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Gas bubbles in crucibles for Czochralski (Cz) silicon growth are both necessary and detrimental: In the outer, bubble-containing (BC) layer of the crucible, they are required for mechanical stability, while in the inner, bubble-free (BF) layer, bubbles can cause the release of particles from the crucible into the melt which may disrupt the single-crystalline growth. In this work, a vacuum bake-out test (VBT) procedure was set up for unused crucible parts and a microscopic characterization routine was developed to systematically investigate bubble formation and growth. Longer process time, higher temperature, and lower atmospheric pressure lead to an increased bubble growth in both, the BC and BF layer. During the VBT, no new bubbles form in the BF layer, while existing bubbles grow. The comparison to experimental data from crucibles used in an industrial Cz process indicates that VBTs can simulate this process. This allows the prediction of the gas-bubble formation in Cz crucibles using a cost-effective and less time-consuming analyzation method.

The grain structure of high-performance (HP) multicrystalline silicon (mc-Si) is characterized by a small initial grain size with randomly oriented grains and a high length fraction of random grain boundaries. However, the remaining unmelted feedstock at the ingot bottom used as seeding layer for achieving the HP mc-Si properties in the standard crystallization procedure causes yield loss. To overcome this disadvantage, the influence of wetting angle, and surface roughness of non-Si nucleation layers at the crucible bottom on the grain structure properties of mc-Si ingots with a weight of 14.5 kg was investigated and compared to classical HP mc-Si. For that purpose, SiC and SiO 2 nucleation layers realized by spraying and embedding of particles with different sizes resulting in different surface morphologies and wetting angles were studied. Nucleation on rough layers of both materials with a root mean square roughness value greater than 100 µm yielded an initially fine grain structure comparable to HP mc-Si. This did not necessarily result in a random orientation distribution and high length fraction of random grain boundaries. Nucleation on SiC layers caused random grain boundary length fractions between 20 and 30% and non-uniform grain distributions. But, nucleation on SiO 2 layers yielded increased random grain boundary length fractions between 50 and 70% and homogenous grain distributions, both values are similar to HP mc-Si. These differences are discussed in terms of the thermal conductivity of the different nucleation layers.

Northern red oak (Quercus rubraL.) is one of the most important introduced tree species in the Czech Republic, occupying about 6,000 ha with ca. 900,000 m3of the standing volume. The presented study aims to evaluate its soil forming effects on natural oak sites. Soil chemistry of the upper soil layers (F+H, Ah, B horizons) was studied in three pairs of stands of both species. In each stand, four bulk samples were taken separately for particular horizons, each consisting of 5 soil-borer cores. The soil characteristics analysed were: pH (active and potential), soil adsorption complex characteristics (content of bases, exchangeable cation capacity, base saturation), exchangeable acidity (exchangeable Al and H), total carbon and nitrogen content, and plant available nutrients content (P, K, Ca, Mg). Total macronutrient content (P, K, Ca, Mg) was analysed only in holorganic horizons. Results confirmed acidification effects of red oak on the upper forest soil layers such as decreased pH, base content, base saturation, all nutrient contents in total as well as plant-available form and increased soil exchangeable acidity (exchangeable Al) in comparison to the sessile oak stands, especially in holorganic horizons and in the uppermost mineral layer (Ahhorizon). Northern red oak can be considered as a slightly site-soil degrading species in the studied sites and environmental conditions in comparison to native oak species.

Northern red oak (Quercus rubra L. syn. Q. borealis F. Michx.) is a valuable broadleaved tree species originating from the eastern half of the USA and Canada. It was introduced to Europe in 1691 and currently covers over 350 000 ha, being found all over the continent, except the coldest part of Scandinavia. It is a fast-growing and valuable broadleaved tree due to its ecological characteristics, good wood properties and high economic value. Northern red oak prefers deep, loose, moderately humid and acid soils, without compact horizons and of at least moderate fertility. It does not grow well on dry, calcareous soils as well as waterlogged or poorly drained soils. It is either naturally regenerated using a group shelterwood system or planted using seedlings of European provenance, collected in certified seed stands. As northern red oak is light-demanding, its management should be ‘dynamic’ and includes heavy interventions (cleaning–respacing and thinning from above), in order to minimize crown competition between the final crop trees. These should produce large diameter trees for valuable end uses (e.g. veneer, solid furniture, lumber, etc.) within a rotation period generally of 80–100 years. The necessity for pruning (both formative and high) depends on the stand stocking at establishment, the subsequent silvicultural interventions as well as the occurrence of forking. The adaptation potential of northern red oak to predicted climate change, especially drought, seems to be higher than for European native oaks, the importance of the species is expected to increase in the future.

