We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,th...We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,the system admits no ground state for anyλ>0.Moreover,there exist two positive numbers,M*andλ*(N),such that if N<M*,then for anyλ>λ*(N),the system admits at least one ground state.Asλ→∞,for any fixed N<M*,we give a detailed description for the limit behavior of both positive and semi-trivial ground states.展开更多
This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the li...This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ = {u ∈ H^1; fRN ｜x｜^2｜u｜^2dx 〈 ＋∞）}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that ｜u（t, x）｜^2→ ｜｜Q｜｜L^2 2 δx=x1 as t → T.展开更多
In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the co...In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.展开更多
In this paper, the near-critical and super-critical asymptotic behavior of a reversible Markov process as a chemical model for polymerization was studied. The results of the present paper, together with an analysis of...In this paper, the near-critical and super-critical asymptotic behavior of a reversible Markov process as a chemical model for polymerization was studied. The results of the present paper, together with an analysis of the sub-critical stage, establish the existence of three distinct stages (sub-critical, near-critical and super-critical stages) of polymerization (in the thermodynamic limit as N --> +infinity,),depending on the value of strength of the fragmentation reaction. These three stages correspond to the size of the largest length of polymers of size N to be itself of order log N, Nm/m+1 (m greater than or equal to 2, m not equal 4n, n greater than or equal to 1) and N, respectively.展开更多
The authors consider the limiting behavior of various branches in a uniform recursive tree with size growing to infinity. The limiting distribution of ξn,m, the number of branches with size m in a uniform recursive t...The authors consider the limiting behavior of various branches in a uniform recursive tree with size growing to infinity. The limiting distribution of ξn,m, the number of branches with size m in a uniform recursive tree of order n, converges weakly to a Poisson distribution with parameter 1/m with convergence of all moments. The size of any large branch tends to infinity almost surely.展开更多
We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantu...We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.展开更多
An electrically conducting fluid is driven by a stretching sheet, in the presence of a magnetic field that is strong enough to produce significant Hall current. The sheet is porous, allowing mass transfer through suct...An electrically conducting fluid is driven by a stretching sheet, in the presence of a magnetic field that is strong enough to produce significant Hall current. The sheet is porous, allowing mass transfer through suction or injection. The limiting behavior of the flow is studied, as the magnetic field strength grows indefinitely. The flow variables are properly scaled, and uniformly valid asymptotic expansions of the velocity components are obtained through parameter straining. The leading order approximations show sinusoidal behavior that is decaying exponentially, as we move away from the surface. The two-term expansions of the surface shear stress components, as well as the far field inflow speed, compare well with the corresponding finite difference solutions;even at moderate magnetic fields.展开更多
The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid■where d≥2.It is known that for each∈>0 and all sufficiently small initial data(u_(0),n_(0),c_(0))belongs to certain Fourie...The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid■where d≥2.It is known that for each∈>0 and all sufficiently small initial data(u_(0),n_(0),c_(0))belongs to certain Fourier space,the problem possesses a unique global solution(u^(∈),n^(∈),c^(∈))in Fourier space.The present work asserts that these solutions stabilize to(u^(∞),n^(∞),c^(∞))as∈^(-1)→0.Moreover,we show that c^(∈)(t)has the initial layer as∈^(-1)→0.As one expects its limit behavior maybe give a new viewlook to understand the system.展开更多
In this paper, the focus is on the boundary stability of a nanolayer in diffusion-reaction systems, taking into account a nonlinear boundary control condition. The authors focus on demonstrating the boundary stability...In this paper, the focus is on the boundary stability of a nanolayer in diffusion-reaction systems, taking into account a nonlinear boundary control condition. The authors focus on demonstrating the boundary stability of a nanolayer using the Lyapunov function approach, while making certain regularity assumptions and imposing appropriate control conditions. In addition, the stability analysis is extended to more complex systems by studying the limit problem with interface conditions using the epi-convergence approach. The results obtained in this article are then tested numerically to validate the theoretical conclusions.展开更多
We consider a modified Lnshnikov process as a model of a chemical polymer ization anf study the asymptotic behavior (in the thermodynamic limit;as N →∞)of a particular probability distribution on the set of N-dimens...We consider a modified Lnshnikov process as a model of a chemical polymer ization anf study the asymptotic behavior (in the thermodynamic limit;as N →∞)of a particular probability distribution on the set of N-dimensional vectors,tile kth component of which is the number of k-mers.The study study establisles the existence of three stages (subcritical,near-critical and supercritical stages)of polymerization,dependenting upon the ratio of association and dissociation rates of f polymers.The present paper concentrates on the analysis of tile subcritical stage.In the sibcritical.stages we show that tile size of the largest length of polymers of stize N is of the order.log N as N →+∞.展开更多
基金supported by NSFC(12075102 and 11971212)the Fundamental Research Funds for the Central Universities(lzujbky-2020-pd01)。
文摘We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,the system admits no ground state for anyλ>0.Moreover,there exist two positive numbers,M*andλ*(N),such that if N<M*,then for anyλ>λ*(N),the system admits at least one ground state.Asλ→∞,for any fixed N<M*,we give a detailed description for the limit behavior of both positive and semi-trivial ground states.
