共查询到20条相似文献,搜索用时 15 毫秒
1.
Infrared asymptotic behavior of a scalar field, passively advected by a random shear flow, is studied by means of the field
theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in time, with
correlation function of the form μ d(t-t¢) / k^d-1+x\propto\delta(t-t') / k_{\bot}^{d-1+\xi}, where k
⊥=|k
⊥| and k
⊥ is the component of the wave vector, perpendicular to the distinguished direction (‘direction of the flow’)—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (Commun. Math. Phys. 131:381, 1990). The structure functions of the scalar field in the infrared range exhibit scaling behavior with exactly known critical
dimensions. It is strongly anisotropic in the sense that the dimensions related to the directions parallel and perpendicular
to the flow are essentially different. In contrast to the isotropic Kraichnan’s rapid-change model, the structure functions
show no anomalous (multi)scaling and have finite limits when the integral turbulence scale tends to infinity. On the contrary,
the dependence of the internal scale (or diffusivity coefficient) persists in the infrared range. Generalization to the velocity
field with a finite correlation time is also obtained. Depending on the relation between the exponents in the energy spectrum
E μ k^1-e\mathcal{E} \propto k_{\bot}^{1-\varepsilon} and in the dispersion law w μ k^2-h\omega\propto k_{\bot}^{2-\eta}, the infrared behavior of the model is given by the limits of vanishing or infinite correlation time, with the crossover
at the ray η=0, ε>0 in the ε–η plane. The physical (Kolmogorov) point ε=8/3, η=4/3 lies inside the domain of stability of the rapid-change regime; there is no crossover line going through this point. 相似文献
2.
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
tr( (-D)2 - CHRd,2\frac1|x|4 - V(x) )-g £ Cgò\mathbbRd V(x)+g+ \fracd4 dx, g 3 1 - \frac d 4,\mathrm{tr}\left( (-\Delta)^2 - C^{\mathrm{HR}}_{d,2}\frac{1}{|x|^4} - V(x) \right)_-^{\gamma}\leq C_\gamma\int\limits_{\mathbb{R}^d} V(x)_+^{\gamma + \frac{d}{4}}\,\mathrm{d}x, \quad \gamma \geq 1 - \frac d 4, 相似文献
3.
Fluorescence lifetimes of formaldehyde excited at 352 nm (
A2 –
A1 401 band) were measured as a function of bath gas pressure. He, N2, O2, CO2 and HCHO were investigated for the bath gas and the temperature dependence between 298 and 500 K for N2 and O2 bath gases was also examined. It was found that the non-linear pressure dependence of the lifetime is successfully reproduced by the model formula
4.
We study the two-dimensional Gross-Pitaevskii theory of a rotating Bose gas in a disc-shaped trap with Dirichlet boundary
conditions, generalizing and extending previous results that were obtained under Neumann boundary conditions. The focus is
on the energy asymptotics, vorticity and qualitative properties of the minimizers in the parameter range |log ε|≪Ω≲ε
−2|log ε|−1 where Ω is the rotational velocity and the coupling parameter is written as ε
−2 with ε≪1. Three critical speeds can be identified. At
\varOmega = \varOmegac1 ~ |loge|\varOmega=\varOmega_{\mathrm{c_{1}}}\sim |\log\varepsilon| vortices start to appear and for
|loge| << \varOmega < \varOmegac2 ~ e-1|\log\varepsilon|\ll\varOmega< \varOmega_{\mathrm{c_{2}}}\sim \varepsilon^{-1} the vorticity is uniformly distributed over the disc. For
\varOmega 3 \varOmega c2\varOmega\geq\varOmega _{\mathrm{c_{2}}} the centrifugal forces create a hole around the center with strongly depleted density. For Ω≪ε
−2|log ε|−1 vorticity is still uniformly distributed in an annulus containing the bulk of the density, but at
\varOmega = \varOmegac3 ~ e-2|loge|-1\varOmega=\varOmega_{\mathrm {c_{3}}}\sim\varepsilon ^{-2}|\log\varepsilon |^{-1} there is a transition to a giant vortex state where the vorticity disappears from the bulk. The energy is then well approximated
by a trial function that is an eigenfunction of angular momentum but one of our results is that the true minimizers break
rotational symmetry in the whole parameter range, including the giant vortex phase. 相似文献
5.
