Measurements and simulations of particle dispersion in a turbulent flow

A particle imaging technique has been used to collect droplet displacement statistics in a round turbulent jet of air. Droplets are injected on the jet axis, and a laser sheet and position-sensitive photomultiplier tube are used to track their radial displacement and time-of-flight. Dispersion statistics can be computed which are Lagrangian or Eulerian in nature. The experiments have been simulated numerically using a second-order closure scheme for the jet and a stochastic simulation for the particle trajectories. Results are presented for non-vaporizing droplets of sizes from 35 to 160 μm. The simulations have underscored the importance of initial conditions and early droplet displacement history on the droplet trajectory for droplets with large inertia relative to the turbulence. Estimates of initial conditions have been made and their effect on dispersion is quantified.     

Separation and determination of m-phenoxybenzaldehyde reaction products by capillary gas chromatography

A capillary GC method employing an internal standard has been developed and successfully used for quantitative determination both of the raw materials used for the manufacture of m-phenoxybenzaldehyde and for the components of the reaction mixtures obtained at various stages of the development of the process. A complete analysis can be performed in a single temperature programmed run.     

Time resolved spectroscopic NMR imaging using hyperpolarized Xe

We have visualized the melting and dissolution processes of xenon (Xe) ice into different solvents using the methods of nuclear magnetic resonance (NMR) spectroscopy, imaging, and time resolved spectroscopic imaging by means of hyperpolarized ¹²⁹Xe. Starting from the initial condition of a hyperpolarized solid Xe layer frozen on top of an ethanol (ethanol/water) ice block we measured the Xe phase transitions as a function of time and temperature. In the pure ethanol sample, pieces of Xe ice first fall through the viscous ethanol to the bottom of the sample tube and then form a thin layer of liquid Xe/ethanol. The xenon atoms are trapped in this liquid layer up to room temperature and keep their magnetization over a time period of 11 min. In the ethanol/water mixture (80 vol%/20%), most of the polarized Xe liquid first stays on top of the ethanol/water ice block and then starts to penetrate into the pores and cracks of the ethanol/water ice block. In the final stage, nearly all the Xe polarization is in the gas phase above the liquid and trapped inside the pores. NMR spectra of homogeneous samples of pure ethanol containing thermally polarized Xe and the spectroscopic images of the melting process show that very high concentrations of hyperpolarized Xe (about half of the density of liquid Xe) can be stored or delivered in pure ethanol.     

1,1‐Organoboration of bis(trimethylstannyl)ethyne with trimethylsilyl‐ and dimethylsilyl‐dialkylboryl‐substituted alkenes: organometallic‐substituted allenes

The reactions of bis(trimethylstannyl)ethyne, Me₃Sn–C?C–SnMe₃ ( 4 ), with trimethylsilyl‐ or dimethylsilyl‐dialkylboryl‐substituted alkenes 1 – 3 afford organometallic‐substituted allenes 5 , 6 and 8 , 9 in high yield. In the case of (E)‐2‐trimethylsilyl‐3‐diethylboryl‐2‐pentene ( 1) , a butadiene derivative 7 could be detected as an intermediate prior to rearrangement into the allene. All reactions were monitored by ²⁹Si and ¹¹⁹Sn NMR, and the products were characterized by an extensive NMR data set (¹H, ¹¹B, ¹³C, ²⁹Si, ¹¹⁹Sn NMR). Copyright © 2003 John Wiley & Sons, Ltd.     

A class of multivariate skew-normal models

The existing model for multivariate skew normal data does not cohere with the joint distribution of a random sample from a univariate skew normal distribution. This incoherence causes awkward interpretation for data analysis in practice, especially in the development of the sampling distribution theory. In this paper, we propose a refined model that is coherent with the joint distribution of the univariate skew normal random sample, for multivariate skew normal data. The proposed model extends and strengthens the multivariate skew model described in Azzalini (1985,Scandinavian Journal of Statistics,12, 171–178). We present a stochastic representation for the newly proposed model, and discuss a bivariate setting, which confirms that the newly proposed model is more plausible than the one given by Azzalini and Dalla Valle (1996,Biometrika,83, 715–726).     

Rate of Convergence of a Stochastic Particle System for the Smoluchowski Coagulation Equation

By continuing the probabilistic approach of Deaconu et al. (2001), we derive a stochastic particle approximation for the Smoluchowski coagulation equations. A convergence result for this model is obtained. Under quite stringent hypothesis we obtain a central limit theorem associated with our convergence. In spite of these restrictive technical assumptions, the rate of convergence result is interesting because it is the first obtained in this direction and seems to hold numerically under weaker hypothesis. This result answers a question closely connected to the Open Problem 16 formulated by Aldous (1999).     

Stationary Distributions of GI/M/c Queue with PH Type Vacations

We study a GI/M/c type queueing system with vacations in which all servers take vacations together when the system becomes empty. These servers keep taking synchronous vacations until they find waiting customers in the system at a vacation completion instant.The vacation time is a phase-type (PH) distributed random variable. Using embedded Markov chain modeling and the matrix geometric solution methods, we obtain explicit expressions for the stationary probability distributions of the queue length at arrivals and the waiting time. To compare the vacation model with the classical GI/M/c queue without vacations, we prove conditional stochastic decomposition properties for the queue length and the waiting time when all servers are busy. Our model is a generalization of several previous studies.     

The Resonance Phenomena Associated with the Time Asymmetry in Non-Hermitian Quantum Mechanics

Resonances are defined as the poles of the scattering matrix. The poles are associated with the complex eigenvalues of the Hamiltonian which are embedded in the lower half of the complex plane. The asymptotes of the corresponding eigenfunctions are exponentially diverged. Therefore, the resonance eigenfunctions are not embedded in the Hermitian domain of the Hamiltonian. The time asymmetric problem is discussed for these types of non-Hermitian Hamiltonians and several solutions of this problem are proposed.     

Performance of noise barriers with various edge shapes and acoustical conditions

The performances of barriers having different shapes and surface conditions were tested using the boundary element method in a well-controlled environment. The heights and widths of the barriers were standardized and the insertion losses for six receiver positions were averaged and compared. Figures displaying the results allow for straightforward barrier performance estimation. It was shown that absorbing and soft edges significantly improve the efficiency of the barrier, but configuration modifications provide only a slight improvement. The soft T-shaped barrier produces the highest performance. A 3 m high T-shaped barrier provides the same performance as a 10 m high plain barrier. The spectral efficiency was also investigated. The insertion loss spectra for the absorbing and the soft barriers exhibit a similar shape, but the rigid barrier differs from these two.