Seedlots of sycamore maple ( Acer pseudoplatanus L.) originating from three different provenance regions were collected in autumn 2012. The seed quality, namely vitality and germination rate, was assessed according to Czech conventions. There were four replications within each seedlot, i.e. twelve treatments altogether for each experimental variant. The effect of gibberellic acid on germination and vitality was studied using three treatments including a control for germination capacity and three treatments including a control for emergence rate. The data shows that the gib - berellic acid did not substitute for the stratification procedure as it did not improve the germination capacity of seeds with pericarp when compared with stratified seeds; however for seeds without pericarp the gibberellic acid improved the germination capacity to the level of stratified seeds. The data also shows the positive influence of gibberellic acid on emergence rate. All variants where acid gibberellic was applied have a statistically higher emergence rate than the control. The increase was about 50% higher than in the control, i.e. without the influence of gibberellic acid.

In this work one high performance multi-crystalline silicon ingot and one conventional multi-crystalline silicon ingot, each with an extraordinary ingot height of 710 mm, were replicated by the successive growth of eight G1 ingots to evaluate the potential advantage of extraordinary tall HPM ingots in industrial production. By analyzing different grain structure parameters like mean grain size, grain orientation and grain boundary type distribution as well as the recombination active dislocation area over the complete ingot height, it was observed that the material properties strongly differ in the initial state of growth for the two material types. However, at ingot heights above 350 mm, the difference has vanished and the grain structure properties for both materials appear similar. It is shown that the evolution of the grain structure in both material types can be explained by the same grain selection and grain boundary generation/annihilation mechanisms whereas the current grain structure determines which mechanisms are the most dominant at a specific ingot height. Since the grain structure directly influences the dislocation content in the silicon material, also the recombination active dislocation area becomes equal in high performance and conventional multi-crystalline silicon material at ingot heights above 350 mm. From these results it is concluded that the advantage of high performance silicon material is limited to the first grown 350 mm of the ingot.

Sycamore (Acer pseudoplatanus L.) seeds are frequently used in forest nurseries and therefore the knowl- edge of their proper treatment is desirable. Seed stratification recommended by the Czech standard is two months but there are not many studies which review the appropriate length in Central European conditions. The paper evaluates the influence of seed stratification length on their germination capacity. The seed samples were treated in differ- ent ways to evaluate their reaction to these different handling conditions. The data proved a significant increase of germination after 42 days of stratification. The data also suggests that the better stratification medium is a substrate than wet filter paper.

We study the mean first time that two monomers, located on the same polymer, encounter in a confined microdomain. Approximating the confined geometry by a harmonic potential well, we obtain an asymptotic expression for the mean first encounter time (MFETC) as a function of the radius e around one monomer. By studying the end-to-end distance of the polymer in a ball using the Edwards’ formalism, we derive an other estimation of the MFETC. We validate the asymptotic formulas using Brownian simulations and derive their range of validity in terms of the polymer length. We apply the present models to compute the mean time for a gene located far away from a promoter site to be activated during looping in confined genomic territories.

