Fold, transcritical and pitchfork singularities for time-reversible systems

This paper deals with a class of singularly perturbed reversible planar vector fields around the origin where the normal hyperbolicity assumption is not assumed. We exhibit conditions for the existence of infinitely many periodic orbits and hetero-clinic cycles converging to singular orbits with respect to the Hausdorf distance. In addition, generic normal forms of such singularities are presented.

Singular perturbation problems for time-reversible systems

In this paper singularly perturbed reversible vector fields defined in R-n without normal hyperbolicity conditions are discussed. The main results give conditions for the existence of infinitely many periodic orbits and heteroclinic cycles converging to singular orbits with respect to the Hausdorff distance.

Path formulation for multiparameter D3-equivariant bifurcation problems

We implement a singularity theory approach, the path formulation, to classify D3-equivariant bifurcation problems of corank 2, with one or two distinguished parameters, and their perturbations. The bifurcation diagrams are identified with sections over paths in the parameter space of a Ba-miniversal unfolding f0 of their cores. Equivalence between paths is given by diffeomorphisms liftable over the projection from the zero-set of F0 onto its unfolding parameter space. We apply our results to degenerate bifurcation of period-3 subharmonics in reversible systems, in particular in the 1:1-resonance.

Campos de vetores lineares reversíveis equivariantes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Homoclinic bifurcations in reversible Hamiltonian systems

We study the existence of homoclic solutions for reversible Hamiltonian systems taking the family of differential equations u(iv) + au - u +f(u, b) = 0 as a model, where fis an analytic function and a, b real parameters. These equations are important in several physical situations such as solitons and in the existence of finite energy stationary states of partial differential equations, but no assumptions of any kind of discrete symmetry is made and the analysis here developed can be extended to others Hamiltonian systems and successfully employed in situations where standard methods fail. We reduce the problem of computing these orbits to that of finding the intersection of the unstable manifold with a suitable set and then apply it to concrete situations. We also plot the homoclinic values configuration in parameters space, giving a picture of the structural distribution and a geometrical view of homoclinic bifurcations. (c) 2005 Published by Elsevier B.V.

The sigma-isotypic decomposition and the sigma-index of reversible-equivariant systems

This work is concerned with dynamical systems in presence of symmetries and reversing symmetries. We describe a construction process of subspaces that are invariant by linear Gamma-reversible-equivariant mappings, where Gamma is the compact Lie group of all the symmetries and reversing symmetries of such systems. These subspaces are the sigma-isotypic components, first introduced by Lamb and Roberts in (1999) [10] and that correspond to the isotypic components for purely equivariant systems. In addition, by representation theory methods derived from the topological structure of the group Gamma, two algebraic formulae are established for the computation of the sigma-index of a closed subgroup of Gamma. The results obtained here are to be applied to general reversible-equivariant systems, but are of particular interest for the more subtle of the two possible cases, namely the non-self-dual case. Some examples are presented. (C) 2011 Elsevier BM. All rights reserved.

Stochastic Modeling of Reversible Biochemical Reaction-Diffusion Systems and High-Resolution Shock-Capturing Methods for Fluid Interfaces

Thesis (Ph.D.)--University of Washington, 2016-08

Conditional entropy and predictability for non-reversible Markov systems

The purpose of this thesis is to clarify the role of non-equilibrium stationary currents of Markov processes in the context of the predictability of future states of the system. Once the connection between the predictability and the conditional entropy is established, we provide a comprehensive approach to the definition of a multi-particle Markov system. In particular, starting from the well-known theory of random walk on network, we derive the non-linear master equation for an interacting multi-particle system under the one-step process hypothesis, highlighting the limits of its tractability and the prop- erties of its stationary solution. Lastly, in order to study the impact of the NESS on the predictability at short times, we analyze the conditional entropy by modulating the intensity of the stationary currents, both for a single-particle and a multi-particle Markov system. The results obtained analytically are numerically tested on a 5-node cycle network and put in correspondence with the stationary entropy production. Furthermore, because of the low dimensionality of the single-particle system, an analysis of its spectral properties as a function of the modulated stationary currents is performed.

Reversible Photorheology in Solutions of Cetyltrimethylammonium Bromide, Salicylic Acid, and trans-2,4,4 '-Trihydroxychalcone

We show photorheology in aqueous solutions of weakly entangled wormlike micelles prepared with cetyltrimethylammonium bromide (CTAB), salicylic acid (HSal), and dilute amounts of the photochromic multistate compound trans-2,4,4'-trihydroxychalcone (Ct). Different chemical species of Ct are associated with different colorations and propensities to reside within or outside CTAB micelles. A light-induced transfer between the intra- and intermicellar space is used to alter the mean length of wormlike micelles and hence the rheological properties of the fluid, studied in steady-state shear Bow and in dynamic rheological measurements. Light-induced changes of fluid rheology are reversible by a the relaxation process. at relaxation rates which depend on pH and which are consistent with photochromic reversion rates measured by UV-vis absorption spectroscopy. Parameterizing viscoelostic rheological states by their effective relaxation time tau(c) and corresponding response modulus G(c), we find the light and dark states of the system to fall onto a characteristic state curve defined by comparable experiments conducted without photosensitive components. These reference experiments were prepared with the same concentration of CTAB, but different concentrations of HSal or sodium salicylote (NaSal), and tested at different temperatures.

