In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the hyperbolic magnetohydrodynamics(MHD) equations in R^3. Then we establish that the solutions with initial data belo...In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the hyperbolic magnetohydrodynamics(MHD) equations in R^3. Then we establish that the solutions with initial data belonging to H^m(R^3) ∩ L^1(R^3) have the following time decay rate:║▽~mu(x, t) ║~2+║ ▽~mb(x, t)║~ 2+ ║▽^(m+1)u(x, t)║~ 2+ ║▽^(m+1)b(x, t) ║~2≤ c(1 + t)^(-3/2-m)for large t, where m = 0, 1.展开更多
In this paper, we show the existence and regularity of mild solutions depending on the small initial data in Besov spaces to the fractional porous medium equation. When 1 < <em>α</em> ≤ 2, we prove gl...In this paper, we show the existence and regularity of mild solutions depending on the small initial data in Besov spaces to the fractional porous medium equation. When 1 < <em>α</em> ≤ 2, we prove global well-posedness for initial data <img src="Edit_b7b43d4c-00d8-49d6-9066-97151fb5c337.bmp" alt="" /> with 1 ≤ <em>p</em> < ∞, 1 ≤ <em>q</em> ≤ ∞, and analyticity of solutions with 1 < <em>p</em> < ∞, 1 ≤ <em>q</em> ≤ ∞. In particular, we also proved that when <em>α</em> = 1, both <em>u</em> and <img src="Edit_a5af0853-8adc-4a08-b8a2-b9a70ea0f409.bmp" alt="" /> belong to <img src="Edit_03a932cc-aa58-4568-83ad-f16416cc7b71.bmp" alt="" />. We solve this equation through the contraction mapping method based on Littlewood-Paley theory and Fourier multiplier. Furthermore, we can get time decay estimates of global solutions in Besov spaces, which is <img src="Edit_083986e9-4e1c-4494-ac5d-a7d30a12df97.bmp" alt="" /> as <em>t</em> → ∞.展开更多
In this paper,it is proved that the weak solution to the Cauchy problem for the scalar viscous conservation law,with nonlinear viscosity,different far field states and periodic perturbations,not only exists globally i...In this paper,it is proved that the weak solution to the Cauchy problem for the scalar viscous conservation law,with nonlinear viscosity,different far field states and periodic perturbations,not only exists globally in time,but also converges towards the viscous shock wave of the corresponding Riemann problem as time goes to infinity.Furthermore,the decay rate is shown.The proof is given by a technical energy method.展开更多
In this paper, we study the optimal time decay rate of isentropic Navier-Stokes equations under the low regularity assumptions about initial data. In the previous works about optimal time decay rate, the initial data ...In this paper, we study the optimal time decay rate of isentropic Navier-Stokes equations under the low regularity assumptions about initial data. In the previous works about optimal time decay rate, the initial data need to be small in H^[N/2]＋2（R^N）. Our work combined negative Besov space estimates and the conventional energy estimates in Besov space framework which is developed by Danchim Through our methods, we can get optimal time decay rate with initial data just small in B^N/2-1,N/2＋1∩^N/2-1,N/2 and belong to some negative Besov space （need not to be small）. Finally, combining the recent results in [25] with our methods, we only need the initial data to be small in homogeneous Besov space B^N/2-2,N/2 ∩B^N/2-1 to get the optimal time decay rate in space L2.展开更多
For the accurate extraction of cavity decay time, a selection of data points is supplemented to the weighted least square method. We derive the expected precision, accuracy and computation cost of this improved method...For the accurate extraction of cavity decay time, a selection of data points is supplemented to the weighted least square method. We derive the expected precision, accuracy and computation cost of this improved method, and examine these performances by simulation. By comparing this method with the nonlinear least square fitting （NLSF） method and the linear regression of the sum （LRS） method in derivations and simulations, we find that this method can achieve the same or even better precision, comparable accuracy, and lower computation cost. We test this method by experimental decay signals. The results are in agreement with the ones obtained from the nonlinear least square fitting method.展开更多
