A drought is when reduced rainfall leads to a water crisis,impacting daily life.Over recent decades,droughts have affected various regions,including South Sulawesi,Indonesia.This study aims to map the probability of m...A drought is when reduced rainfall leads to a water crisis,impacting daily life.Over recent decades,droughts have affected various regions,including South Sulawesi,Indonesia.This study aims to map the probability of meteo-rological drought months using the 1-month Standardized Precipitation Index(SPI)in South Sulawesi.Based on SPI,meteorological drought characteristics are inversely proportional to drought event intensity,which can be modeled using a Non-Homogeneous Poisson Process,specifically the Power Law Process.The estimation method employs Maximum Likelihood Estimation(MLE),where drought event intensities are treated as random variables over a set time interval.Future drought months are estimated using the cumulative Power Law Process function,with theβandγparameters more significant than 0.The probability of drought months is determined using the Non-Homogeneous Poisson Process,which models event occurrence over time,considering varying intensities.The results indicate that,of the 24 districts/cities in South Sulawesi,14 experienced meteorological drought based on the SPI and Power Law Process model.The estimated number of months of drought occurrence in the next 12 months is one month of drought with an occurrence probability value of 0.37 occurring in November in the Selayar,Bulukumba,Bantaeng,Jeneponto,Takalar and Gowa areas,in October in the Sinjai,Barru,Bone,Soppeng,Pinrang and Pare-pare areas,as well as in December in the Maros and Makassar areas.展开更多
Finite-volume extrapolation is an important step for extracting physical observables from lattice calculations.However,it is a significant challenge for systems with long-range interactions.We employ symbolic regressi...Finite-volume extrapolation is an important step for extracting physical observables from lattice calculations.However,it is a significant challenge for systems with long-range interactions.We employ symbolic regression to regress the finite-volume extrapolation formula for both short-range and long-range interactions.The regressed formula still holds the exponential form with a factor L^(n) in front of it.The power decreases with the decreasing range of the force.When the range of the force becomes sufficiently small,the power converges to-1,recovering the short-range formula as expected.Our work represents a significant advancement in leveraging machine learning to probe uncharted territories within particle physics.展开更多
The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of ...The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. FinaJ1y, some exact solutions for a particular case of this equation are obtained after solving the reduced equation.展开更多
We present an experimental method to obtain neutral beam injection （NBI） power scaling laws with operating parameters of the NBI system on HL-2A, including the beam divergence angle, the beam power transmission effi...We present an experimental method to obtain neutral beam injection （NBI） power scaling laws with operating parameters of the NBI system on HL-2A, including the beam divergence angle, the beam power transmission efficiency, the neutralization efficiency and so on. With the empirical scaling laws, the estimating power can be obtained in every shot of experiment on time, therefore the important parameters such as the energy confinement time can be obtained precisely. The simulation results by the tokamak simulation code （TSC） show that the evolution of the plasma parameters is in good agreement with the experimental results by using the NBI power from the empirical scaling law.展开更多
In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)an...In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)and the novel dual powerlaw scale distribution theory.The effects of linear,homogeneous,and non-homogeneous temperature fields on the frequency and buckling temperature of FGM microplates are evaluated in detail.The results show that the porosity greatly affects the mechanical properties of FGM plates,reducing their frequency and flexural temperature compared with non-porous plates.Different temperature profiles alter plate frequencies and buckling temperatures.The presence and pattern of scale effect parameters are also shown to be crucial for the mechanical response of FGM plates.The present research aims to provide precise guidelines for the micro-electro-mechanical system(MEMS)fabrication by elucidating the complex interplay between thermal,material,and structural factors that affect the performance of FGM plates in advanced applications.展开更多
