Coupling techniques for nonlinear hyperbolic equations. III. The well-balanced approximation of thick interfaces

We continue our analysis of the coupling between nonlinear hyperbolic problems across possibly resonant interfaces. In the first two parts of this series, we introduced a new framework for coupling problems which is based on the so-called thin interface model and uses an augmented formulation and an additional unknown for the interface location; this framework has the advantage of avoiding any explicit modeling of the interface structure. In the present paper, we pursue our investigation of the augmented formulation and we introduce a new coupling framework which is now based on the so-called thick interface model. For scalar nonlinear hyperbolic equations in one space variable, we observe that the Cauchy problem is well-posed. Then, our main achievement in the present paper is the design of a new well-balanced finite volume scheme which is adapted to the thick interface model, together with a proof of its convergence toward the unique entropy solution (for a broad class of nonlinear hyperbolic equations). Due to the presence of a possibly resonant interface, the standard technique based on a total variation estimate does not apply, and DiPerna's uniqueness theorem must be used. Following a method proposed by Coquel and LeFloch, our proof relies on discrete entropy inequalities for the coupling problem and an estimate of the discrete entropy dissipation in the proposed scheme.Comment: 21 page

New DRIE-Patterned Electrets for Vibration Energy Harvesting

This paper is about a new manufacturing process aimed at developing stable SiO2/Si3N4 patterned electrets using a Deep Reactive Ion Etching (DRIE) step for an application in electret-based Vibration Energy Harvesters (e-VEH). This process consists in forming continuous layers of SiO2/Si3N4 electrets in order to limit surface conduction phenomena and is a new way to see the problem of electret patterning. Experimental results prove that patterned electrets charged by a positive corona discharge show excellent stability with high surface charge densities that may reach 5mC/m^2 on 1.1\mu m-thick layers, even with fine patterning and harsh temperature conditions (up to 250{\deg}C). This paves the way to new e-VEH designs and manufacturing processes.Comment: Proc. European Energy Conference, 201

Searching a bitstream in linear time for the longest substring of any given density

Given an arbitrary bitstream, we consider the problem of finding the longest substring whose ratio of ones to zeroes equals a given value. The central result of this paper is an algorithm that solves this problem in linear time. The method involves (i) reformulating the problem as a constrained walk through a sparse matrix, and then (ii) developing a data structure for this sparse matrix that allows us to perform each step of the walk in amortised constant time. We also give a linear time algorithm to find the longest substring whose ratio of ones to zeroes is bounded below by a given value. Both problems have practical relevance to cryptography and bioinformatics.Comment: 22 pages, 19 figures; v2: minor edits and enhancement

Is there a best Büchi automaton for explicit model checking?

LTL to Büchi automata (BA) translators are traditionally optimized to produce automata with a small number of states or a small number of non-deterministic states. In this paper, we search for properties of Büchi automata that really influence the performance of explicit model checkers. We do that by manual analysis of several automata and by experiments with common LTL-to-BA translators and realistic verification tasks. As a result of these experiences, we gain a better insight into the characteristics of automata that work well with Spin.Překladače LTL na Büchiho automaty jsou obvykle optimalizovány tak, aby produkovaly automaty s co nejmenším počtem stavů, či s co nejmenším počtem nedeterministických stavů. V této publikaci hledáme vlastnosti Büchiho automatů, které skutečně ovlivňují výkon nástrojů pro explicitní metodu ověřování modelu (model checking). A to pomocí manuální analýzy několika automatů a experimenty s běžnými překladače LTL na automaty a realistickými verifikačními úlohami. Výsledkem těchto experimentů je lepší porozumění charakteristik automatů, které jsou dobré pro model checker Spin

Mutation Bias is the Driving Force of Codon Usage in the Gallus gallus genome

Synonymous codons are used with different frequencies both among species and among genes within the same genome and are controlled by neutral processes (such as mutation and drift) as well as by selection. Up to now, a systematic examination of the codon usage for the chicken genome has not been performed. Here, we carried out a whole genome analysis of the chicken genome by the use of the relative synonymous codon usage (RSCU) method and identified 11 putative optimal codons, all of them ending with uracil (U), which is significantly departing from the pattern observed in other eukaryotes. Optimal codons in the chicken genome are most likely the ones corresponding to highly expressed transfer RNA (tRNAs) or tRNA gene copy numbers in the cell. Codon bias, measured as the frequency of optimal codons (Fop), is negatively correlated with the G + C content, recombination rate, but positively correlated with gene expression, protein length, gene length and intron length. The positive correlation between codon bias and protein, gene and intron length is quite different from other multi-cellular organism, as this trend has been only found in unicellular organisms. Our data displayed that regional G + C content explains a large proportion of the variance of codon bias in chicken. Stepwise selection model analyses indicate that G + C content of coding sequence is the most important factor for codon bias. It appears that variation in the G + C content of CDSs accounts for over 60% of the variation of codon bias. This study suggests that both mutation bias and selection contribute to codon bias. However, mutation bias is the driving force of the codon usage in the Gallus gallus genome. Our data also provide evidence that the negative correlation between codon bias and recombination rates in G. gallus is determined mostly by recombination-dependent mutational patterns

Molecular machines open cell membranes

Beyond the more common chemical delivery strategies, several physical techniques are used to open the lipid bilayers of cellular membranes. These include using electric and magnetic fields, temperature, ultrasound or light to introduce compounds into cells, to release molecular species from cells or to selectively induce programmed cell death (apoptosis) or uncontrolled cell death (necrosis). More recently, molecular motors and switches that can change their conformation in a controlled manner in response to external stimuli have been used to produce mechanical actions on tissue for biomedical applications. Here we show that molecular machines can drill through cellular bilayers using their molecular-scale actuation, specifically nanomechanical action. Upon physical adsorption of the molecular motors onto lipid bilayers and subsequent activation of the motors using ultraviolet light, holes are drilled in the cell membranes. We designed molecular motors and complementary experimental protocols that use nanomechanical action to induce the diffusion of chemical species out of synthetic vesicles, to enhance the diffusion of traceable molecular machines into and within live cells, to induce necrosis and to introduce chemical species into live cells. We also show that, by using molecular machines that bear short peptide addends, nanomechanical action can selectively target specific cell-surface recognition sites. Beyond the in vitroapplications demonstrated here, we expect that molecular machines could also be used in vivo, especially as their design progresses to allow two-photon, near-infrared and radio-frequency activation