Mixing properties of colourings of the ℤ d lattice

2020 ◽  
pp. 1-14 ◽  
Author(s):  
Noga Alon ◽  
Raimundo Briceño ◽  
Nishant Chandgotia ◽  
Alexander Magazinov ◽  
Yinon Spinka
Keyword(s):  
Finite Subset ◽  
Side Length ◽  
Mixing Properties

Abstract We study and classify proper q-colourings of the ℤ d lattice, identifying three regimes where different combinatorial behaviour holds. (1) When $q\le d+1$ , there exist frozen colourings, that is, proper q-colourings of ℤ d which cannot be modified on any finite subset. (2) We prove a strong list-colouring property which implies that, when $q\ge d+2$ , any proper q-colouring of the boundary of a box of side length $n \ge d+2$ can be extended to a proper q-colouring of the entire box. (3) When $q\geq 2d+1$ , the latter holds for any $n \ge 1$ . Consequently, we classify the space of proper q-colourings of the ℤ d lattice by their mixing properties.

scholarly journals A criterion for the positivity of the Liapunov characteristic exponent

1984 ◽  
Vol 4 (4) ◽  
pp. 527-539 ◽  
Author(s):  
Eric Cornelis ◽  
Maciej Wojtkowski
Keyword(s):  
Finite Subset ◽  
Sufficient Conditions ◽  
Characteristic Exponent ◽  
Two Dimensional ◽  
Dimensional Torus ◽  
Liapunov Exponent ◽  
Mixing Properties ◽  
Analytical Formulation

AbstractWe formulate sufficient conditions under which, for a finite subset of SL (2, ℝ), the maximal Liapunov exponent is positive. These conditions are based on the notion of compatible hyperbolicity. We then give an analytical formulation of such a condition and we apply this criterion to prove mixing properties of a particular transformation of the two-dimensional torus.

scholarly journals Wheat Grinding Process with Low Moisture Content: A New Approach for Wholemeal Flour Production

Processes ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 32
Author(s):  
Waleed H. Hassoon ◽  
Dariusz Dziki ◽  
Antoni Miś ◽  
Beata Biernacka
Keyword(s):  
Particle Size ◽  
Moisture Content ◽  
Average Particle Size ◽  
Average Particle ◽  
Grinding Process ◽  
Mixing Properties ◽  
New Approach ◽  
Grain Moisture ◽  
Flour Production ◽  
And Storage

The objective of this study was to determine the grinding characteristics of wheat with a low moisture content. Two kinds of wheat—soft spelt wheat and hard Khorasan wheat—were dried at 45 °C to reduce the moisture content from 12% to 5% (wet basis). Air drying at 45 °C and storage in a climatic chamber (45 °C, 10% relative humidity) were the methods used for grain dehydration. The grinding process was carried out using a knife mill. After grinding, the particle size distribution, average particle size and grinding energy indices were determined. In addition, the dough mixing properties of wholemeal flour dough were studied using a farinograph. It was observed that decreasing the moisture content in wheat grains from 12% to 5% made the grinding process more effective. As a result, the average particle size of the ground material was decreased. This effect was found in both soft and hard wheat. Importantly, lowering the grain moisture led to about a twofold decrease in the required grinding energy. Moreover, the flour obtained from the dried grains showed higher water absorption and higher dough stability during mixing. However, the method of grain dehydration had little or no effect on the results of the grinding process or dough properties.

scholarly journals Local stationarity in exponential last-passage percolation

2021 ◽  
Author(s):  
Márton Balázs ◽  
Ofer Busani ◽  
Timo Seppäläinen
Keyword(s):  
Brownian Motion ◽  
Total Variation ◽  
High Probability ◽  
Probabilistic Methods ◽  
Side Length ◽  
Last Passage Percolation ◽  
Last Passage Times ◽  
Starting Point ◽  
Point To Point ◽  
Passage Times

AbstractWe consider point-to-point last-passage times to every vertex in a neighbourhood of size $$\delta N^{\nicefrac {2}{3}}$$ δ N 2 3 at distance N from the starting point. The increments of the last-passage times in this neighbourhood are shown to be jointly equal to their stationary versions with high probability that depends only on $$\delta $$ δ . Through this result we show that (1) the $$\text {Airy}_2$$ Airy 2 process is locally close to a Brownian motion in total variation; (2) the tree of point-to-point geodesics from every vertex in a box of side length $$\delta N^{\nicefrac {2}{3}}$$ δ N 2 3 going to a point at distance N agrees inside the box with the tree of semi-infinite geodesics going in the same direction; (3) two point-to-point geodesics started at distance $$N^{\nicefrac {2}{3}}$$ N 2 3 from each other, to a point at distance N, will not coalesce close to either endpoint on the scale N. Our main results rely on probabilistic methods only.

scholarly journals Simulation of Thermal Effects on the Flow Field in a Pilot-Scale Kiln

2021 ◽  
Author(s):  
I. A. Sofia Larsson ◽  
Anna-Lena Ljung ◽  
B. Daniel Marjavaara
Keyword(s):  
Flow Field ◽  
Coal Combustion ◽  
Thermal Effects ◽  
Iron Ore ◽  
Combustion Process ◽  
Pilot Scale ◽  
Mixing Properties ◽  
Process Gas ◽  
Mixing Rates ◽  
Computational Fluid Dynamics Cfd

AbstractThe flow field and coal combustion process in a pilot-scale iron ore pelletizing kiln is simulated using a computational fluid dynamics (CFD) model. The objective of the work is to investigate how the thermal effects from the flame affect the flow field. As expected, the combustion process with the resulting temperature rise and volume expansion leads to an increase of the velocity in the kiln. Apart from that, the overall flow field looks similar regardless of whether combustion is present or not. The flow field though affects the combustion process by controlling the mixing rates of fuel and air, governing the flame propagation. This shows the importance of correctly predicting the flow field in this type of kiln, with a large amount of process gas circulating, in order to optimize the combustion process. The results also justify the use of down-scaled, geometrically similar, water models to investigate kiln aerodynamics in general and mixing properties in particular. Even if the heat release from the flame is neglected, valuable conclusions regarding the flow field can still be drawn.

ON THE DENSITY OF HAUSDORFF DIMENSIONS OF BOUNDED TYPE CONTINUED FRACTION SETS: THE TEXAN CONJECTURE

2004 ◽  
Vol 04 (01) ◽  
pp. 63-76 ◽  
Author(s):  
OLIVER JENKINSON
Keyword(s):  
Hausdorff Dimension ◽  
Finite Subset ◽  
Continued Fraction ◽  
Cantor Set ◽  
Computational Method ◽  
Accurate Approximation ◽  
Natural Numbers ◽  
Important Special Case ◽  
The One ◽  
Special Case

Given a non-empty finite subset A of the natural numbers, let EA denote the set of irrationals x∈[0,1] whose continued fraction digits lie in A. In general, EA is a Cantor set whose Hausdorff dimension dim (EA) is between 0 and 1. It is shown that the set [Formula: see text] intersects [0,1/2] densely. We then describe a method for accurately computing dimensions dim (EA), and employ it to investigate numerically the way in which [Formula: see text] intersects [1/2,1]. These computations tend to support the conjecture, first formulated independently by Hensley, and by Mauldin & Urbański, that [Formula: see text] is dense in [0,1]. In the important special case A={1,2}, we use our computational method to give an accurate approximation of dim (E{1,2}), improving on the one given in [18].

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