On the initiation of boudinage and folding instabilities in layered elasto-visco-plastic solids - Insights from natural microstructures and numerical simulations

The present understanding of the initiation of boudinage and folding structures is based on viscosity contrasts and stress exponents, considering an intrinsically unstable state of the layer. The criterion of localization is believed to be prescribed by geometry-material interactions, which are often encountered in natural structures. An alternative localization phenomenon has been established for ductile materials, in which instability emerges for critical material parameters and loading rates from homogeneous conditions. In this thesis, conditions are sought under which this type of instability prevails and whether localization in geological materials necessarily requires a trigger by geometric imperfections. The relevance of critical deformation conditions, material parameters and the spatial configuration of instabilities are discussed in a geological context. In order to analyze boudinage geometries, a numerical eigenmode analysis is introduced. This method allows determining natural frequencies and wavelengths of a structure and inducing perturbations on these frequencies. In the subsequent coupled thermo-mechanical simulations, using a grain size evolution and end-member flow laws, localization emerges when material softening through grain size sensitive viscous creep sets in. Pinch-and-swell structures evolve along slip lines through a positive feedback between the matrix response and material bifurcations inside the layer, independent from the mesh-discretization length scale. Since boudinage and folding are considered to express the same general instability, both structures should arise independently of the sign of the loading conditions and for identical material parameters. To this end, the link between material to energy instabilities is approached by means of bifurcation analyses of the field equations and finite element simulations of the coupled system of equations. Boudinage and folding structures develop at the same critical energy threshold, where dissipative work by temperature-sensitive creep overcomes the diffusive capacity of the layer. This finding provides basis for a unified theory for strain localization in layered ductile materials. The numerical simulations are compared to natural pinch-and-swell microstructures, tracing the adaption of grain sizes, textures and creep mechanisms in calcite veins. The switch from dislocation to diffusion creep relates to strain-rate weakening, which is induced by dissipated heat from grain size reduction, and marks the onset of continuous necking. The time-dependent sequence uncovers multiple steady states at different time intervals. Microstructurally and mechanically stable conditions are finally expressed in the pinch-and-swell end members. The major outcome of this study is that boudinage and folding can be described as the same coupled energy-mechanical bifurcation, or as one critical energy attractor. This finding allows the derivation of critical deformation conditions and fundamental material parameters directly from localized structures in the field.

Functionality, Robustness and Control of Nonlinear Network Dynamics: Modeling and Understanding the C. elegans Connectome

Thesis (Ph.D.)--University of Washington, 2016-06

Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.

Entanglement and bifurcations in Jahn-Teller models

We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The Exbeta system models the coupling of a two-level electronic system, or qubit, to a single-oscillator mode, while the Exepsilon models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the Exbeta system, the ground states of the Exepsilon model always exhibit entanglement. For the Exbeta case we aim to clarify results from previous work, alluding to a link between the ground-state entanglement characteristics and a bifurcation of a fixed point in the classical analog. In the Exepsilon case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.

Quantum entanglement and fixed-point bifurcations

How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state-the ground state-achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.

Chaulioleptos haywardi n. gen., n. sp (Digenea : Sanguinicolidae) from Filimanus heptadactyla (Perciformes : Polynemidae) of Moreton Bay, Australia

Here we describe the first Species of sanguinicolid blood fluke (Trematoda: Digenea) from a polynemid fish. Chaulioleptos haywardi n. gen., n. sp. is described from Filimanus heptadacryla Cuvier, 1829 (Perciformes: Polynemidae), the sevenfinger threadfin from Sandgate, Moreton Bay (southeast Queensland, Australia). Chaidioleptos haywardi differs from existing sanguinicolid genera in the combined possession of the following 7 characters: 2 testes, an entirely postovarian uterus, a uterine chamber, separate genital pores, an H-shaped intestine with abbreviated anterior caeca, tegumental spines in incomplete ventromarginal transverse rows that are continuous along the length of the body, and vitelline follicles that are tightly compacted and subsequently appear to form a solid branching mass occupying the area anterior to intestinal bifurcation and extending posteriorly to the level of the posterior margin of the anterior testis. Chaulioleptos haywardi is most closely related to Paracardicola Martin, 1960 and Adelomyllos Nolan and Cribb, 2004.

Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

Global behavior of positive solutions of nonlinear three-point boundary value problems

We investigate the structure of the positive solution set for nonlinear three-point boundary value problems of the form u('') + h(t) f(u) = 0, u(0) = 0, u(1) = lambdau(eta), where eta epsilon (0, 1) is given lambda epsilon (0, 1/n) is a parameter, f epsilon C ([0, infinity), [0, infinity)) satisfies f (s) > 0 for s > 0, and h epsilon C([0, 1], [0, infinity)) is not identically zero on any subinterval of [0, 1]. Our main results demonstrate the existence of continua of positive solutions of the above problem. (C) 2004 Elsevier Ltd. All rights reserved.

Stability and cycles in a cobweb model with heterogeneous expectations

We investigate the dynamics of a cobweb model with heterogeneous beliefs, generalizing the example of Brock and Hommes (1997). We examine situations where the agents form expectations by using either rational expectations, or a type of adaptive expectations with limited memory defined from the last two prices. We specify conditions that generate cycles. These conditions depend on a set of factors that includes the intensity of switching between beliefs and the adaption parameter. We show that both Flip bifurcation and Neimark-Sacker bifurcation can occur as primary bifurcation when the steady state is unstable.

Pendant drop formation of shear-thinning and yield stress fluids

A volume-of-fluid numerical method is used to predict the dynamics of shear-thinning liquid drop formation in air from a circular orifice. The validity of the numerical calculation is confirmed for a Newtonian liquid by comparison with experimental measurements. For particular values of Weber number and Froude number, predictions show a more rapid pinch-off, and a reduced number of secondary droplets, with increasing shear-thinning. Also a minimum in the limiting drop length occurs for the smallest Weber number as the zero-shear viscosity is varied. At the highest viscosity, the drop length is reduced due to shear-thinning, whereas at lower viscosities there is little effect of shear-thinning. The evolution of predicted drop shape, drop thickness and length, and the configuration at pinch-off are discussed for shear-thinning drops. The evolution of a drop of Bingham yield stress liquid is also considered as a limiting case. In contrast to the shear-thinning cases, it exhibits a plug flow prior to necking, an almost step-change approach to pinch-off of a torpedo shaped drop following the onset of necking, and a much smaller neck length; no secondary drops are formed. The results demonstrate the potential of the numerical model as a design tool in tailoring the fluid rheology for controlling drop formation behaviour. (c) 2006 Elsevier Inc. All rights reserved.

An exceptionally rich complex of Sanguinicolidae von Graff, 1907 (Platyhelminthes : Trematoda) from Siganidae, Labridae and Mullidae (Teleostei : Perciformes) from the Indo-West Pacific Region

