Excellent fits were obtained by Talantsev (MPLB 33, 1950195, 2019) to the temperature (T)-dependent upper critical field (H<sub>c</sub><sub>2</sub>(T)) data of H<sub>3</sub>S report...Excellent fits were obtained by Talantsev (MPLB 33, 1950195, 2019) to the temperature (T)-dependent upper critical field (H<sub>c</sub><sub>2</sub>(T)) data of H<sub>3</sub>S reported by Mozaffari et al. [Nature Communications 10, 2522 (2019)] by employing four alternative phenomenological models, each of which invoked two or more properties from its sample-specific set S<sub>1</sub> = {T<sub>c</sub>, gap, coherence length, penetration depth, jump in sp.ht.} and a single value of the effective mass (m*) of an electron. Based on the premise that the variation of H<sub>c</sub><sub>2</sub>(T) is due to the variation of the chemical potential μ(T), we report here fits to the same data by employing a T-, μ- and m*-dependent equation for H<sub>c</sub><sub>2</sub>(T) and three models of μ(T), viz. the linear, the parabolic and the concave-upward model. For temperatures up to which the data are available, each of these provides a good fit. However, for lower values of T, their predictions differ. Notably, the predicted values of H<sub>c</sub><sub>2</sub>(0) are much higher than in any of the models dealt with by Talantsev. In sum, we show here that the addressed data are explicable in a framework comprising the set S<sub>2</sub> = {μ, m*, interaction parameter λ<sub>m</sub>, Landau index N<sub>L</sub>}, which is altogether different from S<sub>1</sub>.展开更多
This work represents the extraction of oil with high free fatty acid content from spent bleaching earth using sub-critical water technology as a greener production pathway. The extraction efficiencies under different ...This work represents the extraction of oil with high free fatty acid content from spent bleaching earth using sub-critical water technology as a greener production pathway. The extraction efficiencies under different conditions were investigated. The studied parameters include temperatures in the range of 180 to 270°C, the feed to solventfeed-to-solvent (in this case water) ratio (1:1, 1:2, 1:3, 1:4 and 1:5) and extraction times in the range of 5-60 minutes. The results showed that the optimum temperature, feed to solventfeed-to-solvent ratio, and extraction time were 270°C, 1:3, and 20 minutes, respectively. In another experiment, the extracted free fatty acids were converted into mono-, di-, and triglycerides through esterification with glycerol to increase the value added of the extracted products. The kinetics of the extraction process was found to be corresponding to an irreversible consecutive unimolecular-type first order reaction, consisting of the extraction step followed by the decomposition reaction step. Both reaction rates of extraction and decomposition were estimated using the reaction rate equations utilizing the nonlinear regression method. The apparent activation energy was calculated to be 46.1 kJ·mol-1. This result indicates a diffusion controlled reaction. For more exploration and deep understanding of the extraction mechanism, other thermodynamic parameters were also calculated and analyzed including,ΔH#, ΔS#, and ΔG# of the extraction step.展开更多
The strata movement induced by sub-critical extraction is a problem not receiving due attention because of its relatively small magnitude of deformation. However, with the increase of mining depth, sub-critical extrac...The strata movement induced by sub-critical extraction is a problem not receiving due attention because of its relatively small magnitude of deformation. However, with the increase of mining depth, sub-critical extraction has become a general phenomenon. This calls for an in-depth investigation into the characteristics of ground movements observed under different extents of sub-critical extraction, so as to determine the appropriate mining technique for use. Following a discussion of the factors influencing the extent of super-critical extraction, the super-critical extraction extent evaluation criteria was presented, the characteristics and laws of the strata and ground movements caused by such an extraction condition were systematically analyzed, and the mechanism of surface subsidence induced by sub-critical extraction was revealed. The result of study may serve as a basis for the development of the strata and ground movement prediction model and the mining techniques appropriate for use at depth beneath surface structures and buildings.展开更多
