Stanley Katz

Bio: Stanley Katz is an academic researcher from City University of New York. The author has contributed to research in topics: Radical polymerization & Stochastic modelling. The author has an hindex of 14, co-authored 30 publications receiving 609 citations. Previous affiliations of Stanley Katz include City College of New York.

The Extent of Correlations in a Stochastic Coalescence Process

Abstract: A stochastic model of coalescence is set up and solved for the probabilities of all possible histories of particle growth. The full stochastic model is compared with the so-called kinetic model to which it reduces in the absence of correlations. A primary objective is the assessment of the extent of correlations in poorly mixed systems or in systems of small populations. The study shows that insofar as the total number of particles is concerned, regardless of their size distribution, the results from the kinetic equations match the true stochastic averages even for very small initial populations. But, when size distributors are considered, then, in systems of small population or in large systems that are poorly mixed, the results of the kinetic equations may differ substantially from the stochastic means in the long-term tail; apart from the tail, the distributions from the full stochastic and kinetic models match quite well.

Scale‐up criteria for stirred tank reactors

Abstract: A method is derived for the design of stirred tank reactors for homogeneous reactions. A simple mixing model proposed previously by Curl (4) is used to compute the effects of finite mixing time on complex chemical reactions. It is also shown how the parameters of the model can be obtained by tracer experiments, or estimated theoretically by the assumption of isotropic turbulence. It is shown that in many practical cases the assumption of ideal mixing is a good approximation. However, the effects of imperfect mixing are more likely to be felt in a large reactor than in a pilot plant. Some quantitative examples are discussed. Methods are derived to compute the average outlet concentration for complex systems such as autothermic reactions, polymerization, crystallization, etc.

Dynamic behavior of the well-mixed isothermal crystallizer.

Abstract: Industrial crystallization operations are still something of an art, and often depend to a considerable degree on the skill of the operator. This paper attempts to aid in the understanding of the dynamic behavior and stability of such systems.

Dynamic behavior of the well‐mixed isothermal crystallizer

Abstract: Under some conditions, continuous crystallization exhibits cyclic changes of the particle size even with constant input conditions. A linearized stability analysis has been performed to determine under what conditions this behavior can be expected. Numerical solutions of the actual nonlinear system equations were carried out to follow the cyclic behavior and to compute the cycle time and the amplitude of the fluctuations. The effect of seeding on the stability limits and product distribution was also evaluated.

Combinatorial Stochastic Processes

Abstract: Preliminaries.- Bell polynomials, composite structures and Gibbs partitions.- Exchangeable random partitions.- Sequential constructions of random partitions.- Poisson constructions of random partitions.- Coagulation and fragmentation processes.- Random walks and random forests.- The Brownian forest.- Brownian local times, branching and Bessel processes.- Brownian bridge asymptotics for random mappings.- Random forests and the additive coalescent.

Deterministic and stochastic models for coalescence (aggregation and coagulation): a review of the mean-field theory for probabilists

Abstract: Author(s): Aldous, DJ | Abstract: Consider N particles, which merge into clusters according to the following rule: a cluster of size x and a cluster of size y merge at (stochastic) rate K(x, y)/N, were AT is a specified rate kernel. This Marcus-Lushnikov model of stochastic coalescence and the underlying deterministic approximation given by the Smoluchowski coagulation equations have an extensive scientific literature. Some mathematical literature (Kingman's coalescent in population genetics; component sizes in random graphs) implicitly studies the special cases K(x, y) = 1 and K(x, y) = xy. We attempt a wide-ranging survey. General kernels are only now starting to be studied rigorously; so many interesting open problems appear. © 1999 ISI/BS.

Particle-turbulence interactions in atmospheric clouds

Abstract: ▪ Abstract Turbulence is ubiquitous in atmospheric clouds, which have enormous turbulence Reynolds numbers owing to the large range of spatial scales present. Indeed, the ratio of energy-containing and dissipative length scales is on the order of 105 for a typical convective cloud, with a corresponding large-eddy Reynolds number on the order of 106 to 107. A characteristic trait of high-Reynolds-number turbulence is strong intermittency in energy dissipation, Lagrangian acceleration, and scalar gradients at small scales. Microscale properties of clouds are determined to a great extent by thermodynamic and fluid-mechanical interactions between droplets and the surrounding air, all of which take place at small spatial scales. Furthermore, these microscale properties of clouds affect the efficiency with which clouds produce rain as well as the nature of their interaction with atmospheric radiation and chemical species. It is expected, therefore, that fine-scale turbulence is of direct importance to the evolu...

Perspectives on shear banding in complex fluids

Abstract: In this review, I present an idiosyncratic view of the current state of shear banding in complex fluids. Particular attention is paid to some of the outstanding issues and questions facing the field, including the applicability of models that have “traditionally” been used to model experiments; future directions and challenges for experimentalists; and some of the issues surrounding vorticity banding, which has been discussed theoretically and whose experiments are fewer in number yet, in many ways, more varied in character.

Model identification and control of solution crystallization processes: a review

Abstract: The modeling of crystal quality (size, shape, and purity) is discussed. Numerical methods for the model solution are reviewed including collocation and Galerkin's method on finite elements. Measurement technologies for on-line crystal size distribution are presented. The difficulties with laser light scattering methods are discussed in detail. Parameter estimation is reviewed and new methods based on nonlinear optimization are presented. Sample calculations of parameters and their uncertainty from experimental data are included. The research literature covering control of continuous and batch crystallization is reviewed, and sample calculations of optimal cooling profiles for batch crystallizers are presented