The Probability Density Function Related to Shallow Cumulus Entrainment Rate and Its Influencing Factors in a Large-Eddy Simulation

The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus clouds.Accurately obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization scheme.In this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy simulation.The results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved variables.The probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous studies.Further analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the future.The results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.

Combining stochastic density functional theory with deep potential molecular dynamics to study warm dense matter

In traditional finite-temperature Kohn–Sham density functional theory(KSDFT),the partial occupation of a large number of high-energy KS eigenstates restricts the use of first-principles molecular dynamics methods at extremely high temperatures.However,stochastic density functional theory(SDFT)can overcome this limitation.Recently,SDFT and the related mixed stochastic–deterministic density functional theory,based on a plane-wave basis set,have been implemented in the first-principles electronic structure software ABACUS[Q.Liu and M.Chen,Phys.Rev.B 106,125132(2022)].In this study,we combine SDFT with the Born–Oppenheimer molecular dynamics method to investigate systems with temperatures ranging from a few tens of eV to 1000 eV.Importantly,we train machine-learning-based interatomic models using the SDFT data and employ these deep potential models to simulate large-scale systems with long trajectories.Subsequently,we compute and analyze the structural properties,dynamic properties,and transport coefficients of warm dense matter.

A probability theory for filtered ghost imaging

Based on probability density functions,we present a theoretical model to explain filtered ghost imaging(FGI)we first proposed and experimentally demonstrated in 2017[Opt.Lett.425290(2017)].An analytic expression for the joint intensity probability density functions of filtered random speckle fields is derived according to their probability distributions.Moreover,the normalized second-order intensity correlation functions are calculated for the three cases of low-pass,bandpass and high-pass filterings to study the resolution and visibility in the FGI system.Numerical simulations show that the resolution and visibility predicted by our model agree well with the experimental results,which also explains why FGI can achieve a super-resolution image and better visibility than traditional ghost imaging.

Probability Distribution Characteristics of Strong Nonlinear Waves Under Typhoon Conditions in the Northern South China Sea

The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.

Probability Laws Derived from the Gamma Function

Several densities or probability laws of continuous random variables derive from the Euler Gamma function. These laws form the basis of sampling theory, namely hypothesis testing and estimation. Namely the gamma, beta, and Student law, through the chi-square law and the normal law are all distributions resulting from applications of Euleur functions.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

High-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer based on probability density evolution method

This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel.Subsequently,the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform.Furthermore,the probability density evolution method(PDEM)is developed to high-dimensional uncertainty quantification of projectile motion.The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation(MCS).Finally,the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed.The results show that the disturbance of the pitch angular,pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle,and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle.

Integrating host biological and ecological variables to predict probability of haemosporidian infection in raptors

Variations in host traits that influence their exposure and susceptibility may impact probability of vector-transmitted diseases.Therefore,identifying the predictors of infection probability is necessary to understand the risk of disease outbreaks during expanding environmental perturbation.Here,we conducted a large survey based on microscopic examination and molecular analysis of haemosporidian parasite infection in raptors rescued at the Beijing Raptor Rescue Centre.Combining these data with biological and ecological variables of the raptors,we determined predictors that affect the probability of haemosporidian infection using generalized linear mixed models and multimodel inference.Our results showed that infection probability exhibited considerable variation across host species in raptors,and body mass,sex,and evolutionary history played relatively weaker roles in driving infection probability.Instead,activity pattern,age,geographic range size,migration distance,and nest type were important predictors of the probability of haemosporidian infection,and the role of each predictor differed in the three main haemosporidian genera(Plasmodium,Haemoproteus,and Leucocytozoon).This macro-ecological analysis will add to our understanding of host traits that influence the probability of avian haemosporidian infection and will help inform risk of emerging diseases.

Secrecy Outage Probability Minimization in Wireless-Powered Communications Using an Improved Biogeography-Based Optimization-Inspired Recurrent Neural Network

