The matrix version of Symmetric Successive Over Relaxation(matrix-SSOR)scheme has been proved to be more efficient than the standard Lower-Upper Symmetric Gauss-Seidel(LUSGS),but less robust for high-speed flows.In or...The matrix version of Symmetric Successive Over Relaxation(matrix-SSOR)scheme has been proved to be more efficient than the standard Lower-Upper Symmetric Gauss-Seidel(LUSGS),but less robust for high-speed flows.In order to ulteriorly improve the convergence rate as well as numerical stability of matrix-SSOR,two improvements regarding entropy fix and local time step have been proposed and validated.Firstly,an augmented entropy fix method is imposed on the inviscid Jacobian matrix and proved to be effective in two high-speed flows,in which the key parameter in entropy fix is discussed and found to be insensitive within appropriate range of values.Since the time step also has great effects on the numerical stability and convergence rate,a modified cell residual adapted local time step method with consideration of the residual history is developed,which is found to be effective for increasing the convergence rate when the matrix-SSOR is applied,but invalid when the LU-SGS is used.The proposed modified local time step method is also insensitive to the key parameter within appropriate range of values.The two modifications can be conveniently implanted into analogous matrix-type implicit schemes to improve the numerical performance.展开更多
This article discusses the problem of existence of jointly continuous self-intersection local time for an additive levy process. Here, 'local time' is understood in the sense of occupation density, and by an a...This article discusses the problem of existence of jointly continuous self-intersection local time for an additive levy process. Here, 'local time' is understood in the sense of occupation density, and by an additive Levy process the authors mean a process X = {X(t),t∈ R+N} which has the decomposition X = Xi X2 … XN, each Xl has the lower index αl, α= min{α1,…, αN}. Let Z = (Xt2 - Xt1, …, Xtr - Xtr-1). They prove that if Nrα > d(r-1), then a jointly continuous local time of Z, i.e. the self-intersection local time of X, can be obtained.展开更多
This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the...This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the satellite orbit design and the orbit injection deviation are the causes for the initial shift velocity, whereas the atmospheric drag and the sun gravitational perturbation produce the shift acceleration. To deal with these shift factors, a shift control method is put forward, through such methods as orbit variation design, orbit altitude, and inclination keeping control. The simulation experiment and practical application have proved the effectiveness of this control method.展开更多
In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the ...In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its＇ chaos expansion. Key words Collision local time; fractional Ornstein-Uhlenbeck processes; generalized white noise functionals; choas expansion展开更多
Let X1 XN be independent, classical Levy processes on R^d with Levy exponents ψ1,…, ψN, respectively. The corresponding additive Levy process is defined as the following N-parameter random field on R^d, X（t） △=...Let X1 XN be independent, classical Levy processes on R^d with Levy exponents ψ1,…, ψN, respectively. The corresponding additive Levy process is defined as the following N-parameter random field on R^d, X（t） △= X1（t1） ＋ ... ＋ XN（tN）, At∈N. Under mild regularity conditions on the ψi＇s, we derive estimate for the local and uniform moduli of continuity of local times of X = {X（t）; t ∈R^N}.展开更多
In this paper, the generalized local time of the indefinite Wiener integral Xt is discussed through white noise approach, which means to regard the local time as a Hida distribution. Moreover, similar result is also o...In this paper, the generalized local time of the indefinite Wiener integral Xt is discussed through white noise approach, which means to regard the local time as a Hida distribution. Moreover, similar result is also obtained in case of two independent Brownian motions by using the similar approach.展开更多
In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its loca...In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.展开更多
The representation of additive functionals and local times for jump Markov processes are obtained.The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.
