Maximizing measures for endomorphisms of the circle

We study a given fixed continuous function phi : S(1) -> R and an endomorphism f : S(1)-> S(1), whose f-invariant probability measures maximize integral phi d mu. We prove that the set of endomorphisms having a f maximizing invariant measure supported on a periodic orbit is C(0) dense.

On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.

Multiple Brake Orbits and Homoclinics in Riemannian Manifolds

Let (M, g) be a complete Riemannian manifold, Omega subset of Man open subset whose closure is homeomorphic to an annulus. We prove that if a,Omega is smooth and it satisfies a strong concavity assumption, then there are at least two distinct geodesics in starting orthogonally to one connected component of a,Omega and arriving orthogonally onto the other one. Using the results given in Giamb et al. (Adv Differ Equ 10:931-960, 2005), we then obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a class of Hamiltonian systems. Under a further symmetry assumption, the result is improved by showing the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinic orbits. In our proof we shall use recent deformation results proved in Giamb et al. (Nonlinear Anal Ser A: Theory Methods Appl 73:290-337, 2010).

A full family of multimodal maps on the circle

We exhibit a family of trigonometric polynomials inducing a family of 2m-multimodal maps on the circle which contains all relevant dynamical behavior.

Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence

Let M be a compact, connected non-orientable surface without boundary and of genus g >= 3. We investigate the pure braid groups P,(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 -> P(m)(M \ {x(1), ..., x(n)}) hooked right arrow P(n+m)(M) (P*) under right arrow P(n)(M) -> 1, where m, n >= 1, and p* is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p: F(n+m)(M) -> F(n)(M) of configuration spaces, defined by p((x(1), ..., x(n), x(n+1), ..., x(n+m))) = (x(1), ..., x(n)). We show that p and p* admit a section if and only if n = 1. Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups. (C) 2009 Elsevier B.V. All rights reserved.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

NONSTATIONARY MIXING AND THE UNIQUE ERGODICITY OF ADIC TRANSFORMATIONS

We define topological and measure-theoretic mixing for nonstationary dynamical systems and prove that for a nonstationary subshift of finite type, topological mixing implies the minimality of any adic transformation defined on the edge space, while if the Parry measure sequence is mixing, the adic transformation is uniquely ergodic. We also show this measure theoretic mixing is equivalent to weak ergodicity of the edge matrices in the sense of inhomogeneous Markov chain theory.

Henon-like maps with arbitrary stationary combinatorics

We extend the renormalization operator introduced in [A. de Carvalho, M. Martens and M. Lyubich. Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669] from period-doubling Henon-like maps to Henon-like maps with arbitrary stationary combinatorics. We show that the renonnalization picture also holds in this case if the maps are taken to be strongly dissipative. We study infinitely renormalizable maps F and show that they have an invariant Cantor set O on which F acts like a p-adic adding machine for some p > 1. We then show, as for the period-doubling case in the work of de Carvalho, Martens and Lyubich [Renormalization in the Henon family, I: universality but non-rigidity. J. Stat. Phys. 121(5/6) (2005), 611-669], that the sequence of renormalizations has a universal form, but that the invariant Cantor set O is non-rigid. We also show that O cannot possess a continuous invariant line field.

An analysis of the transition between strain dependent and independent softening in austenite

The post-deformation softening behaviour of austenite has been studied for various compositions and deformation conditions. The strain at which the transition from strain dependent to strain independent post-deformation softening behaviour occurs (ε*) has been found to coincide closely with the strain to the peak stress (εp) under certain conditions but not under others. It has been proposed that the relationship between ε* and εp may be described geometrically using the initial grain size and the dynamically recrystallised grain size.

Exploiting geometry for improved hybrid AOA/TDOA-based localization

In this paper we examine the geometrically constrained optimization approach to localization with hybrid bearing (angle of arrival, AOA) and time difference of  arrival (TDOA) sensors. In particular, we formulate a constraint on the measurement errors which is then used along with constraint-based optimization tools in order to estimate the maximum likelihood values of the errors given an appropriate cost function. In particular we focus on deriving a localization algorithm for stationary target localization in the so-called adverse localization geometries where the relative positioning of the sensors and the target do not readily permit accurate or convergent localization using traditional approaches. We illustrate this point via simulation and we compare our approach to a number of different techniques that are discussed in the literature.

Performance of smart antennas with receive diversity in wireless sensor networks

In this paper we propose a Geometrically Based Single Bounce Elliptical Model (GBSBEM) for multipath components involving randomly placed scatterers in the scattering region with sensors deployed on a field. The system model assumes a cluster based wireless sensor network (WSN) which collects information from the sensors, filters and modulates the data and transmit it through a wireless channel to be collected at the receiver. We first develop a GBSBE model and based on this model we develop our channel model. Use of Smart antenna system at the receiver end, which exploits various receive diversity combining techniques like Maximal Ratio Combining (MRC), Equal Gain Combining (EGC), and Selection Combining (SC), adds novelty to this system. The performance of these techniques have been proved through matlab simulations and further ahead based on different number of antenna elements present at the receiver array, we calculate the performance of our system in terms of bit-error-rate (BER). Based on the transmission power we quantify for the energy efficiency of our communication model.

