Is diffusion limited aggregation scale invariant?

Recent work showing evidence for multiscaling in large two dimensional DLA clusters is reviewed. A connection between multiscaling and multifractality is also shown resulting in a weak localization of the growth sites (δ-sites) in shells around the cluster seed.     

各向异性扩散控制聚集集团的豪斯道夫维数

本文通过解析计算,给出了各向异性扩散控制聚集集团有效外半角β=min{β_x,β_y},修正了文献[1]关于有效外半角β=max{β_x,β_y}的假设,对各向异性扩散控制聚集集团的豪斯道夫维数D随各向异性扩散几率p的变化公式也作了相应的修正,并进行了计算机模拟实验,发现修正后的公式与实验符合较好,与Jullien等人的计算机模拟结果进行了比较,在p≥1/4时两者的结果是一致的。 关键词：     

Symmetries and Modular Intersections of Von Neumann Algebras

Let be von Neumann algebras acting on a Hilbert space and let be a common cyclic and separating vector. We say that have the modular intersection property with respect to if(1) -half-sided modular inclusions,(2) (If (1) holds the strong limit exists.) We show that under these conditions the modular groups of and generate a 2-dim. Lie group.This observation is the basis for obtaining group representations of Sl(2, )/Z ₂ generated by modular groups.     

Heat transport in turbulent rayleigh-Benard convection

We present measurements of the Nusselt number N as a function of the Rayleigh number R in cylindrical cells with aspect ratios 0. 510(7) they are consistent with N = asigma-1/12R1/4+bsigma-1/7R3/7 as proposed by Grossmann and Lohse for sigma greater, similar2.     

Nusselt number measurements for turbulent Rayleigh-Bénard convection

We present high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for a cylindrical sample of water (Prandtl number sigma=4.4) of height L approximately equal to 50 cm and aspect ratio Gamma identical with D/L approximately equal to 1 (D is the diameter) for 3 x 10(9)< or =R< or =6 x 10(10). For R approximately 3 x 10(9) the data are consistent with existing results for acetone (sigma=4.0, R< or =3 x 10(9)). There the measurements are also consistent with a model by Grossmann and Lohse (GL). As R increases, the measurements fall below the GL prediction. Near R=6 x 10(10) the prediction is 8% above the data.     

Fracture surfaces as multiscaling graphs

Fracture paths in quasi-two-dimensional (2D) media (e.g., thin layers of materials or paper) are analyzed as self-affine graphs h(x) of height h as a function of length x. We show that these are multiscaling, in the sense that nth order moments of the height fluctuations across any distance l scale with a characteristic exponent that depends nonlinearly on the order of the moment. Having demonstrated this, one rules out a widely held conjecture that fracture in 2D belongs to the universality class of directed polymers in random media. In fact, 2D fracture does not belong to any of the known kinetic roughening models. The presence of multiscaling offers a stringent test for any theoretical model; we show that a recently introduced model of quasistatic fracture passes this test.     

各向异性扩散DLA的标度性质

本文利用坐标变换的方法讨论了各向异性扩散对DLA集团标度行为的影响。对二维正方形点阵,解析计算了各向异性扩散DLA集团的Hausdorff维数。结果表明,此时生长集困的Hausdorff维数D随各向异性扩散概率p连续变化,其最大值为5/3,最小值为3/2,还将这里所得到的理论结果与Jullien等人的数值结果进行了比较,发现它们符合得很好。最后,还解析讨论并计算了各向异性扩散DLA的广义维数D_q(p)。     

Finite size effect of harmonic measure estimation in a DLA model: Variable size of probe particles

A finite size effect in the probing of the harmonic measure in simulation of diffusion-limited aggregation (DLA) growth is investigated. We introduce a variable size of probe particles, to estimate harmonic measure and extract the fractal dimension of DLA clusters taking two limits, of vanishingly small probe particle size and of infinitely large size of a DLA cluster. We generate 1000 DLA clusters consisting of 50 million particles each, using an off-lattice killing-free algorithm developed in the early work. The introduced method leads to unprecedented accuracy in the estimation of the fractal dimension. We discuss the variation of the probability distribution function with the size of probing particles.     