We studied the problem of existence of jointly continuous local time for an additive process. Here, 'local time' is understood in the sence of occupation density, and by an additive Levy process we mean a proc...We studied the problem of existence of jointly continuous local time for an additive process. Here, 'local time' is understood in the sence of occupation density, and by an additive Levy process we mean a process X = {X(t), t ∈ R^d_+ ) } which has the decomposition X= X_1, X_2 ... X_N. We prove that if the product of it slower index and N is greater than d, then a jointly continuous local time can he obtained via Berman's method.展开更多
Let X,X1,X2 be i. i. d. random variables with EX^2＋δ〈∞ （for some δ〉0）. Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ＊ （n）=supx∈zζ（x,n）,ζ（x,n） =#{0≤k≤n：[Sk]=x}. A s...Let X,X1,X2 be i. i. d. random variables with EX^2＋δ〈∞ （for some δ〉0）. Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ＊ （n）=supx∈zζ（x,n）,ζ（x,n） =#{0≤k≤n：[Sk]=x}. A strong approximation of ζ（n） by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ＊（n） are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ＊（n） is proved.展开更多
Let W be a standard Brownian motion,and define Y(t) =∫t 0 ds W(s) as Cauchy' s principal value related to the local time of W.We study some limitresults on lag increments of Y(t) and obtain various results all...Let W be a standard Brownian motion,and define Y(t) =∫t 0 ds W(s) as Cauchy' s principal value related to the local time of W.We study some limitresults on lag increments of Y(t) and obtain various results all of which are related to earlier work by Hanson and Russo in 1 983展开更多
Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existen...Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existence of the local times of X^H(u)(u)and establish its joint continuity and the Holder regularity.These results generalize the corresponding results about fractional stable sheets to multifractional stable sheets.展开更多
The objective of this paper is to study the local time and Tanaka formula of symmetric G-martingales.We introduce the local time of G-martingales and show that it belongs to the G-expectation space LG^2(ΩT).By a loca...The objective of this paper is to study the local time and Tanaka formula of symmetric G-martingales.We introduce the local time of G-martingales and show that it belongs to the G-expectation space LG^2(ΩT).By a localization argument,we obtain the bicontinuous modification of local time.Furthermore,we give the Tanaka formula for convex functions of G-martingales.展开更多
In this paper,we study the inverse local times at 0 of one-dimensional reflected diffusions on[0,∞)and establish a comparison principle for these inverse local times.We also provide applications to Green function est...In this paper,we study the inverse local times at 0 of one-dimensional reflected diffusions on[0,∞)and establish a comparison principle for these inverse local times.We also provide applications to Green function estimates for non-local operators.展开更多
The azimuthal morphology of Earth's ring currents has consistently shown asymmetry during extreme space weather events at low latitudes,particularly during geomagnetic storms.A dawn-dusk pattern has been detected ...The azimuthal morphology of Earth's ring currents has consistently shown asymmetry during extreme space weather events at low latitudes,particularly during geomagnetic storms.A dawn-dusk pattern has been detected during the storm main phase through near-Earth and in-situ magnetic measurements.This asymmetry is believed to arise from asymmetric solar windmagnetosphere coupling and is linked to the closure of the ring current.Recent evidence has confirmed the existence of asymmetric ring currents during quiet times and the storm recovery phase.This phenomenon may be closely related to the evolution of ring currents,including plasma injection and decay processes.In this study,the local time asymmetry of the ring current is estimated using data from low-Earth-orbit Swarm and Macao Science Satellite-1(MSS-1)missions.Spherical harmonics models are developed to quantify the magnetic field of ring currents through external Gauss coefficients during both quiet periods and the storm recovery phase.Several features of dawn-dusk asymmetry are observed in various cases in different months.(1)The maximum difference in magnetic value across local time ranges from 3 to 10 nT,showing relative invariance compared with various Sym-H levels.(2)Stronger magnetic signals are detected at the premidnight sector during quiet times and at the afternoon sector during the storm recovery phase.(3)Magnetic perturbations remain at a lower level during the postmidnight and morning sectors.Although the pattern of local time asymmetry differs between quiet times and the recovery phase,dawn-dusk asymmetry remains the most pronounced feature,affecting the trapping and loss of charged particles in the inner magnetosphere.Combining Swarm and MSS-1 magnetic observations can enable convenient monitoring of the detailed azimuthal local time effects of the ring current at various disturbance levels in the future.展开更多
