Numerical simulation of water and water emulsion droplets evaporation in flames with different temperatures

The models of heat and mass transfer and phase transition for “water droplet – flame” system have been developed using non-stationary nonlinear partial differential equations. The system of differential equations was solved by the finite-difference method. The locally one-dimensional method was used to solve the difference analogous of differential equations. One-dimensional differential equations were solved using an implicit four-point difference scheme. Nonlinear equations were solved by the iteration method. The evaporation rates of water droplets (with sizes from 0.05 mm to 5 mm) in the flame zone (at the temperatures from 500 K to 1200 K) were determined. Theoretical analysis established essentially nonlinear (close to exponential) form of dependence of the water droplet evaporation rate on the temperature of the external gas area and the temperature of a droplet surface. In particular, the water droplet evaporation rate varies from 0.25 to 0.29 kg/(m2s), when the temperature of external gas area is about 1100 K. On the other hand, the water droplet evaporation rate does not exceed 0.01 kg/(m2s) when the temperature of external gas area is about 350 K. Besides, it has been found out that droplets warm up at different rates depending on their initial temperature and velocity. As a result, the integral characteristics of droplet evaporation can increase substantially, when droplets move through the external gas area at the same temperature. We performed a similar investigation or droplet streams with droplet concentration 0.001–0.005 m3 in 1 m3 of gas area (typical parameters for modern spray extinguishing systems)

DFAs and PFAs with Long Shortest Synchronizing Word Length

It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching this bound was only given for $n \leq 4$, and with bounds on the number of symbols for $n \leq 10$. Here we give the full analysis for $n \leq 6$, without bounds on the number of symbols. For PFAs the bound is much higher. For $n \leq 6$ we do a similar analysis as for DFAs and find the maximal shortest synchronizing word lengths, exceeding $(n-1)^2$ for $n =4,5,6$. For arbitrary n we give a construction of a PFA on three symbols with exponential shortest synchronizing word length, giving significantly better bounds than earlier exponential constructions. We give a transformation of this PFA to a PFA on two symbols keeping exponential shortest synchronizing word length, yielding a better bound than applying a similar known transformation.Comment: 16 pages, 2 figures source code adde

Synchronizing heuristics for weakly connected automata with various topologies

Since the problem of finding a shortest synchronizing sequence for an automaton is known to be NP-hard, heuristics algorithms are used to find synchronizing sequences. There are several heuristic algorithms in the literature for this purpose. However, even the most efficient heuristic algorithm in the literature has a quadratic complexity in terms of the number of states of the automaton, and therefore can only scale up to a couple of thousands of states. It was also shown before that if an automaton is not strongly connected, then these heuristic algorithms can be used on each strongly connected component separately. This approach speeds up these heuristic algorithms and allows them to scale to much larger number of states easily. In this paper, we investigate the effect of the topology of the automaton on the performance increase obtained by these heuristic algorithms. To this end, we consider various topologies and provide an extensive experimental study on the performance increase obtained on the existing heuristic algorithms. Depending on the size and the number of components, we obtain speed-up values as high as 10000x and more

On the Number of Synchronizing Colorings of Digraphs

We deal with $k$-out-regular directed multigraphs with loops (called simply \emph{digraphs}). The edges of such a digraph can be colored by elements of some fixed $k$-element set in such a way that outgoing edges of every vertex have different colors. Such a coloring corresponds naturally to an automaton. The road coloring theorem states that every primitive digraph has a synchronizing coloring. In the present paper we study how many synchronizing colorings can exist for a digraph with $n$ vertices. We performed an extensive experimental investigation of digraphs with small number of vertices. This was done by using our dedicated algorithm exhaustively enumerating all small digraphs. We also present a series of digraphs whose fraction of synchronizing colorings is equal to $1-1/k^d$, for every $d \ge 1$ and the number of vertices large enough. On the basis of our results we state several conjectures and open problems. In particular, we conjecture that $1-1/k$ is the smallest possible fraction of synchronizing colorings, except for a single exceptional example on 6 vertices for $k=2$.Comment: CIAA 2015. The final publication is available at http://link.springer.com/chapter/10.1007/978-3-319-22360-5_1