Rb(5PJ)与He,N2的碰撞精细结构混合和猝灭

在气体样品池条件下,研究了Rb(5PJ) (He,N2)碰撞能量转移过程.用调频半导体激光器激发Rb原子至Rb(5P3/2)态,在不同的He或N2气压下,测量了直接5P3/2→5S1/2荧光和转移5P1/2→5S1/2荧光.对于Rb(5PJ)与He的碰撞,只发生精细结构转移(略去碰撞猝灭效应),电子态能量仅能转移为He原子的平动能.在与N2的碰撞中,向分子振转态的转移是重要的.本实验中,Rb的密度为4.5×1011 cm-3,由辐射陷获理论得到5P1/2→5S1/2的有效辐射率为2.47×107 s-1.利用速率方程分析,可以得到碰撞转移速率系数,对于He,5P3/2→5S1/2转移速率系数kHe21=2.61×10 12 cm3·s.对于N2,测量5PJ He和5PJ N2两种情况下直接荧光与敏化荧光的相对强度比,利用最小二乘法确定5Pa/2→5S1/2转移速率系数kN212=2.36×10-11 cm3·s,5PJ态猝灭速率系数kN2=1.44×10-11 cm3·s-1.由实验结果证实了Cs-N2主要是直线式碰撞传能机制,与其他实验结果进行了比较.     

Lacunarity and multifractal analysis of the large DLA mass distribution

We show the methodology used to analyze fractal and mass-multifractal properties of very large Diffusion-Limited Aggregation (DLA) clusters with a maximum of 10⁹${10}^9$ particles for 2D aggregates and 10⁸${10}^8$ particles for 3D clusters, to support our main result; the scaling behavior obtained by our experimental results corresponds to the expected performance of monofractal objects. In order to estimate lacunarity measures for large DLA clusters, we develop a variant of the gliding-box algorithm which reduces the computer time needed to obtain experimental results. We show how our mass multifractal data have a tendency to present monofractal behavior for the mass distribution of the cases presented in this paper in the limit of very large clusters. Lacunarity analysis shows, provided we study small clusters mass distributions, data which might be interpreted as two different values of fractal dimensions while the cluster grows; however, this effect tends to vanish when the cluster size increases further, in such a way that monofractality is achieved. The outcomes of this paper lead us to conclude that the previously reported mass multifractality behavior (Vicsek et al., 1990  [13]) detected for DLA clusters is a consequence of finite size effects and floating point precision limitations and not an intrinsic feature of the phenomena, since the scaling behavior of our DLA clusters space corresponds to monofractal objects, being this situation remarkably noticeable in the limit of very large clusters.     

Observation of decays B0-->Ds(*)+ pi- and B0-->Ds(*)- K+

We report the observation of decays B{0}-->D{s}{(*)+}pi- and B{0}-->D{s}{(*)-}K+ in a sample of 230 x 10(6) Upsilon(4S)-->BB[over] events recorded with the BABAR detector at the SLAC PEP-II asymmetric-energy e+ e- storage ring. We measure the branching fractions B(B{0}-->D{s}{+}pi-)=(1.3+/-0.3(stat)+/-0.2(syst))x10(-5), B(B{0}-->D{s}{-} K+)=(2.5+/-0.4(stat)+/-0.4(syst))x10(-5), B(B{0}-->D{s}{*+}pi-)=(2.8+/-0.6(stat)+/-0.5(syst))x10(-5), and B(B{0}-->D{s}{*-}K+)=(2.0+/-0.5(stat)+/-0.4(syst))x10(-5). The significances of the measurements to differ from zero are 5, 9, 6, and 5 standard deviations, respectively. This is the first observation of B{0}-->D{s}{+}pi-, B{0}-->D{s}{*+}pi-, and B{0}-->D{s}{*-}K+ decays.     