We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),...We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.展开更多
In this paper,we consider the derivatives of intersection local time for two independent d-dimensional symmetricα-stable processes X^(α) and X^(α)with respective indices α and α.We first study the sufficient cond...In this paper,we consider the derivatives of intersection local time for two independent d-dimensional symmetricα-stable processes X^(α) and X^(α)with respective indices α and α.We first study the sufficient condition for the existence of the derivatives,which makes us obtain the exponential integrability and H?lder continuity.Then we show that this condition is also necessary for the existence of derivatives of intersection local time at the origin.Moreover,we also study the power variation of the derivatives.展开更多
This paper is concerned with the smoothness （in the sense of Meyer- Watanabe） of the local times of Gaussian random fields. Sufficient and necessary conditions for the existence and smoothness of the local times, co...This paper is concerned with the smoothness （in the sense of Meyer- Watanabe） of the local times of Gaussian random fields. Sufficient and necessary conditions for the existence and smoothness of the local times, collision local times, and self-intersection local times are established for a large class of Gaussian random fields, including fractional Brownian motions, fractional Brownian sheets and solutions of stochastic heat equations driven by space-time Gaussian noise.展开更多
A 2D axisymmetric numerical model was established to investigate the variations of molten pool with different melt rates during the vacuum arc remelting of 8Cr4Mo4V high-strength steel,and the ingot growth was simulat...A 2D axisymmetric numerical model was established to investigate the variations of molten pool with different melt rates during the vacuum arc remelting of 8Cr4Mo4V high-strength steel,and the ingot growth was simulated by dynamic mesh techniques.The results show that as the ingot grows,the molten pool profile changes from shallow and flat to V-shaped,and both the molten pool depth and the mushy width increase.Meanwhile,the variation of both the molten pool shape and the mushy width melt rate is clarified by the thermal equilibrium analysis.As melt rate increases,both the molten pool depth and the mushy width increase.It is caused by the increment in sensible heat stored in the ingot due to the limitation of the cooling capacity of the mold.The nonlinear increment in sensible heat leads to a nonlinear increase in the mushy width.In addition,as melt rate increases,the local solidification time(LST)of ingot decreases obviously at first and then increases.When melt rate is controlled in a suitable range,LST is the lowest and the secondary dendrite arm spacing of the ingot is the smallest,which can effectively improve the compactness degree of 8Cr4Mo4V high-strength steel.展开更多
In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the ex...In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12272397 and 11902334),the National Numerical Wind Tunnel Project,China。
文摘The matrix version of Symmetric Successive Over Relaxation(matrix-SSOR)scheme has been proved to be more efficient than the standard Lower-Upper Symmetric Gauss-Seidel(LUSGS),but less robust for high-speed flows.In order to ulteriorly improve the convergence rate as well as numerical stability of matrix-SSOR,two improvements regarding entropy fix and local time step have been proposed and validated.Firstly,an augmented entropy fix method is imposed on the inviscid Jacobian matrix and proved to be effective in two high-speed flows,in which the key parameter in entropy fix is discussed and found to be insensitive within appropriate range of values.Since the time step also has great effects on the numerical stability and convergence rate,a modified cell residual adapted local time step method with consideration of the residual history is developed,which is found to be effective for increasing the convergence rate when the matrix-SSOR is applied,but invalid when the LU-SGS is used.The proposed modified local time step method is also insensitive to the key parameter within appropriate range of values.The two modifications can be conveniently implanted into analogous matrix-type implicit schemes to improve the numerical performance.
基金Supported by the National Natural Science Foundation and the Doctoral Programme Foundation of China.
文摘This article discusses the problem of existence of jointly continuous self-intersection local time for an additive levy process. Here, 'local time' is understood in the sense of occupation density, and by an additive Levy process the authors mean a process X = {X(t),t∈ R+N} which has the decomposition X = Xi X2 … XN, each Xl has the lower index αl, α= min{α1,…, αN}. Let Z = (Xt2 - Xt1, …, Xtr - Xtr-1). They prove that if Nrα > d(r-1), then a jointly continuous local time of Z, i.e. the self-intersection local time of X, can be obtained.