A novel series of Ce^3＋-doped Yb3 Al（5-x）GaxO（12）（x = 0, 1,2, 3,4, 5） powders of ytterbium aluminum gallium garnets were synthesized by high temperature solid-state reaction in a carbon reducing atmosphere. The...A novel series of Ce^3＋-doped Yb3 Al（5-x）GaxO（12）（x = 0, 1,2, 3,4, 5） powders of ytterbium aluminum gallium garnets were synthesized by high temperature solid-state reaction in a carbon reducing atmosphere. The ytterbium aluminum garnets were characterized by X-ray powder diffraction, UV-Vis diffuse reflectance spectra, photoluminescence spectra and decay curves. Moreover, the substitution effect for the Al^3＋ sites with Ga^3＋ in 0.5 at%Ce：Yb3 Al（5-x）GaxO（12）（x = 0,1, 2, 3, 4, 5） garnets were discussed. With the increase of Ga^3＋ ion concentration, the visible absorption peaks within 400-450 nm have blue shift phenomenon,while the absorption peaks in the range of 330-350 nm and the absorption band edge red shifts.Furthermore, the short decay times are very short with less than 10 ns due to the Yb^3＋ ＋ Ce^3＋→ Yb^2＋ ＋ Ce^4＋ electron transfer reaction.展开更多
In this review article, we present recent developments and improvements in magnetic resonance sounding （MRS）, a newly established geophysical exploration method that provides unique information about hydrogeophysica...In this review article, we present recent developments and improvements in magnetic resonance sounding （MRS）, a newly established geophysical exploration method that provides unique information about hydrogeophysical properties due to its direct sensitivity to hydrogen protons and proton dynamics. Starting with the most sophisticated and complete MRS formulation, we give a detailed view on how to solve the equation, i.e., inverting exactly for all model parameters： water content, decay time, and resistivity. Giving a short review of general inversion schemes used in geophysics, the special properties of MRS inversion are evaluated and the development of MRS inversion over recent years is shown. We present the extension of MRS to magnetic resonance tomography （MRT）, i.e., the extension to two-dimensional investigations and appropriate inversions. Finally, we address restrictions, limitations, and inconsistencies as well as future developments.展开更多
The photoplethysmogram(PPG) of a pulse wave,similar in appearance to the arterial blood pressure(ABP) waveform,contains rich information about the cardiovascular system.The decay time constant RC,equal to the product ...The photoplethysmogram(PPG) of a pulse wave,similar in appearance to the arterial blood pressure(ABP) waveform,contains rich information about the cardiovascular system.The decay time constant RC,equal to the product of peripheral resistance R and total arterial compliance C,is a meaningful cardiovascular model parameter in vascular assessment.Using or ameliorating the existing ABP methods does not achieve a satisfactory estimation of RC from the PPG volume pulse(VRC).Thus,a novel non-iterative shape method(NSM) of evaluating VRC is introduced in this paper.The mathematic expression between a novel,readily available morphological parameter called the area difference ratio(ADR) and VRC was established.As it was difficult to calculate VRC from the complicated expression analytically,we recommend estimating it using a piecewise linear interpolation criterion.Also,since the effect of the PPG magnitude is eliminated in the calculation of ADR,precaliberation or normalization is dispensable in the NSM.Results of human experiments indicated that the NSM was computationally efficient,and the simulation experiments confirmed that the NSM was theoretically available for ABP.展开更多
We study the theoretical effect of k-cubic （i.e, cubic-in-momentum） Dresselhaus spin-orbit coupling on the decay time of persistent spin helix states in semiconductor two-dimensional electron gases. We show that the...We study the theoretical effect of k-cubic （i.e, cubic-in-momentum） Dresselhaus spin-orbit coupling on the decay time of persistent spin helix states in semiconductor two-dimensional electron gases. We show that the decay time of persistent spin helix states may be suppressed substantially by k-cubic Dresselhaus spin-orbit coupling, and after taking the effect of k-cubic Dresselhaus spin-orbit interaction into account, the theoretical results obtained accord both qualitatively and quantitatively with other recent experimental results.展开更多
In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, w...In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, we show that the existence, uniqueness and time-asymptotic stability of time periodic solutions when the space dimension n 〉 5. Our proof is based on a combination of the energy method and the contraction mapping theorem.展开更多
