Stability of a spherical flame ball in a porous medium

Gaseous flame balls and their stability to symmetric disturbances are studied numerically and asymptotically, for large activation temperature, within a porous medium that serves only to exchange heat with the gas. Heat losses to a distant ambient environment, affecting only the gas, are taken to be radiative in nature and are represented using two alternative models. One of these treats the heat loss as being constant in the burnt gases and linearizes the radiative law in the unburnt gas (as has been studied elsewhere without the presence of a solid). The other does not distinguish between burnt and unburnt gas and is a continuous dimensionless form of Stefan's law, having a linear part that dominates close to ambient temperatures and a fourth power that dominates at higher temperatures.Numerical results are found to require unusually large activation temperatures in order to approach the asymptotic results. The latter involve two branches of solution, a smaller and a larger flame ball, provided heat losses are not too high. The two radiative heat loss models give completely analogous steady asymptotic solutions, to leading order, that are also unaffected by the presence of the solid which therefore only influences their stability. For moderate values of the dimensionless heat-transfer time between the solid and gas all flame balls are unstable for Lewis numbers greater than unity. At Lewis numbers less than unity, part of the branch of larger flame balls becomes stable, solutions with the continuous radiative law being stable over a narrower range of parameters. In both cases, for moderate heat-transfer times, the stable region is increased by the heat capacity of the solid in a way that amounts, simply, to decreasing an effective Lewis number for determining stability, just as if the heat-transfer time was zero

Stochasticity from function -- why the Bayesian brain may need no noise

An increasing body of evidence suggests that the trial-to-trial variability of spiking activity in the brain is not mere noise, but rather the reflection of a sampling-based encoding scheme for probabilistic computing. Since the precise statistical properties of neural activity are important in this context, many models assume an ad-hoc source of well-behaved, explicit noise, either on the input or on the output side of single neuron dynamics, most often assuming an independent Poisson process in either case. However, these assumptions are somewhat problematic: neighboring neurons tend to share receptive fields, rendering both their input and their output correlated; at the same time, neurons are known to behave largely deterministically, as a function of their membrane potential and conductance. We suggest that spiking neural networks may, in fact, have no need for noise to perform sampling-based Bayesian inference. We study analytically the effect of auto- and cross-correlations in functionally Bayesian spiking networks and demonstrate how their effect translates to synaptic interaction strengths, rendering them controllable through synaptic plasticity. This allows even small ensembles of interconnected deterministic spiking networks to simultaneously and co-dependently shape their output activity through learning, enabling them to perform complex Bayesian computation without any need for noise, which we demonstrate in silico, both in classical simulation and in neuromorphic emulation. These results close a gap between the abstract models and the biology of functionally Bayesian spiking networks, effectively reducing the architectural constraints imposed on physical neural substrates required to perform probabilistic computing, be they biological or artificial

Multi-stage Inspection of Laser Welding Defects using Machine Learning

As welding processes become faster and components consist of many more welds compared to previous applications, there is a need for fast but still precise quality inspection. The aim of this paper is to compare already existing approaches, namely single-sensor systems (SSS) and multi-sensor systems (MSS) with a proposed cascaded system (CS). The introduced CS is characterized by the fact that not all available data are analyzed, but only cleverly selected ones. The different approaches consisting of neural networks are compared in terms of their accuracy and computational effort. The data are recorded from scratch and include two common sensor systems for quality control, namely a photodiode (PD) and a high-speed camera (HSC). As a result, when the CS makes half of the final decisions based on a SSS with PD signals and the other half based on a SSS with HSC images, the estimated computational effort is reduced by almost 50% compared to the SSS with HSC images as input. At the same time, the accuracy decreases only by 0.25% to 95.96%. Additionally, based on the CS, a general cascaded system (GCS) for quality inspection is proposed

Seeing the wood for the trees: the role of woody resources for the construction of gender specific household cultural artefacts in non-traditional communities in the Eastern Cape, South Africa

There is a growing wealth of data capturing the direct-use values of the environment and recognition of forests and wild resources as representing ‘‘the poor man’s overcoat’’. This focus has however resulted in an emphasis on the utilitarian values of wild resources for rural livelihoods and has for the most part overlooked their cultural values. In tangent to these developments within the field of anthropology there has been increased attention directed towards the relationship between biodiversity and human diversity over the past decade. This has resulted in the recognition of what the Declaration of Belem calls an ‘inextricable link’ between biological and cultural diversity. The term bio-cultural diversity has been introduced as a concept denoting this link. Consequently there is a need for more elaborate assessments of the various ways in which different groups of people find value in biodiversity. The aim of this paper is to demonstrate the cultural significance of wild harvested plant resources for the maintenance of two gender specific cultural artefacts for amaXhosa people in South Africa, to assess the persistence of these practices in rapidly modernizing communities. We demonstrate the endurance of these ancient cultural artefacts in present-day peri-urban communities and suggest that they point to the need for improved understanding of the significance of bio-cultural diversity. The findings of the study should not be interpreted as illustrating stagnation in the traditional past, but rather as pointing at the need for improved understanding of the significance of bio-cultural diversity in a dynamic sense

