Two innovative equivalent statements of the third law of thermodynamics

It is found from textbooks and literature that there are three different statements for the third law of thermodynamics,i.e., the Nernst theorem, the unattainability statement of absolute zero temperature, and the heat capacity statement. It is pointed out that such three statements correspond to three thermodynamic parameters, which are, respectively, the entropy,temperature, and heat capacity, and can be obtained by extrapolating the experimental results of different parameters at ultralow temperatures to absolute zero. It is expounded that because there is no need for additional assumptions in the derivation of the Nernst equation, the Nernst theorem should be renamed as the Nernst statement. Moreover, it is proved that both the Nernst statement and the heat capacity statement are mutually deducible and equivalent, while the unattainability of absolute zero temperature is only a corollary of the Nernst statement or the heat capacity statement so that it is unsuitably referred to as one statement of the third law of thermodynamics. The conclusion is that the Nernst statement and the heat capacity statement are two equivalent statements of the third law of thermodynamics.

Literature overview of basic characteristics and flotation laws of flocs

Flocculation flotation is the most efficient method for recovering fine-grained minerals,and its essence lies in flotation and recovery of flocs.Fundamental physical characteristics of flocs are mainly determined by their apparent particle size and structure(density and morphology).Substantial researches have been conducted regarding the effect of floc characteristics on particle settling and water treatment.However,the influence of floc characteristics on flotation has not been widely studied.Based on the floc formation and flocculation flotation,this study reviews the fundamental physical characteristics of flocs from the perspectives of floc particle size and structure,summarizing the interaction between floc particle size and structure.Moreover,it thoroughly discusses the effect of floc particle size and structure on floc floatability,further revealing the influence of floc characteristics on bubble collision and adhesion and elucidating the mechanisms of interaction between flocs and bubbles.Thus,it is observed that floc particle size is not the only factor influencing flocculation flotation.Within the appropriate apparent particle size range,flocs with a compact structure exhibit higher efficiency in bubble collision and adhesion during flotation,thereby resulting in enhanced flotation performance.This study aims to provide a reference for flocculation flotation,targeting the development of more efficient and refined flocculation flotation processes in the future.

Distribution law and susceptibility of geohazards across a gradient belt of the Western Sichuan Plateau

Across a gradient belt of the Western Sichuan Plateau,geohazards have seriously limited economic and social development.According to incomplete statistics,15,673 geohazards have been recorded in the study area.In order to mitigate the threat of geohazards to human engineering activities in the region,an overall understanding of the distribution pattern of geohazards and susceptibility assessment are necessary.In this paper,a gradient belt of the Western Sichuan Plateau and its zoning criteria were defined.Subsequently,on the basis of relief amplitude,distance to faults,rainfall,and human activities,three indicators of endogenic process were introduced:Bouguer gravity anomaly gradient,vertical deformation gradient,and horizontal deformation gradient.Thereafter,the distribution patterns of geohazards were investigated through mathematical statistics and ArcGIS software.By randomly selecting 10,449 hazards,a geohazard susceptibility map was generated using the Information Value(IV)model.Finally,the IV model was validated against 5224 hazards using the Area Under Curve(AUC)method.The results show that 47.6%of the geohazards were distributed in the zone of steep slope.Geohazards showed strong responses to distance to faults,human activities,and annual rainfall.The distribution of geohazards in the gradient belt of the Western Sichuan Plateau is more sensitive to vertical internal dynamics factors(such as vertical deformation gradient and Bouguer gravity anomaly gradient)without any apparent sensitivity to horizontal internal dynamics factors.The areas of high and very-high risk account for up to 32.22%,mainly distributed in the Longmenshan and Anning River faults.According to the AUC plot,the success rate of the IV model for generating the susceptibility map is 76%.This susceptibility map and geohazard distribution pattern can provide a reference for geological disaster monitoring,preparation of post-disaster emergency measures,and town planning.