We describe an unprecedented radiation of sanguinicolid blood flukes ( Digenea: Sanguinicolidae) from two species of Labridae (Choerodon venustus and C. cauteroma), seven species of Mullidae (Mulloidichthys vanicolensis, Parupeneus barberinoides, P. barberinus, P. bifasciatus, P. cyclostomus, P. indicus and P. multifasciatus) and ten species of Siganidae (Siganus argenteus, S. corallinus, S. doliatus, S. fuscescens, S. lineatus, S. margaritiferus, S. puellus, S. punctatus, S. virgatus and S. vulpinus) from sites off Australia and Palau. The flukes were morphologically similar in having the combination of a long thread-like body, tegumental spines in lateral transverse rows, a vestigial oral sucker bearing concentric rows of fine spines, an H-shaped intestine, a cirrussac, a notch level with the male genital pore, a lateral or post-ovarian uterus, a uterine chamber and separate genital pores. These species are divided into two genera on the basis of testis number. Sanguinicolids from Siganus fuscescens have a single large testis between the intestinal bifurcation and the ovary and are placed in Ankistromeces Nolan & Cribb, 2004. Species from the remaining nine species of Siganidae, Labridae and Mullidae are placed in Phthinomita n. g.; these species have two testes, the anterior testis being large and between the intestinal bifurcation and the ovary whereas the small posterior testis is at the posterior end of the body and appears rudimentary or degenerate and probably non-functional. The second internal transcribed spacer (ITS2) of ribosomal DNA ( rDNA) from 29 host/parasite/location combinations (h/p/l) was sequenced together with that of Ankistromeces mariae Nolan & Cribb, 2004 for comparison. From 135 samples we found 19 distinct genotypes which were interpreted as representing at least that many species. Replicate sequences were obtained for 25 of 30 h/p/l combinations ( including A. mariae); there was no intraspecific variation between replicates sequences for any of these. Interspecific variation ranged from 1 - 41 base differences (0.3 - 12.7% sequence divergence). The 19 putative species were difficult to recognise by morphological examination. We describe 13 new species; we do not describe (= name) six species characterised solely by molecular sequences and three putative species for which morphological data is available but for which molecular data is not. We have neither morphological nor molecular data for sanguinicolids harboured in five hosts species ( Siganus margaritiferus, S. puellus, Choerodon cauteroma, Parupeneus indicus and P. multifasciatus) in which we have seen infections. Where host species were infected in different localities they almost always harboured distinct species. Some host species ( for example, S. argenteus and S. lineatus from Lizard Island) harboured two or three species in a single geographical location. This suggests that, for parts of this system, parasite speciation has outstripped host speciation. Distance analysis of ITS2 showed species from each host family ( Siganidae, Mullidae and Labridae) did not form monophyletic clades to the exclusion of species from other host families. However, a host defined clade was formed by the sequences from sanguinicolids from S. fuscescens.

Comparative proteomic analysis to study molecular events during gonad development in mice

Sex determination represents a critical bifurcation in the road of embryonic development. It is based on a finely regulated network of gene activity, as well as protein-protein interactions and activation or silencing of signaling pathways. Despite the identification of a number of critical genes, many aspects of the molecular cascade that drives the differentiation of the embryonic gonad into either a testis or an ovary remain poorly understood. To identify new proteins involved in this cascade, we employed two-dimensional gel electrophoresis and mass spectrometry to compare the protein expression profiles of fetal mouse testes and ovaries. Three proteins, hnRPA1, TRA1, and HSC71, were found to be expressed in a male-specific manner and this expression was confirmed by real-time reverse transcriptase polymerase chain reaction (RT-PCR) and in situ hybridization. Moreover, HSC71 was found to be hyperphosphorylated in male compared to female gonads, emphasizing the advantage of the proteomic approach in allowing the detection of posttranslational modifications.

Investigating the performance analysis of EASI algorithm and EKENS algorithm in nonlinear model

This paper investigates the performance of EASI algorithm and the proposed EKENS algorithm for linear and nonlinear mixtures. The proposed EKENS algorithm is based on the modified equivariant algorithm and kernel density estimation. Theory and characteristic of both the algorithms are discussed for blind source separation model. The separation structure of nonlinear mixtures is based on a nonlinear stage followed by a linear stage. Simulations with artificial and natural data demonstrate the feasibility and good performance of the proposed EKENS algorithm.

Bifurcating trajectory of non-diffractive electromagnetic airy pulse

The explicit expression for spatial-temporal Airy pulse is derived from the Maxwell's equations in paraxial approximation. The trajectory of the pulse in the time-space coordinates is analysed. The existence of a bifurcation point that separates regions with qualitatively different features of the pulse propagation is demonstrated. At this point the velocity of the pulse becomes infinite and the orientation of it changes to the opposite.