This paper focuses on wireless-powered communication systems,which are increasingly relevant in the Internet of Things(IoT)due to their ability to extend the operational lifetime of devices with limited energy.The main contribution of the paper is a novel approach to minimize the secrecy outage probability(SOP)in these systems.Minimizing SOP is crucial for maintaining the confidentiality and integrity of data,especially in situations where the transmission of sensitive data is critical.Our proposed method harnesses the power of an improved biogeography-based optimization(IBBO)to effectively train a recurrent neural network(RNN).The proposed IBBO introduces an innovative migration model.The core advantage of IBBO lies in its adeptness at maintaining equilibrium between exploration and exploitation.This is accomplished by integrating tactics such as advancing towards a random habitat,adopting the crossover operator from genetic algorithms(GA),and utilizing the global best(Gbest)operator from particle swarm optimization(PSO)into the IBBO framework.The IBBO demonstrates its efficacy by enabling the RNN to optimize the system parameters,resulting in significant outage probability reduction.Through comprehensive simulations,we showcase the superiority of the IBBO-RNN over existing approaches,highlighting its capability to achieve remarkable gains in SOP minimization.This paper compares nine methods for predicting outage probability in wireless-powered communications.The IBBO-RNN achieved the highest accuracy rate of 98.92%,showing a significant performance improvement.In contrast,the standard RNN recorded lower accuracy rates of 91.27%.The IBBO-RNN maintains lower SOP values across the entire signal-to-noise ratio(SNR)spectrum tested,suggesting that the method is highly effective at optimizing system parameters for improved secrecy even at lower SNRs.

Functional microfluidics:theory,microfabrication,and applications

Microfluidic devices are composed of microchannels with a diameter ranging from ten to a few hundred micrometers.Thus,quite a small(10-9–10-18l)amount of liquid can be manipulated by such a precise system.In the past three decades,significant progress in materials science,microfabrication,and various applications has boosted the development of promising functional microfluidic devices.In this review,the recent progress on novel microfluidic devices with various functions and applications is presented.First,the theory and numerical methods for studying the performance of microfluidic devices are briefly introduced.Then,materials and fabrication methods of functional microfluidic devices are summarized.Next,the recent significant advances in applications of microfluidic devices are highlighted,including heat sinks,clean water production,chemical reactions,sensors,biomedicine,capillaric circuits,wearable electronic devices,and microrobotics.Finally,perspectives on the challenges and future developments of functional microfluidic devices are presented.This review aims to inspire researchers from various fields engineering,materials,chemistry,mathematics,physics,and more—to collaborate and drive forward the development and applications of functional microfluidic devices,specifically for achieving carbon neutrality.

Contract Mechanism of Water Environment Regulation for Small and Medium Sized Enterprises Based on Optimal Control Theory

The small and scattered enterprise pattern in the county economy has formed numerous sporadic pollution sources, hindering the centralized treatment of the water environment, increasing the cost and difficulty of treatment. How enterprises can make reasonable decisions on their water environment behavior based on the external environment and their own factors is of great significance for scientifically and effectively designing water environment regulation mechanisms. Based on optimal control theory, this study investigates the design of contractual mechanisms for water environmental regulation for small and medium-sized enterprises. The enterprise is regarded as an independent economic entity that can adopt optimal control strategies to maximize its own interests. Based on the participation of multiple subjects including the government, enterprises, and the public, an optimal control strategy model for enterprises under contractual water environmental regulation is constructed using optimal control theory, and a method for calculating the amount of unit pollutant penalties is derived. The water pollutant treatment cost data of a paper company is selected to conduct empirical numerical analysis on the model. The results show that the increase in the probability of government regulation and public participation, as well as the decrease in local government protection for enterprises, can achieve the same regulatory effect while reducing the number of administrative penalties per unit. Finally, the implementation process of contractual water environmental regulation for small and medium-sized enterprises is designed.

Prospect Theory Based Individual Irrationality Modelling and Behavior Inducement in Pandemic Control

Understanding and modeling individuals’behaviors during epidemics is crucial for effective epidemic control.However,existing research ignores the impact of users’irrationality on decision-making in the epidemic.Meanwhile,existing disease control methods often assume users’full compliance with measures like mandatory isolation,which does not align with the actual situation.To address these issues,this paper proposes a prospect theorybased framework to model users’decision-making process in epidemics and analyzes how irrationality affects individuals’behaviors and epidemic dynamics.According to the analysis results,irrationality tends to prompt conservative behaviors when the infection risk is low but encourages risk-seeking behaviors when the risk is high.Then,this paper proposes a behavior inducement algorithm to guide individuals’behaviors and control the spread of disease.Simulations and real user tests validate our analysis,and simulation results show that the proposed behavior inducement algorithm can effectively guide individuals’behavior.

Density functional theory study of B- and Si-doped carbons and their adsorption interactions with sulfur compounds

Understanding the adsorption interactions between carbon materials and sulfur compounds has far-reaching impacts,in addition to their well-known important role in energy storage and conversion,such as lithium-ion batteries.In this paper,properties of intrinsic B or Si single-atom doped,and B-Si codoped graphene(GR)and graphdiyne(GDY)were investigated by using density functional theory-based calculations,in which the optimal doping configurations were explored for potential applications in adsorbing sulfur compounds.Results showed that both B or Si single-atom doping and B-Si codoping could substantially enhance the electron transport properties of GR and GDY,improving their surface activity.Notably,B and Si atoms displayed synergistic effects for the codoped configurations,where B-Si codoped GR/GDY exhibited much better performance in the adsorption of sulfurcontaining chemicals than single-atom doped systems.In addition,results demonstrated that,after B-Si codoping,the adsorption energy and charge transfer amounts of GDY with sulfur compounds were much larger than those of GR,indicating that B-Si codoped GDY might be a favorable material for more effectively interacting with sulfur reagents.

