THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

Self-organized distribution of periodicity and chaos in an electrochemical oscillator

We report a detailed numerical investigation of a prototype electrochemical oscillator, in terms of high-resolution phase diagrams for an experimentally relevant section of the control (parameter) space. The prototype model consists of a set of three autonomous ordinary differential equations which captures the general features of electrochemical oscillators characterized by a partially hidden negative differential resistance in an N-shaped current-voltage stationary curve. By computing Lyapunov exponents, we provide a detailed discrimination between chaotic and periodic phases of the electrochemical oscillator. Such phases reveal the existence of an intricate structure of domains of periodicity self-organized into a chaotic background. Shrimp-like periodic regions previously observed in other discrete and continuous systems were also observed here, which corroborate the universal nature of the occurrence of such structures. In addition, we have also found a structured period distribution within the order region. Finally we discuss the possible experimental realization of comparable phase diagrams.

Complex Oscillatory Response of a PEM Fuel Cell Fed with H(2)/CO and Oxygen

Oscillatory kinetics is commonly observed in the electrocatalytic oxidation of most species that can be used in fuel cell devices. Examples include formic acid, methanol, ethanol, ethylene glycol, and hydrogen/carbon monoxide mixtures, and most papers refer to half-cell experiments. We report in this paper the experimental investigation of the oscillatory dynamics in a proton exchange membrane (PEM) fuel cell at 30 degrees C. The system consists of a Pt/C cathode fed with oxygen and a PtRu (1:1)/C anode fed with H(2) mixed with 100 ppm of CO, and was studied at different cell currents and anode flow rates. Many different states including periodic and nonperiodic series were observed as a function of the cell current and the H(2)/CO flow rate. In general, aperiodic/chaotic states were favored at high currents and low flow rates. The dynamics was further characterized in terms of the relationship between the oscillation amplitude and the subsequent time required for the anode to get poisoned by carbon monoxide. Results are discussed in terms of the mechanistic aspects of the carbon monoxide adsorption and oxidation. (C) 2010 The Electrochemical Society. [DOI: 10.1149/1.3463725] All rights reserved.

Morphology and biology of a new Pseudopolydora (Annelida: Spionidae) species from Brazil

Adults of Pseudopolydora rosebelae sp. nov. inhabit silty tubes on muddy bottoms in shallow water in southern Brazil, states of Sao Paulo and Rio de Janeiro. They are rare and extremely delicate, attaining 20 mm long for 55 chaetigers. The worms are distinctive by their colourful yellow and black pigmentation on the anterior part of body and palps, prominent transverse hood on the dorsal anterior edge of chaetiger 3, and lack of coloured respiratory pigment in blood. Of 12 examined individuals, all were females. Oogenesis is intraovarian; oocytes develop from chaetigers 14-15 to chaetigers 24-36. Recently laid oocytes were about 150 mu m in diameter, with embryos and developing larvae found in capsules inside female tubes in March-June. Broods comprised up to 23 capsules with 400 propagules. Capsules were joined to each other in a string and each attached by a single thin stalk to the inner wall of the tube. Larvae hatched at the 4-chaetiger stage and fed on plankton. Pelagic larvae are unique among Pseudopolydora in having large ramified mid-dorsal melanophores from chaetiger 3 onwards. Competent larvae are able to settle and metamorphose at the 15-chaetiger stage, but can remain planktonic up to 18 chaetigers. They have one pair of unpigmented ocelli and three pairs of black eyes in the prostomium, unpaired ramified mid-dorsal melanophores on chaetiger 1 and on the pygidium, ramified lateral melanophores on chaetigers 5-10, prominent yellow chromatophores in the prostomium, peristomium, on dorsal and ventral sides of chaetigers and in the pygidium. Branchiae are present on chaetigers 7-10, and gastrotrochs are arranged on chaetigers 3, 5, 7 and 12. Provisional serrated bristles are present in all notopodia, and hooks are present in neuropodia from chaetiger 8 onwards. Two pairs of provisional protonephridia are present in chaetigers 1 and 2, and adult metanephridia are present from chaetiger 4.