Membrane fouling is often considered as a hindrance for the application of microfiltration/ultrafiltration(MF/UF) for drinking water production. A novel process of photocatalytic membrane reactor/dynamic membrane(PMR/...Membrane fouling is often considered as a hindrance for the application of microfiltration/ultrafiltration(MF/UF) for drinking water production. A novel process of photocatalytic membrane reactor/dynamic membrane(PMR/DM), operating in a continuous mode under sub-critical flux, was proposed for the mitigation of membrane fouling caused by humic acids(HAs) in water. The mechanism of membrane fouling alleviation with synergistic photocatalytic oxidation and dynamic layer isolating effect was comprehensively investigated from the characterization of foulant evolution responsible for the reversible and irreversible fouling. The results showed that the PMR/DM utilized photocatalytic oxidation to enhance the porosity and hydrophilicity of the fouling layer by converting the high molecular weight(MW) and hydrophobic HA molecules with carboxylic functional groups and aromatic structures into low-MW hydrophilic or transphilic fractions, including tryptophan-like or fulvic-like substances. The fouling layer formed in the PMR/DM by combination of photocatalytic oxidation and DM running at a sub-critical flux of 100 L·h^-1·m^-2, was more hydrophilic and more porous, resulting in the lowest trans-membrane pressure(TMP) growth rates, as compared to the processes of ceramic membrane(CM), DM and PMR/CM.Meanwhile, the dynamic layer prevented the foulants, particularly the high-MW hydrophobic fractions,from contacting the primary membrane, which enabled the membrane permeability to be restored easily.展开更多
In-plane shear crack sub-critical propagation of rock at high temperature was studied by finite element method and shear-box(i.e.compression-shear) test with newly designed electrically conductive adhesive method.Nume...In-plane shear crack sub-critical propagation of rock at high temperature was studied by finite element method and shear-box(i.e.compression-shear) test with newly designed electrically conductive adhesive method.Numerical and experimental results show that the normalized shear(Mode Ⅱ) stress intensity factors,K ⅡT/KT0 is decreased as the temperature increases because high temperature can improve stress distribution at crack tip and reduce the Mode Ⅱ stress intensity factor.Microscopic features of fractured surface are of little pits and secondary micro-cracks in the vicinity(1.5-4.0 mm) of the crack tip.The chevron-shape secondary cracks gradually merge in the length of about 4-5 mm and disappear along the direction of crack propagation.Stable shear crack propagation time is increased with the increasing temperature while the stable shear crack propagation rate is decreased with the increasing temperature,since high temperature can increase the shear(Mode Ⅱ) fracture toughness and prevent the crack growth.It is necessary to ensure the ligament of specimen long enough to measure the maximum unstable crack propagation rate of rock.展开更多
Shear-box(i.e.compression-shear) test and newly designed electrically conductive adhesive method were used to measure shear crack sub-critical propagation time and rate of sandstone specimen.Different cubic specimens ...Shear-box(i.e.compression-shear) test and newly designed electrically conductive adhesive method were used to measure shear crack sub-critical propagation time and rate of sandstone specimen.Different cubic specimens with and without holes were tested to study the effect of holes on the shear crack sub-critical propagation.Numerical and experimental results show that three independent variables of hole,the interval distance S,the distance between the center of hole and the crack tip L,and hole radius R,have different contribution to the ratio of stress intensity factor of the specimen with holes to that of the specimen without hole,KⅡ/KⅡ0.Increasing S and decreasing L and R will result in the decrease of KⅡ/KⅡ0 and help crack arrest.The weight relation of the independent variables for KⅡ/KⅡ0 is S>L>R.The specimen DH3 with the largest value of S and the smallest values of L and R has the longest sub-critical crack propagation time and the smallest sub-critical crack propagation rate.Adding two suitable holes symmetrically to the original crack plane in rock specimen is considered to be a potential method for crack arrest of rock.展开更多
