the end-walls of the cell,due to different viscosities.The effect of films forming can find application in technological processes to intensify mass transfer at interphase boundaries.

Optimal confrontation position selecting games model and its application to one-on-one air combat

In the air combat process,confrontation position is the critical factor to determine the confrontation situation,attack effect and escape probability of UAVs.Therefore,selecting the optimal confrontation position becomes the primary goal of maneuver decision-making.By taking the position as the UAV’s maneuver strategy,this paper constructs the optimal confrontation position selecting games(OCPSGs)model.In the OCPSGs model,the payoff function of each UAV is defined by the difference between the comprehensive advantages of both sides,and the strategy space of each UAV at every step is defined by its accessible space determined by the maneuverability.Then we design the limit approximation of mixed strategy Nash equilibrium(LAMSNQ)algorithm,which provides a method to determine the optimal probability distribution of positions in the strategy space.In the simulation phase,we assume the motions on three directions are independent and the strategy space is a cuboid to simplify the model.Several simulations are performed to verify the feasibility,effectiveness and stability of the algorithm.