On Undecidable Dynamical Properties of Reversible One-Dimensional Cellular Automata

Cellular automata are models for massively parallel computation. A cellular automaton consists of cells which are arranged in some kind of regular lattice and a local update rule which updates the state of each cell according to the states of the cell's neighbors on each step of the computation. This work focuses on reversible one-dimensional cellular automata in which the cells are arranged in a two-way in_nite line and the computation is reversible, that is, the previous states of the cells can be derived from the current ones. In this work it is shown that several properties of reversible one-dimensional cellular automata are algorithmically undecidable, that is, there exists no algorithm that would tell whether a given cellular automaton has the property or not. It is shown that the tiling problem of Wang tiles remains undecidable even in some very restricted special cases. It follows that it is undecidable whether some given states will always appear in computations by the given cellular automaton. It also follows that a weaker form of expansivity, which is a concept of dynamical systems, is an undecidable property for reversible one-dimensional cellular automata. It is shown that several properties of dynamical systems are undecidable for reversible one-dimensional cellular automata. It shown that sensitivity to initial conditions and topological mixing are undecidable properties. Furthermore, non-sensitive and mixing cellular automata are recursively inseparable. It follows that also chaotic behavior is an undecidable property for reversible one-dimensional cellular automata.

Towards a better energy efficiency through a systems approach in an industrial forklift

The purpose of this study is to improve the potential energy recovery to electric energy in an electrohydraulic forklift system. The initial achieved result for energy saving ratio after structural optimization is 40 %. Component optimization is applied to the tested drive which consists of a DTC controlled electric servo motor directly running a reversible hydraulic pump. According to the study the energy efficiency and the energy recovery from the electro-hydraulic forklift system can be increased by 11 % units. New ideas and directions of further research were obtained during the study.

Viologen based electroactive polymers and composites for durable electrochromic systems

Electrochromism, the phenomenon of reversible color change induced by a small electric charge, forms the basis for operation of several devices including mirrors, displays and smart windows. Although, the history of electrochromism dates back to the 19th century, only the last quarter of the 20th century has its considerable scientific and technological impact. The commercial applications of electrochromics (ECs) are rather limited, besides top selling EC anti-glare mirrors by Gentex Corporation and airplane windows by Boeing, which made a huge commercial success and exposed the potential of EC materials for future glass industry. It is evident from their patents that viologens (salts of 4,4ʹ-bipyridilium) were the major active EC component for most of these marketed devices, signifying the motivation of this thesis focusing on EC viologens. Among the family of electrochromes, viologens have been utilized in electrochromic devices (ECDs) for a while, due to its intensely colored radical cation formation induced by applying a small cathodic potential. Viologens can be synthesized as oligomer or in the polymeric form or as functionality to conjugated polymers. In this thesis, polyviologens (PVs) were synthesized starting from cyanopyridinium (CNP) based monomer precursors. Reductive coupling of cross-connected cyano groups yields viologen and polyviologen under successive electropolymerization using for example the cyclic voltammetry (CV) technique. For further development, a polyviologen-graphene composite system was fabricated, focusing at the stability of the PV electrochrome without sacrificing its excellent EC properties. High electrical conductivity, high surface area offered by graphene sheets together with its non-covalent interactions and synergism with PV significantly improved the electrochrome durability in the composite matrix. The work thereby continued in developing a CNP functionalized thiophene derivative and its copolymer for possible utilization of viologen in the copolymer blend. Furthermore, the viologen functionalized thiophene derivative was synthesized and electropolymerized in order to explore enhancement in the EC contrast and overall EC performance. The findings suggest that such electroactive viologen/polyviologen systems and their nanostructured composite films as well as viologen functionalized conjugated polymers, can be potentially applied as an active EC material in future ECDs aiming at durable device performances.

A general synthesis of macrocyclic pi-electron-acceptor systems

Cyclocondensations of aromatic diamines with 1,1'-bis(2,4-dinitrophenyl)-4,4'-bipyridinium salts afford doubly or quadruply charged, macrocyclic, N,N'-diarylbipyridinium cations. These are tolerant of a wide range of acids, bases, and nucleophiles, although they appear to undergo reversible, one-electron reduction by tertiary amines. Single-crystal X-ray analysis demonstrates the presence of a macrocycle conformation in which the 4,4'-bipyridinium and 4,4'-biphenylenedisulfonyl residues are suitably spaced and aligned for complexation with pi-donor arenes, and NMR studies in solution indeed confirm binding to 1,5-bis[hydroxy(ethoxy)ethoxy]naphthalene.

Healable Polymer Systems

Polymers are used in many everyday technologies and their degradation due to environmental exposure has lead to great interest in materials which can heal and repair themselves. In order to design new self healing polymers it's important to understand the fundamental healing mechanisms behind the material.Healable Polymer Systems will outline the key concepts and mechanisms underpinning the design and processing of healable polymers, and indicate potential directions for progress in the future development and applications of these fascinating and potentially valuable materials. The book covers the different techniques developed successfully to date for both autonomous healable materials (those which do not require an external stimulus to promote healing) and rehealable or remendable materials (those which only recover their original physical properties if a specific stimulus is applied). These include the encapsulated-monomer approach, reversible covalent bond formation, irreversible covalent bond formation and supramolecular self-assembly providing detailed insights into their chemistry.Written by leading experts, the book provides polymer scientists with a compact and readily accessible source of reference for healable polymer systems.