共查询到20条相似文献,搜索用时 531 毫秒
1.
If X = X(t, ξ) is the solution to the stochastic porous media equation in O ì Rd, 1 £ d £ 3,{\mathcal{O}\subset \mathbf{R}^d, 1\le d\le 3,} modelling the self-organized criticality (Barbu et al. in Commun Math Phys 285:901–923, 2009) and X
c
is the critical state, then it is proved that
ò¥0m(O\Ot0)dt < ¥,\mathbbP-a.s.{\int^{\infty}_0m(\mathcal{O}{\setminus}\mathcal{O}^t_0)dt<{\infty},\mathbb{P}\hbox{-a.s.}} and
limt?¥ òO|X(t)-Xc|dx = l < ¥, \mathbbP-a.s.{\lim_{t\to{\infty}} \int_\mathcal{O}|X(t)-X_c|d\xi=\ell<{\infty},\ \mathbb{P}\hbox{-a.s.}} Here, m is the Lebesgue measure and Otc{\mathcal{O}^t_c} is the critical region {x ? O; X(t,x)=Xc(x)}{\{\xi\in\mathcal{O}; X(t,\xi)=X_c(\xi)\}} and X
c
(ξ) ≤ X(0, ξ) a.e. x ? O{\xi\in\mathcal{O}}. If the stochastic Gaussian perturbation has only finitely many modes (but is still function-valued), limt ? ¥ òK|X(t)-Xc|dx = 0{\lim_{t \to {\infty}} \int_K|X(t)-X_c|d\xi=0} exponentially fast for all compact K ì O{K\subset\mathcal{O}} with probability one, if the noise is sufficiently strong. We also recover that in the deterministic case ℓ = 0. 相似文献
2.
We describe the fundamental solution of the equation that is obtained by linearization of the coagulation equation with kernel K(x, y) = (xy)λ/2, around the steady state f(x) = x ?(3+λ)/2 with ${\lambda \in (1, 2)}We describe the fundamental solution of the equation that is obtained by linearization of the coagulation equation with kernel
K(x, y) = (xy)λ/2, around the steady state f(x) = x
−(3+λ)/2 with l ? (1, 2){\lambda \in (1, 2)} . Detailed estimates on its asymptotics are obtained. Some consequences are deduced for the flux properties of the particles
distributions described by such models. 相似文献
3.
In this paper, we consider the global wellposedness of the 3-D incompressible anisotropic Navier-Stokes equations with initial
data in the critical Besov-Sobolev type spaces B{\mathcal{B}} and
B-\frac12,\frac124{\mathcal{B}^{-\frac12,\frac12}_4} (see Definitions 1.1 and 1.2 below). In particular, we proved that there exists a positive constant C such that (ANS
ν
) has a unique global solution with initial data u0 = (u0h, u03){u_0 = (u_0^h, u_0^3)} which satisfies
||u0h||B exp(\fracCn4 ||u03||B4) £ c0n{\|u_0^h\|_{\mathcal{B}} \exp\bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}}^4\bigr) \leq c_0\nu} or
||u0h||B-\frac12,\frac124 exp(\fracCn4 ||u03||B-\frac12,\frac1244) £ c0n{\|u_0^h\|_{\mathcal{B}^{-\frac12,\frac12}_{4}} \exp \bigl(\frac{C}{\nu^4} \|u_0^3\|_{\mathcal{B}^{-\frac12,\frac12}_{4}}^4\bigr)\leq c_0\nu} for some c
0 sufficiently small. To overcome the difficulty that Gronwall’s inequality can not be applied in the framework of Chemin-Lerner
type spaces, [(Lpt)\tilde](B){\widetilde{L^p_t}(\mathcal{B})}, we introduced here sort of weighted Chemin-Lerner type spaces, [(L2t, f)\tilde](B){\widetilde{L^2_{t, f}}(\mathcal{B})} for some apropriate L
1 function f(t). 相似文献
4.