In this paper,we study the global existence and decay rates of strong solutions to the three dimensional compressible Phan-Thein-Tanner model.By a refined energy method,we prove the global existence under the assumpti...In this paper,we study the global existence and decay rates of strong solutions to the three dimensional compressible Phan-Thein-Tanner model.By a refined energy method,we prove the global existence under the assumption that the H^(3) norm of the initial data is small,but that the higher order derivatives can be large.If the initial data belong to homogeneous Sobolev spaces or homogeneous Besov spaces,we obtain the time decay rates of the solution and its higher order spatial derivatives.Moreover,we also obtain the usual L^(p)-L^(2)(1≤p≤2)type of the decay rate without requiring that the Lpnorm of initial data is small.展开更多
We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove ...We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove the local existence and the global existence of integral solutions for the different initial data under some conditions that involve the size of the initial data.On the other hand,in the case of global solutions,we obtain their optimal time decay by Gronwall’s lemma.展开更多
This study investigates the effect of the magnetic field on the transient density of excess minority charge carriers in the base of a series-connected vertical junction silicon solar cell. The solar cell is presented ...This study investigates the effect of the magnetic field on the transient density of excess minority charge carriers in the base of a series-connected vertical junction silicon solar cell. The solar cell is presented in open circuit transient operation. The magnetic field through the Laplace force which deflects the photogenerated carriers from their initial trajectory towards the lateral surfaces reducing their mobility, diffusion and conduction, will certainly influence the decay time of the transient regime. The transient density of excess minority carriers in the base is a sum of infinite terms whose decay time of the different harmonics is studied.展开更多
In this study,we comprehensively characterized and optimized a cryogenic pure CsI(pCsI)detector.We utilized a 2 cm×2 cm×2 cm cube crystal coupled with a HAMAMATSU R11065 photomultiplier tube,achieving a rema...In this study,we comprehensively characterized and optimized a cryogenic pure CsI(pCsI)detector.We utilized a 2 cm×2 cm×2 cm cube crystal coupled with a HAMAMATSU R11065 photomultiplier tube,achieving a remarkable light yield of 35.2 PE/ke V_(ee)and an unprecedented energy resolution of 6.9%at 59.54 ke V.Additionally,we measured the scintillation decay time of pCsI,which was significantly shorter than that of CsI(Na)at room temperature.Furthermore,we investigated the impact of temperature,surface treatment and crystal shape on light yield.Notably,the light yield peaked at approximately 20 K and remained stable within the range of 70–100 K.The light yield of the polished crystals was approximately 1.5 times greater than that of the ground crystals,whereas the crystal shape exhibited minimal influence on the light yield.These results are crucial for the design of the 10 kg pCsI detector for the future CLOVERS(coherent elastic neutrino(V)-nucleus scattering at China Spallation Neutron Source(CSNS))experiment.展开更多
In this manuscript,we consider two kinds of the Fokker-Planck-type systems in the whole space.The first part involves proving the global existence and the algebraic time decay rates of the mild solutions to the Fokker...In this manuscript,we consider two kinds of the Fokker-Planck-type systems in the whole space.The first part involves proving the global existence and the algebraic time decay rates of the mild solutions to the Fokker-Planck-Boltzmann equation near Maxwellians if initial data satisfies some smallness in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2)∩L_(k)^(p)L_(T)^(∞)L_(v)^(2).The second part proves the global existence of the mild solutions to the Vlasov-Poisson-Fokker-Planck system in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2),and we also obtain the exponential time decay rates,which are different from the algebraic time decay rates of the Fokker-Planck-Boltzmann equation.Our analysis is based on Lk1LT∞Lv2function space introduced by Duan et al.(Comm Pure Appl Math,2021,74:932-1020),the L_(k)^(1)∩L_(k)^(p) approach developed by Duan et al.(SIAM J Math Anal,2024,56:762-800),and the coercivity property of the Fokker-Planck operator.However,it is worth pointing out that the L_(k)^(1)∩L_(k)^(p)approach is not required for the Vlasov-Poisson-Fokker-Planck system,due to the influence of the electric field term,which is different from the Fokker-Planck-Boltzmann equation in this paper and in the work of Duan et al.(SIAM J Math Anal,2024,56:762-800).展开更多