Equivariant pretheories and invariants of torsors

In the present paper we introduce and study the notion of an equivariant pretheory: basic examples include equivariant Chow groups, equivariant K-theory and equivariant algebraic cobordism. To extend this set of examples we define an equivariant (co)homology theory with coefficients in a Rost cycle module and provide a version of Merkurjev's (equivariant K-theory) spectral sequence for such a theory. As an application we generalize the theorem of Karpenko-Merkurjev on G-torsors and rational cycles; to every G-torsor E and a G-equivariant pretheory we associate a graded ring which serves as an invariant of E. In the case of Chow groups this ring encodes the information concerning the motivic J-invariant of E and in the case of Grothendieck's K_0 -- indexes of the respective Tits algebras.Comment: 23 pages; this is an essentially extended version of the previous preprint: the construction of an equivariant cycle (co)homology and the spectral sequence (generalizing the long exact localization sequence) are adde

Rapid Mixing for Lattice Colorings with Fewer Colors

We provide an optimally mixing Markov chain for 6-colorings of the square lattice on rectangular regions with free, fixed, or toroidal boundary conditions. This implies that the uniform distribution on the set of such colorings has strong spatial mixing, so that the 6-state Potts antiferromagnet has a finite correlation length and a unique Gibbs measure at zero temperature. Four and five are now the only remaining values of q for which it is not known whether there exists a rapidly mixing Markov chain for q-colorings of the square lattice.Comment: Appeared in Proc. LATIN 2004, to appear in JSTA

Structural and chemical investigations of adapted Siemens feed rods for an optimized float zone process

The optimization of the float zone process for industrial application is a promising way to crystallize high purity silicon for high efficiency solar cells with reduced process costs. We investigated two differently produced Siemens rods which should be used as feed material for the float zone process. The aim is to identify and to improve material properties of the feed rods which have a high impact to the float zone process. We show here microstructural and chemical analysis comparing feed rods manufactured under standard conditions and under float zone adapted conditions. To resolve the growth behavior of the grains SEM/EBSD mappings are performed at different positions. TEM analyses are used to investigate the interface region between the mono- and the multicrystalline silicon within the Siemens feed rod. Additionally, drilled cores are cut out from the feed rods containing the region of the slim rod. Afterwards, the drilled cores are crystallized with the float zone process. Finally, carbon and oxygen measurements with FT-IR spectrometry on different positions of the crystallized drilled cores of the Siemens feed rods show the influence of the slim rod material to the float zone process

Influence of slim rod material properties to the Siemens feed rod and the float zone process

The identification and understanding of material properties influencing the float zone process is important to crystallize high purity silicon for high efficiency solar cells. Also the knowledge of minimal requirements to crystallize monocrystalline silicon with the float zone process is of interest from an economic point of view. In the present study, feed rods for the float zone process composed of a central slim rod and the deposited silicon from the Siemens process are investigated. Previous studies have shown that the slim rod has a significant impact on the purity and suitability for further crystallization processes. In particular, contaminations like substitutional carbon and the presence of precipitates as well as the formation of oxide layers play an important role and are investigated in detail. For this purpose different slim rod materials were used in deposition and float zone crystallization experiments. Samples were prepared by cross sectioning and core drilling of Siemens rods, which were recrystallized with the float zone process. Recrystallized drilled cores are analyzed with FT-IR spectrometry concerning the carbon and oxygen content. To estimate the grain growth behavior on the slim rod surface in dependence of the used slim rod material, EBSD mappings inside a SEM are performed on squared and circular slim rods. TEM analysis was used to investigate the presence of an oxide layer at the interface between slim rod and deposited polycrystalline silicon. Additionally the influence of a nitrogen-containing gas atmosphere during the slim rod pulling is investigated by IR microscopy and ToF-SIMS regarding Si3N4 precipitation

Cohomogeneity one manifolds and selfmaps of nontrivial degree

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we extend identity and transposition to an infinite family of selfmaps of every odd degree. The compositions of these selfmaps with the power maps realize all possible degrees of selfmaps of SU(3).Comment: v2, v3: minor improvement