We obtain convergent multi-scale expansions for the one-and two-point correlation functions of the low temperature lattice classical N - vector spin model in d S 3 dimensions, N S 2. The Gibbs factor is taken as exp[-b(1/2 ||?f||2 +l/8 || |f|2 - 1 ||2 + v/2||f- h||2)], \exp [-\beta (1/2 ||\partial \phi||^2 +\lambda/8 ||\, |\phi|^2 - 1 ||^2 + v/2||\phi - h||^2)], where f(x), h ? RN\phi(x), h \in R^N, x ? Zdx \in Z^d, |h|=1, b < ¥|h|=1, \beta < \infty, l 3 ¥\lambda \geq \infty are large and 0 < v h 1. In the thermodynamic and v ˉ 0v \downarrow 0 limits, with h = e1, and j L ½ , the expansion gives áf1(x)? = 1+0(1/b1/2)\langle \phi_1(x)\rangle = 1+0(1/\beta^{1/2}) (spontaneous magnetization), áf1(x)fi(y)? = 0\langle \phi_1(x)\phi_i(y)\rangle=0, áfi (x)fi (y)? = c0 D-1(x,y)+R(x,y)\langle \phi_i (x)\phi_i (y)\rangle = c_0 \Delta^{-1}(x,y)+R(x,y) (Goldstone Bosons), i = 2, 3, ?, Ni= 2, 3,\,\ldots, N, and áf1(x)f1(y)?T=R¢(x,y)\langle \phi_1(x)\phi_1(y)\rangle^T=R'(x,y), where |R(x,y)||R(x,y)|, |R¢(x,y)| < 0(1)(1+|x-y|)d-2+r|R'(x,y)|< 0(1)(1+|x-y|)^{d-2+\rho} for some > 0, and c0 is aprecisely determined constant. 相似文献
5.
Vladimir Rabinovich 《Russian Journal of Mathematical Physics》2012,19(1):107-120
The propagation of electromagnetic waves issued by modulated moving sources of the form j( t,x ) = a( t )e - iw0 t [(x)\dot]0 ( t )d( x - x0 ( t ) )j\left( {t,x} \right) = a\left( t \right)e^{ - i\omega _0 t} \dot x_0 \left( t \right)\delta \left( {x - x_0 \left( t \right)} \right) is considered, where j(t, x) stands for the current density vector, x = (x
1, x
2, x
3) ∈ ℝ3 for the space variables, t ∈ ℝ for time, t → x
0(t) ∈ ℝ3 for the vector function defining the motion of the source, ω
0 for the eigenfrequency of the source, a(t) for a narrow-band amplitude, and δ for the standard δ function. Suppose that the media under consideration are dispersive. This means that the electric and magnetic permittivity
ɛ(ω), μ(ω) depends on the frequency ω. We obtain a representation of electromagnetic fields in the form of time-frequency oscillating integrals whose phase contains
a large parameter λ > 0 characterizing the slowness of the change of the amplitude a(t) and the velocity [(x)\dot]0 ( t )\dot x_0 \left( t \right) and a large distance between positions of the source and the receiver. Applying the two-dimensional stationary phase method
to the integrals, we obtain explicit formulas for the electromagnetic field and for the Doppler effects. As an application
of our approach, we consider the propagation of electromagnetic waves produced by moving source in a cold nonmagnetized plasma
and the Cherenkov radiation in dispersive media. 相似文献
6.
We construct a family of self-adjoint operators D N , ${N\in{\mathbb Z}}We construct a family of self-adjoint operators D
N
,
N ? \mathbb Z{N\in{\mathbb Z}} , which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space
\mathbb CPlq{{\mathbb C}{\rm P}^{\ell}_q} , for any ℓ ≥ 2 and 0 < q < 1. They provide 0+-dimensional equivariant even spectral triples. If ℓ is odd and
N=\frac12(l+1){N=\frac{1}{2}(\ell+1)} , the spectral triple is real with KO-dimension 2ℓ mod 8. 相似文献
7.
We analyze the long time behavior of solutions of the Schrödinger equation ${i\psi_t=(-\Delta-b/r+V(t,x))\psi}We analyze the long time behavior of solutions of the Schr?dinger equation iyt=(-D-b/r+V(t,x))y{i\psi_t=(-\Delta-b/r+V(t,x))\psi},
x ? \mathbbR3{x\in\mathbb{R}^3}, r = |x|, describing a Coulomb system subjected to a spatially compactly supported time periodic potential V(t, x) = V(t + 2π/ω, x) with zero time average. 相似文献
8.