In reactor physics tests, it is important to monitor sub-criticality continuously during criticality approach. Reactivity measurements by the inverse kinetics method are widely used during the operation of a nuclear r...In reactor physics tests, it is important to monitor sub-criticality continuously during criticality approach. Reactivity measurements by the inverse kinetics method are widely used during the operation of a nuclear reactor. This technique is successfully applied at sufficiently high power level or to a core without an external neutron source where the neutron source term in point reactor kinetics equations may be neglected. For operation at low power levels or in the sub-critical domain, the increase in the fluctuation of the neutron signal may cause difficulties in the evaluation of reactivity and the effect of direct emission from the external neutron source may not be neglected. Therefore, contribution of the neutron source must be taken into account and this implies knowledge of a quantity proportional to the source strength, which calls the source term and then it should be determined. The research work has been conducted to measure reactivity with source term using a dedicated reactivity measurement system by the Least Square Inverse Kinetics Method (LSIKM). Application to a simulator of HANARO research reactor, Korea Atomic Energy Research Institute (KAERI), with known source strength and reactivity worth has showed consistent and satisfactory agreement.展开更多
Sub-critical water extraction is a brand-new separation technology. This paper mainly discussed the principle, advantages of sub-critical water extraction, and its applications ranging from the medicinal plants tradit...Sub-critical water extraction is a brand-new separation technology. This paper mainly discussed the principle, advantages of sub-critical water extraction, and its applications ranging from the medicinal plants traditionally used in Europe and Asia to produce pharmaceutical extracts (such as volatile oil, tannins, flavonoids, anthraquinone, lactone, etc.). Meanwhile, the prospect of sub-critical water extraction in plant extractives is also explored. It will be widely used in the field of medical plants, bringing huge economic benefits, environmental benefits and social benefits.展开更多
[Objectives] To study the optimal conditions for extracting procyanidins fromLycium ruthenicum Murr. with sub-critical fluid R134 a( 1,1,1,2-tetrafluoroethane) in 1 L extraction kettle. [Methods]Taking the extraction ...[Objectives] To study the optimal conditions for extracting procyanidins fromLycium ruthenicum Murr. with sub-critical fluid R134 a( 1,1,1,2-tetrafluoroethane) in 1 L extraction kettle. [Methods]Taking the extraction rate of procyanidins as an indicator,the influence of pressure,temperature,and extraction time on extraction rate of procyanidins fromL. Ruthenicum Murr. was studied by single factor experimental methods and orthogonal array design. [Results]The order of factors affecting extraction rate of procyanidins was extraction temperature > extraction pressure > extraction time. The optimum extraction conditions were as follows: the extraction rate of procyanidins fromL. ruthenicum Murr. was the highest with extraction pressure of 1. 2 MPa,extraction temperature of 50℃ and extraction time of 90 min. The content of procyanidins in L. ruthenicum Murr. from different producing areas was determined by vanillin-HCl method under the optimal conditions. [Conclusions] The method has the advantages of easy operation,good selectivity,low extraction temperature and high extraction efficiency,which is suitable for extraction of procyanidins in L. ruthenicum Murr.展开更多
