Wigner Function：from Ensemble Average of Density Operator to Its Matrix Element in Entangled Pure States

We show that the Wigner function (an ensemble average of the density operator ρ, Δ is the Wigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting from quantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangled states are defined in the enlarged Fock space with a fictitious freedom.

More on half-wormholes and ensemble averages

We continue our study Half-Wormholes and Ensemble Averages about the half-wormhole proposal.By generalizing the original proposal of the half-wormhole,we propose a new way to detect half-wormholes.The crucial idea is to decompose the observables into self-averaged sectors and non-self-averaged sectors.We find the contributions from different sectors have interesting statistics in the semi-classical limit.In particular,dominant sectors tend to condense and the condensation explains the emergence of half-wormholes and we expect that the appearance of condensation is a signal of possible bulk description.We also initiate the study of multi-linked half-wormholes using our approach.

Climate change in the Tianshan and northern Kunlun Mountains based on GCM simulation ensemble with Bayesian model averaging

Climate change in mountainous regions has significant impacts on hydrological and ecological systems. This research studied the future temperature, precipitation and snowfall in the 21^（st） century for the Tianshan and northern Kunlun Mountains（TKM） based on the general circulation model（GCM） simulation ensemble from the coupled model intercomparison project phase 5（CMIP5） under the representative concentration pathway（RCP） lower emission scenario RCP4.5 and higher emission scenario RCP8.5 using the Bayesian model averaging（BMA） technique. Results show that（1） BMA significantly outperformed the simple ensemble analysis and BMA mean matches all the three observed climate variables;（2） at the end of the 21^（st） century（2070–2099） under RCP8.5, compared to the control period（1976–2005）, annual mean temperature and mean annual precipitation will rise considerably by 4.8°C and 5.2%, respectively, while mean annual snowfall will dramatically decrease by 26.5%;（3） precipitation will increase in the northern Tianshan region while decrease in the Amu Darya Basin. Snowfall will significantly decrease in the western TKM. Mean annual snowfall fraction will also decrease from 0.56 of 1976–2005 to 0.42 of 2070–2099 under RCP8.5; and（4） snowfall shows a high sensitivity to temperature in autumn and spring while a low sensitivity in winter, with the highest sensitivity values occurring at the edge areas of TKM. The projections mean that flood risk will increase and solid water storage will decrease.

Reliability ensemble averaging reduces surface wind speed projection uncertainties in the 21st century over China

Accurate prediction of future surface wind speed(SWS)changes is the basis of scientific planning for wind turbines.Most studies have projected SWS changes in the 21st century over China on the basis of the multi-model ensemble(MME)of the 6th Coupled Model Intercomparison Project(CMIP6).However,the simulation capability for SWS varies greatly in CMIP6 multi-models,so the MME results still have large uncertainties.In this study,we used the reliability ensemble averaging(REA)method to assign each model different weights according to their performances in simulating historical SWS changes and project the SWS under different shared socioeconomic pathways(SSPs)in 2015-2099.The results indicate that REA considerably improves the SWS simulation capacity of CMIP6,eliminating the overestimation of SWS by the MME and increasing the simulation capacity of spatial distribution.The spatial correlations with observations increased from 0.56 for the MME to 0.85 for REA.Generally,REA could eliminate the overestimation of the SWS by 33%in 2015-2099.Except for southeastern China,the SWS generally decreases over China in the near term(2020-2049)and later term(2070-2099),particularly under high-emission scenarios.The SWS reduction projected by REA is twice as high as that by the MME in the near term,reaching-4%to-3%.REA predicts a larger area of increased SWS in the later term,which expands from southeastern China to eastern China.This study helps to reduce the projected SWS uncertainties.

