Nonlinear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate

We consider the axial compression of a thin sheet wrapped around a rigid cylindrical substrate. In contrast to the wrinkling-to-fold transitions exhibited in similar systems, we find that the sheet always buckles into a single symmetric fold, while periodic solutions are unstable. Upon further compression, the solution breaks symmetry and stabilizes into a recumbent fold. Using linear analysis and numerics, we theoretically predict the buckling force and energy as a function of the compressive displacement. We compare our theory to experiments employing cylindrical neoprene sheets and find remarkably good agreement.Comment: 20 pages, 5 figure

Making big steps in trajectories

We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of trajectories up to the area where discontinuous jumps appear, applicable for holomorphic flow functions. Examples with a prototypical implementation illustrate that the algorithm might provide results with higher precision than well-known ODE solvers at a similar computation time

Parameterized Uniform Complexity in Numerics: from Smooth to Analytic, from NP-hard to Polytime

The synthesis of classical Computational Complexity Theory with Recursive Analysis provides a quantitative foundation to reliable numerics. Here the operators of maximization, integration, and solving ordinary differential equations are known to map (even high-order differentiable) polynomial-time computable functions to instances which are `hard' for classical complexity classes NP, #P, and CH; but, restricted to analytic functions, map polynomial-time computable ones to polynomial-time computable ones -- non-uniformly! We investigate the uniform parameterized complexity of the above operators in the setting of Weihrauch's TTE and its second-order extension due to Kawamura&Cook (2010). That is, we explore which (both continuous and discrete, first and second order) information and parameters on some given f is sufficient to obtain similar data on Max(f) and int(f); and within what running time, in terms of these parameters and the guaranteed output precision 2^(-n). It turns out that Gevrey's hierarchy of functions climbing from analytic to smooth corresponds to the computational complexity of maximization growing from polytime to NP-hard. Proof techniques involve mainly the Theory of (discrete) Computation, Hard Analysis, and Information-Based Complexity

Nitroreductase (GlNR1) increases susceptibility of Giardia lamblia and Escherichia coli to nitro drugs

Objectives The protozoan parasite Giardia lamblia causes the intestinal disease giardiasis, which may lead to acute and chronic diarrhoea in humans and various animal species. For treatment of this disease, several drugs such as the benzimidazole albendazole, the nitroimidazole metronidazole and the nitrothiazolide nitazoxanide are currently in use. Previously, a G. lamblia nitroreductase 1 (GlNR1) was identified as a nitazoxanide-binding protein. The aim of the present project was to elucidate the role of this enzyme in the mode of action of the nitro drugs nitazoxanide and metronidazole. Methods Recombinant GlNR1 was overexpressed in both G. lamblia and Escherichia coli (strain BL21). The susceptibility of the transfected bacterial and giardial cell lines to nitazoxanide and metronidazole was analysed. Results G. lamblia trophozoites overexpressing GlNR1 had a higher susceptibility to both nitro drugs. E. coli were fully resistant to nitazoxanide under both aerobic and semi-aerobic growth conditions. When grown semi-aerobically, bacteria overexpressing GlNR1 became susceptible to nitazoxanide. Conclusions These findings suggest that GlNR1 activates nitro drugs via reduction yielding a cytotoxic produc

Rhodium-catalysed hydroformylation of N-(2-propenyl)-β-lactams as a key step in the synthesis of functionalised N-[4-(2-oxoazetidin-1-yl)but-1-enyl]acetamides

Biologically relevant functionalised N-[4-(2-oxoazetidin-1-yl)but-1-enyl]acetamides have been prepared in a two-step approach starting from N-(2-propenyl)-beta-lactams, involving initial rhodium-catalysed hydroformylation followed by subjection of the obtained aldehydes to Staudinger reaction conditions after initial imination

Computed tomography-osteoaboorptiometry

A method of making a visual display of subchondral mineralization in the major synovial joints is described. Unlike existing procedures, it can be used on the living subject. A modified application of computed tomography-densitometry, computed tomography-osteoabsorptiometry makes it possible to explore the mechanical adaptability to the prevailing mechanical force. This claim is based upon the comparison of information obtained from 20 anatomical specimens with CT-osteoabsorptiometry and x-ray densitometry of sections; both methods yielding virtually identical results. The distribution of the subchondral density was then expressed as a map of the articular surface with the aid of an image analyser. This method can make a useful contribution to basic clinical research, as well as providing a diagnostic technique which can also be used for observing progress after a corrective osteotomy or any other procedure causing a change in mechanical function. Examples of its use on living patients are given

Foundation of Computer (Algebra) ANALYSIS Systems: Semantics, Logic, Programming, Verification

We propose a semantics of operating on real numbers that is sound, Turing-complete, and practical. It modifies the intuitive but super-recursive Blum-Shub-Smale model (formalizing Computer ALGEBRA Systems), to coincide in power with the realistic but inconvenient Type-2 Turing machine underlying Computable Analysis: reconciling both as foundation to a Computer ANALYSIS System. Several examples illustrate the elegance of rigorous numerical coding in this framework, formalized as a simple imperative programming language ERC with denotational semantics for REALIZING a real function $f$: arguments $x$ are given as exact real numbers, while values $y=f(x)$ suffice to be returned approximately up to absolute error $2^p$ with respect to an additionally given integer parameter $p\to-\infty$. Real comparison (necessarily) becomes partial, possibly 'returning' the lazy Kleenean value UNKNOWN (subtly different from $\bot$ for classically undefined expressions like 1/0). This asserts closure under composition, and in fact 'Turing-completeness over the reals': All and only functions computable in the sense of Computable Analysis can be realized in ERC. Programs thus operate on a many-sorted structure involving real numbers and integers, the latter connected via the 'error' embedding $Z\ni p\mapsto 2^p\in R$, whose first-order theory is proven decidable and model-complete. This logic serves for formally specifying and formally verifying correctness of ERC programs