This paper deals with a first-principle mathematical model that describes the electrostatic coalescer unitsdevoted to the separation of water from oil in water-in-oil emulsions, which are typical of the upstreamoperat...This paper deals with a first-principle mathematical model that describes the electrostatic coalescer unitsdevoted to the separation of water from oil in water-in-oil emulsions, which are typical of the upstreamoperations in oil fields. The main phenomena governing the behavior of the electrostatic coalescer are denscribed, starting from fundamental laws. In addition, the gradual coalescence of the emulsion droplets isconsidered in the mathematical modeling in a dynamic fashion, as the phenomenon is identified as a keystep in the overall yield of the unit operation. The resulting differential system with boundary conditionsis then integrated via performing numerical libraries, and the simulation results confirm the available lit-erature and the industrial data. A sensitivity analysis is provided with respect to the main parameters. Themathematical model results in a flexible tool that is useful for the purposes of design, unit behavior predic-tion. performance rnoniroring, and ontimization.展开更多
A rigorous spectral representation of relativistic random-phase approximation is presented.Explicit expression is derived for the effective particle-hole interaction which contains the direct term Kan,the exchange ter...A rigorous spectral representation of relativistic random-phase approximation is presented.Explicit expression is derived for the effective particle-hole interaction which contains the direct term Kan,the exchange term KaQ and the kernel for the fermion line renormalization K_(fr).It is shown that according to our method,not only K_(an) but also K_(sc) and K_(fr) can be given rigorously in a form which depends only on one ω(energy)-variable and they all take account of the retardation effect properly.展开更多
Rigorous Coupled-Wave Approach (RCWA) has been used successfully and accurately to study simple grating structures, such as one-layer gratings, one-whole gratings. In this paper, RCWA is expanded to solve Sandwich gra...Rigorous Coupled-Wave Approach (RCWA) has been used successfully and accurately to study simple grating structures, such as one-layer gratings, one-whole gratings. In this paper, RCWA is expanded to solve Sandwich gratings (SG), which is composed of two identical planar dielectric gratings adjoined by thin metallic or dielectric film. The electromagnetic analytic expressions for each layer of SG structure are given and rigorous coupled-wave equations are deduced. The numerical investigations for the diffraction spectra of SG by our theoretical and computer programs are in good agreement with the results of classical RCWA in the condition when a Sandwish grating is simplified to a classical one-layer grating. The calculations by our programs of another condition when a Sandwish grating is degenerated to a classical single planar structure also conform to the results of classical electromagnetic theory. The research results above indicate that the extended theoretical formula has backwards compatibility and is self-consistent with the classical theory.展开更多
In order to make more available methods for natural jadeite quality evaluation,this study applied rigorous coupled wave theory to calculate and simulate the reflection characteristics of various natural jadeites,and e...In order to make more available methods for natural jadeite quality evaluation,this study applied rigorous coupled wave theory to calculate and simulate the reflection characteristics of various natural jadeites,and establish evaluation standard based on the relationship between refractive index and reflectivity and responses of reflection efficiency to refractive index,grating thickness and incident angles,etc.The results suggest that reflection efficiency varies significantly as a function of the natural jadeite quality,which can provide a new method to evaluate natural jadeite.展开更多
Continuous time random walk on fractals is studied.Asymptotic forms of<r^(2)(t)>,S(t)and P(t)are obtained rigorously by the generalized Blackwell theorem,where<r^(2)(t)>is the mean-square displacement,S(t)...Continuous time random walk on fractals is studied.Asymptotic forms of<r^(2)(t)>,S(t)and P(t)are obtained rigorously by the generalized Blackwell theorem,where<r^(2)(t)>is the mean-square displacement,S(t)the number of distinct sites visited in time t,and P(t)the probability of return at time t.The spatial disorder turns out to be predominant for long time.展开更多