Deduction and Validation of an Eulerian-Eulerian Model for Turbulent Dilute Two-Phase Flows by Means of the Phase Indicator Function-Disperse Elements Probability Density Function

A statistical formalism overcoming some conceptual and practical difficulties arising in existing two-phase flow (2PHF) mathematical modelling has been applied to propose a model for dilute 2PHF turbulent Hows. Phase interaction terms with a clear physical meaning enter the equations and the formalism provides some guidelines for the avoidance of closure assumptions or the rational approximation of these terms. Continuous phase averaged continuity, momentum, turbulent kinetic energy and turbulence dissipation rate equations have been rigorously and systematically obtained in a single step. These equations display a structure similar to that for single-phase flows. It is also assumed that dispersed phase dynamics is well described by a probability density function (pdf) equation and Eulerian continuity, momentum and fluctuating kinetic energy equations for the dispersed phase are deduced. An extension of the standard k-e turbulence model for the continuous phase is used. A gradient transport model is adopted for the dispersed phase fluctuating fluxes of momentum and kinetic energy at the non-colliding, large inertia limit. This model is then used to predict the behaviour of three axisymmetric turbulent jets of air laden with solid particles varying in size and concentration. Qualitative and quantitative numerical predictions compare reasonably well with the three different sets of experimental results, studying the influence of particle size, loading ratio and flow confinement velocity.

Effective Elastic Properties of 3-Phase Particle Reinforced Composites with Randomly Dispersed Elastic Spherical Particles of Different Sizes Dedicated to Professor Karl Stark Pister for his 95th birthday

Higher-order multiscale structures are proposed to predict the effective elastic properties of 3-phase particle reinforced composites by considering the probabilistic spherical particles spatial distribution,the particle interactions,and utilizing homogenization with ensemble volume average approach.The matrix material,spherical particles with radius a1,and spherical particles with radius a2,are denoted as the 0th phase,the 1st phase,and the 2nd phase,respectively.Particularly,the two inhomogeneity phases are different particle sizes and the same elastic material properties.Improved higher-order(in ratio of spherical particle sizes to the distance between the centers of spherical particles)bounds on effective elastic properties of 3-phase particle reinforced proposed Formulation II and Formulation I derive composites.As a special case,i.e.,particle size of the 1st phase is the same as that of the 2nd phase,the proposed formulations reduce to 2-phase formulas.Our theoretical predictions demonstrate excellent agreement with selected experimental data.In addition,several numerical examples are presented to demonstrate the competence of the proposed frameworks.

Hybrid Sine Cosine and Stochastic Fractal Search for Hemoglobin Estimation

The sample’s hemoglobin and glucose levels can be determined by obtaining a blood sample from the human body using a needle and analyzing it.Hemoglobin(HGB)is a critical component of the human body because it transports oxygen from the lungs to the body’s tissues and returns carbon dioxide from the tissues to the lungs.Calculating the HGB level is a critical step in any blood analysis job.TheHGBlevels often indicate whether a person is anemic or polycythemia vera.Constructing ensemble models by combining two or more base machine learning(ML)models can help create a more improved model.The purpose of this work is to present a weighted average ensemble model for predicting hemoglobin levels.An optimization method is utilized to get the ensemble’s optimum weights.The optimum weight for this work is determined using a sine cosine algorithm based on stochastic fractal search(SCSFS).The proposed SCSFS ensemble is compared toDecision Tree,Multilayer perceptron(MLP),Support Vector Regression(SVR)and Random Forest Regressors as model-based approaches and the average ensemble model.The SCSFS results indicate that the proposed model outperforms existing models and provides an almost accurate hemoglobin estimate.

On the necessity of an integrative approach to understand protein structural dynamics

Proteins are dynamic,fluctuating between multiple conformational states.Protein dynamics,spanning orders of magnitude in time and space,allow proteins to perform specific functions.Moreover,under certain conditions,proteins can morph into a different set of conformations.Thus,a complete understanding of protein structural dynamics can provide mechanistic insights into protein function.Here,we review the latest developments in methods used to determine protein ensemble structures and to characterize protein dynamics.Techniques including X-ray crystallography,cryogenic electron microscopy,and small angle scattering can provide structural information on specific conformational states or on the averaged shape of the protein,whereas techniques including nuclear magnetic resonance,fluorescence resonance energy transfer(FRET),and chemical cross-linking coupled with mass spectrometry provide information on the fluctuation of the distances between protein domains,residues,and atoms for the multiple conformational states of the protein.In particular,FRET measurements at the single-molecule level allow rapid resolution of protein conformational states,where information is otherwise obscured in bulk measurements.Taken together,the different techniques complement each other and their integrated use can offer a clear picture of protein structure and dynamics.