Dynamic stabilization of L2 periodic orbits using attitude-orbit coupling effects

Numerical explorations show how the known periodic solutions of the Hill problem are modified in the case of the attitude-orbit coupling that may occur for large satellite structures. We focus on the case in which the elongation is the dominant satellite?s characteristic and find that a rotating structure may remain with its largest dimension in a plane parallel to the plane of the primaries. In this case, the effect produced by the non-negligible physical dimension is dynamically equivalent to the perturbation produced by an oblate central body on a masspoint satellite. Based on this, it is demonstrated that the attitude-orbital coupling of a long enough body may change the dynamical characteristics of a periodic orbit about the collinear Lagrangian points.

Temporal task allocation in periodic environments. An approach based on synchronization

In this paper, we study a robot swarm that has to perform task allocation in an environment that features periodic properties. In this environment, tasks appear in different areas following periodic temporal patterns. The swarm has to reallocate its workforce periodically, performing a temporal task allocation that must be synchronized with the environment to be effective. We tackle temporal task allocation using methods and concepts that we borrow from the signal processing literature. In particular, we propose a distributed temporal task allocation algorithm that synchronizes robots of the swarm with the environment and with each other. In this algorithm, robots use only local information and a simple visual communication protocol based on light blinking. Our results show that a robot swarm that uses the proposed temporal task allocation algorithm performs considerably more tasks than a swarm that uses a greedy algorithm.

Gromov hyperbolicity of periodic planar graphs

The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it. The main result in this paper is a very simple characterization of the hyperbolicity of a large class of periodic planar graphs.

Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given

Vortex pinning vs superconducting wire network: origin of periodic oscillations induced by applied magnetic fields in superconducting films with arrays of nanomagnets

Hybrid magnetic arrays embedded in superconducting films are ideal systems to study the competition between different physical (such as the coherence length) and structural length scales such as are available in artificially produced structures. This interplay leads to oscillation in many magnetically dependent superconducting properties such as the critical currents, resistivity and magnetization. These effects are generally analyzed using two distinct models based on vortex pinning or wire network. In this work, we show that for magnetic dot arrays, as opposed to antidot (i.e. holes) arrays, vortex pinning is the main mechanism for field induced oscillations in resistance R(H), critical current Ic(H), magnetization M(H) and ac-susceptibility χ ac(H) in a broad temperature range. Due to the coherence length divergence at Tc, a crossover to wire network behaviour is experimentally found. While pinning occurs in a wide temperature range up to Tc, wire network behaviour is only present in a very narrow temperature window close to Tc. In this temperature interval, contributions from both mechanisms are operational but can be experimentally distinguished.

Application of the homogenization techniques to the determination of the effective flexure constants of plate structural systems

A Mindlin plate with periodically distributed ribs patterns is analyzed by using homogenization techniques based on asymptotic expansion methods. The stiffness matrix of the homogenized plate is found to be dependent on the geometrical characteristics of the periodical cell, i.e. its skewness, plan shape, thickness variation etc. and on the plate material elastic constants. The computation of this plate stiffness matrix is carried out by averaging over the cell domain some solutions of different periodical boundary value problems. These boundary value problems are defined in variational form by linear first order differential operators on the cell domain and the boundary conditions of the variational equation correspond to a periodic structural problem. The elements of the stiffness matrix of homogenized plate are obtained by linear combinations of the averaged solution functions of the above mentioned boundary value problems. Finally, an illustrative example of application of this homogenization technique to hollowed plates and plate structures with ribs patterns regularly arranged over its area is shown. The possibility of using in the profesional practice the present procedure to the actual analysis of floors of typical buildings is also emphasized.

Periodic variation in side-chain polarities of T-cell antigenic peptides correlates with their structure and activity.