Homogenization in a thin domain with an oscillatory boundary

In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type R(epsilon) = {(x(1), x(2)) is an element of R(2) vertical bar x(1) is an element of (0, 1), 0 < x(2) < epsilon G(x(1), x(1)/epsilon)} where the function G(x, y) is periodic in y of period L. Observe that the upper boundary of the thin domain presents a highly oscillatory behavior and, moreover, the height of the thin domain, the amplitude and period of the oscillations are all of the same order, given by the small parameter epsilon. (C) 2011 Elsevier Masson SAS. All rights reserved.

Analytical calculation of the transition to complete phase synchronization in coupled oscillators

Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to the total synchronization. We are able to develop exact solutions for the value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions as well as for a chain with fixed ends. We compare the results with those calculated numerically.

Comparative analysis of triple band S-C-L erbium-doped fibre and semiconductor optical amplifier for CWDM applications

The authors present a comparative analysis between a triple-band S-C-L erbium-doped fibre amplifier and a commercial semiconductor optical amplifier in a CWDM application scenario. Both technologies were characterised for gain and noise figures from 1480 to 1610 nm (S, C and L bands) and their systemic performances were evaluated in terms of bit error rate measurements for a wide range of optical power levels.

Chaotic communication based on the particle-in-a-box electronic circuit

A secure communication system based on the error-feedback synchronization of the electronic model of the particle-in-a-box system is proposed. This circuit allows a robust and simple electronic emulation of the mechanical behavior of the collisions of a particle inside a box, exhibiting rich chaotic behavior. The required nonlinearity to emulate the box walls is implemented in a simple way when compared with other analog electronic chaotic circuits. A master/slave synchronization of two circuits exhibiting a rich chaotic behavior demonstrates the potentiality of this system to secure communication. In this system, binary data stream information modulates the bifurcation parameter of the particle-in-a-box electronic circuit in the transmitter. In the receiver circuit, this parameter is estimated using Pecora-Carroll synchronization and error-feedback synchronization. The performance of the demodulation process is verified through the eye pattern technique applied on the recovered bit stream. During the demodulation process, the error-feedback synchronization presented better performance compared with the Pecora-Carroll synchronization. The application of the particle-in-a-box electronic circuit in a secure communication system is demonstrated.

Analytical formulae for electromechanical effective properties of 3-1 longitudinally porous piezoelectric materials

A unidirectional fiber composite is considered here, the fibers of which are empty cylindrical holes periodically distributed in a transversely isotropic piezoelectric matrix, The empty-fiber cross-section is circular and the periodicity is the same in two directions at an angle pi/2 or pi/3. Closed-form formulae for all electromechanical effective properties of these 3-1 longitudinally periodic porous piezoelectric materials are presented. The derivation of such expressions is based on the asymptotic homogenization method as a limit of the effective properties of two-phase transversely isotropic parallel fiber-reinforced composites when the fibers properties tend to zero. The plane effective coefficients satisfy the corresponding Schulgasser-Benveniste-Dvorak universal type of relations, A new relation among the antiplane effective constants from the solutions of two antiplane strains and potential local problems is found. This relation is valid for arbitrary shapes of the empty-fiber cross-sections. Based on such a relation, and using recent numerical results for isotropic conductive composites, the antiplane effective properties are computed for different geometrical shapes of the empty-fiber cross-section. Comparisons with other analytical and numerical theories are presented. (c) 2008 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A simple way to introduce fibers into FEM models

This communication proposes a simple way to introduce fibers into finite element modelling. This is a promising formulation to deal with fiber-reinforced composites by the finite element method (FEM), as it allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced into the pre-existent finite element numerical system to consider any distribution of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic is the reduced work required by the user to introduce fibers, avoiding `rebar` elements, node-by-node geometrical definitions or even complex mesh generation. An additional characteristic of the technique is the possibility of representing unbounded stresses at the end of fibers using a finite number of degrees of freedom. Further studies are required for non-linear applications in which localization may occur. Along the text the linear formulation is presented and the bounded connection between fibers and continuum is considered. Four examples are presented, including non-linear analysis, to validate and show the capabilities of the formulation. Copyright (c) 2007 John Wiley & Sons, Ltd.