Time decay of solutions to the cauchy problem for time-dependent Schrödinger-Hartree equations

We consider the time-dependent Schrödinger-Hartree equation (1) $$iu_t + \Delta u = \left( {\frac{1}{r}*|u|^2 } \right)u + \lambda \frac{u}{r},(t, x) \in \mathbb{R} \times \mathbb{R}^3 ,$$ (2) $$u(0,x) = \phi (x) \in \Sigma ^{2,2} ,x \in \mathbb{R}^3 ,$$ where λ≧0 and \(\Sigma ^{2,2} = \{ g \in L^2 ;\parallel g\parallel _{\Sigma ^{2,2} }^2 = \sum\limits_{|a| \leqq 2} {\parallel D^a g\parallel _2^2 + \sum\limits_{|\beta | \leqq 2} {\parallel x^\beta g\parallel _2^2< \infty } } \} \) . We show that there exists a unique global solutionu of (1) and (2) such that $$u \in C(\mathbb{R};H^{1,2} ) \cap L^\infty (\mathbb{R};H^{2,2} ) \cap L_{loc}^\infty (\mathbb{R};\Sigma ^{2,2} )$$ with $$u \in L^\infty (\mathbb{R};L^2 ).$$ Furthermore, we show thatu has the following estimates: $$\parallel u(t)\parallel _{2,2} \leqq C,a.c. t \in \mathbb{R},$$ and $$\parallel u(t)\parallel _\infty \leqq C(1 + |t|)^{ - 1/2} ,a.e. t \in \mathbb{R}.$$      

Cs(6P)+(Ne,N2)碰撞能量转移

在气体样品池条件下,研究了Cs(6P3/2) (Ne,N2)碰撞能量转移过程.用调频半导体激光器激发Cs原子至Cs(6P3/2)态,在不同的Ne或N2气压下,测量了直接6P3/2→6S1/2荧光和转移6P1/2→6S1/2荧光,对于6P3/2与Ne的碰撞,电子态能量仅能转移为Ne原子的平动能.在与N2的碰撞中,向分子振转态的转移是重要的.利用速率方程分析,可以得到碰撞转移速率系数,对于Ne,6PJ精细结构碰撞转移速率系数为1.45×10-12cm3·s-1.对于N2,测量6P Ne和6P N2二种情况下荧光的相对强度比,确定精细结构速率系数为1.64×10-12cm3·s-1,6P态猝灭速率系数为4.88×10-12cm3·s-1.     

Two-loop effective theory analysis of pi (K)-->enu[over ]_{e}[gamma] branching ratios

We study the ratios R_{e/mu};{(P)} identical withGamma(P-->enu[over ]_{e}[gamma])/Gamma(P-->munu[over ]_{mu}[gamma]) (P=pi, K) in Chiral Perturbation Theory to order e;{2}p;{4}. We complement the two-loop effective theory results with a matching calculation of the counterterm, finding R_{e/mu};{(pi)}=(1.2352+/-0.0001)x10;{-4} and R_{e/mu};{(K)}=(2.477+/-0.001)x10;{-5}.     

The isomonodromy approach to matric models in 2D quantum gravity

We consider the double-scaling limit in the hermitian matrix model for 2D quantum gravity associated with the measure exp . We show that after the appropriate modification of the contour of integration the Cross-Migdal-Douglas-Shenker limit to the Painlevé I equation (in the generic case of the pure gravity) is valid and calculate the nonperturbative parameters of the corresponding Painlevé function. Our approach is based on the WKB-analysis of the L-A pair corresponding to the discrete string equation in the framework of the Inverse Monodromy Method. Here we extend our results, which were obtained before for the particular casesN=2,3. Our analysis complements the isomonodromy approach proposed by G. Moore to the general string equations that come from the matrix model in the continuous limit and differ in that we apply the isomonodromy technique to investigate the double scaling limit itself.     