Critical concentrations of α-(1→3)-D-glucan L-FV-Ⅱ from Lentinus edodes were studied by viscometry andfluorescence probe techniques. The dependence of the reduced viscosity on concentration of the glucan in 0.5 mol...Critical concentrations of α-(1→3)-D-glucan L-FV-Ⅱ from Lentinus edodes were studied by viscometry andfluorescence probe techniques. The dependence of the reduced viscosity on concentration of the glucan in 0.5 mol/L NaOHaqueous solutions with or without urea showed two turning points corresponding to the dynamic contact concentration c_s andthe overlap concentration c~* of the polymer. The values of c_s and c~* were found to be 1×10^(-3) g cm^(-3) and 1.1×10^(-2) g cm^(-3),respectively, for L-FV-Ⅱ in 0.5 mol/L NaOH aqueous solutions. The two critical concentrations of L-FV-Ⅱ in 0.5 mol/LNaOH aqueous solutions were also found to be 1.2×10^(-3) g cm^(-3) fbr c_s and 9.2×10^(-3) g cm^(-3) for c~* from the concentrationdependence of phenanthrene fluorescence intensities. The overlap concentration c~* of L-FV-Ⅱ in 0.5 mol/L NaOH aqueoussolutions was lower than that of polystyrene with same molecular weight in benzene, owing to the fact that polysaccharidetends to undergo aggregation caused by intermolecular hydrogen bonding. A normal viscosity behavior of L-FV-Ⅱ in 0.5 mol/L urea/0.5 mol/L NaOH aqueous solutions can still be observed in an extremely low concentration range at 25℃.展开更多
In this article, by applying the super-solution and sub-solution methods, instead of energy estimate methods, the authors investigate the critical extinction exponents for a polytropic filtration equation with a nonlo...In this article, by applying the super-solution and sub-solution methods, instead of energy estimate methods, the authors investigate the critical extinction exponents for a polytropic filtration equation with a nonlocal source and an absorption term, and give a classification of the exponents and coefficients for the solutions to vanish in finite time or not, which improve one of our results (Applicable Analysis, 92(2013), 636-650) and the results of Zheng et al (Math. Meth. Appl. Sci., 36(2013), 730-743).展开更多
Based on μ-, T- and H-dependent pairing and number equations and the premise that μ(T) is predominantly the cause of the variation of the upper critical field H<sub>c</sub><sub>2</sub>(T), wh...Based on μ-, T- and H-dependent pairing and number equations and the premise that μ(T) is predominantly the cause of the variation of the upper critical field H<sub>c</sub><sub>2</sub>(T), where μ, T and H denote the chemical potential, temperature and the applied field, respectively, we provide in this paper fits to the empirical H<sub>c</sub><sub>2</sub>(T) data of H<sub>3</sub>S reported by Mozaffari, et al. (2019) and deal with the issue of whether or not H<sub>3</sub>S exhibits the Meissner effect. Employing a variant of the template given by Dogan and Cohen (2021), we examine in detail the results of Hirsch and Marsiglio (2022) who have claimed that H<sub>3</sub>S does not exhibit the Meissner effect and Minkov, et al. (2023) who have claimed that it does. We are thus led to suggest that monitoring the chemical potential (equivalently, the number density of Cooper pairs N<sub>s</sub> at T = T<sub>c</sub>) should shed new light on the issue being addressed.展开更多
文摘Excellent fits were obtained by Talantsev (MPLB 33, 1950195, 2019) to the temperature (T)-dependent upper critical field (H<sub>c</sub><sub>2</sub>(T)) data of H<sub>3</sub>S reported by Mozaffari et al. [Nature Communications 10, 2522 (2019)] by employing four alternative phenomenological models, each of which invoked two or more properties from its sample-specific set S<sub>1</sub> = {T<sub>c</sub>, gap, coherence length, penetration depth, jump in sp.ht.} and a single value of the effective mass (m*) of an electron. Based on the premise that the variation of H<sub>c</sub><sub>2</sub>(T) is due to the variation of the chemical potential μ(T), we report here fits to the same data by employing a T-, μ- and m*-dependent equation for H<sub>c</sub><sub>2</sub>(T) and three models of μ(T), viz. the linear, the parabolic and the concave-upward model. For temperatures up to which the data are available, each of these provides a good fit. However, for lower values of T, their predictions differ. Notably, the predicted values of H<sub>c</sub><sub>2</sub>(0) are much higher than in any of the models dealt with by Talantsev. In sum, we show here that the addressed data are explicable in a framework comprising the set S<sub>2</sub> = {μ, m*, interaction parameter λ<sub>m</sub>, Landau index N<sub>L</sub>}, which is altogether different from S<sub>1</sub>.