Regulating Effect of Substrate Temperature on Sputteringgrown Ge/Si QDs under Low Ge Deposition

The effect of deposition temperature on the morphology and optoelectronic performance of Ge/Si QDs grown by magnetron sputtering under low Ge deposition(~4 nm)was investigated by atomic force microscopy,Raman spectroscopy,and photoluminescence(PL)tests.The experimental results indicate that temperatures higher than 750℃effectively increase the crystallization rate and surface smoothness of the Si buffer layer,and temperatures higher than 600℃significantly enhance the migration ability of Ge atoms,thus increasing the probability of Ge atoms meeting and nucleating to form QDs on Si buffer layer,but an excessively high temperature will cause the QDs to undergo an Ostwald ripening process and thus develop into super large islands.In addition,some PL peaks were observed in samples containing small-sized,high-density Ge QDs,the photoelectric properties reflected by these peaks were in good agreement with the corresponding structural characteristics of the grown QDs.Our results demonstrate the viability of preparing high-quality QDs by magnetron sputtering at high deposition rate,and the temperature effect is expected to work in conjunction with other controllable factors to further regulate QD growth,which paves an effective way for the industrial production of QDs that can be used in future devices.

Nuclear magnetic resonance experiments on the time-varying law of oil viscosity and wettability in high-multiple waterflooding sandstone cores

A simulated oil viscosity prediction model is established according to the relationship between simulated oil viscosity and geometric mean value of T2spectrum,and the time-varying law of simulated oil viscosity in porous media is quantitatively characterized by nuclear magnetic resonance(NMR)experiments of high multiple waterflooding.A new NMR wettability index formula is derived based on NMR relaxation theory to quantitatively characterize the time-varying law of rock wettability during waterflooding combined with high-multiple waterflooding experiment in sandstone cores.The remaining oil viscosity in the core is positively correlated with the displacing water multiple.The remaining oil viscosity increases rapidly when the displacing water multiple is low,and increases slowly when the displacing water multiple is high.The variation of remaining oil viscosity is related to the reservoir heterogeneity.The stronger the reservoir homogeneity,the higher the content of heavy components in the remaining oil and the higher the viscosity.The reservoir wettability changes after water injection:the oil-wet reservoir changes into water-wet reservoir,while the water-wet reservoir becomes more hydrophilic;the degree of change enhances with the increase of displacing water multiple.There is a high correlation between the time-varying oil viscosity and the time-varying wettability,and the change of oil viscosity cannot be ignored.The NMR wettability index calculated by considering the change of oil viscosity is more consistent with the tested Amott(spontaneous imbibition)wettability index,which agrees more with the time-varying law of reservoir wettability.

Development and Application of a Power Law Constitutive Model for Eddy Current Dampers

Eddy current dampers (ECDs) have emerged as highly desirable solutions for vibration control due to theirexceptional damping performance and durability. However, the existing constitutive models present challenges tothe widespread implementation of ECD technology, and there is limited availability of finite element analysis (FEA)software capable of accurately modeling the behavior of ECDs. This study addresses these issues by developing anewconstitutivemodel that is both easily understandable and user-friendly for FEAsoftware. By utilizing numericalresults obtained from electromagnetic FEA, a novel power law constitutive model is proposed to capture thenonlinear behavior of ECDs. The effectiveness of the power law constitutive model is validated throughmechanicalproperty tests and numerical seismic analysis. Furthermore, a detailed description of the application process ofthe power law constitutive model in ANSYS FEA software is provided. To facilitate the preliminary design ofECDs, an analytical derivation of energy dissipation and parameter optimization for ECDs under harmonicmotionis performed. The results demonstrate that the power law constitutive model serves as a viable alternative forconducting dynamic analysis using FEA and optimizing parameters for ECDs.

Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws

In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results apply to all nonlinear scalar conservation laws and to nonlinear hyperbolic systems of two equations.

Analysis of the Characterization of the Old Man in“The Law of Life”from the Narrative Perspective

“The Law of Life”is one of Jack London’s representative works,depicting the story of an elderly Native American abandoned by his family,alone and waiting for life to fade away.This paper,based on narrative theory,aims to explore how the author employs narrative techniques to present the image of the old man in the short story.The narrative techniques of dual focalization and dual narrative timelines in the text demonstrate the abandonment of the old man’s homeland and his inescapable death under a naturalistic view of life and reflect a desolate life picture of resignation towards death under naturalistic determinism,depicting a grim elderly world under the naturalistic concept of“survival of the fittest.”Studying this short story helps us reflect on the living conditions of the elderly and provides insights into how to better care for the elderly population amid the global trend of aging.