Macro-Fiber Composite Actuators for Flow Control of a Variable Camber Airfoil

This research employs solid-state actuators for delay of flow separation seen in airfoils at low Reynolds numbers. The flow control technique investigated here is aimed for a variable camber airfoil that employs two active surfaces and a single four-bar (box) mechanism as the internal structure. To reduce separation, periodic excitation to the flow around the leading edge of the airfoil is induced by a total of nine piezocomposite actuated clamped-free unimorph benders distributed in the spanwise direction. An electromechanical model is employed to design an actuator capable of high deformations at the desired frequency for lift improvement at post-stall angles. The optimum spanwise distribution of excitation for increasing lift coefficient is identified experimentally in the wind tunnel. A 3D (non-uniform) excitation distribution achieved higher lift enhancement in the post-stall region with lower power consumption when compared to the 2D (uniform) excitation distribution. A lift coefficient increase of 18.4% is achieved with the identified non-uniform excitation mode at the bender resonance frequency of 125 Hz, the flow velocity of 5 m/s and at the reduced frequency of 3.78. The maximum lift (Clmax) is increased 5.2% from the baseline. The total power consumption of the flow control technique is 639 mW(RMS).

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Piezoceramic Composite Actuators for Flow Control in Low Reynolds Number Airflow

The research presented here employs solid-state actuators for flow separation delay or for forced attachment of separated flow seen in airfoils at low Reynolds numbers. To reduce separation, periodic excitation to the flow around the leading edge of the airfoil is induced by Macro-Fiber Composite actuated clamped-free unimorph benders. An electromechanical model of the unimorph is briefly presented and parametric study is conducted to aid the design of a unimorph to output high deformation at a desired frequency. The optimum frequency and amplitude for lift improvement at post-stall angles are identified experimentally. Along with aerodynamic force and structural displacement measurements, helium bubble flow visualization is used to verify existing separated flow, and the attached flow induced by flow control. The lift enhancement induced by several flow control techniques is compared. A symmetric and non-uniform (3D) flow excitation results in the maximum lift enhancement at post-stall region at the lowest power consumption level. A maximum lift coefficient increase of 27.5% (in the post-stall region) is achieved at 125 Hz periodic excitation, with the 3D symmetric actuation mode at 5 m/s and the reduced frequency of 3.78. C(l,max) is increased 7.6% from the baseline.

Whirlwind: a new cryptographic hash function

A new cryptographic hash function Whirlwind is presented. We give the full specification and explain the design rationale. We show how the hash function can be implemented efficiently in software and give first performance numbers. A detailed analysis of the security against state-of-the-art cryptanalysis methods is also provided. In comparison to the algorithms submitted to the SHA-3 competition, Whirlwind takes recent developments in cryptanalysis into account by design. Even though software performance is not outstanding, it compares favourably with the 512-bit versions of SHA-3 candidates such as LANE or the original CubeHash proposal and is about on par with ECHO and MD6.

A family of implementation-friendly BN elliptic curves

For the last decade, elliptic curve cryptography has gained increasing interest in industry and in the academic community. This is especially due to the high level of security it provides with relatively small keys and to its ability to create very efficient and multifunctional cryptographic schemes by means of bilinear pairings. Pairings require pairing-friendly elliptic curves and among the possible choices, Barreto-Naehrig (BN) curves arguably constitute one of the most versatile families. In this paper, we further expand the potential of the BN curve family. We describe BN curves that are not only computationally very simple to generate, but also specially suitable for efficient implementation on a very broad range of scenarios. We also present implementation results of the optimal ate pairing using such a curve defined over a 254-bit prime field. (C) 2001 Elsevier Inc. All rights reserved.