In this article I conduct a short review of the proofs of the area inside a circle. These include intuitive as well as rigorous analytic proofs. This discussion is important not just from mathematical view point but a...In this article I conduct a short review of the proofs of the area inside a circle. These include intuitive as well as rigorous analytic proofs. This discussion is important not just from mathematical view point but also because pedagogically the calculus books still use circular reasoning today to prove the area inside a circle (also that of an ellipse) on this important historical topic, first illustrated by Archimedes. I offer an innovative approach through the introduction of a theorem, which will lead to proving the area inside a circle avoiding circular argumentation.展开更多
Global mean sea level budget is rigorously adjusted during the period 2005-2015.The emphasis is to provide the best estimates for the linear rates of changes(trends)of the global mean sea level budget components durin...Global mean sea level budget is rigorously adjusted during the period 2005-2015.The emphasis is to provide the best estimates for the linear rates of changes(trends)of the global mean sea level budget components during this period subject to the constraint:Earth’s hydrosphere conserves water.The newly simultaneously adjusted trends of the budget components suggest a larger correction for the global mean sea level trend implicated by the other budget components’trends under the budget constraint.The simultaneous estimation of the linear trends of the budget components subject to the constraint for closure improves their uncertainties and enables a holistic assessment of the global mean sea budget,which has implications for future sea level science studies,including the future Intergovernmental Panel on Climate Change(IPCC)Assessment Reports,and the US Climate Assessment Reports.展开更多
In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwis...In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach.Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.展开更多
We present quasi-exact ab initio path integral Monte Carlo(PIMC)results for the partial static density responses and local field factors of hydrogen in the warm dense matter regime,from solid density conditions to the...We present quasi-exact ab initio path integral Monte Carlo(PIMC)results for the partial static density responses and local field factors of hydrogen in the warm dense matter regime,from solid density conditions to the strongly compressed case.The full dynamic treatment of electrons and protons on the same footing allows us to rigorously quantify both electronic and ionic exchange–correlation effects in the system,and to compare the results with those of earlier incomplete models such as the archetypal uniform electron gas or electrons in a fixed ion snapshot potential that do not take into account the interplay between the two constituents.The full electronic density response is highly sensitive to electronic localization around the ions,and our results constitute unambiguous predictions for upcoming X-ray Thomson scattering experiments with hydrogen jets and fusion plasmas.All PIMC results are made freely available and can be used directly for a gamut of applications,including inertial confinement fusion calculations and the modeling of dense astrophysical objects.Moreover,they constitute invaluable benchmark data for approximate but computationally less demanding approaches such as density functional theory or PIMC within the fixed-node approximation.展开更多
文摘This paper deals with a first-principle mathematical model that describes the electrostatic coalescer unitsdevoted to the separation of water from oil in water-in-oil emulsions, which are typical of the upstreamoperations in oil fields. The main phenomena governing the behavior of the electrostatic coalescer are denscribed, starting from fundamental laws. In addition, the gradual coalescence of the emulsion droplets isconsidered in the mathematical modeling in a dynamic fashion, as the phenomenon is identified as a keystep in the overall yield of the unit operation. The resulting differential system with boundary conditionsis then integrated via performing numerical libraries, and the simulation results confirm the available lit-erature and the industrial data. A sensitivity analysis is provided with respect to the main parameters. Themathematical model results in a flexible tool that is useful for the purposes of design, unit behavior predic-tion. performance rnoniroring, and ontimization.
基金Supported by the National Natural Science Foundation of China and the Foundation of State Education Commission.
文摘A rigorous spectral representation of relativistic random-phase approximation is presented.Explicit expression is derived for the effective particle-hole interaction which contains the direct term Kan,the exchange term KaQ and the kernel for the fermion line renormalization K_(fr).It is shown that according to our method,not only K_(an) but also K_(sc) and K_(fr) can be given rigorously in a form which depends only on one ω(energy)-variable and they all take account of the retardation effect properly.