C?t?lin I. Carstea 《Communications in Mathematical Physics》2010,300(2):487-528
The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}The existence of co-rotational finite time blow up solutions to the wave map problem from
\mathbbR2+1 ? N{\mathbb{R}^{2+1} \to N} , where N is a surface of revolution with metric d
ρ
2 + g(ρ)2
dθ2, g an entire function, is proven. These are of the form u(t,r)=Q(l(t)t)+R(t,r){u(t,r)=Q(\lambda(t)t)+\mathcal{R}(t,r)} , where Q is a time independent solution of the co-rotational wave map equation −u
tt
+ u
rr
+ r
−1
u
r
= r
−2
g(u)g′(u), λ(t) = t
−1-ν, ν > 1/2 is arbitrary, and R{\mathcal{R}} is a term whose local energy goes to zero as t → 0. 相似文献
9.
John T. Cannon 《Communications in Mathematical Physics》1974,35(3):215-233
Nelson's free Markoff field on ? l+1 is a natural generalization of the Ornstein-Uhlenbeck process on ?1, mapping a class of distributions φ(x,t) on ? l ×?1 to mean zero Gaussian random variables φ with covariance given by the inner product \(\left( {\left( {m^2 - \Delta - \frac{{\partial ^2 }}{{\partial t^2 }}} \right)^{ - 1} \cdot , \cdot } \right)_2 \) . The random variables φ can be considered functions φ〈q〉=∝ φ(x,t)q(x,t)d x dt on a space of functionsq(x,t). In the O.U. case,l=0, the classical Wiener theorem asserts that the underlying measure space can be taken as the space of continuous pathst →q(t). We find analogues of this, in the casesl>0, which assert that the underlying measure space of the random variables φ which have support in a bounded region of ? l+1 can be taken as a space of continuous pathst →q(·,t) taking values in certain Soboleff spaces. 相似文献
10.
For a q × q matrix x = (x i, j ) we let ${J(x)=(x_{i,j}^{-1})}For a q × q matrix x = (x
i, j
) we let J(x)=(xi,j-1){J(x)=(x_{i,j}^{-1})} be the Hadamard inverse, which takes the reciprocal of the elements of x. We let I(x)=(xi,j)-1{I(x)=(x_{i,j})^{-1}} denote the matrix inverse, and we define K=I°J{K=I\circ J} to be the birational map obtained from the composition of these two involutions. We consider the iterates Kn=K°?°K{K^n=K\circ\cdots\circ K} and determine the degree complexity of K, which is the exponential rate of degree growth d(K)=limn?¥( deg(Kn) )1/n{\delta(K)=\lim_{n\to\infty}\left( deg(K^n) \right)^{1/n}} of the degrees of the iterates. Earlier studies of this map were restricted to cyclic matrices, in which case K may be represented by a simpler map. Here we show that for general matrices the value of δ(K) is equal to the value conjectured by Anglès d’Auriac, Maillard and Viallet. 相似文献
11.
Some authors found that, in different coordinates, the tunneling approach gives different Hawking temperature for the Schwarzschild
black hole recently. In this paper, by studying the Hawking radiation of the Kerr black hole arising from the scalar and Dirac
particles, we find that, to obtain the Hawking temperature by using tunneling effect, the coordinate representations for the
stationary Kerr black hole should satisfy two conditions: (a) to keep the Killing vectors x(t)m{{\xi_{(t)}^\mu}} and x(j)m{{\xi_{(\varphi)}^\mu}} invariant; and (b) the radial coordinate transformation is a regular and non-zero function. 相似文献
12.
