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.

Fournier polarography revisited

A theory for Fournier polarography and higher order harmonics is presented. This is valid for reversible systems under semi-infinite diffusion to stationary and expanding plane electrodes. The algorithm is simple, accurate and exploits the identities holding for the interfacial concentrations. The computations — minimal in nature — can be carried out easily and the results given here were evaluated taking into account the presence of harmonics to, at least, the twenty-fifth order.

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

Optimal camera planning under versatile user constraints in multi-camera image processing systems

The selection of optimal camera configurations (camera locations, orientations, etc.) for multi-camera networks remains an unsolved problem. Previous approaches largely focus on proposing various objective functions to achieve different tasks. Most of them, however, do not generalize well to large scale networks. To tackle this, we propose a statistical framework of the problem as well as propose a trans-dimensional simulated annealing algorithm to effectively deal with it. We compare our approach with a state-of-the-art method based on binary integer programming (BIP) and show that our approach offers similar performance on small scale problems. However, we also demonstrate the capability of our approach in dealing with large scale problems and show that our approach produces better results than two alternative heuristics designed to deal with the scalability issue of BIP. Last, we show the versatility of our approach using a number of specific scenarios.

Reversible addition fragmentation chain transfer (RAFT) polymerization : mechanism, process and applications

The present article gives an overview of the reversible addition fragmentation chain transfer (RAFT) process. RAFT is one of the most versatile living radical polymerization systems and yields polymers of predictable chain length and narrow molecular weight distribution. RAFT relies on the rapid exchange of thiocarbonyl thio groups between growing polymeric chains. The key strengths of the RAFT process for polymer design are its high tolerance of monomer functionality and reaction conditions, the wide range of well-controlled polymeric architectures achievable, and its (in-principle) non-rate-retarding nature. This article introduces the mechanism of polymerization, the range of polymer molecular weights achievable, the range of monomers in which polymerization is controlled by RAFT, the various polymeric architectures that can be obtained, the type of end-group functionalities available to RAFT-made polymers, and the process of RAFT polymerization.

Reversible transdifferentiation of blood vascular endothelial cells to a lymphatic-like phenotype in vitro

Blood vascular cells and lymphatic endothelial cells (BECs and LECs, respectively) form two separate vascular systems and are functionally distinct cell types or lineages with characteristic gene expression profiles. Interconversion between these cell types has not been reported. Here, we show that in conventional in vitro angiogenesis assays, human BECs of fetal or adult origin show altered gene expression that is indicative of transition to a lymphatic-like phenotype. This change occurs in BECs undergoing tubulogenesis in fibrin, collagen or Matrigel assays, but is independent of tube formation per se, because it is not inhibited by a metalloproteinase inhibitor that blocks tubulogenesis. It is also reversible, since cells removed from 3D tubules revert to a BEC expression profile upon monolayer culture. Induction of the lymphatic-like phenotype is partially inhibited by co-culture of HUVECs with perivascular cells. These data reveal an unexpected plasticity in endothelial phenotype, which is regulated by contact with the ECM environment and/or cues from supporting cells.

Interactions of nandrolone and psychostimulant drugs on central monoaminergic systems