文摘Rigorous Coupled-Wave Approach (RCWA) has been used successfully and accurately to study simple grating structures, such as one-layer gratings, one-whole gratings. In this paper, RCWA is expanded to solve Sandwich gratings (SG), which is composed of two identical planar dielectric gratings adjoined by thin metallic or dielectric film. The electromagnetic analytic expressions for each layer of SG structure are given and rigorous coupled-wave equations are deduced. The numerical investigations for the diffraction spectra of SG by our theoretical and computer programs are in good agreement with the results of classical RCWA in the condition when a Sandwish grating is simplified to a classical one-layer grating. The calculations by our programs of another condition when a Sandwish grating is degenerated to a classical single planar structure also conform to the results of classical electromagnetic theory. The research results above indicate that the extended theoretical formula has backwards compatibility and is self-consistent with the classical theory.
文摘In order to make more available methods for natural jadeite quality evaluation,this study applied rigorous coupled wave theory to calculate and simulate the reflection characteristics of various natural jadeites,and establish evaluation standard based on the relationship between refractive index and reflectivity and responses of reflection efficiency to refractive index,grating thickness and incident angles,etc.The results suggest that reflection efficiency varies significantly as a function of the natural jadeite quality,which can provide a new method to evaluate natural jadeite.
文摘Continuous time random walk on fractals is studied.Asymptotic forms of<r^(2)(t)>,S(t)and P(t)are obtained rigorously by the generalized Blackwell theorem,where<r^(2)(t)>is the mean-square displacement,S(t)the number of distinct sites visited in time t,and P(t)the probability of return at time t.The spatial disorder turns out to be predominant for long time.
文摘In this article I conduct a short review of the proofs of the area inside a circle. These include intuitive as well as rigorous analytic proofs. This discussion is important not just from mathematical view point but also because pedagogically the calculus books still use circular reasoning today to prove the area inside a circle (also that of an ellipse) on this important historical topic, first illustrated by Archimedes. I offer an innovative approach through the introduction of a theorem, which will lead to proving the area inside a circle avoiding circular argumentation.
基金partially supported by the Natural Science Foundation of China(Grant No.41974040)。
文摘Global mean sea level budget is rigorously adjusted during the period 2005-2015.The emphasis is to provide the best estimates for the linear rates of changes(trends)of the global mean sea level budget components during this period subject to the constraint:Earth’s hydrosphere conserves water.The newly simultaneously adjusted trends of the budget components suggest a larger correction for the global mean sea level trend implicated by the other budget components’trends under the budget constraint.The simultaneous estimation of the linear trends of the budget components subject to the constraint for closure improves their uncertainties and enables a holistic assessment of the global mean sea budget,which has implications for future sea level science studies,including the future Intergovernmental Panel on Climate Change(IPCC)Assessment Reports,and the US Climate Assessment Reports.
基金supported by the National Natural Science Foundation of China(Grant No.11771265).
文摘In this article,some new rigorous perturbation bounds for the SR decomposition un-der normwise or componentwise perturbations for a given matrix are derived.Also,the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach.Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.
基金supported by the Center for Advanced Systems Understanding(CASUS),financed by Germany’s Federal Ministry of Education and Research(BMBF)and the Saxon State Government out of the State Budget approved by the Saxon State Parliamentfunding from the European Research Council(ERC)under the European Union’s Horizon 2022 Research and Innovation Program(Grant Agreement No.101076233,“PREXTREME”).
文摘We present quasi-exact ab initio path integral Monte Carlo(PIMC)results for the partial static density responses and local field factors of hydrogen in the warm dense matter regime,from solid density conditions to the strongly compressed case.The full dynamic treatment of electrons and protons on the same footing allows us to rigorously quantify both electronic and ionic exchange–correlation effects in the system,and to compare the results with those of earlier incomplete models such as the archetypal uniform electron gas or electrons in a fixed ion snapshot potential that do not take into account the interplay between the two constituents.The full electronic density response is highly sensitive to electronic localization around the ions,and our results constitute unambiguous predictions for upcoming X-ray Thomson scattering experiments with hydrogen jets and fusion plasmas.All PIMC results are made freely available and can be used directly for a gamut of applications,including inertial confinement fusion calculations and the modeling of dense astrophysical objects.Moreover,they constitute invaluable benchmark data for approximate but computationally less demanding approaches such as density functional theory or PIMC within the fixed-node approximation.