This is a survey paper on the study of compressible Navier-Stokes-Poisson equations. The emphasis is on the long time behavior of global solutions to multi-dimensional compressible Navier-Stokes-Poisson equations, and...This is a survey paper on the study of compressible Navier-Stokes-Poisson equations. The emphasis is on the long time behavior of global solutions to multi-dimensional compressible Navier-Stokes-Poisson equations, and the optimal decay rates for both unipolar and bipolar compressible Navier-Stokes-Poisson equations are discussed.展开更多
The compressible non-isentropic bipolar Navier-Stokes-Poisson （BNSP） sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being ...The compressible non-isentropic bipolar Navier-Stokes-Poisson （BNSP） sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in Hl（R3） （R3） for 1 〉 4 and s E （0, 1], it is shown that the density and temperature for each charged particle （like electron or ion） decay at the same optimal rate （1 ＋ t）-3/4, but the momentum for each particle decays at the optimal rate （1 ＋ t）-1/4-3/2 which is slower than the rate （1 ＋ t）-3/4-3/2 for the compressible Navier-Stokes （NS） equations [19] for same initial data. However, the total momentum tends to the constant state at the rate （1 ＋t）-3/4 as well, due to the interplay interaction of charge particles which counteracts the influence of electric field.展开更多
In this paper, we consider the Vlasov-Maxwell-Fokker-Planck system with relativistic transport in the whole space. The global solutions to this system near the relativistic Maxwellian are constructed and the optimal t...In this paper, we consider the Vlasov-Maxwell-Fokker-Planck system with relativistic transport in the whole space. The global solutions to this system near the relativistic Maxwellian are constructed and the optimal time decay rate of global solutions are also obtained by an approach by combining the compensating function and energy method.展开更多
In the recent work, we have developed a decay framework in general Lp critical spaces and established optimal time-decay estimates for barotropic compressible Navier-Stokes equations. Those decay rates of Lq-Lr type o...In the recent work, we have developed a decay framework in general Lp critical spaces and established optimal time-decay estimates for barotropic compressible Navier-Stokes equations. Those decay rates of Lq-Lr type of the solution and its derivatives are available in the critical regularity framework, which were exactly firstly observed by Matsumura ＆ Nishida, and subsequently generalized by Ponce for solutions with high Sobolev regularity. We would like to mention that our approach is likely to be effective for other hyperbolic/parabolic systems that are encountered in fluid mechanics or mathematical physics. In this paper, a new observation is involved in the high frequency, which enables us to improve decay exponents for the high frequencies of solutions.展开更多
We consider the optimal time-convergence rates of the global solution to the Cauchy problem for the Boltzmann equation in R3.We show that the global solution tends to the global Maxwellian at the optimal time-decay ra...We consider the optimal time-convergence rates of the global solution to the Cauchy problem for the Boltzmann equation in R3.We show that the global solution tends to the global Maxwellian at the optimal time-decay rate(1+t)-3/4,where the macroscopic density,momentum and energy decay at the optimal rate(1+t)-3/4 and the microscopic part decays at the optimal rate(1+t)-5/4.We also show that the solution tends to the Maxwellian at the optimal time-decay rate(1+t).5/4 in the case of the macroscopic part of the initial data is zero,where the macroscopic density,momentum and energy decay at the optimal rate(1+t)-5/4 and the microscopic part decays at the optimal rate(1+t)-7/4.These convergence rates are shown to be optimal for the Boltzmann equation.展开更多
基金Supported by NSFC(11271290)GSPT of Zhejiang Province(2014R424062)
文摘In this paper, we first show the global existence, uniqueness and regularity of weak solutions for the hyperbolic magnetohydrodynamics(MHD) equations in R^3. Then we establish that the solutions with initial data belonging to H^m(R^3) ∩ L^1(R^3) have the following time decay rate:║▽~mu(x, t) ║~2+║ ▽~mb(x, t)║~ 2+ ║▽^(m+1)u(x, t)║~ 2+ ║▽^(m+1)b(x, t) ║~2≤ c(1 + t)^(-3/2-m)for large t, where m = 0, 1.