A self-organization formation configuration based assignment probability and collision detection

The formation control of multiple unmanned aerial vehicles(multi-UAVs)has always been a research hotspot.Based on the straight line trajectory,a multi-UAVs target point assignment algorithm based on the assignment probability is proposed to achieve the shortest overall formation path of multi-UAVs with low complexity and reduce the energy consumption.In order to avoid the collision between UAVs in the formation process,the concept of safety ball is introduced,and the collision detection based on continuous motion of two time slots and the lane occupation detection after motion is proposed to avoid collision between UAVs.Based on the idea of game theory,a method of UAV motion form setting based on the maximization of interests is proposed,including the maximization of self-interest and the maximization of formation interest is proposed,so that multi-UAVs can complete the formation task quickly and reasonably with the linear trajectory assigned in advance.Finally,through simulation verification,the multi-UAVs target assignment algorithm based on the assignment probability proposed in this paper can effectively reduce the total path length,and the UAV motion selection method based on the maximization interests can effectively complete the task formation.

Local thermal conductivity of inhomogeneous nano-fluidic films:A density functional theory perspective

Combining the mean field Pozhar-Gubbins(PG)theory and the weighted density approximation,a novel method for local thermal conductivity of inhomogeneous fluids is proposed.The correlation effect that is beyond the mean field treatment is taken into account by the simulation-based empirical correlations.The application of this method to confined argon in slit pore shows that its prediction agrees well with the simulation results,and that it performs better than the original PG theory as well as the local averaged density model(LADM).In its further application to the nano-fluidic films,the influences of fluid parameters and pore parameters on the thermal conductivity are calculated and investigated.It is found that both the local thermal conductivity and the overall thermal conductivity can be significantly modulated by these parameters.Specifically,in the supercritical states,the thermal conductivity of the confined fluid shows positive correlation to the bulk density as well as the temperature.However,when the bulk density is small,the thermal conductivity exhibits a decrease-increase transition as the temperature is increased.This is also the case in which the temperature is low.In fact,the decrease-increase transition in both the small-bulk-density and low-temperature cases arises from the capillary condensation in the pore.Furthermore,smaller pore width and/or stronger adsorption potential can raise the critical temperature for condensation,and then are beneficial to the enhancement of the thermal conductivity.These modulation behaviors of the local thermal conductivity lead immediately to the significant difference of the overall thermal conductivity in different phase regions.

The “Dead Universe” Theory: Natural Separation of Galaxies Driven by the Remnants of a Supermassive Dead Universe

This article explores the dead universe theory as a novel interpretation for the origin and evolution of the universe, suggesting that our cosmos may have originated from the remnants of a preceding universe. This perspective challenges the conventional Big Bang theory, particularly concerning dark matter, the expansion of the universe, and the interpretation of phenomena such as gravitational waves.

Comparative study on phase transition behaviors of fractional molecular field theory and random-site Ising model

Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to verify the feasibility of this theory,this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional(2D)random-site Ising model(2D-RSIM).The results indicate that the FMFT deviates from the 2D-RSIM significantly.The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution,where the real order parameter is spatially heterogeneous and has no symmetry of space translation,but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.

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.

Corrigendum to“Atomic-scale electromagnetic theory bridging optics in microscopic world and macroscopic world”

The signs of the electric field markers in Figs.2 and 4 of the paper[Chin.Phys.B 32104211(2023)]have been corrected.These modifications do not affect the results derived in the paper.

Foundations of the Scale-Symmetric Theory and the Illusory Total Width of the Off-Shell Higgs Bosons

Here we present the foundations of the Scale-Symmetric Theory (SST), i.e. the fundamental phase transitions of the initial inflation field, the atom-like structure of baryons and different types of black holes. Within SST we show that the transition from the nuclear strong interactions in the off-shell Higgs boson production to the nuclear weak interactions causes that the real total width of the Higgs boson from the Higgs line shape (i.e. 3.3 GeV) decreases to 4.3 MeV that is the illusory total width. Moreover, there appear some glueballs/condensates with the energy 3.3 GeV that accompany the production of the off-shell Higgs bosons.