We present an analysis that synthesizes information on the sequence, structure, and motifs of antigenic peptides, which previously appeared to be in conflict. Fourier analysis of T-cell antigenic peptides indicates a periodic variation in amino acid polarities of 3-3.6 residues per period, suggesting an amphipathic alpha-helical structure. However, the diffraction patterns of major histocompatibility complex (MHC) molecules indicate that their ligands are in an extended non-alpha-helical conformation. We present two mutually consistent structural explanations for the source of the alpha-helical periodicity, based on an observation that the side chains of MHC-bound peptides generally partition with hydrophobic (hydrophilic) side chains pointing into (out of) the cleft. First, an analysis of haplotype-dependent peptide motifs indicates that the locations of their defining residues tend to force a period 3-4 variation in hydrophobicity along the peptide sequence, in a manner consistent with the spacing of pockets in the MHC. Second, recent crystallographic determination of the structure of a peptide bound to a class II MHC molecule reveals an extended but regularly twisted peptide with a rotation angle of about 130 degrees. We show that similar structures with rotation angles of 100-130 degrees are energetically acceptable and also span the length of the MHC cleft. These results provide a sound physical chemical and structural basis for the existence of a haplotype-independent antigenic motif which can be particularly important in limiting the search time for antigenic peptides.

Rectification and signal averaging of weak electric fields by biological cells.

Oscillating electric fields can be rectified by proteins in cell membranes to give rise to a dc transport of a substance across the membrane or a net conversion of a substrate to a product. This provides a basis for signal averaging and may be important for understanding the effects of weak extremely low frequency (ELF) electric fields on cellular systems. We consider the limits imposed by thermal and "excess" biological noise on the magnitude and exposure duration of such electric field-induced membrane activity. Under certain circumstances, the excess noise leads to an increase in the signal-to-noise ratio in a manner similar to processes labeled "stochastic resonance." Numerical results indicate that it is difficult to reconcile biological effects with low field strengths.

Tilted excitation implies odd periodic resonances

This work was supported by the Brazilian agencies FAPESP and CNPq. MSB also acknowledges the Engineering and Physical Sciences Research Council grant Ref. EP/I032606/1. GID thanks Felipe A. C. Pereira for fruitful discussions.

THE DESIGN AND SYNTHESIS OF SILOXANE PRECURSORS FOR CHIRAL PERIODIC MESOPOROUS ORGANOSILICA MATERIALS

The development of cost-effective and reliable methods for the synthesis and separation of asymmetric compounds is paramount in helping to meet society’s ever-growing demand for chiral small molecules. Of these methods, chiral heterogeneous supports are particularly appealing as they allow for the reuse of the chiral source. One such support, based on the synergy between chiral organic units and structurally stable inorganic silicon scaffolds are periodic mesoporous organosilicas (PMOs). In the work described herein, I examine some of the factors governing the transmission of chirality between chiral dopants and prochiral bulk phases in chiral PMO materials. In particular, the exploration of 1,1’-binaphthalene-bridged chiral dopants with a focus on the point of attachment into the materials. Moreover, the effects of ordering in the materials are examined and reveal that chirality transfer is more facile in materials with molecular-scale order then those containing amorphous walls. Secondly, the issues surrounding the synthesis and purification of aryl-triethoxysilanes as siloxane precursors are addressed. Both the introduction of a two-carbon linker and the direct attachment of allyl and mixed allyldiethoxysilane species are explored. This work demonstrates that allyldiethoxysilanes are ideal, in that they are stable enough to permit facile synthesis, while still being able to hydrolyze completely to produce well-ordered materials. Lastly, the production of new bulk phases for chiral PMO materials is examined by introducing new prochiral nitrogen-containing siloxane precursors. Biphenyldiamine and bipyridine-bridged siloxane precursors are readily synthesized on reasonable scales. Their use as the bulk siloxane precursor in the production of PMO materials however, is precluded by insufficient gelation and additional siloxane precursors are necessary for the production of ordered materials. In addition to the research detailed above that forms the body of this thesis, two short works are appended. The first details the production of polythiophene assemblies mediated through coordination nanospaces, while the second explores the production of N-heterocyclic carbene functionalized gold nanoparticles through ligand exchange.

Dynamical Equations For The Period Vectors In A Periodic System Under Constant External Stress

The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton’s second law applied to halves of the system. Later statistics over indistinguishable translated states and forces associated with transport of momentum are applied to the resulting dynamical equations. In the final expressions, the period vectors are driven by the imbalance between internal and external stresses. The internal stress is shown to have both full interaction and kinetic-energy terms.