文摘This work represents the extraction of oil with high free fatty acid content from spent bleaching earth using sub-critical water technology as a greener production pathway. The extraction efficiencies under different conditions were investigated. The studied parameters include temperatures in the range of 180 to 270°C, the feed to solventfeed-to-solvent (in this case water) ratio (1:1, 1:2, 1:3, 1:4 and 1:5) and extraction times in the range of 5-60 minutes. The results showed that the optimum temperature, feed to solventfeed-to-solvent ratio, and extraction time were 270°C, 1:3, and 20 minutes, respectively. In another experiment, the extracted free fatty acids were converted into mono-, di-, and triglycerides through esterification with glycerol to increase the value added of the extracted products. The kinetics of the extraction process was found to be corresponding to an irreversible consecutive unimolecular-type first order reaction, consisting of the extraction step followed by the decomposition reaction step. Both reaction rates of extraction and decomposition were estimated using the reaction rate equations utilizing the nonlinear regression method. The apparent activation energy was calculated to be 46.1 kJ·mol-1. This result indicates a diffusion controlled reaction. For more exploration and deep understanding of the extraction mechanism, other thermodynamic parameters were also calculated and analyzed including,ΔH#, ΔS#, and ΔG# of the extraction step.
基金Project supported by Doctoral Study Courses Foundation and Post-Doctoral Scientific Foundation .
文摘The strata movement induced by sub-critical extraction is a problem not receiving due attention because of its relatively small magnitude of deformation. However, with the increase of mining depth, sub-critical extraction has become a general phenomenon. This calls for an in-depth investigation into the characteristics of ground movements observed under different extents of sub-critical extraction, so as to determine the appropriate mining technique for use. Following a discussion of the factors influencing the extent of super-critical extraction, the super-critical extraction extent evaluation criteria was presented, the characteristics and laws of the strata and ground movements caused by such an extraction condition were systematically analyzed, and the mechanism of surface subsidence induced by sub-critical extraction was revealed. The result of study may serve as a basis for the development of the strata and ground movement prediction model and the mining techniques appropriate for use at depth beneath surface structures and buildings.
基金Supported by the National Natural Science Foundation of China(21566013,51562016)Youth Science Foundation of Jiangxi Provincial Department of Education,China(GJJ170970)the Natural Science Foundation of Jiangxi Province(20171BAB206015)
文摘Membrane fouling is often considered as a hindrance for the application of microfiltration/ultrafiltration(MF/UF) for drinking water production. A novel process of photocatalytic membrane reactor/dynamic membrane(PMR/DM), operating in a continuous mode under sub-critical flux, was proposed for the mitigation of membrane fouling caused by humic acids(HAs) in water. The mechanism of membrane fouling alleviation with synergistic photocatalytic oxidation and dynamic layer isolating effect was comprehensively investigated from the characterization of foulant evolution responsible for the reversible and irreversible fouling. The results showed that the PMR/DM utilized photocatalytic oxidation to enhance the porosity and hydrophilicity of the fouling layer by converting the high molecular weight(MW) and hydrophobic HA molecules with carboxylic functional groups and aromatic structures into low-MW hydrophilic or transphilic fractions, including tryptophan-like or fulvic-like substances. The fouling layer formed in the PMR/DM by combination of photocatalytic oxidation and DM running at a sub-critical flux of 100 L·h^-1·m^-2, was more hydrophilic and more porous, resulting in the lowest trans-membrane pressure(TMP) growth rates, as compared to the processes of ceramic membrane(CM), DM and PMR/CM.Meanwhile, the dynamic layer prevented the foulants, particularly the high-MW hydrophobic fractions,from contacting the primary membrane, which enabled the membrane permeability to be restored easily.