We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to + (equal to ?). For β large enough we show that for any ${\varepsilon >0 }We consider the Glauber dynamics for the 2D Ising model in a box of side L, at inverse temperature β and random boundary conditions τ whose distribution P either stochastically dominates the extremal plus phase (hence the quotation marks in the title) or is stochastically dominated
by the extremal minus phase. A particular case is when P is concentrated on the homogeneous configuration identically equal to + (equal to −). For β large enough we show that for any ${\varepsilon >0 }${\varepsilon >0 } there exists c=c(b,e){c=c(\beta,\varepsilon)} such that the corresponding mixing time T
mix satisfies limL?¥ P(Tmix 3 exp(cLe)) = 0{{\rm lim}_{L\to\infty}\,{\bf P}\left(T_{\rm mix}\ge {\rm exp}({cL^\varepsilon})\right) =0}. In the non-random case τ ≡ + (or τ ≡ −), this implies that Tmix £ exp(cLe){T_{\rm mix}\le {\rm exp}({cL^\varepsilon})}. The same bound holds when the boundary conditions are all + on three sides and all − on the remaining one. The result,
although still very far from the expected Lifshitz behavior T
mix = O(L
2), considerably improves upon the previous known estimates of the form
Tmix £ exp(c L\frac 12 + e){T_{\rm mix}\le {\rm exp}({c L^{\frac 12 + \varepsilon}})}. The techniques are based on induction over length scales, combined with a judicious use of the so-called “censoring inequality”
of Y. Peres and P. Winkler, which in a sense allows us to guide the dynamics to its equilibrium measure. 相似文献
13.
Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on?Lattice Strips 总被引:1,自引:0,他引:1
We determine the general structure of the partition function of the q-state Potts model in an external magnetic field, Z(G,q,v,w) for arbitrary q, temperature variable v, and magnetic field variable w, on cyclic, M?bius, and free strip graphs G of the square (sq), triangular (tri), and honeycomb (hc) lattices with width L
y
and arbitrarily great length L
x
. For the cyclic case we prove that the partition function has the form
Z(L,Ly×Lx,q,v,w)=?d=0Ly[(c)\tilde](d)Tr[(TZ,L,Ly,d)m]Z(\Lambda,L_{y}\times L_{x},q,v,w)=\sum_{d=0}^{L_{y}}\tilde{c}^{(d)}\mathrm{Tr}[(T_{Z,\Lambda,L_{y},d})^{m}]
, where Λ denotes the lattice type,
[(c)\tilde](d)\tilde{c}^{(d)}
are specified polynomials of degree d in q,
TZ,L,Ly,dT_{Z,\Lambda,L_{y},d}
is the corresponding transfer matrix, and m=L
x
(L
x
/2) for Λ=sq,tri (hc), respectively. An analogous formula is given for M?bius strips, while only
TZ,L,Ly,d=0T_{Z,\Lambda,L_{y},d=0}
appears for free strips. We exhibit a method for calculating
TZ,L,Ly,dT_{Z,\Lambda,L_{y},d}
for arbitrary L
y
and give illustrative examples. Explicit results for arbitrary L
y
are presented for
TZ,L,Ly,dT_{Z,\Lambda,L_{y},d}
with d=L
y
and d=L
y
−1. We find very simple formulas for the determinant
det(TZ,L,Ly,d)\mathrm{det}(T_{Z,\Lambda,L_{y},d})
. We also give results for self-dual cyclic strips of the square lattice. 相似文献
14.
In appropriate units, the Brown-Ravenhall Hamiltonian for a system of 1 electron relativistic molecules with K fixed nuclei having charge and position Zk, Rk, k=1,2, ?,Kk=1,2, \ldots,K, is of the form \bB1,K = L+ ( D0 + aVc) L+ \bB_{1,K}= \Lambda_+ \bigl( D_0 + \alpha V_c\bigr) \Lambda_+ , where v+ is the projection onto the positive spectral subspace of the free Dirac operator D0 and Vc = - ?k=1K \fracaZk\lmod \bx-Rk \rmod + ?k < l, k,l=1K \fracaZk Zl\lmod Rk-Rl \rmod V_c= - \sum_{k=1}^K \frac{\alpha Z_k}{\lmod \bx-R_k \rmod} + \sum_{kZk £ aZc = \frac2p/2 + 2/ p\alpha Z_k \leq \alpha Z_c = \frac{2}{\pi /2 + 2/ \pi}, k=1,2, ?,Kk=1,2, \ldots,K, and a £ \frac2 p(p2+4)(2+?{1+ p/2})\alpha \leq \frac{2 \pi}{(\pi^2+4)(2+\sqrt{1+ \pi /2})}, \ \bB1,K 3 \operatornameconst \cdotp K\bB_{1,K} \geq \operatorname{const} \cdotp K. 相似文献
15.
