Scaling dynamics for solvable coagulation equations with dust and gel

We study limiting behavior of rescaled size distributions that evolve by Smoluchowski's rate equations for coagulation, with rate kernel K=2, x+y or xy. We find that the dynamics naturally extend to probability distributions on the half-line with zero and infinity appended, representing populations of clusters of zero and infinite size. The “scaling attractor” (set of subsequential limits) is compact and has a Levy-Khintchine-type representation that linearizes the dynamics and allows one to establish several signatures of chaos. In particular, for any given solution trajectory, there is a dense family of initial distributions (with the same initial tail) that yield scaling trajectories that shadow the given one for all time. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An examination of the pumping requirements for multiphoton deexcitations of isomeric levels

Deexcitation of isomeric levels via virtual excitation of higher levels with short lifetimes is calculated for a variety of circumstances. On and off resonance processes as well as single and multiple photon excitations are considered. Parameters characteristic of atomic and nuclear systems are contrasted. For the nuclear systems, the small excitation cross sections resulting from the small nuclear size leads to enormous intensity requirements for the pumping of nuclear isomers.     

Universality Classes in Burgers Turbulence

We establish necessary and sufficient conditions for the shock statistics to approach self-similar form in Burgers turbulence with Lévy process initial data. The proof relies upon an elegant closure theorem of Bertoin and Carraro and Duchon that reduces the study of shock statistics to Smoluchowski’s coagulation equation with additive kernel, and upon our previous characterization of the domains of attraction of self-similar solutions for this equation.     

Void-fraction measurements in a steady-state mercury-nitrogen flow loop

 A steady-state vertical mercury-nitrogen flow system has been investigated using three tomographic algorithms. Void-fraction profiles have been reconstructed by the data collected by a 60 mCi gamma-ray source and a single Na(Tl) detector. The results indicate excellent agreement (within ±1%) between the least-squares-solution and the chord-segment-inversion algorithms. The data-collection time for each data-ray was varied so that in each case 3000 counts could be collected to reduce the detrimental effect of Poisson statistics in the reconstructed profiles. Eleven sets of data have been collected for nitrogen flow-rates between 0.00123 and 0.00884  kg/s. The mercury flow-rates were between 17.6 and 34.1 kg/s. The resulting cross-sectional average void varied between 0.10 and 0.38. Received: 13 March 1997/Accepted: 12 September 1997     

Approach to self‐similarity in Smoluchowski's coagulation equations

We consider the approach to self‐similarity (or dynamical scaling) in Smoluchowski's equations of coagulation for the solvable kernels K(x, y) = 2, x + y and xy. In addition to the known self‐similar solutions with exponential tails, there are one‐parameter families of solutions with algebraic decay, whose form is related to heavy‐tailed distributions well‐known in probability theory. For K = 2 the size distribution is Mittag‐Leffler, and for K = x + y and K = xy it is a power‐law rescaling of a maximally skewed α‐stable Lévy distribution. We characterize completely the domains of attraction of all self‐similar solutions under weak convergence of measures. Our results are analogous to the classical characterization of stable distributions in probability theory. The proofs are simple, relying on the Laplace transform and a fundamental rigidity lemma for scaling limits. © 2003 Wiley Periodicals, Inc.     

Continuous and discrete Bessel wavelet transforms

Using the theory of Hankel convolution, continuous and discrete Bessel wavelet transforms are defined. Certain boundedness results and inversion formula for the continuous Bessel wavelet transform are obtained. Important properties of the discrete Bessel wavelet transform are given.     

Relative photodissociation cross-section of NaCs molecule,using argon ion laser lines

Laser-induced photodissociation of NaCs molecule has been observed when a mixture of Na and Cs metal vapour in a glass cell was irradiated by most of the lines of an argon ion laser. The photodissociation results in the 3P state of Na atoms which is correlated with theF ¹Σ⁺ and G¹π molecular states of NaCs. Distribution of photofragments over fine structure components 3² P _3/2 and 3² P _1/2 of Na has been studied. The ratio of intensity ofD ₂ line (5890 Å) toD ₁ line (5896 Å) of Na varies from around 2 at 5145 Å to about 3.5 at 4579 Å. The relative photodissociation cross-section increases monotonically as the wave-length of laser light decreases from 5145 Å to 4579 Å. It is seen that the 4579 Å photon is about 200 times more effective than the 5145 Å photon in causing the photoreaction NaCs + (Ar⁺ photon) → Na*(3P) + Cs(6S).