基金Project(50374073) supported by the National Natural Science Foundation of ChinaProject(1343-77239) supported by the Graduate Education Innovation Project of Central South University,China
文摘In-plane shear crack sub-critical propagation of rock at high temperature was studied by finite element method and shear-box(i.e.compression-shear) test with newly designed electrically conductive adhesive method.Numerical and experimental results show that the normalized shear(Mode Ⅱ) stress intensity factors,K ⅡT/KT0 is decreased as the temperature increases because high temperature can improve stress distribution at crack tip and reduce the Mode Ⅱ stress intensity factor.Microscopic features of fractured surface are of little pits and secondary micro-cracks in the vicinity(1.5-4.0 mm) of the crack tip.The chevron-shape secondary cracks gradually merge in the length of about 4-5 mm and disappear along the direction of crack propagation.Stable shear crack propagation time is increased with the increasing temperature while the stable shear crack propagation rate is decreased with the increasing temperature,since high temperature can increase the shear(Mode Ⅱ) fracture toughness and prevent the crack growth.It is necessary to ensure the ligament of specimen long enough to measure the maximum unstable crack propagation rate of rock.
基金Project(50374073) supported by the National Natural Science Foundation of ChinaProject(1343-77239) supported by the Graduate Education Innovation Project of Central South University,China
文摘Shear-box(i.e.compression-shear) test and newly designed electrically conductive adhesive method were used to measure shear crack sub-critical propagation time and rate of sandstone specimen.Different cubic specimens with and without holes were tested to study the effect of holes on the shear crack sub-critical propagation.Numerical and experimental results show that three independent variables of hole,the interval distance S,the distance between the center of hole and the crack tip L,and hole radius R,have different contribution to the ratio of stress intensity factor of the specimen with holes to that of the specimen without hole,KⅡ/KⅡ0.Increasing S and decreasing L and R will result in the decrease of KⅡ/KⅡ0 and help crack arrest.The weight relation of the independent variables for KⅡ/KⅡ0 is S>L>R.The specimen DH3 with the largest value of S and the smallest values of L and R has the longest sub-critical crack propagation time and the smallest sub-critical crack propagation rate.Adding two suitable holes symmetrically to the original crack plane in rock specimen is considered to be a potential method for crack arrest of rock.
文摘In reactor physics tests, it is important to monitor sub-criticality continuously during criticality approach. Reactivity measurements by the inverse kinetics method are widely used during the operation of a nuclear reactor. This technique is successfully applied at sufficiently high power level or to a core without an external neutron source where the neutron source term in point reactor kinetics equations may be neglected. For operation at low power levels or in the sub-critical domain, the increase in the fluctuation of the neutron signal may cause difficulties in the evaluation of reactivity and the effect of direct emission from the external neutron source may not be neglected. Therefore, contribution of the neutron source must be taken into account and this implies knowledge of a quantity proportional to the source strength, which calls the source term and then it should be determined. The research work has been conducted to measure reactivity with source term using a dedicated reactivity measurement system by the Least Square Inverse Kinetics Method (LSIKM). Application to a simulator of HANARO research reactor, Korea Atomic Energy Research Institute (KAERI), with known source strength and reactivity worth has showed consistent and satisfactory agreement.
文摘Sub-critical water extraction is a brand-new separation technology. This paper mainly discussed the principle, advantages of sub-critical water extraction, and its applications ranging from the medicinal plants traditionally used in Europe and Asia to produce pharmaceutical extracts (such as volatile oil, tannins, flavonoids, anthraquinone, lactone, etc.). Meanwhile, the prospect of sub-critical water extraction in plant extractives is also explored. It will be widely used in the field of medical plants, bringing huge economic benefits, environmental benefits and social benefits.