文摘In this paper, we show the existence and regularity of mild solutions depending on the small initial data in Besov spaces to the fractional porous medium equation. When 1 < <em>α</em> ≤ 2, we prove global well-posedness for initial data <img src="Edit_b7b43d4c-00d8-49d6-9066-97151fb5c337.bmp" alt="" /> with 1 ≤ <em>p</em> < ∞, 1 ≤ <em>q</em> ≤ ∞, and analyticity of solutions with 1 < <em>p</em> < ∞, 1 ≤ <em>q</em> ≤ ∞. In particular, we also proved that when <em>α</em> = 1, both <em>u</em> and <img src="Edit_a5af0853-8adc-4a08-b8a2-b9a70ea0f409.bmp" alt="" /> belong to <img src="Edit_03a932cc-aa58-4568-83ad-f16416cc7b71.bmp" alt="" />. We solve this equation through the contraction mapping method based on Littlewood-Paley theory and Fourier multiplier. Furthermore, we can get time decay estimates of global solutions in Besov spaces, which is <img src="Edit_083986e9-4e1c-4494-ac5d-a7d30a12df97.bmp" alt="" /> as <em>t</em> → ∞.
文摘In this paper,it is proved that the weak solution to the Cauchy problem for the scalar viscous conservation law,with nonlinear viscosity,different far field states and periodic perturbations,not only exists globally in time,but also converges towards the viscous shock wave of the corresponding Riemann problem as time goes to infinity.Furthermore,the decay rate is shown.The proof is given by a technical energy method.
基金Supported by the National Natural Science Foundation of China(Grant No.11501439)the Postdoctoral Science Foundation Pro ject of China(Grant No.2017T100733)
文摘In this paper, we study the optimal time decay rate of isentropic Navier-Stokes equations under the low regularity assumptions about initial data. In the previous works about optimal time decay rate, the initial data need to be small in H^[N/2]＋2（R^N）. Our work combined negative Besov space estimates and the conventional energy estimates in Besov space framework which is developed by Danchim Through our methods, we can get optimal time decay rate with initial data just small in B^N/2-1,N/2＋1∩^N/2-1,N/2 and belong to some negative Besov space （need not to be small）. Finally, combining the recent results in [25] with our methods, we only need the initial data to be small in homogeneous Besov space B^N/2-2,N/2 ∩B^N/2-1 to get the optimal time decay rate in space L2.
基金supported by the Preeminent Youth Fund of Sichuan Province,China(Grant No.2012JQ0012)the National Natural Science Foundation of China(Grant Nos.11173008,10974202,and 60978049)the National Key Scientific and Research Equipment Development Project of China(Grant No.ZDYZ2013-2)
文摘For the accurate extraction of cavity decay time, a selection of data points is supplemented to the weighted least square method. We derive the expected precision, accuracy and computation cost of this improved method, and examine these performances by simulation. By comparing this method with the nonlinear least square fitting （NLSF） method and the linear regression of the sum （LRS） method in derivations and simulations, we find that this method can achieve the same or even better precision, comparable accuracy, and lower computation cost. We test this method by experimental decay signals. The results are in agreement with the ones obtained from the nonlinear least square fitting method.