基金supported by the China Postdotoral Science Foundation(20060401004)
文摘This article analyzes the shift factors of the descending node local time for sun-synchronous satellites and proposes a shift control method to keep the local time shift within an allowance range. It is found that the satellite orbit design and the orbit injection deviation are the causes for the initial shift velocity, whereas the atmospheric drag and the sun gravitational perturbation produce the shift acceleration. To deal with these shift factors, a shift control method is put forward, through such methods as orbit variation design, orbit altitude, and inclination keeping control. The simulation experiment and practical application have proved the effectiveness of this control method.
基金supported by the National Natural Science Fundation of China(71561017)the Science and Technology Plan of Gansu Province(1606RJZA041)+1 种基金the Youth Plan of Academic Talent of Lanzhou University of Finance and Economicssupported by the Fundamental Research Funds for the Central Universities(HUST2015QT005)
文摘In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its＇ chaos expansion. Key words Collision local time; fractional Ornstein-Uhlenbeck processes; generalized white noise functionals; choas expansion
文摘Let X1 XN be independent, classical Levy processes on R^d with Levy exponents ψ1,…, ψN, respectively. The corresponding additive Levy process is defined as the following N-parameter random field on R^d, X（t） △= X1（t1） ＋ ... ＋ XN（tN）, At∈N. Under mild regularity conditions on the ψi＇s, we derive estimate for the local and uniform moduli of continuity of local times of X = {X（t）; t ∈R^N}.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1106103230973586)
文摘In this paper, the generalized local time of the indefinite Wiener integral Xt is discussed through white noise approach, which means to regard the local time as a Hida distribution. Moreover, similar result is also obtained in case of two independent Brownian motions by using the similar approach.
基金supported by the National Natural Science Foundation of China (No. 10871177)the Ph. D.Programs Foundation of Ministry of Education of China (No. 20060335032)the Natural Science Foundation of Zhejiang Province of China (No. Y7080044)
文摘In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.
基金supported by the National Nature Science Foundation of China(10271091)
文摘The representation of additive functionals and local times for jump Markov processes are obtained.The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.
基金the National Natural Science Foundation of China
文摘We studied the problem of existence of jointly continuous local time for an additive process. Here, 'local time' is understood in the sence of occupation density, and by an additive Levy process we mean a process X = {X(t), t ∈ R^d_+ ) } which has the decomposition X= X_1, X_2 ... X_N. We prove that if the product of it slower index and N is greater than d, then a jointly continuous local time can he obtained via Berman's method.
文摘Let X,X1,X2 be i. i. d. random variables with EX^2＋δ〈∞ （for some δ〉0）. Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ＊ （n）=supx∈zζ（x,n）,ζ（x,n） =#{0≤k≤n：[Sk]=x}. A strong approximation of ζ（n） by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ＊（n） are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ＊（n） is proved.
文摘Let W be a standard Brownian motion,and define Y(t) =∫t 0 ds W(s) as Cauchy' s principal value related to the local time of W.We study some limitresults on lag increments of Y(t) and obtain various results all of which are related to earlier work by Hanson and Russo in 1 983
文摘Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existence of the local times of X^H(u)(u)and establish its joint continuity and the Holder regularity.These results generalize the corresponding results about fractional stable sheets to multifractional stable sheets.
基金Supported by the National Natural Science Foundation of China(No.11601282)the Natural Science Foundation of Shandong Province(No.ZR2016AQ10)
文摘The objective of this paper is to study the local time and Tanaka formula of symmetric G-martingales.We introduce the local time of G-martingales and show that it belongs to the G-expectation space LG^2(ΩT).By a localization argument,we obtain the bicontinuous modification of local time.Furthermore,we give the Tanaka formula for convex functions of G-martingales.
基金supported by Simons Foundation(Grant No.520542)supported by National Natural Science Foundation of China(Grant Nos.11801283 and 12171252)。
文摘In this paper,we study the inverse local times at 0 of one-dimensional reflected diffusions on[0,∞)and establish a comparison principle for these inverse local times.We also provide applications to Green function estimates for non-local operators.