Li-Yun Hu Qi Wang Zi-Sheng Wang Xue-xiang Xu 《International Journal of Theoretical Physics》2012,51(2):331-349
Using the thermal entangled state representation 〈η|, we examine the master equation (ME) describing phase-sensitive reservoirs. We present the analytical expression of solution
to the ME, i.e., the Kraus operator-sum representation of density operator ρ is given, and its normalization is also proved by using the IWOP technique. Further, by converting the characteristic function
χ(λ) into an overlap between two “pure states” in enlarged Fock space, i.e., χ(λ)=〈η
=−λ
|ρ|η
=0〉, we consider time evolution of distribution functions, such as Wigner, Q- and P-function. As applications, the photon-count
distribution and the evolution of Wigner function of photon-added coherent state are examined in phase-sensitive reservoirs.
It is shown that the Wigner function has a negative value when
kt\leqslant\frac 12ln( 1+m¥) \kappa t\leqslant\frac {1}{2}\ln ( 1+\mu_{\infty}) is satisfied, where μ
∞ depends on the squeezing parameter |M|2 of environment, and increases as the increase of |M|. 相似文献
6.
Percolation theory is extensively studied in statistical physics and mathematics with applications in diverse fields. However,
the research is focused on systems with only one type of links, connectivity links. We review a recently developed mathematical
framework for analyzing percolation properties of realistic scenarios of networks having links of two types, connectivity
and dependency links. This formalism was applied to study Erdős-Rényi (ER) networks that include also dependency links. For
an ER network with average degree [`(k)]\bar{k} that is composed of dependency clusters of size s, the fraction of nodes that belong to the giant component, P
∞, is given by P¥=ps-1[1-exp(-[`(k)]pP¥) ]sP_{\infty}=p^{s-1}[1-\exp{(-\bar{k}pP_{\infty})} ]^{s} where 1−p is the initial fraction of randomly removed nodes. Here, we apply the formalism to the study of random-regular (RR) networks
and find a formula for the size of the giant component in the percolation process: P
∞=p
s−1(1−r
k
)
s
where r is the solution of r=p
s
(r
k−1−1)(1−r
k
)+1, and k is the degree of the nodes. These general results coincide, for s=1, with the known equations for percolation in ER and RR networks respectively without dependency links. In contrast to s=1, where the percolation transition is second order, for s>1 it is of first order. Comparing the percolation behavior of ER and RR networks we find a remarkable difference regarding
their resilience. We show, analytically and numerically, that in ER networks with low connectivity degree or large dependency
clusters, removal of even a finite number (zero fraction) of the infinite network nodes will trigger a cascade of failures
that fragments the whole network. Specifically, for any given s there exists a critical degree value, [`(k)]min\bar{k}_{\min}, such that an ER network with [`(k)] £ [`(k)]min\bar{k}\leq \bar{k}_{\min} is unstable and collapse when removing even a single node. This result is in contrast to RR networks where such cascades
and full fragmentation can be triggered only by removal of a finite fraction of nodes in the network. 相似文献
7.
We prove that the small scale structures of the stochastically forced Navier–Stokes equations approach those of the naturally associated Ornstein–Uhlenbeck process as the scales get smaller. Precisely, we prove that the rescaled kth spatial Fourier mode converges weakly on path space to an associated Ornstein–Uhlenbeck process as |k| . In addition, we prove that the Navier–Stokes equations and the naturally associated Ornstein–Uhlenbeck process induce equivalent transition densities if the viscosity is replaced with hyper-viscosity. This gives a simple proof of unique ergodicity for the hyperviscous Navier–Stokes system. We show how different strengthened hyperviscosity produce varying levels of equivalence. 相似文献
8.
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
9.
In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic
shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the
product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Müller (Philos
Mag A 66(5):697–715, 1992), is defined by the following functional:
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