Method for Particle Size Control During the Drying and Granulation in Fluidized Bed

The fluidized bed process presented in this paper is suitable for recovery of solids from solutions in the form of granules. The solution is sprayed into the bed and as solvent evaporates, solid material is deposited on the surface of fluidizing particles. During this process, particle growth takes place by surface layering and/or agglomeration. A special grinder is used in the fluidized bed to control particle growth by causing selective disintegration of large particles. For steady state operation, the most important task is to determine the existing particle size distribution in the fluidized bed. A special method was developed to measure torque and stress fluctuations* in the bed of particles. Using a correlation between torque and stress fluctuations and particle size, this method and device can be used for direct control of the rotation speed of the grinder to produce granules of given size in the fluidized bed. Results of torque and stress measurements and their correlation to particle size are presented

Particle Size Control by Torque Measurements in Fluidized Beds during Drying and Granulation from Solutions

The fluidized bed process presented in this paper is suitable to recover solids from solution in form of granules. Solution is sprayed into the bed and, as the solvent evaporates, solid material is deposited on the surface of fluidizing particles. During this process, particle growth takes place by surface layering and/or agglomeration. A special grinder is used in the fluidized bed to control particle growth by causing selective disintegration of large particles. For steady state operation, the most important task is to determine the existing particle size distribution in the fluidized bed. A special method was developed to measure torque and stress fluctuations in the bed of particles. Using a correlation between torque and particle size, this method and device can be used for direct control of the rotation speed of the grinder to produce granules of given size in the fluidized bed. In this paper, the results of torque measurements and their correlation with particle size are presented

Torque Measurements and DEM Simulations in a Couette-type Device with Application to Particle Size Measurements

A continuously operating modified Cuette-type shearing device has been developed for in-situ measurements to estimate the average particle size during size enlargement processes in fluidized bed granulator. It was proven by experiments that well-defined correlation exists between the mean torque and the average particle size being in the device. DEM simulations revealed interesting aspects of this method

Polychromatic Coloring for Half-Planes

We prove that for every integer $k$, every finite set of points in the plane can be $k$-colored so that every half-plane that contains at least $2k-1$ points, also contains at least one point from every color class. We also show that the bound $2k-1$ is best possible. This improves the best previously known lower and upper bounds of $\frac{4}{3}k$ and $4k-1$ respectively. We also show that every finite set of half-planes can be $k$ colored so that if a point $p$ belongs to a subset $H_p$ of at least $3k-2$ of the half-planes then $H_p$ contains a half-plane from every color class. This improves the best previously known upper bound of $8k-3$. Another corollary of our first result is a new proof of the existence of small size \eps-nets for points in the plane with respect to half-planes.Comment: 11 pages, 5 figure

Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds

"Concentrated differential privacy" was recently introduced by Dwork and Rothblum as a relaxation of differential privacy, which permits sharper analyses of many privacy-preserving computations. We present an alternative formulation of the concept of concentrated differential privacy in terms of the Renyi divergence between the distributions obtained by running an algorithm on neighboring inputs. With this reformulation in hand, we prove sharper quantitative results, establish lower bounds, and raise a few new questions. We also unify this approach with approximate differential privacy by giving an appropriate definition of "approximate concentrated differential privacy.

Deterministic Random Walks on the Integers

Jim Propp's P-machine, also known as the "rotor router model" is a simple deterministic process that simulates a random walk on a graph. Instead of distributing chips to randomly chosen neighbors, it serves the neighbors in a fixed order. We investigate how well this process simulates a random walk. For the graph being the infinite path, we show that, independent of the starting configuration, at each time and on each vertex, the number of chips on this vertex deviates from the expected number of chips in the random walk model by at most a constant c_1, which is approximately 2.29. For intervals of length L, this improves to a difference of O(log L), for the L_2 average of a contiguous set of intervals even to O(sqrt{log L}). All these bounds are tight

Particle Size Control by Torque and Stress Measurement in Fluidized Bed Drying and Granulation from Solutions

The fluidized bed process presented in this paper is suitable for recovery of solids from solutions in the form of granules. The solution is sprayed into the bed and as solvent evaporates, solid material is deposited on the surface of fluidizing particles. During this process, particle growth takes place by surface layering and/or agglomeration. A special grinder is used in the fluidized bed to control particle growth by causing selective disintegration of large particles. For steady state operation, the most important task is to determine the existing particle size distribution in the fluidized bed. A special method was developed to measure torque and stress fluctuations* in the bed of particles. Using a correlation between torque and stress fluctuations and particle size, this method and device can be used for direct control of the rotation speed of the grinder to produce granules of given size in the fluidized bed. Results of torque and stress measurements and their correlation to particle size are presented

Conflict-free colorings of graphs and hypergraphs Probability and Computing

A colouring of the vertices of a hypergraph H is called conflict-free if each hyperedge E of H contains a vertex of 'unique' colour that does not get repeated in E. The smallest number of colours required for such a colouring is called the conflict-free chromatic number of H, and is denoted by chi(CF)(H). This parameter wits first introduced by Even, Lotker, Ron and Smorodinsky (FOCS 2002) in a geometric setting, in connection with frequency assignment problems for cellular networks. Here we analyse this notion for general hypergraphs. It is shown that chi(CF)(H) = 3. Using Lovasz's Local Lemma, the same result holds for hypergraphs in which the size of every edge is at least 2t - 1 and every edge intersects at most tit others. We give efficient polynomial-time algorithms to obtain such colourings

Partitioning multi-dimensional sets in a small number of ``uniform'' parts

In this paper we prove that every finite subset of ZxZ can be partitioned into a small number of subsets so that, in each part all vertical sections have aproximately the same size and all horyzontal sections have aproximately the same size. The generalization of this statement is used to give a combinatorial interpretation to every information inequality