基金Supported by 2016 Instrument Functional Development Project of Lanzhou Regional Center of Resources and Environmental Science Instrument,CAS(2018gl11)
文摘[Objectives] To study the optimal conditions for extracting procyanidins fromLycium ruthenicum Murr. with sub-critical fluid R134 a( 1,1,1,2-tetrafluoroethane) in 1 L extraction kettle. [Methods]Taking the extraction rate of procyanidins as an indicator,the influence of pressure,temperature,and extraction time on extraction rate of procyanidins fromL. Ruthenicum Murr. was studied by single factor experimental methods and orthogonal array design. [Results]The order of factors affecting extraction rate of procyanidins was extraction temperature > extraction pressure > extraction time. The optimum extraction conditions were as follows: the extraction rate of procyanidins fromL. ruthenicum Murr. was the highest with extraction pressure of 1. 2 MPa,extraction temperature of 50℃ and extraction time of 90 min. The content of procyanidins in L. ruthenicum Murr. from different producing areas was determined by vanillin-HCl method under the optimal conditions. [Conclusions] The method has the advantages of easy operation,good selectivity,low extraction temperature and high extraction efficiency,which is suitable for extraction of procyanidins in L. ruthenicum Murr.
基金This work was supported by the National Natural Science Foundation of China (No. 29374170) and the Research Grant Council of Hong Kong Government Earmarked Grant (CUHK 4161/99M).
文摘Critical concentrations of α-(1→3)-D-glucan L-FV-Ⅱ from Lentinus edodes were studied by viscometry andfluorescence probe techniques. The dependence of the reduced viscosity on concentration of the glucan in 0.5 mol/L NaOHaqueous solutions with or without urea showed two turning points corresponding to the dynamic contact concentration c_s andthe overlap concentration c~* of the polymer. The values of c_s and c~* were found to be 1×10^(-3) g cm^(-3) and 1.1×10^(-2) g cm^(-3),respectively, for L-FV-Ⅱ in 0.5 mol/L NaOH aqueous solutions. The two critical concentrations of L-FV-Ⅱ in 0.5 mol/LNaOH aqueous solutions were also found to be 1.2×10^(-3) g cm^(-3) fbr c_s and 9.2×10^(-3) g cm^(-3) for c~* from the concentrationdependence of phenanthrene fluorescence intensities. The overlap concentration c~* of L-FV-Ⅱ in 0.5 mol/L NaOH aqueoussolutions was lower than that of polystyrene with same molecular weight in benzene, owing to the fact that polysaccharidetends to undergo aggregation caused by intermolecular hydrogen bonding. A normal viscosity behavior of L-FV-Ⅱ in 0.5 mol/L urea/0.5 mol/L NaOH aqueous solutions can still be observed in an extremely low concentration range at 25℃.
基金supported by NSFC(11271154,11401252)Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Education,the 985 program of Jilin University+1 种基金Fundamental Research Funds of Jilin University(450060501179)supported by Graduate Innovation Fund of Jilin University(2014084)
文摘In this article, by applying the super-solution and sub-solution methods, instead of energy estimate methods, the authors investigate the critical extinction exponents for a polytropic filtration equation with a nonlocal source and an absorption term, and give a classification of the exponents and coefficients for the solutions to vanish in finite time or not, which improve one of our results (Applicable Analysis, 92(2013), 636-650) and the results of Zheng et al (Math. Meth. Appl. Sci., 36(2013), 730-743).
文摘Based on μ-, T- and H-dependent pairing and number equations and the premise that μ(T) is predominantly the cause of the variation of the upper critical field H<sub>c</sub><sub>2</sub>(T), where μ, T and H denote the chemical potential, temperature and the applied field, respectively, we provide in this paper fits to the empirical H<sub>c</sub><sub>2</sub>(T) data of H<sub>3</sub>S reported by Mozaffari, et al. (2019) and deal with the issue of whether or not H<sub>3</sub>S exhibits the Meissner effect. Employing a variant of the template given by Dogan and Cohen (2021), we examine in detail the results of Hirsch and Marsiglio (2022) who have claimed that H<sub>3</sub>S does not exhibit the Meissner effect and Minkov, et al. (2023) who have claimed that it does. We are thus led to suggest that monitoring the chemical potential (equivalently, the number density of Cooper pairs N<sub>s</sub> at T = T<sub>c</sub>) should shed new light on the issue being addressed.