基金Project supported by National Natural Science Foundation of China(11475242,51272263)K.C.Wong Magna Fund in Ningbo University
文摘A novel series of Ce^3＋-doped Yb3 Al（5-x）GaxO（12）（x = 0, 1,2, 3,4, 5） powders of ytterbium aluminum gallium garnets were synthesized by high temperature solid-state reaction in a carbon reducing atmosphere. The ytterbium aluminum garnets were characterized by X-ray powder diffraction, UV-Vis diffuse reflectance spectra, photoluminescence spectra and decay curves. Moreover, the substitution effect for the Al^3＋ sites with Ga^3＋ in 0.5 at%Ce：Yb3 Al（5-x）GaxO（12）（x = 0,1, 2, 3, 4, 5） garnets were discussed. With the increase of Ga^3＋ ion concentration, the visible absorption peaks within 400-450 nm have blue shift phenomenon,while the absorption peaks in the range of 330-350 nm and the absorption band edge red shifts.Furthermore, the short decay times are very short with less than 10 ns due to the Yb^3＋ ＋ Ce^3＋→ Yb^2＋ ＋ Ce^4＋ electron transfer reaction.
基金supported by the German Scientific Council as part of a program on Magnetic Resonance
文摘In this review article, we present recent developments and improvements in magnetic resonance sounding （MRS）, a newly established geophysical exploration method that provides unique information about hydrogeophysical properties due to its direct sensitivity to hydrogen protons and proton dynamics. Starting with the most sophisticated and complete MRS formulation, we give a detailed view on how to solve the equation, i.e., inverting exactly for all model parameters： water content, decay time, and resistivity. Giving a short review of general inversion schemes used in geophysics, the special properties of MRS inversion are evaluated and the development of MRS inversion over recent years is shown. We present the extension of MRS to magnetic resonance tomography （MRT）, i.e., the extension to two-dimensional investigations and appropriate inversions. Finally, we address restrictions, limitations, and inconsistencies as well as future developments.
基金Project (No.81070885) supported by the National Natural Science Foundation of China
文摘The photoplethysmogram(PPG) of a pulse wave,similar in appearance to the arterial blood pressure(ABP) waveform,contains rich information about the cardiovascular system.The decay time constant RC,equal to the product of peripheral resistance R and total arterial compliance C,is a meaningful cardiovascular model parameter in vascular assessment.Using or ameliorating the existing ABP methods does not achieve a satisfactory estimation of RC from the PPG volume pulse(VRC).Thus,a novel non-iterative shape method(NSM) of evaluating VRC is introduced in this paper.The mathematic expression between a novel,readily available morphological parameter called the area difference ratio(ADR) and VRC was established.As it was difficult to calculate VRC from the complicated expression analytically,we recommend estimating it using a piecewise linear interpolation criterion.Also,since the effect of the PPG magnitude is eliminated in the calculation of ADR,precaliberation or normalization is dispensable in the NSM.Results of human experiments indicated that the NSM was computationally efficient,and the simulation experiments confirmed that the NSM was theoretically available for ABP.
基金Project supported by the National Natural Science Foundation of China (Grant No.10874049)
文摘We study the theoretical effect of k-cubic （i.e, cubic-in-momentum） Dresselhaus spin-orbit coupling on the decay time of persistent spin helix states in semiconductor two-dimensional electron gases. We show that the decay time of persistent spin helix states may be suppressed substantially by k-cubic Dresselhaus spin-orbit coupling, and after taking the effect of k-cubic Dresselhaus spin-orbit interaction into account, the theoretical results obtained accord both qualitatively and quantitatively with other recent experimental results.
基金Supported by National Natural Science Foundation of China(11271305)
文摘In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, we show that the existence, uniqueness and time-asymptotic stability of time periodic solutions when the space dimension n 〉 5. Our proof is based on a combination of the energy method and the contraction mapping theorem.