Purpose:The goal of this study is to analyze the relationship between funded and unfunded papers and their citations in both basic and applied sciences.Design/methodology/approach:A power law model analyzes the relati...Purpose:The goal of this study is to analyze the relationship between funded and unfunded papers and their citations in both basic and applied sciences.Design/methodology/approach:A power law model analyzes the relationship between research funding and citations of papers using 831,337 documents recorded in the Web of Science database.Findings:The original results reveal general characteristics of the diffusion of science in research fields:a)Funded articles receive higher citations compared to unfunded papers in journals;b)Funded articles exhibit a super-linear growth in citations,surpassing the increase seen in unfunded articles.This finding reveals a higher diffusion of scientific knowledge in funded articles.Moreover,c)funded articles in both basic and applied sciences demonstrate a similar expected change in citations,equivalent to about 1.23%,when the number of funded papers increases by 1%in journals.This result suggests,for the first time,that funding effect of scientific research is an invariant driver,irrespective of the nature of the basic or applied sciences.Originality/value:This evidence suggests empirical laws of funding for scientific citations that explain the importance of robust funding mechanisms for achieving impactful research outcomes in science and society.These findings here also highlight that funding for scientific research is a critical driving force in supporting citations and the dissemination of scientific knowledge in recorded documents in both basic and applied sciences.Practical implications:This comprehensive result provides a holistic view of the relationship between funding and citation performance in science to guide policymakers and R&D managers with science policies by directing funding to research in promoting the scientific development and higher diffusion of results for the progress of human society.展开更多
Given n samples(viewed as an n-tuple)of aγ-regular discrete distributionπ,in this article the authors concern with the weighted and unweighted graphs induced by the n samples.They first prove a series of SLLN result...Given n samples(viewed as an n-tuple)of aγ-regular discrete distributionπ,in this article the authors concern with the weighted and unweighted graphs induced by the n samples.They first prove a series of SLLN results(of Dvoretzky-Erdos'type).Then they show that the vertex weights of the graphs under investigation obey asymptotically power law distributions with exponent 1+γThey also give a conjecture that the degrees of unweighted graphs would exhibit asymptotically power law distributions with constant exponent 2.This exponent is obviously independent of the parameterγ∈(0,1),which is a surprise to us at first sight.展开更多
Power-law distributions and other skew distributions,observed in various models and real systems,are considered.A model,describing evolving systems with increasing number of elements,is considered to study the distrib...Power-law distributions and other skew distributions,observed in various models and real systems,are considered.A model,describing evolving systems with increasing number of elements,is considered to study the distribution over element sizes.Stationary power-law distributions are found.Certain non-stationary skew distributions are obtained and analyzed,based on exact solutions and numerical simulations.展开更多
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 tot...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.展开更多
This paper examines the spatial and temporal distribution of all COVID-19 cases from January to June 2020 against the underlying distribution of population in the United States.It is found that,as time passes,COVID-19...This paper examines the spatial and temporal distribution of all COVID-19 cases from January to June 2020 against the underlying distribution of population in the United States.It is found that,as time passes,COVID-19 cases become a power law with cutoff,resembling the underlying spatial distribution of populations.The power law implies that many states and counties have a low number of cases,while only a few highly populated states and counties have a high number of cases.To further differentiate patterns between the underlying populations and COVID-19 cases,we derived their inherent hierarchy or spatial heterogeneity characterized by the ht-index.We found that the ht-index of COVID-19 cases persistently approaches that of the populations;that is,5 and 7 at the state and county levels,respectively.Mapping the ht-index of COVID-19 cases against that of populations shows that the pandemic is largely shaped by the underlying population with the R-square value between infection and population up to 0.82.展开更多
The newly revised and enlarged main contents of the Law of Prevention and Control of Atmospheric Pollution are described, The macro impacts of the law on the power industry development are analyzed mainly in respects ...The newly revised and enlarged main contents of the Law of Prevention and Control of Atmospheric Pollution are described, The macro impacts of the law on the power industry development are analyzed mainly in respects to power demand and readjustment of power structure and layout. clean production and pollution control level, scientific management of environmental protection, in accordance with law as well as changes of construction and operation costs. And finally, several questions worthy to be noted in course of implementation of the new law are enumerated.展开更多