A Schrödinger inverse scattering problem with a spectral dependence in the potential

The inverse scattering problem for the scalar Schrödinger equation , is considered. It is solved by reduction to the inverse scattering problem for a matrix Schrödinger equation: .This work has been done as part of the program Recherche Coopérative sur Programme No. 264: Etude interdisciplinaire des problèmes inverses.Physique Mathématique et Théorique, Equipe de recherche associée au CNRS, No. 154.     

piN and pipiN couplings of the Delta(1232) and its chiral partners

We investigate the interactions and chiral properties of the four spin-3/2 baryons N(-)(D13), N+(P13), Delta+(P33), and Delta(-)(D33) together with the nucleon. We construct the SU(2)R x SU(2)L invariant interactions between the spin-1/2 and spin-3/2 baryons with the aid of a new, specially developed spin and isospin projection technique for these baryon fields, where the chiral invariant interactions contain one- and two-pion couplings. We obtain simple relations for the coupling constants of the one- and two-pion spin-1/2-3/2 transitions terms. The relation for the one-pion interactions reasonably agrees with the experiments, which suggests that these spin-3/2 baryons are chiral partners.     

Evidence for the decay D0-->K(-)pi(+)pi(-)e(+)nu(e)

Using a 281 pb{-1} data sample collected at the psi(3770) with the CLEO-c detector, we present the first absolute branching fraction measurement of the decay D0-->K(-)pi(+)pi(-)e(+)nu(e) at a statistical significance of about 4.0 standard deviations. We find 10 candidates consistent with the decay D0-->K(-)pi(+)pi(-)e(+)nu(e). The probability that a background fluctuation accounts for this signal is less than 4.1 x 10{-5}. We find B(D0-->K(-)pi(+)pi(-)e(+)nu(e)) = [2.8{-1.1}{+1.4}(stat)+/-0.3(syst)]x10{-4}. By restricting the invariant mass of the hadronic system to be consistent with K1(1270), we obtain the product of branching fractions B(D{0}-->K{1}{-}(1270)e{+}nu{e})xB(K1-(1270)-->K{-}pi{+}pi{-})=[2.5{-1.0}{+1.3}(stat)+/-0.2(syst)]x10{-4}. Using B(K1-(1270)-->K{-}pi{+}pi{-})=(33+/-3)%, we obtain B(D{0}-->K{1}{-}(1270)e{+}nu{e})=[7.6{-3.0}{+4.1}(stat)+/-0.6(syst)+/-0.7]x10{-4}. The last error accounts for the uncertainties in the measured K1-(1270)-->K{-}pi{+}pi{-} branching fractions.     

Universal order statistics of random walks

We study analytically the order statistics of a time series generated by the positions of a symmetric random walk of n steps with step lengths of finite variance σ(2). We show that the statistics of the gap d(k,n) = M(k,n)-M(k+1,n) between the kth and the (k+1)th maximum of the time series becomes stationary, i.e., independent of n as n → ∞ and exhibits a rich, universal behavior. The mean stationary gap exhibits a universal algebraic decay for large k, ~d(k,∞)-/σ 1/sqrt[2πk], independent of the details of the jump distribution. Moreover, the probability density (pdf) of the stationary gap exhibits scaling, Pr(d(k,∞) = δ) ~/= (sqrt[k]/σ)P(δsqrt[k]/σ), in the regime δ~ (d(k,∞)). The scaling function P(x) is universal and has an unexpected power law tail, P(x) ~ x(-4) for large x. For δ> (d(k,∞)) the scaling breaks down and the pdf gets cut off in a nonuniversal way. Consequently, the moments of the gap exhibit an unusual multiscaling behavior.