Evolutional dynamics of 45S and 5S ribosomal DNA in ancient allohexaploid Atropa belladonna

Background: Polyploid hybrids represent a rich natural resource to study molecular evolution of plant genes and genomes. Here, we applied a combination of karyological and molecular methods to investigate chromosomal structure, molecular organization and evolution of ribosomal DNA (rDNA) in nightshade, Atropa belladonna (fam. Solanaceae), one of the oldest known allohexaploids among flowering plants. Because of their abundance and specific molecular organization (evolutionarily conserved coding regions linked to variable intergenic spacers, IGS), 45S and 5S rDNA are widely used in plant taxonomic and evolutionary studies. Results: Molecular cloning and nucleotide sequencing of A. belladonna 45S rDNA repeats revealed a general structure characteristic of other Solanaceae species, and a very high sequence similarity of two length variants, with the only difference in number of short IGS subrepeats. These results combined with the detection of three pairs of 45S rDNA loci on separate chromosomes, presumably inherited from both tetraploid and diploid ancestor species, example intensive sequence homogenization that led to substitution/elimination of rDNA repeats of one parent. Chromosome silver-staining revealed that only four out of six 45S rDNA sites are frequently transcriptionally active, demonstrating nucleolar dominance. For 5S rDNA, three size variants of repeats were detected, with the major class represented by repeats containing all functional IGS elements required for transcription, the intermediate size repeats containing partially deleted IGS sequences, and the short 5S repeats containing severe defects both in the IGS and coding sequences. While shorter variants demonstrate increased rate of based substitution, probably in their transition into pseudogenes, the functional 5S rDNA variants are nearly identical at the sequence level, pointing to their origin from a single parental species. Localization of the 5S rDNA genes on two chromosome pairs further supports uniparental inheritance from the tetraploid progenitor. Conclusions: The obtained molecular, cytogenetic and phylogenetic data demonstrate complex evolutionary dynamics of rDNA loci in allohexaploid species of Atropa belladonna. The high level of sequence unification revealed in 45S and 5S rDNA loci of this ancient hybrid species have been seemingly achieved by different molecular mechanisms

Droplet evaporation in water jet at the motion through high temperature gases

Abstract. Heat and mass transfer model for the numerical investigation of the evaporation process of a single droplet in water jet when moving through high temperature gases was developed. The integral characteristics of the process under investigation were calculated. The macroscopic regularities of water droplet evaporation, as elements of jet, in the high temperature gas mixture (as exemplified by combustion products of typical condensed substances) were determined

Water Droplet With Carbon Particles Moving Through High-Temperature Gases

An experimental investigation was carried out on the influence of solid inclusions (nonmetallic particles with sizes from a few tens to hundreds of micrometers) on water droplet evaporation during motion through high-temperature gases (more than 1000 K). Optical methods for diagnostics of two-phase (gas and vapor-liquid) flows (particle image velocimetry (PIV) and interferometric particle imaging (IPI)) were used. It was established that introducing foreign solid particles into the water droplets intensifies evaporation rate in high-temperature gas severalfold. Dependence of liquid evaporation on sizes and concentration of solid inclusion were obtained

A Fast Algorithm Finding the Shortest Reset Words

In this paper we present a new fast algorithm finding minimal reset words for finite synchronizing automata. The problem is know to be computationally hard, and our algorithm is exponential. Yet, it is faster than the algorithms used so far and it works well in practice. The main idea is to use a bidirectional BFS and radix (Patricia) tries to store and compare resulted subsets. We give both theoretical and practical arguments showing that the branching factor is reduced efficiently. As a practical test we perform an experimental study of the length of the shortest reset word for random automata with $n$ states and 2 input letters. We follow Skvorsov and Tipikin, who have performed such a study using a SAT solver and considering automata up to $n=100$ states. With our algorithm we are able to consider much larger sample of automata with up to $n=300$ states. In particular, we obtain a new more precise estimation of the expected length of the shortest reset word $\approx 2.5\sqrt{n-5}$.Comment: COCOON 2013. The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-642-38768-5_1