Combined constraints on modified Chaplygin gas model from cosmological observed data: Markov Chain Monte Carlo approach 总被引:1,自引:0,他引:1
We use the Markov Chain Monte Carlo method to investigate a global constraints on the modified Chaplygin gas (MCG) model as
the unification of dark matter and dark energy from the latest observational data: the Union2 dataset of type supernovae Ia
(SNIa), the observational Hubble data (OHD), the cluster X-ray gas mass fraction, the baryon acoustic oscillation (BAO), and
the cosmic microwave background (CMB) data. In a flat universe, the constraint results for MCG model are, Wbh2 = 0.02263+0.00184-0.00162 (1s)+0.00213-0.00195 (2s){\Omega_{b}h^{2}\,{=}\,0.02263^{+0.00184}_{-0.00162} (1\sigma)^{+0.00213}_{-0.00195} (2\sigma)}, Bs = 0.7788+0.0736-0.0723(1s)+0.0918-0.0904 (2s){B_{s}\,{=}\,0.7788^{+0.0736}_{-0.0723}(1\sigma)^{+0.0918}_{-0.0904} (2\sigma)}, a = 0.1079+0.3397-0.2539 (1s)+0.4678-0.2911 (2s){\alpha\,{=}\,0.1079^{+0.3397}_{-0.2539} (1\sigma)^{+0.4678}_{-0.2911} (2\sigma)}, B = 0.00189+0.00583-0.00756(1s)+0.00660-0.00915 (2s){B\,{=}\,0.00189^{+0.00583}_{-0.00756}(1\sigma)^{+0.00660}_{-0.00915} (2\sigma)}, and H0=70.711+4.188-3.142 (1s)+5.281-4.149(2s){H_{0}=70.711^{+4.188}_{-3.142} (1\sigma)^{+5.281}_{-4.149}(2\sigma)}. 相似文献
16.
Gustav Holzegel 《Communications in Mathematical Physics》2010,294(1):169-197
The massive wave equation ${\square_{g}\psi - \alpha \frac{\Lambda}{3}\psi = 0}The massive wave equation
\squaregy- a\fracL3y = 0{\square_{g}\psi - \alpha \frac{\Lambda}{3}\psi = 0} is studied on a fixed Kerr-anti de Sitter background (M,gM,a,L){\left(\mathcal{M},g_{M,a,\Lambda}\right)}. We first prove that in the Schwarzschild case (a = 0), ψ remains uniformly bounded on the black hole exterior provided that
a < \frac94{\alpha < \frac{9}{4}}, i.e. the Breitenlohner-Freedman bound holds. Our proof is based on vectorfield multipliers and commutators: The total flux
of the usual energy current arising from the timelike Killing vector field T (which fails to be non-negative pointwise) is shown to be non-negative with the help of a Hardy inequality after integration
over a spacelike slice. In addition to T, we construct a vectorfield whose energy identity captures the redshift producing good estimates close to the horizon. The
argument is finally generalized to slowly rotating Kerr-AdS backgrounds. This is achieved by replacing the Killing vectorfield
T = ∂
t
with K=?t + l?f{K=\partial_t + \lambda \partial_\phi} for an appropriate λ ~ a, which is also Killing and–in contrast to the asymptotically flat case–everywhere causal on the black hole exterior. The
separability properties of the wave equation on Kerr-AdS are not used. As a consequence, the theorem also applies to spacetimes
sufficiently close to the Kerr-AdS spacetime, as long as they admit a causal Killing field K which is null on the horizon. 相似文献
17.
Tomá? Dohnal Michael Plum Wolfgang Reichel 《Communications in Mathematical Physics》2011,308(2):511-542
We consider the nonlinear Schr?dinger equation
(-D+V(x))u = G(x) |u|p-1u, x ? \mathbb Rn(-\Delta +V(x))u = \Gamma(x) |u|^{p-1}u, \quad x\in {\mathbb R}^n 相似文献
18.
This paper considers Hardy–Lieb–Thirring inequalities for higher order differential operators. A result for general fourth-order
operators on the half-line is developed, and the trace inequality
|