基金partially supported by the National Natural Science Foundation of China(11926354,11971496)Natural Science Foundation of Guangdong Province(2019A1515011320,2021A1515010292,2214050001249)+2 种基金Innovative team project of ordinary universities of Guangdong Province(2020KCXTD024)Characteristic innovation projects of ordinary colleges and universities in Guangdong Province(2020KTSCX134)the Education Research Platform Project of Guangdong Province(2018179)。
文摘In this paper,we study the global existence and decay rates of strong solutions to the three dimensional compressible Phan-Thein-Tanner model.By a refined energy method,we prove the global existence under the assumption that the H^(3) norm of the initial data is small,but that the higher order derivatives can be large.If the initial data belong to homogeneous Sobolev spaces or homogeneous Besov spaces,we obtain the time decay rates of the solution and its higher order spatial derivatives.Moreover,we also obtain the usual L^(p)-L^(2)(1≤p≤2)type of the decay rate without requiring that the Lpnorm of initial data is small.
文摘We consider the global existence and decay of integral solutions to the parabolic-parabolic Keller-Segel system in d-dimension.On the one hand,by Banach fixed point theorem and some properties of heat kernel,we prove the local existence and the global existence of integral solutions for the different initial data under some conditions that involve the size of the initial data.On the other hand,in the case of global solutions,we obtain their optimal time decay by Gronwall’s lemma.
文摘This study investigates the effect of the magnetic field on the transient density of excess minority charge carriers in the base of a series-connected vertical junction silicon solar cell. The solar cell is presented in open circuit transient operation. The magnetic field through the Laplace force which deflects the photogenerated carriers from their initial trajectory towards the lateral surfaces reducing their mobility, diffusion and conduction, will certainly influence the decay time of the transient regime. The transient density of excess minority carriers in the base is a sum of infinite terms whose decay time of the different harmonics is studied.
基金supported by the National Key R&D Program of China(No.2022YFA1602204)the National Natural Science Foundation of China(Nos.12175241,12221005)+2 种基金the Fundamental Research Funds for the Central Universitiesthe International Partnership Program of the Chinese Academy of Sciences(No.211134KYSB20200057)the Double First-Class University Project Foundation of USTC。
文摘In this study,we comprehensively characterized and optimized a cryogenic pure CsI(pCsI)detector.We utilized a 2 cm×2 cm×2 cm cube crystal coupled with a HAMAMATSU R11065 photomultiplier tube,achieving a remarkable light yield of 35.2 PE/ke V_(ee)and an unprecedented energy resolution of 6.9%at 59.54 ke V.Additionally,we measured the scintillation decay time of pCsI,which was significantly shorter than that of CsI(Na)at room temperature.Furthermore,we investigated the impact of temperature,surface treatment and crystal shape on light yield.Notably,the light yield peaked at approximately 20 K and remained stable within the range of 70–100 K.The light yield of the polished crystals was approximately 1.5 times greater than that of the ground crystals,whereas the crystal shape exhibited minimal influence on the light yield.These results are crucial for the design of the 10 kg pCsI detector for the future CLOVERS(coherent elastic neutrino(V)-nucleus scattering at China Spallation Neutron Source(CSNS))experiment.
基金supported by the National Natural Science Foundation of China(11801285,12326337)。
文摘In this manuscript,we consider two kinds of the Fokker-Planck-type systems in the whole space.The first part involves proving the global existence and the algebraic time decay rates of the mild solutions to the Fokker-Planck-Boltzmann equation near Maxwellians if initial data satisfies some smallness in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2)∩L_(k)^(p)L_(T)^(∞)L_(v)^(2).The second part proves the global existence of the mild solutions to the Vlasov-Poisson-Fokker-Planck system in the function space L_(k)^(1)L_(T)^(∞)L_(v)^(2),and we also obtain the exponential time decay rates,which are different from the algebraic time decay rates of the Fokker-Planck-Boltzmann equation.Our analysis is based on Lk1LT∞Lv2function space introduced by Duan et al.(Comm Pure Appl Math,2021,74:932-1020),the L_(k)^(1)∩L_(k)^(p) approach developed by Duan et al.(SIAM J Math Anal,2024,56:762-800),and the coercivity property of the Fokker-Planck operator.However,it is worth pointing out that the L_(k)^(1)∩L_(k)^(p)approach is not required for the Vlasov-Poisson-Fokker-Planck system,due to the influence of the electric field term,which is different from the Fokker-Planck-Boltzmann equation in this paper and in the work of Duan et al.(SIAM J Math Anal,2024,56:762-800).