基金Supported by National Science Foundation of China (11071177)Excellent Youth Foundation of Sichuan Province (2012JQ0011)
文摘This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ = {u ∈ H^1; fRN ｜x｜^2｜u｜^2dx 〈 ＋∞）}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that ｜u（t, x）｜^2→ ｜｜Q｜｜L^2 2 δx=x1 as t → T.
文摘In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g_φ: for nonnegative function f∈ L^1(R^n),■and ■where f_t(x) =t^(-n)f(t^(-1) x) for t > 0. Meanwhile, the corresponding results for Marcinkiewicz integral and its fractional version with kernels satisfying L_α~q-Dini condition are also given.
基金supported in part by National NaturalScience Foundation of China!196610O3
文摘In this paper, the near-critical and super-critical asymptotic behavior of a reversible Markov process as a chemical model for polymerization was studied. The results of the present paper, together with an analysis of the sub-critical stage, establish the existence of three distinct stages (sub-critical, near-critical and super-critical stages) of polymerization (in the thermodynamic limit as N --> +infinity,),depending on the value of strength of the fragmentation reaction. These three stages correspond to the size of the largest length of polymers of size N to be itself of order log N, Nm/m+1 (m greater than or equal to 2, m not equal 4n, n greater than or equal to 1) and N, respectively.
基金This work was supported by the National Natural Science Foundation of China(10671188)and Special Foundation of USTC.
文摘The authors consider the limiting behavior of various branches in a uniform recursive tree with size growing to infinity. The limiting distribution of ξn,m, the number of branches with size m in a uniform recursive tree of order n, converges weakly to a Poisson distribution with parameter 1/m with convergence of all moments. The size of any large branch tends to infinity almost surely.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11105133)
文摘We study the long-time limit behavior of the solution to an atom＇s master equation. For the first time we derive that the probability of the atom being in the α-th （α = j ＋ 1 -jz, j is the angular momentum quantum number, jz is the z-component of angular momentum） state is {（1 - K/G）/[1 - （K/G）2j＋1]}（K/G）^α-1 as t → ＋∞, which coincides with the fact that when K/G 〉 1, the larger the a is, the larger the probability of the atom being in the α-th state （the lower excited state） is. We also consider the case for some possible generaizations of the atomic master equation.
文摘An electrically conducting fluid is driven by a stretching sheet, in the presence of a magnetic field that is strong enough to produce significant Hall current. The sheet is porous, allowing mass transfer through suction or injection. The limiting behavior of the flow is studied, as the magnetic field strength grows indefinitely. The flow variables are properly scaled, and uniformly valid asymptotic expansions of the velocity components are obtained through parameter straining. The leading order approximations show sinusoidal behavior that is decaying exponentially, as we move away from the surface. The two-term expansions of the surface shear stress components, as well as the far field inflow speed, compare well with the corresponding finite difference solutions;even at moderate magnetic fields.
基金supported by the National Key Research and Development Program of China(No.2018YFA0707300)the National Natural Science Foundation of China(Nos.51901151,51905372,52275362,52171122)China Postdoctoral Science Foundation(Nos.2020M680918,2021T140503)。
基金partial supported by the National Natural Science Foundation of China(Grant Nos.71774073,71988101)Social Scienceof Jiangxi Provincial(Grant No.20YJ02)+1 种基金Natural Science Foundation of Jiangxi Provincial(Grant No.20171BAA208019)partial supported by Jiangxi Provincial Department of Education Science and Technology Research Project(GJJ213110)。
文摘The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid■where d≥2.It is known that for each∈>0 and all sufficiently small initial data(u_(0),n_(0),c_(0))belongs to certain Fourier space,the problem possesses a unique global solution(u^(∈),n^(∈),c^(∈))in Fourier space.The present work asserts that these solutions stabilize to(u^(∞),n^(∞),c^(∞))as∈^(-1)→0.Moreover,we show that c^(∈)(t)has the initial layer as∈^(-1)→0.As one expects its limit behavior maybe give a new viewlook to understand the system.
文摘In this paper, the focus is on the boundary stability of a nanolayer in diffusion-reaction systems, taking into account a nonlinear boundary control condition. The authors focus on demonstrating the boundary stability of a nanolayer using the Lyapunov function approach, while making certain regularity assumptions and imposing appropriate control conditions. In addition, the stability analysis is extended to more complex systems by studying the limit problem with interface conditions using the epi-convergence approach. The results obtained in this article are then tested numerically to validate the theoretical conclusions.
文摘We consider a modified Lnshnikov process as a model of a chemical polymer ization anf study the asymptotic behavior (in the thermodynamic limit;as N →∞)of a particular probability distribution on the set of N-dimensional vectors,tile kth component of which is the number of k-mers.The study study establisles the existence of three stages (subcritical,near-critical and supercritical stages)of polymerization,dependenting upon the ratio of association and dissociation rates of f polymers.The present paper concentrates on the analysis of tile subcritical stage.In the sibcritical.stages we show that tile size of the largest length of polymers of stize N is of the order.log N as N →+∞.