The current manuscript is reported about the eiectro-osmotic Couette-Poiseuille ftow of power law Al2O3- PVC nanofluid through a channel, in which upper wall is moving with constant velocity. The influences of magneti...The current manuscript is reported about the eiectro-osmotic Couette-Poiseuille ftow of power law Al2O3- PVC nanofluid through a channel, in which upper wall is moving with constant velocity. The influences of magnetic field, mixed convection, joule heating, and viscous dissipation are also incorporated. The flow is generated because of constant pressure gradient in axial direction. The resulting flow problem is coupled nonlinear ordinary differential equations, which are at first modeled and then transform into dimensionless form through appropriate transformation. Analytical solution of the governing is carried out. The impact of modified Brinkman number, modified Magnetic field, electro-osmotic parameters on velocity and temperature are examined graphically. From the results, it is concluded that the Skin friction at moving isolated wail decreases with the increase of electro-osmotic parameter and reverse behavior for Nusselt number at heated stationary wall occur.展开更多
Due to the simplicity and flexibility of the power law process,it is widely used to model the failures of repairable systems.Although statistical inference on the parameters of the power law process has been well deve...Due to the simplicity and flexibility of the power law process,it is widely used to model the failures of repairable systems.Although statistical inference on the parameters of the power law process has been well developed,numerous studies largely depend on complete failure data.A few methods on incomplete data are reported to process such data,but they are limited to their specific cases,especially to that where missing data occur at the early stage of the failures.No framework to handle generic scenarios is available.To overcome this problem,from the point of view of order statistics,the statistical inference of the power law process with incomplete data is established in this paper.The theoretical derivation is carried out and the case studies demonstrate and verify the proposed method.Order statistics offer an alternative to the statistical inference of the power law process with incomplete data as they can reformulate current studies on the left censored failure data and interval censored data in a unified framework.The results show that the proposed method has more flexibility and more applicability.展开更多
This paper is concerned with the mechanism of blackouts in China power system from the viewpoint of self-organized criticality. By using two estimation algorithms of scaled window variance （SWV） and rescaled rangest...This paper is concerned with the mechanism of blackouts in China power system from the viewpoint of self-organized criticality. By using two estimation algorithms of scaled window variance （SWV） and rescaled rangestatistics （R/S）, this paper studies the blackout data in China power system during 1988-1997. The result of analysis shows that the blackout data of 1994-1997 coincides well with the autocorrelation. Furthermore, it is found that the function of blackout probability vs. blackout size exhibits power law distribution.展开更多
Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or...Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.展开更多
The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstr...The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with Uw 〉〉 U∞, or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.展开更多
This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or u...This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.展开更多
Considering Brinkman⁃Forchheimer extended Darcy flow and local thermal non⁃equilibrium effect,a general model of forced convection with viscous dissipation in power⁃law fluid saturated porous media channel was establi...Considering Brinkman⁃Forchheimer extended Darcy flow and local thermal non⁃equilibrium effect,a general model of forced convection with viscous dissipation in power⁃law fluid saturated porous media channel was established.The dimensionless temperature profiles and Nusselt number were numerically solved using the classical fourth⁃order Runge Kutta method under a constant heat flux boundary condition.The conclusion showed that the fluid⁃solid temperature distributions were significantly affected by dimensionless Bi,k,Da,Br,and F,and the effects of power⁃law indexes on convection heat transfer characteristics were also non⁃negligible.展开更多
基金funded by Hasanuddin University,grant number 00309/UN4.22/PT.01.03/2024.