The Rule of Law is the Most Important Means of Human Rights Protection

Today,we are here to commemorate the 75^(th) anniversary of the adoption of the Universal Declaration of Human Rights.In this Declaration,which consists of only30 articles,seven articles are related to the constitution,law,court,and the rule of law,making it a declaration filled with the rule of law.Coincidentally,today is also the 10^(th) National Constitution Day of China.Nineteen years ago,“the state respects and protects human rights”was enshrined in the Constitution,becoming a constitutional principle.Since then,human rights protection in China has been based on fundamental law.

Malawi Opens Tourism Doors No visa’s needed for Chinese tourists and others,as Malawi makes visits more convenient

When Malawian President Lazarus Chakwera delivered a State of the Nation Address at the 50th Parliamentary Session and Budget Meeting in February,tourism was top of mind.

Scaling law of resolved-scale isotropic turbulence and its application in large-eddy simulation

Eddy-damping quasinormal Markovian （EDQNM） theory is employed to calculate the resolved-scale spectrum and transfer spectrum, based on which we investigate the resolved-scale scaling law. Results show that the scaling law of the resolved-scale turbulence, which is affected by several factors, is far from that of the full-scale turbulence and should be corrected. These results are then applied to an existing subgrid model to improve its performance. A series of simulations are performed to verify the necessity of a fixed scaling law in the subgrid modeling.

The law of barrel wear and its application

A power function relation between number of rounds and barrel wear amount is created based on the test data from firing of large-caliber barrels. The function is optimized to fully fit the test data. A new concept of diameter change rate of bore is proposed and the law of barrel wear is put forward by means of comparing the diameter change rates for large-caliber barrels with different calibers. It is shown that the law of barrel wear is successful in barrel life prediction.

Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws

This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance laws.The basic idea is that the“meaningful objects”are the fluxes,evaluated across domain boundaries over time intervals.The fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional setting.It implies that a weak solution indeed satisfies the balance law.In fact,it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the boundary.It should be emphasized that the weak solutions considered here need not be entropy solutions.Furthermore,the assumption imposed on the flux f(u)is quite minimal-just that it is locally bounded.

Broader applicability of the metacoupling framework than Tobler’s first law of geography for global sustainability:A systematic review

Complex sustainability issues in the Anthropocene,with rapid globalization and global environmental changes,are increasingly interlinked between not only nearby systems but also distant systems.Tobler’s first law of geog-raphy(TFL)states“near things are more related than distant things”.Evidence suggests that TFL is not infallible for sustainability issues.Recently,the integrated framework of metacoupling(MCF;human-nature interactions within as well as between adjacent and distant systems)has been applied to analyze the interactions between nearby and distant coupled human and natural systems simultaneously.However,previous work has been scat-tered and fragmented.It is crucial to understand the extent to which TFL and MCF apply across pressing issues in sustainability.Therefore,we reviewed and synthesized sustainability literature that used TFL and MCF across seven major topics:land change,species migration,tourism,trade,agricultural development,conservation,and governance.Results indicate MCF had a much broader applicability than TFL for these topics.The literature using MCF generally did not or likely did not obey TFL,especially in trade,governance,and agricultural de-velopment.In the TFL literature,most topics obeyed TFL,except for species migration and trade.The findings suggest the need to rethink and further test TFL’s relevance to sustainability issues,and highlight the potential of MCF to address complex interactions between both adjacent and distant systems across the world for global sustainability.

THE LAW OF THE ITERATED LOGARITHM FOR SPATIAL AVERAGES OF THE STOCHASTIC HEAT EQUATION

Let u(t,x)be the solution to the one-dimensional nonlinear stochastic heat equation driven by space-time white noise with u(0,x)=1 for all x∈R.In this paper,we prove the law of the iterated logarithm(LIL for short)and the functional LIL for a linear additive functional of the form∫[0,R]u(t,x)dx and the nonlinear additive functionals of the form∫[0,R]g(u(t,x))dx,where g:R→R is nonrandom and Lipschitz continuous,as R→∞for fixed t>0,using the localization argument.