In the present paper the effect of the furnace interior materials on the carbon and oxygen concentrations in multicrystalline silicon (mc-Si) is studied. Mc-Si ingots were produced in a high-vacuum induction furnace by means of the vertical Bridgman technique. Growth experiments with or without graphite components in the furnace as well as with crucible coatings of different oxygen concentrations were performed. The concentration of carbon monoxide in the growth chamber is found to depend significantly on the setup used. A standard, graphite-containing setup results in pronounced CO formation, which can be completely suppressed by applying graphite-free elements. Oxygen in the crucible coating is shown to influence the concentration of carbon monoxide via the formation of SiO. Growth under a CO enriched atmosphere is associated with the formation of a SiC/SiO2 melt surface layer, which pins the carbon concentration in the melt or crystal near its solubility limit, whereas in graphite- or CO-free growth the dissolved carbon segregates approximately according to Scheil’s law. On the other hand, the effect of carbon monoxide on oxygen concentration in the grown crystals appears to be negligible. Instead, the oxygen concentration is directly related to the oxygen content of the crucible coating.

AbStr Act : Natural regeneration and its relationship to micro-relief and weed competition were studied on 6 re search plots in mountain spruce forests in the Sumava Mountains. The data on density regeneration, total height and height increment of each seedling were recorded on 50 by 5 m transects. The position of each seedling was adjusted by a satellite system “Field map”. The data show that an elevation is a significantly (significance level P = 0.99) preferable micro-relief for seedlings in most cases (7 of the total 9 cases). The regeneration density is low in a high-competition environment, i.e. in grass and ferns, where the number of seedlings is significantly low on all surveyed plots. But dead wood, which is also an elevation in terms of the micro-relief, is the most preferable micro-site. The data show no sig nificant differences in seedling heights due to differently dominant competing plants. Neither was the hypothesis about the beneficial influence of stem or stump in close surroundings on seedlings confirmed by our data.

Several years ago, we decided to switch our main focus of interest toward the field of modeling cellular biology. Several reasons motivated this move: first cellular and molecular biology offer a fantastic new source of physical and mathematical problems. Second, to understand the function of cellular microdomains, modeling and computer simulations are necessary tools to organize and structure experimental observations. We review here some questions we have started to address.

The study analyses the growth of beech seedling fine roots and their development in the first five years. The research plots were established in 1997-2003 in community forests of Starý Plzenec (Western Bohemia, Czech Republic). The data are based on annual reviews of beech samplings extracted from surveyed plots. The whole root volume as well as the fine root volume is significantly (on a 95% significance level) growing during the first years after outplanting and there is not any disruption of growth immediately after outplanting.

The search by swimmers for a small target in a bounded domain is ubiquitous in cellular biology, where a prominent case is that of the search by spermatozoa for an egg in the uterus. This is one of the severest selection processes in animal reproduction. We present here a mathematical model of the search, its analysis, and numerical simulations. In the proposed model the swimmers’ trajectories are rectilinear and the speed is constant. When a trajectory hits an obstacle or the boundary, it is reflected at a random angle and continues the search with the same speed. Because hitting a small target by a trajectory is a rare event, asymptotic approximations and stochastic simulations are needed to estimate the mean search time in various geometries. We consider searches in a disk, in convex planar domains, and in domains with cusps. The exploration of the parameter space for spermatozoa motion in different uterus geometries leads to scaling laws for the search process.

This paper deals with sub-Riemannian metrics onR 3 in the contact case. We study the singularities of the exponential mapping in the neighborhood of its pole. This is in stark contrast with the Riemannian case where this situation never occurs.

Using a novel theoretical approach, we study the mean first-encounter time (MFET) between the two ends of a polymer. Previous approaches used various simplifications that reduced the complexity of the problem, leading, however, to incompatible results. We construct here for the first time a general theory that allows us to compute the MFET. The method is based on estimating the mean time for a Brownian particle to reach a narrow domain in the polymer configuration space. In dimension two and three, we find that the MFET depends mainly on the first eigenvalue of the associated Fokker-Planck operator and provide precise estimates that are confirmed by Brownian simulations. Interestingly, although many time scales are involved in the encounter process, its distribution can be well approximated by a single exponential, which has several consequences for modeling chromosome dynamics in the nucleus. Another application of our result is computing the mean time for a DNA molecule to form a closed loop (when its two ends meet for the first time).

In this paper I want to report on work done in collaboration with J.P. Gauthier and A. Hammouri in several publications. (see [GHK], [GK]).