文摘A drought is when reduced rainfall leads to a water crisis,impacting daily life.Over recent decades,droughts have affected various regions,including South Sulawesi,Indonesia.This study aims to map the probability of meteo-rological drought months using the 1-month Standardized Precipitation Index(SPI)in South Sulawesi.Based on SPI,meteorological drought characteristics are inversely proportional to drought event intensity,which can be modeled using a Non-Homogeneous Poisson Process,specifically the Power Law Process.The estimation method employs Maximum Likelihood Estimation(MLE),where drought event intensities are treated as random variables over a set time interval.Future drought months are estimated using the cumulative Power Law Process function,with theβandγparameters more significant than 0.The probability of drought months is determined using the Non-Homogeneous Poisson Process,which models event occurrence over time,considering varying intensities.The results indicate that,of the 24 districts/cities in South Sulawesi,14 experienced meteorological drought based on the SPI and Power Law Process model.The estimated number of months of drought occurrence in the next 12 months is one month of drought with an occurrence probability value of 0.37 occurring in November in the Selayar,Bulukumba,Bantaeng,Jeneponto,Takalar and Gowa areas,in October in the Sinjai,Barru,Bone,Soppeng,Pinrang and Pare-pare areas,as well as in December in the Maros and Makassar areas.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.12375072,12375073,12275259,and 12135011)supported by Guangdong Provincial Funding(Grant No.2019QN01X172)supported by the National Security Academic Fund(Grant No.U2330401)。
文摘Finite-volume extrapolation is an important step for extracting physical observables from lattice calculations.However,it is a significant challenge for systems with long-range interactions.We employ symbolic regression to regress the finite-volume extrapolation formula for both short-range and long-range interactions.The regressed formula still holds the exponential form with a factor L^(n) in front of it.The power decreases with the decreasing range of the force.When the range of the force becomes sufficiently small,the power converges to-1,recovering the short-range formula as expected.Our work represents a significant advancement in leveraging machine learning to probe uncharted territories within particle physics.
基金Supported by the Fundamental Research Funds for the Central Universities under Grant No.2013XK03the National Natural Science Foundation of China under Grant No.11371361
文摘The conservation laws for the （1＋2）-dimensional Zakharov-Kuznetsov modified equal width （ZK-MEW） equation with power law nonlinearity are constructed by using Noether＇s approach through an interesting method of increasing the order of this equation. With the aid of an obtained conservation law, the generalized double reduction theorem is applied to this equation. It can be shown that the reduced equation is a second order nonlinear ODE. FinaJ1y, some exact solutions for a particular case of this equation are obtained after solving the reduced equation.
文摘We present an experimental method to obtain neutral beam injection （NBI） power scaling laws with operating parameters of the NBI system on HL-2A, including the beam divergence angle, the beam power transmission efficiency, the neutralization efficiency and so on. With the empirical scaling laws, the estimating power can be obtained in every shot of experiment on time, therefore the important parameters such as the energy confinement time can be obtained precisely. The simulation results by the tokamak simulation code （TSC） show that the evolution of the plasma parameters is in good agreement with the experimental results by using the NBI power from the empirical scaling law.
基金Project supported by the National Key Research and Development Program of China(No.2022YFB3207100)Hubei Provincial Strategic Scientist Training Plan(No.2022EJD009)the Fundamental Research Funds for the Central Universities of China(No.2042023kf1041)。
文摘In this study,the thermodynamic behaviors of the intrinsic frequency and buckling temperature of rectangular plates of functionally graded materials(FGMs)are explored based on the modified couple stress theory(MCST)and the novel dual powerlaw scale distribution theory.The effects of linear,homogeneous,and non-homogeneous temperature fields on the frequency and buckling temperature of FGM microplates are evaluated in detail.The results show that the porosity greatly affects the mechanical properties of FGM plates,reducing their frequency and flexural temperature compared with non-porous plates.Different temperature profiles alter plate frequencies and buckling temperatures.The presence and pattern of scale effect parameters are also shown to be crucial for the mechanical response of FGM plates.The present research aims to provide precise guidelines for the micro-electro-mechanical system(MEMS)fabrication by elucidating the complex interplay between thermal,material,and structural factors that affect the performance of FGM plates in advanced applications.