基金supported by the NSFC (10871134),supported by the NSFC (10871134, 10771008)the NCET support of the Ministry of Education of China+1 种基金the Huo Ying Dong Fund (111033)the funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR201006107)
文摘This is a survey paper on the study of compressible Navier-Stokes-Poisson equations. The emphasis is on the long time behavior of global solutions to multi-dimensional compressible Navier-Stokes-Poisson equations, and the optimal decay rates for both unipolar and bipolar compressible Navier-Stokes-Poisson equations are discussed.
基金supported by the NSFC (10871134)supported by the NSFC (10871134,10910401059)+1 种基金the funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR201006107)supported by the General Research Fund of Hong Kong,City Univ.103108
文摘The compressible non-isentropic bipolar Navier-Stokes-Poisson （BNSP） sys- tem is investigated in R3 in the present paper, and the optimal time decay rates of global strong solution are shown. For initial data being a perturbation of equilibrium state in Hl（R3） （R3） for 1 〉 4 and s E （0, 1], it is shown that the density and temperature for each charged particle （like electron or ion） decay at the same optimal rate （1 ＋ t）-3/4, but the momentum for each particle decays at the optimal rate （1 ＋ t）-1/4-3/2 which is slower than the rate （1 ＋ t）-3/4-3/2 for the compressible Navier-Stokes （NS） equations [19] for same initial data. However, the total momentum tends to the constant state at the rate （1 ＋t）-3/4 as well, due to the interplay interaction of charge particles which counteracts the influence of electric field.
基金supported partially by the NNSFC Grant(11371151)the Scientific Research Foundation of Graduate School of South China Normal University
文摘In this paper, we consider the Vlasov-Maxwell-Fokker-Planck system with relativistic transport in the whole space. The global solutions to this system near the relativistic Maxwellian are constructed and the optimal time decay rate of global solutions are also obtained by an approach by combining the compensating function and energy method.
基金Supported by the National Natural Science Foundation of China(Grant No.11471158)the Program for New Century Excellent Talents in University(Grant No.NCET-13–0857)the Fundamental Research Funds for the Central Universities(Grant No.NE2015005)
文摘In the recent work, we have developed a decay framework in general Lp critical spaces and established optimal time-decay estimates for barotropic compressible Navier-Stokes equations. Those decay rates of Lq-Lr type of the solution and its derivatives are available in the critical regularity framework, which were exactly firstly observed by Matsumura ＆ Nishida, and subsequently generalized by Ponce for solutions with high Sobolev regularity. We would like to mention that our approach is likely to be effective for other hyperbolic/parabolic systems that are encountered in fluid mechanics or mathematical physics. In this paper, a new observation is involved in the high frequency, which enables us to improve decay exponents for the high frequencies of solutions.
基金supported by Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality(Grant No.PHR201006107)the Key Project of the Beijing Municipal Education Commission(Grant No.KZ201210028033)
文摘We consider the optimal time-convergence rates of the global solution to the Cauchy problem for the Boltzmann equation in R3.We show that the global solution tends to the global Maxwellian at the optimal time-decay rate(1+t)-3/4,where the macroscopic density,momentum and energy decay at the optimal rate(1+t)-3/4 and the microscopic part decays at the optimal rate(1+t)-5/4.We also show that the solution tends to the Maxwellian at the optimal time-decay rate(1+t).5/4 in the case of the macroscopic part of the initial data is zero,where the macroscopic density,momentum and energy decay at the optimal rate(1+t)-5/4 and the microscopic part decays at the optimal rate(1+t)-7/4.These convergence rates are shown to be optimal for the Boltzmann equation.