We are interested in conditions under which, for a family of systems depending smoothly on some parameters, there exists a family of diffeomorphisms and feedback transformations, smoothly depending on the parameters, which transform the family of systems into one (independant of the parameters). This paper deals with the relationship between the possibility to define these families of feedback and diffeomorphisms everywhere locally (locally around any point), or globally. No constant rank assumption is made.

In this article we study the time optimality status of singular trajectories, for single-input affine systems. The basic tool is the construction of a semi-normal form under the action of the feedback group and an adapted representation of the input-space, which allow to evaluate the accessibility set.

We deal with controllability of right-invariant control systems on Lie groups. Following the ideas of a series of papers by JURDJEVIC-KUPKA, GAUTHIER-BORNARD, GAUTHIER-KUPKA-SALLET, LEITE-CROUCH, EL ASSOUDI-GAUTHIER, we obtain a generalization of these results in the general case of real semi-simple Lie groups.

1. The authors have calorimetrically determined the energy emitted in the process of mechanical fragmentation of a solid. The difference between this and the energy supplied to the fragmented system is equal to the energy accumulated in the fragmented material. 2. There is found to be a linear relation between the energy irreversibly accumulated in the broken rock and bit and the energy supplied to the system which breaks the material. The same relation is established between the accumulated energy and the energy emitted in the form of heat during the fragmentation process, which can be measured calorimetrically. 3. Solutions are found for the problem of determining experimentally the work required to form unit surface area for isotropic solids of complex composition.

In this paper we give necessary and sufficient conditions for a family of right (or left) invariant vector fields on a Lie group G G to be transitive. The concept of transitivity is essentially that of controllability in the literature on control systems. We consider families of right (resp. left) invariant vector fields on a Lie group G G which is a semidirect product of a compact group K K and a vector space V V on which K K acts linearly. If F \mathcal {F} is a family of right-invariant vector fields, then the values of the elements of F \mathcal {F} at the identity define a subset Γ \Gamma of L ( G ) L(G) the Lie algebra of G G . We say that F \mathcal {F} is transitive on G G if the semigroup generated by ∪ X ∈ Γ { exp ⁡ ( t X ) : t ⩾ 0 } { \cup _{X \in \Gamma }}\{ \exp (tX):t \geqslant 0\} is equal to G G . Our main result is that F \mathcal {F} is transitive if and only if Lie ⁡ ( Γ ) \operatorname {Lie} (\Gamma ) , the Lie algebra generated by Γ \Gamma , is equal to L ( G ) L(G) .

In his very interesting paper [8], Sussmann introduces, among other important concepts, a property he calls (P) and which is equivalent to the openness of accessibility sets of a system on a manifold. He states that property (P) is not stable under small perturbation of the system. To sustain his claim he constructs an example. As the second author has noticed, the example is wrong. It turns out that property (P) is stable: as a consequence of the main result of this paper, it follows that the openness of the accessibility sets implies the complete controllability of the system at least in the case of a compact state space. This last property is stable by the main result of Sussmann’s paper just quoted. Our main theorem is the generalization of the well-known and trivial fact that if the orbits of a connected topological group acting on a connected topological space are open, then the action is transitive. We extend this result to the action on a manifold of pseudo-semigroups satisfying a connectedness property. The extension is not as trivial as the group case since in the semi group case the orbits of the action are not disjoint any more.

Based on the structure of a finite setG of real numbers arithmetic operations onG are defined using the corresponding real operations and a subsequent mapping ? with real domain and range inG. Error estimations are given related to the arithmetic onG depending on ? and numerically critical situations are discussed. Especially a general floating point arithmetic is developed. A definition for simulations (onG) of real functions is given with regard for inaccuracies of arguments and results.

The behavior of the extremal curves in optimal control theory is much more complex than that of their namesakes in the classical calculus of variations. Here we analyze the simplest instances of singular behavior of these extremals. Among others, in sharp contrast to the classical case, a C 0 {C^0} -limit of extremals may not be an extremal. In the simplest cases (elliptic fold and Maxwell points) of this occurrence, the limits are trajectories of a new vector field. A special case of this field showed up in some work of V. I. Arnold. Results related to ours have been obtained in low dimension by I. Ekeland.