文摘Purpose:The goal of this study is to analyze the relationship between funded and unfunded papers and their citations in both basic and applied sciences.Design/methodology/approach:A power law model analyzes the relationship between research funding and citations of papers using 831,337 documents recorded in the Web of Science database.Findings:The original results reveal general characteristics of the diffusion of science in research fields:a)Funded articles receive higher citations compared to unfunded papers in journals;b)Funded articles exhibit a super-linear growth in citations,surpassing the increase seen in unfunded articles.This finding reveals a higher diffusion of scientific knowledge in funded articles.Moreover,c)funded articles in both basic and applied sciences demonstrate a similar expected change in citations,equivalent to about 1.23%,when the number of funded papers increases by 1%in journals.This result suggests,for the first time,that funding effect of scientific research is an invariant driver,irrespective of the nature of the basic or applied sciences.Originality/value:This evidence suggests empirical laws of funding for scientific citations that explain the importance of robust funding mechanisms for achieving impactful research outcomes in science and society.These findings here also highlight that funding for scientific research is a critical driving force in supporting citations and the dissemination of scientific knowledge in recorded documents in both basic and applied sciences.Practical implications:This comprehensive result provides a holistic view of the relationship between funding and citation performance in science to guide policymakers and R&D managers with science policies by directing funding to research in promoting the scientific development and higher diffusion of results for the progress of human society.
基金This work was supported by the National Natural Science Foundation of China(Nos.11871162,11771286,11271255,11271077,11001173,11790273)the Key Laboratory of Mathematics for Non linear Science,Fudan University.
文摘Given n samples(viewed as an n-tuple)of aγ-regular discrete distributionπ,in this article the authors concern with the weighted and unweighted graphs induced by the n samples.They first prove a series of SLLN results(of Dvoretzky-Erdos'type).Then they show that the vertex weights of the graphs under investigation obey asymptotically power law distributions with exponent 1+γThey also give a conjecture that the degrees of unweighted graphs would exhibit asymptotically power law distributions with constant exponent 2.This exponent is obviously independent of the parameterγ∈(0,1),which is a surprise to us at first sight.
文摘Power-law distributions and other skew distributions,observed in various models and real systems,are considered.A model,describing evolving systems with increasing number of elements,is considered to study the distribution over element sizes.Stationary power-law distributions are found.Certain non-stationary skew distributions are obtained and analyzed,based on exact solutions and numerical simulations.
文摘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.
基金This work was partially supported by the Swedish Research Council Formas through the ALEXANDER project with grant number FR-2017/0009.
文摘This paper examines the spatial and temporal distribution of all COVID-19 cases from January to June 2020 against the underlying distribution of population in the United States.It is found that,as time passes,COVID-19 cases become a power law with cutoff,resembling the underlying spatial distribution of populations.The power law implies that many states and counties have a low number of cases,while only a few highly populated states and counties have a high number of cases.To further differentiate patterns between the underlying populations and COVID-19 cases,we derived their inherent hierarchy or spatial heterogeneity characterized by the ht-index.We found that the ht-index of COVID-19 cases persistently approaches that of the populations;that is,5 and 7 at the state and county levels,respectively.Mapping the ht-index of COVID-19 cases against that of populations shows that the pandemic is largely shaped by the underlying population with the R-square value between infection and population up to 0.82.
文摘The newly revised and enlarged main contents of the Law of Prevention and Control of Atmospheric Pollution are described, The macro impacts of the law on the power industry development are analyzed mainly in respects to power demand and readjustment of power structure and layout. clean production and pollution control level, scientific management of environmental protection, in accordance with law as well as changes of construction and operation costs. And finally, several questions worthy to be noted in course of implementation of the new law are enumerated.