It has been hypothesized that abuse of supra-therapeutic doses of anabolic androgenic steroids (AASs) can lead to dependence and function as a gateway to abuse of other drugs. This is supported by behavioral studies on animal models and psychiatric evaluations of human subjects, although their neurochemical effects remain largely unknown. A large body of evidence suggests that the ability of the drugs to induce a strong elevation of extracellular dopamine (DA) levels in the nucleus accumbens (NAc), especially, plays a crucial role in their reinforcing effects. -- This study had four main aims. The first was to explore the effects of nandrolone decanoate on dopaminergic and serotonergic activities in the brains of rats. The second aim was to assess whether or not nandrolone pre-exposure modulates the acute neurochemical and behavioral effects of psychostimulant drugs in experimental animals. The third was to investigate if the AAS-pre-treatment induced changes in brain reward circuitry are reversible. And the fourth main goal was to evaluate the role of androgen and estrogen receptors in the modulation of the dopaminergic and serotonergic effects of acute injections of stimulant drugs by sub-chronic nandrolone treatment. The results showed that nandrolone decanoate at doses, high enough to induce erythropoiesis, significantly increased the levels of DOPAC and 5-HT in the cerebral cortex. Co-administration of AAS and psychostimulant drugs showed that the increase in extracellular DA and 5-HT concentration evoked by amphetamine, MDMA and cocaine in the NAc was attenuated dose-dependently by pretreatment with nandrolone. Nandrolone pre-exposure also attenuated the ability of stimulants to cause increased stereotyped behavior and locomotor activity. Despite the significant decrease in nandrolone concentration in blood, the attenuation of cocaine’s effects remained unchanged after a fairly long period without nandrolone, suggesting that nandrolone effects could be long lasting. Blockade of androgen receptors with flutamide abolished the attenuating effect of nandrolone pretreatment on amphetamine-induced elevation of extracellular DA concentration. --- In conclusion, the results show that AAS-pretreatment is able to inhibit the reward-related neurochemical and behavioral effects of amphetamine, MDMA and cocaine in experimental animals. Furthermore, it seems that these effects could be long lasting and it appears that the ability of nandrolone to modulate reward-related effects of stimulants is dependent on activation of androgen receptors.

Reversible shear-induced crystallization above equilibrium freezing temperature in a lyotropic surfactant system

We demonstrate a unique shear-induced crystallization phenomenon above the equilibrium freezing temperature (T-K(o)) in weakly swollen isotropic (L-i) and lamellar (L-alpha) mesophases with bilayers formed in a cationic-anionic mixed surfactant system. Synchrotron rheological X-ray diffraction study reveals the crystallization transition to be reversible under shear (i.e., on stopping the shear, the nonequilibrium crystalline phase L-c melts back to the equilibrium mesophase). This is different from the shear-driven crystallization below T-K(o), which is irreversible. Rheological optical observations show that the growth of the crystalline phase occurs through a preordering of the L-i phase to an L-alpha phase induced by shear flow, before the nucleation of the Lc phase. Shear diagram of the L-i phase constructed in the parameter space of shear rate ((gamma)) over dot vs. temperature exhibits L-i -> L-c and L-i -> L-alpha transitions above the equilibrium crystallization temperature (T-K(o)), in addition to the irreversible shear-driven nucleation of L-c in the L-i phase below T-K(o). In addition to revealing a unique class of nonequilibrium phase transition, the present study urges a unique approach toward understanding shear-induced phenomena in concentrated mesophases of mixed amphiphilic systems.

Temperature-Induced Reversible First-Order Single Crystal to Single Crystal Phase Transition in Boc-gamma(4)(R)Val-Val-OH: Interplay of Enthalpy and Entropy

Crystals of Boc-gamma y(4)(R)Val-Val-OH undergo a reversible first-order single crystal to single crystal phase transition at T-c approximate to 205 K from the orthorhombic space group P22(1)2(1) (Z' = 1) to the monoclinic space group P2(1) (Z' = 2) with a hysteresis of similar to 2.1 K. The low-temperature monoclinic form is best described as a nonmerohedral twin with similar to 50% contributions from its two components. The thermal behavior of the dipeptide crystals was characterized by differential scanning calorimetry experiments. Visual changes in birefringence of the sample during heating and cooling cycles on a hot-stage microscope with polarized light supported the phase transition. Variable-temperature unit cell check measurements from 300 to 100 K showed discontinuity in the volume and cell parameters near the transition temperature, supporting the first-order behavior. A detailed comparison of the room-temperature orthorhombic form with the low-temperature (100 K) monoclinic form revealed that the strong hydrogen-bonding motif is retained in both crystal systems, whereas the non-covalent interactions involving side chains of the dipeptide differ significantly, leading to a small change in molecular conformation in the monoclinic form as well as a small reorientation of the molecules along the ac plane. A rigid-body thermal motion analysis (translation, libration, screw; correlation of translation and libration) was performed to study the crystal entropy. The reversible nature of the phase transition is probably the result of an interplay between enthalpy and entropy: the low-temperature monoclinic form is enthalpically favored, whereas the room-temperature orthorhombic form is entropically favored.

Macroscopically Dissipative Systems with Underlying Microscopic Dynamics : Properties and Limits of Measurement

While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution.

Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.