Parametric modelling and the tessellation of architectural surfaces

Parametric modelling is gaining in popularity as both a fabrication and design tool, but its application in the architectural design industry has not been widely explored. This form of modelling has the ability to generate complex forms with intuitively reactive components, allowing designers to express and
fabricate structures previously too laborious and geometrically complex to realise. The key aim of the paper is to address the increasing need for seamless and bi-directional connectivity between the design, modelling and
fabrication ambit.

Tribology of lubricated nitrocarburised and titanium carbonitride surfaces

In the current work, two different coatings, nitrocarburised (CN) and titanium carbonitride (TiCN) on M2 grade high speed tool steel, were prepared by commercial diffusion and physical vapour deposition (PVD) techniques, respectively. Properties of the coating were characterised using a variety of techniques such as Glow-Discharge Optical Emission Spectrometry (GD-OES) and Scanning Electron Microscopy (SEM). Three non-commercial, oil-based lubricants with simplified formulations were used for this study. A tribological test was developed in which two nominally geometrically-identical crossed cylinders slide over each other under selected test conditions. This test was used to evaluate the effectiveness of a pre-applied lubricant film and a surface coating for various conditions of sliding wear. Engineered surface coatings can significantly improve wear resistance of the tool surface but their sliding wear performances strongly depend on the type of coating and lubricant combination used. These coating-lubricant interactions can also have a very strong effect on the useful life of the lubricant in a tribological system. Better performance of lubricants during the sliding wear testing was achieved hen used with the nitrocarburised (CN) coating. To understand the nature of the interactions and their possible effects on the coating-lubricant system, several surface analysis techniques were used. The molecular level investigation of Fourier Transform Infrared Spectroscopy (FTIR) revealed that oxidative degradation occurred in all used oil-based lubricants during the sliding wear test but the degradation behaviour of oil-based lubricants varied with the coating-lubricant system and the wear conditions. The main differences in the carbonyl oxidation region of the FTIR spectra (1900-1600 cm-1) between different coating-lubricant systems may relate to the effective lifetime of the lubricant during the sliding wear test. Secondary Ion Mass Spectrometry (SIMS) depth profiling shows that the CN coating has the highest lubricant absorbability among the tested tool surfaces. Diffusion of chlorine (C1), hydrogen (H) and oxygen (O) into the surface of subsurface of the tool suggested that strong interactions occurred between lubricant and tool surface during the sliding wear test. The possible effects of the interactions on the performance of whole tribological system are also discussed. The study of Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS) indicated that the envelope of hydrocarbons (CmHn) of oil lubricant in the positive TOF-SIMS spectra shifted to lower mass fragment after the sliding wear testing due to the breakage of long-chain hydrocarbons to short-chain ones during the degradation of lubricant. The shift of the mass fragment range of the hydrocarbon (CmHn) envelope caries with the type of both tool surface and lubricant, again confirming that variation in the performance of the tool-lubricant system relates to the changes in surface chemistry due to tribochemical interactions at the tool-lubricant interface under sliding wear conditions. The sliding wear conditions resulted in changes not only in topography of the tool surface due to mechanical interactions, as outlined in Chapter 5, but also in surface chemistry due to tribochemical interactions, as discussed in Chapters 6 and 7.

A simple displacement-based quadrilateral laminated composite plate element : Part II : linear analysis

The 4-node, 24-dof quadrilateral displacement-based element (Zhang et al. 2004), which have been developed successfully for linear analysis of thin to thick laminated composite plates, is extended further for geometrically nonlinear analysis in this paper. The proposed element is based on the first-order shear deformation theory (FSDT) and von-Karman's large deflection theory, and the total Lagrangian approach is employed to formulate the element. The deflection and rotation functions of the element boundary are obtained from Timoshenko's laminated composite beam functions. The developed element is simple in formulation, free from shear-locking, and include conventional engineering degrees of freedom. Numerical examples demonstrate that the element is accurate and efficient for large deformation, small rotation geometrically nonlinear analysis of thin to moderately thick laminated composite plates.

Parametric modelling of architectural surfaces

Parametric modelling is gaining in popularity as both a fabrication and design tool, but its application in the architectural design industry has not been widely explored. Parametric modelling has the ability to generate complex forms with intuitively reactive components, allowing designers to express and fabricate structures previously too laborious and geometrically complex to realise. This alIows designers to address a project at both the macro and micro levels of resolution in the governing control surface and the individual repetitive component. This two level modelling control, of component and overall surface, can allow designers to explore new types of form generation subject to parametric constraints. Shading screens have been selected as the focus for this paper and are used as a medium to explore form generation within a given set of functional parameters. Screens can have many applications in a building but for the purpose of the following case studies, lighting quality and passive sun control are the main functional requirement. A set of screen components have been designed within certain shading parameters to create a generic component that can automatically adapt to any given climatic conditions. These will then be applied to surfaces of varying degrees of geometric complexity to be analysed in their ability to correctly tessellate and create a unified screening array true to the lighting requirements placed on the generic component.