文摘The current manuscript is reported about the eiectro-osmotic Couette-Poiseuille ftow of power law Al2O3- PVC nanofluid through a channel, in which upper wall is moving with constant velocity. The influences of magnetic field, mixed convection, joule heating, and viscous dissipation are also incorporated. The flow is generated because of constant pressure gradient in axial direction. The resulting flow problem is coupled nonlinear ordinary differential equations, which are at first modeled and then transform into dimensionless form through appropriate transformation. Analytical solution of the governing is carried out. The impact of modified Brinkman number, modified Magnetic field, electro-osmotic parameters on velocity and temperature are examined graphically. From the results, it is concluded that the Skin friction at moving isolated wail decreases with the increase of electro-osmotic parameter and reverse behavior for Nusselt number at heated stationary wall occur.
基金supported by the National Natural Science Foundation of China(51775090)。
文摘Due to the simplicity and flexibility of the power law process,it is widely used to model the failures of repairable systems.Although statistical inference on the parameters of the power law process has been well developed,numerous studies largely depend on complete failure data.A few methods on incomplete data are reported to process such data,but they are limited to their specific cases,especially to that where missing data occur at the early stage of the failures.No framework to handle generic scenarios is available.To overcome this problem,from the point of view of order statistics,the statistical inference of the power law process with incomplete data is established in this paper.The theoretical derivation is carried out and the case studies demonstrate and verify the proposed method.Order statistics offer an alternative to the statistical inference of the power law process with incomplete data as they can reformulate current studies on the left censored failure data and interval censored data in a unified framework.The results show that the proposed method has more flexibility and more applicability.
基金This work was supported by the National Natural Science Foundation of China (No. 50595411, 50377018)the Project 973 (G2004CB217902).
文摘This paper is concerned with the mechanism of blackouts in China power system from the viewpoint of self-organized criticality. By using two estimation algorithms of scaled window variance （SWV） and rescaled rangestatistics （R/S）, this paper studies the blackout data in China power system during 1988-1997. The result of analysis shows that the blackout data of 1994-1997 coincides well with the autocorrelation. Furthermore, it is found that the function of blackout probability vs. blackout size exhibits power law distribution.
基金This work was supported by the Natural Science Foundation of China(Grant Nos.61673169,11701176,11626101,11601485).
文摘Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models.Amongst them,the significant models of fluids and heat or mass transfer are on priority.Most recently a new idea of fractal-fractional derivative is introduced;however,it is not used for heat transfer in channel flow.In this article,we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem.More exactly,we have considered the free convection heat transfer for a Newtonian fluid.The flow is bounded between two parallel static plates.One of the plates is heated constantly.The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution.The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter.For the influence of temperature and velocity profile,it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator.Therefore,a combined approach of fractal fractional explains the memory of the function better than fractional only.
基金This work is supported by the National Natural Science Foundation of China (No.50476083) and the Cross-Century Talents Projectsby the Ministry Education of China.
文摘The specific problem to be considered here concerns the boundary layer problem of a non-Newtonian fluid on a flat plate in length, whose surface has a constant velocity opposite in the direction to that of the mainstream with Uw 〉〉 U∞, or alternatively when the plate surface velocity is kept fixed but the stream speed is reduced to zero. A theoretical analysis for a boundary layer flow is made and the self-similar equation is determined. Solutions are presented numerically for special power index and the associated transfer behavior is discussed.
文摘This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.
基金Sponsored by the Liaoning Provincial Doctoral Initiation Fund Project(Grant No.2019-BS-030).
文摘Considering Brinkman⁃Forchheimer extended Darcy flow and local thermal non⁃equilibrium effect,a general model of forced convection with viscous dissipation in power⁃law fluid saturated porous media channel was established.The dimensionless temperature profiles and Nusselt number were numerically solved using the classical fourth⁃order Runge Kutta method under a constant heat flux boundary condition.The conclusion showed that the fluid⁃solid temperature distributions were significantly affected by dimensionless Bi,k,Da,Br,and F,and the effects of power⁃law indexes on convection heat transfer characteristics were also non⁃negligible.
