How to mimic the shapes of plant tendrils on the nano and microscale: spirals and helices of electrospun liquid crystalline cellulose derivatives

We show that suspended nano and microfibres electrospun from liquid crystalline cellulosic solutions will curl into spirals if they are supported at just one end, or, if they are supported at both ends, will twist into a helix of one handedness over half of its length and of the opposite handedness over the other half, the two halves being connected by a short straight section. This latter phenomenon, known as perversion, is a consequence of the intrinsic curvature of the fibres and of a topological conservation law. Furthermore, agreement between theory and experiment can only be achieved if account is taken of the intrinsic torsion of the fibres. Precisely the same behaviour is known to be exhibited by the tendrils of climbing plants such as Passiflora edulis, albeit on a lengthscale of millimetres, i.e., three to four orders of magnitude larger than in our fibres. This suggests that the same basic, coarse-grained physical model is applicable across a range of lengthscales.

Benzo[c]thiophene chromophores linked to cationic Fe and Ru derivatives for NLO materials: synthesis characterization and quadratic hyperpolarizabilities

5-Monocyclopentadienyliron(II)/ruthenium(II) complexes of the general formula [M(5-C5H5)(PP)(L1)][PF6] {M = Fe, PP = dppe; M = Ru, PP = dppe or 2PPh3; L1 = 5-[3-(thiophen-2-yl)benzo[c]thiophenyl]thiophene-2-carbonitrile} have been synthesized and studied to evaluate their molecular quadratic hyperpolarizabilities. The compounds were fully characterized by NMR, FTIR and UV/Vis spectroscopy and their electrochemical behaviour studied by cyclic voltammetry. Quadratic hyperpolarizabilities () were determined by hyper-Rayleigh scattering measurements at a fundamental wavelength of 1500 nm. Density functional theory calculations were employed to rationalize the second-order non-linear optical properties of these complexes.

Fractional coins and fractional derivatives

This paper discusses the fundamentals of negative probabilities and fractional calculus. The historical evolution and the main mathematical concepts are discussed, and several analogies between the two apparently unrelated topics are established. Based on the new conceptual perspective, some experiments are performed shading new light into possible future progress.

Optimal controllers with complex order derivatives

This paper studies the optimization of complex-order algorithms for the discrete-time control of linear and nonlinear systems. The fundamentals of fractional systems and genetic algorithms are introduced. Based on these concepts, complexorder control schemes and their implementation are evaluated in the perspective of evolutionary optimization. The results demonstrate not only that complex-order derivatives constitute a valuable alternative for deriving control algorithms, but also the feasibility of the adopted optimization strategy.

On the fractional central differences and derivatives

Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials. The coherence of these definitions is studied by applying the definitions to functions with Fourier transformable functions. Some properties of these derivatives are presented and particular cases studied.

Time-delay and fractional derivatives

This paper proposes the calculation of fractional algorithms based on time-delay systems. The study starts by analyzing the memory properties of fractional operators and their relation with time delay. Based on the Fourier analysis an approximation of fractional derivatives through timedelayed samples is developed. Furthermore, the parameters of the proposed approximation are estimated by means of genetic algorithms. The results demonstrate the feasibility of the new perspective.

Exploiting sensor redundancy for the calculation of fractional derivatives in the presence of noise

In this paper a new method for the calculation of the fractional expressions in the presence of sensor redundancy and noise, is presented. An algorithm, taking advantage of the signal characteristics and the sensor redundancy, is tuned and optimized through genetic algorithms. The results demonstrate the good performance for different types of expressions and distinct levels of noise.

Design, synthesis and biologival evaluation of novel isoniazid derivatives with potente antitubercular activity

The disturbing emergence of multidrug-resistant strains of Mycobacterium tuberculosis (Mtb) has been driving the scientific community to urgently search for new and efficient antitubercular drugs. Despite the various drugs currently under evaluation, isoniazid is still the key and most effective component in all multi-therapeutic regimens recommended by the WHO. This paper describes the QSAR-oriented design, synthesis and in vitro antitubercular activity of several potent isoniazid derivatives (isonicotinoyl hydrazones and isonicotinoyl hydrazides) against H37Rv and two resistant Mtb strains. QSAR studies entailed RFs and ASNNs classification models, as well as MLR models. Strict validation procedures were used to guarantee the models' robustness and predictive ability. Lipophilicity was shown not to be relevant to explain the activity of these derivatives, whereas shorter N-N distances and lengthy substituents lead to more active compounds. Compounds I, 2, 4, 5 and 6, showed measured activities against H37Rv higher than INH (i.e., MIC <= 0.28 mu M), while compound 9 exhibited a six fold decrease in MIC against the katG (S315T) mutated strain, by comparison with INH (Le., 6.9 vs. 43.8 mu M). All compounds were ineffective against H37Rv(INH) (Delta katG), a strain with a full deletion of the katG gene, thus corroborating the importance of KatG in the activation of INH-based compounds. The most potent compounds were also shown not to be cytotoxic up to a concentration 500 times higher than MIC. (C) 2014 Elsevier Masson SAS. All rights reserved.

Towards the rational biosynthesis of substituted phenazines and phenoxazinones by laccases

Laccases are multi-copper oxidases that oxidise a wide range of substrates including phenol and aniline derivatives, which could be further involved in coupling reactions leading to the formation of dimeric and trimeric structures. This paper describes the enzyme-mediated dimerisation of several ortho and meta, para-disubstituted aromatic amines into phenazine ("head-to-tail" dimers) and phenoxazinone chromophores. The redox properties of substituted aromatic amines were studied by cyclic voltammetry and the kinetic constants of CotA and Trametes versicolor laccases were measured for selected aromatic amines. The structure of novel enzymatically synthesised phenazine and phenoxazinone dyes using CotA laccase was assessed by NMR and MS. Overall our data show that this enzymatic green process is an efficient alternative to the classic chemical oxidation of aromatic amines and phenols, with an impact on the broad field of applications of these heterocyclic compounds.

Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms

This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.

The K-Th derivatives of the immanant and the X-symmetric power of an operator

In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.

Fractional central differences and derivatives

Journal of Vibration and Control, Vol. 14, Nº 9-10

Approximating fractional derivatives through the generalized mean

This paper addresses the calculation of fractional order expressions through rational fractions. The article starts by analyzing the techniques adopted in the continuous to discrete time conversion. The problem is re-evaluated in an optimization perspective by tacking advantage of the degree of freedom provided by the generalized mean formula. The results demonstrate the superior performance of the new algorithm.

Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

On the relation between the fractional Brownian motion and the fractional derivatives

Physics Letters A, vol. 372; Issue 7