When can statistical theories be causally closed?

The notion of common cause closedness of a classical, Kolmogorovian probability space with respect to a causal independence relation between the random events is defined, and propositions are presented that characterize common cause closedness for specific probability spaces. It is proved in particular that no probability space with a finite number of random events can contain common causes of all the correlations it predicts; however, it is demonstrated that probability spaces even with a finite number of random events can be common cause closed with respect to a causal independence relation that is stronger than logical independence. Furthermore it is shown that infinite, atomless probability spaces are always common cause closed in the strongest possible sense. Open problems concerning common cause closedness are formulated and the results are interpreted from the perspective of Reichenbach's Common Cause Principle (RCCP)

Drying of Heat Sensitive Materials of High Moisture Content in Mechanically Spouted Bed of Inert Particles

In drying operation the material characteristics such as heat sensitivity, moisture content and particle size are of great importance, which should be taken into account in selection of proper design and conditions for the process. Rigorous quality requirements, i.e. gentle drying of heat sensitive materials, stable, well-controlled and economic operation can be fulfilled by using Mechanically Spouted Bed (MSB) dryer with inert particles developed to eliminate some drawbacks of the conventional spouted bed dryers. In this paper the construction and the main features of MSB-dryer are presented. Different tasks with special quality demands, namely drying of bovine serum albumin and moisture removal from tomato pulp of thermoplastic behaviour, and a method to accomplish these requirements are shown

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

Application of Motionless Mixer in Gas Purification – A case study

The lecture gives a review on the application of motionless mixers in gas purification, where wet dust separation is carried out by water circulation trough vertical tubes filled with FixMix(TM) motionless mixer elements. Dusty gas and water are flowing downwards, co-currently. Solids phase is filtered continuously from the slurry

Finite Jeffrey logic is not finitely axiomatizable

Bayes logics based on Bayes conditionalization as a probability updating mechanism have recently been introduced in [http://philsci-archive.pitt.edu/14136/]. It has been shown that the modal logic of Bayesian belief revision determined by probabilities on a finite set of elementary propositions or on a standard Borel space is not finitely axiomatizable [http://philsci-archive.pitt.edu/14136/]. Apart from Bayes conditionalization there are other methods, extensions of the standard one, of updating a probability measure. One such important method is Jeffrey's conditionalization. In this paper we consider the modal logic \JL_{<\omega} of probability updating based on Jeffrey's conditionalization where the underlying measurable space is finite. By relating this logic to the logic of absolute continuity and to Medvedev's logic of finite problems, we show that \JL_{<\omega} is not finitely axiomatizable. The result is significant because it indicates that axiomatic approaches to belief revision might be severely limited

Chromatic number of the product of graphs, graph homomorphisms, Antichains and cofinal subsets of posets without AC

We have observations concerning the set theoretic strength of the following combinatorial statements without the axiom of choice. 1. If in a partially ordered set, all chains are finite and all antichains are countable, then the set is countable. 2. If in a partially ordered set, all chains are finite and all antichains have size $\aleph_{\alpha}$, then the set has size $\aleph_{\alpha}$ for any regular $\aleph_{\alpha}$. 3. CS (Every partially ordered set without a maximal element has two disjoint cofinal subsets). 4. CWF (Every partially ordered set has a cofinal well-founded subset). 5. DT (Dilworth's decomposition theorem for infinite p.o.sets of finite width). 6. If the chromatic number of a graph $G_{1}$ is finite (say $k<\omega$), and the chromatic number of another graph $G_{2}$ is infinite, then the chromatic number of $G_{1}\times G_{2}$ is $k$. 7. For an infinite graph $G=(V_{G}, E_{G})$ and a finite graph $H=(V_{H}, E_{H})$, if every finite subgraph of $G$ has a homomorphism into $H$, then so has $G$. Further we study a few statements restricted to linearly-ordered structures without the axiom of choice.Comment: Revised versio

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

Maxwell and the normal distribution: A colored story of probability, independence, and tendency toward equilibrium

In the first part of the paper we investigate Maxwell’s attempt to justify the mathematical assumptions behind his 1860 Proposition IV according to which the velocity components of colliding particles follow the normal distribution. Contrary to the com- monly held view we find that his molecular collision model plays a crucial role in reaching this conclusion, and that his model assumptions also permit inference to a non-reversible equalization of mean kinetic energies, which is what he intended to prove in his widely discredited Proposition VI. If we take a charitable reading of his own proof or Proposition VI then it was Maxwell, and not Boltzmann, who gave the first proof of a tendency towards equilibrium. In the second half of the paper we add a further, not yet investigated, piece to the historical and intellectual puzzle surrounding his derivation. We argue that Maxwell’s prior and contemporaneous work on color vision provided him familiarity with and sensitivity to application of statistical reasoning in physics. This includes an encounter with distributions outside the context of error theory. We also call attention to a notion of independence of variables employed in his works on color vision that might have impacted the mistake he made in his proof of Proposition IV

Computer Tomograph Measurements in Shear and Gravity Particle Flows

The paper reports the recent results obtained on the applicability of cross-sectional digital imaging method to study particle flow characteristics in 3D particle beds forced to move by gravity or shear. X-ray CT imaging technique is widely used in medical diagnostics and, during the last decades, its spatial and temporal resolution has been improved significantly. In this study, an attempt was made to use this technique for engineering purposes. Two experimental set-ups with different types of particle flows were investigated using Siemens Somatom Plus type CT equipment. A series of trials were carried out in a small model hopper with flat bottom and almost cylindrical side wall slightly deviating from verticality. Non steady-state flow was studied during the outflow of particulate material from this vessel, through a central hole at the bottom. Further investigation was fulfilled in a modified Cuette-type shearing device to study steady-state shear flow. This equipment consisted of an almost cylindrical vessel identical to that used for gravity flow measurements, and a smaller inner cylinder rotating within this vessel concentrically, around its vertical axis. The surface of the inner cylinder was notched vertically, i.e. perpendicularly to the direction of rotation to increase wall friction between the particles and the cylinder. Almost spherical sucrose granules, also used for gravity flow measurements, were filled into the gap between the rotating cylinder and the outer wall of the equipment. Movement of particles took place due to shear, generated within the particle bed. By using X-ray CT technique, cross-sectional digital images were obtained in every two seconds for both types of particle flows. For this, the cross-sectional variation of the local Hounsfield density values were measured in a matrix of 0.1x0.1x2.0 mm space elements. It was proved that the applied non-invasive crosssectional imaging technique was suitable to distinguish the stationary and moving particle regions, and by this, to estimate the location of the boundary zone between them

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