Comprehensive use of the Gutenberg–Richter law and geotomography for improving seismic hazard evaluation in hard coal mines

Mining-induced seismicity occurs in numerous underground mines worldwide where extraction is conducted at great depths or in areas characterised by complex tectonic structure.It is accompanied by rock bursts,which result in the loss of working functionality and the possibility of accidents among personnel.The issue of a constant and reliable seismic hazard evaluation is of key signifcance for both the safety of miners and the stability of production.Research on its improvement is directed at developing new interpretive solutions and methods.The nature of the presented solution is the complex interpretation of seismological data that characterise rock mass seismicity and of underground measurement results in the form of a map presenting the longitudinal wave propagation velocity distribution in the rock surrounding the mined coal seam.The solution was tested in hard coal mines located in the Upper Silesian Coal Basin.The mines are equipped with a modern seismological system enabling the constant monitoring of seismicity together with hazard level evaluation as well as with seismic apparatus for conducting periodic measurements of the seismic wave propagation velocity before the mining face.Comprehensive seismic hazard evaluation criteria were determined based on the obtained results,involving the anomaly of the Gutenberg–Richter law“b”value and the maximum longitudinal seismic wave propagation velocity in the roof rock.The obtained experience and the result validation of this new comprehensive hazard evaluation method confrm its practical usefulness and indicate the directions of improvement for the solution in question.

Aerodynamic shape and drag scaling law of a flexible fibre in a flowing medium

The study of a flexible body immersed in a flowing medium is one of the best way to find its aerodynamic shape.This Letter revisited the problem that was first studied by Alben et al.(Nature 420,479–481,2002).To determine the aerodynamic shape of the fibre,a simpler approach is proposed.A universal drag scaling law is obtained and the universality of the Alben-Shelley-Zhang scaling law is confirmed by using dimensional analysis.A complete Maple code is provided for finding aerodynamic shape of the fibre in the flowing medium.

Effect of particle gradation on pore structure and seepage law of solution in weathered crust elution-deposited rare earth ores

Both CT and Avizo software were used to explore the effect of particle gradation on the evolution characteristics of pore structure and seepage paths in weathered crust elution-deposited rare earth ores during leaching.The results showed that the pore areas in four kinds of ore samples before leaching were mainly concentrated in 10^(4)–10^(7)μm^(2),whose pore quantities accounted for 96.89%,94.94%,90.48%,and 89.45%,respectively,while the corresponding pore volume only accounted for 30.74%,14.55%,7.58%,and 2.84%of the total pore volume.With the decrease of fractal dimension,the average pore throat length increased,but pore throat quantities,the average pore throat radius and coordination number decreased.Compared with that before leaching,the change degree of pore structure during leaching increased with the fractal dimension decreasing.For example,the reduction rate of the average coordination number of ore samples was 14.36%,21.30%,28.00%,and 32.90%,respectively.Seepage simulation results indicated that seepage paths were uniformly distributed before leaching while the streamline density and seepage velocity increased with the fractal dimension decreasing.Besides,the phenomenon of the streamline interruption gradually reduced during leaching while preferential seepage got more obvious with the decrease of the fractal dimension.

A modified generalized scaling law for the similitude of dynamic strain in centrifuge modeling

Soil strain is the key parameter to control the elasto-plastic deformation and even the failure processes.To overcome the defect that the strain of the model soil is always smaller than that of the prototype in Iai′s generalized scaling law(GSL),a modified scaling law was proposed based on Iai′s GSL to secure the same dynamic shear strain between the centrifuge model and the prototype by modulating the amplitude and frequency of the input motion at the base.A suite of dynamic centrifuge model tests of dry sand level ground was conducted with the same overall scaling factor(λ=200)under different centrifugal accelerations by using the technique of“modeling of models”to validate the modified GSL.The test results show that the modified GSL could achieve the same dynamic strain in model as that of the prototype,leading to better modeling for geotechnical problems where dynamic strain dominates the response or failure of soils.Finally,the applicability of the proposed scaling law and possible constraints on geometry scaling due to the capability limits of existing centrifuge shaking tables are discussed.

Envelope Method and More General New Global Structures of Solutions for Multi-dimensional Conservation Law

For the two-dimensional(2D)scalar conservation law,when the initial data contain two different constant states and the initial discontinuous curve is a general curve,then complex structures of wave interactions will be generated.In this paper,by proposing and investigating the plus envelope,the minus envelope,and the mixed envelope of 2D non-selfsimilar rarefaction wave surfaces,we obtain and the prove the new structures and classifications of interactions between the 2D non-selfsimilar shock wave and the rarefaction wave.For the cases of the plus envelope and the minus envelope,we get and prove the necessary and sufficient criterion to judge these two envelopes and correspondingly get more general new structures of 2D solutions.