基金supported by the National Natural Science Foundation of China(Grant Nos.12250014,and 12250012)the Macao Foundation。
文摘The azimuthal morphology of Earth's ring currents has consistently shown asymmetry during extreme space weather events at low latitudes,particularly during geomagnetic storms.A dawn-dusk pattern has been detected during the storm main phase through near-Earth and in-situ magnetic measurements.This asymmetry is believed to arise from asymmetric solar windmagnetosphere coupling and is linked to the closure of the ring current.Recent evidence has confirmed the existence of asymmetric ring currents during quiet times and the storm recovery phase.This phenomenon may be closely related to the evolution of ring currents,including plasma injection and decay processes.In this study,the local time asymmetry of the ring current is estimated using data from low-Earth-orbit Swarm and Macao Science Satellite-1(MSS-1)missions.Spherical harmonics models are developed to quantify the magnetic field of ring currents through external Gauss coefficients during both quiet periods and the storm recovery phase.Several features of dawn-dusk asymmetry are observed in various cases in different months.(1)The maximum difference in magnetic value across local time ranges from 3 to 10 nT,showing relative invariance compared with various Sym-H levels.(2)Stronger magnetic signals are detected at the premidnight sector during quiet times and at the afternoon sector during the storm recovery phase.(3)Magnetic perturbations remain at a lower level during the postmidnight and morning sectors.Although the pattern of local time asymmetry differs between quiet times and the recovery phase,dawn-dusk asymmetry remains the most pronounced feature,affecting the trapping and loss of charged particles in the inner magnetosphere.Combining Swarm and MSS-1 magnetic observations can enable convenient monitoring of the detailed azimuthal local time effects of the ring current at various disturbance levels in the future.
基金Partial funding in support of this work was provided by the Natural Sciences and Engineering Research Council of Canada(NSERC)the Department of Mathematics at the University of Oregon。
文摘We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.
基金Supported by National Natural Science Foundation of China(Grant Nos.12071003,12201294)Natural Science Foundation of Jiangsu Province,China(Grant No.BK20220865)。
文摘In this paper,we consider the derivatives of intersection local time for two independent d-dimensional symmetricα-stable processes X^(α) and X^(α)with respective indices α and α.We first study the sufficient condition for the existence of the derivatives,which makes us obtain the exponential integrability and H?lder continuity.Then we show that this condition is also necessary for the existence of derivatives of intersection local time at the origin.Moreover,we also study the power variation of the derivatives.
基金Research of Z. Chen and D. Wu was partially supported by the National Natural Science Foundation of China （Grant No. 11371321）. Research of Y. Xiao was partially supported by the NSF Grants DMS-1307470 and DMS-1309856.
文摘This paper is concerned with the smoothness （in the sense of Meyer- Watanabe） of the local times of Gaussian random fields. Sufficient and necessary conditions for the existence and smoothness of the local times, collision local times, and self-intersection local times are established for a large class of Gaussian random fields, including fractional Brownian motions, fractional Brownian sheets and solutions of stochastic heat equations driven by space-time Gaussian noise.
基金financially supported by National Natural Science Foundation of China(Nos.U1908223 and U1960203)Fundamental Research Funds for the Central Universities(Grant No.N2125017)Talent Project of Revitalizing Liaoning(Grant No.XLYC1902046).
文摘A 2D axisymmetric numerical model was established to investigate the variations of molten pool with different melt rates during the vacuum arc remelting of 8Cr4Mo4V high-strength steel,and the ingot growth was simulated by dynamic mesh techniques.The results show that as the ingot grows,the molten pool profile changes from shallow and flat to V-shaped,and both the molten pool depth and the mushy width increase.Meanwhile,the variation of both the molten pool shape and the mushy width melt rate is clarified by the thermal equilibrium analysis.As melt rate increases,both the molten pool depth and the mushy width increase.It is caused by the increment in sensible heat stored in the ingot due to the limitation of the cooling capacity of the mold.The nonlinear increment in sensible heat leads to a nonlinear increase in the mushy width.In addition,as melt rate increases,the local solidification time(LST)of ingot decreases obviously at first and then increases.When melt rate is controlled in a suitable range,LST is the lowest and the secondary dendrite arm spacing of the ingot is the smallest,which can effectively improve the compactness degree of 8Cr4Mo4V high-strength steel.
基金supported by National Natural Science Foundation of China (Grant No.10871103)
文摘In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion.
