Stabilizing the Richardson Algorithm by Controlling Chaos

By viewing the operations of the Richardson purification algorithm as a discrete time dynamical process, we propose a method to overcome the instability of the algorithm by controlling chaos. We present theoretical analysis and numerical results on the behavior and performance of the stabilized algorithm.Comment: Send email to [email protected] or [email protected] for uuencoded tarred gzipped postscript files for the five figure

A new method for isolating turbulent states in transitional stratified plane Couette flow

We present a new adaptive control strategy to isolate and stabilize turbulent states in transitional, stably stratified plane Couette flow in which the gravitational acceleration (non-dimensionalized as the bulk Richardson number$Ri$) is adjusted in time to maintain the turbulent kinetic energy (TKE) of the flow. We demonstrate that applying this method at various stages of decaying stratified turbulence halts the decay process and allows a succession of intermediate turbulent states of decreasing energy to be isolated and stabilized. Once the energy of the initial flow becomes small enough, we identify a single minimal turbulent spot, and lower-energy states decay to laminar flow. Interestingly, the turbulent states which emerge from this process have very similar time-averaged$Ri$, but TKE levels different by an order of magnitude. The more energetic states consist of several turbulent spots, each qualitatively similar to the minimal turbulent spot. This suggests that the minimal turbulent spot may well be the lowest-energy turbulent state which forms a basic building block of stratified plane Couette flow. The fact that a minimal spot of turbulence can be stabilized, so that it neither decays nor grows, opens up exciting opportunities for further study of spatiotemporally intermittent stratified turbulence.The EPSRC grant EP/K034529/1 entitled ‘Mathematical Underpinnings of Stratified Turbulence’ is gratefully acknowledged for supporting the research presented here.This is the author accepted manuscript. The final version is available from Cambridge University Press via https://doi.org/10.1017/jfm.2016.62

Global topological control for synchronized dynamics on networks

A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act on the topology of the inter-nodes contacts to achieve the desired degree of stabilization, without altering the dynamical parameters of the model. Both symmetric and asymmetric couplings are considered. In this latter setting the web of contacts is assumed to be balanced, for the homogeneous equilibrium to exist. The performance of the proposed method are assessed, assuming the Complex Ginzburg-Landau equation as a reference model. In this case, the implemented control allows one to stabilize the synchronous limit cycle, hence time-dependent, uniform solution. A system of coupled real Ginzburg-Landau equations is also investigated to obtain the topological stabilization of a homogeneous and constant fixed point

Control mechanisms for a nonlinear model of international relations

Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race

Functional analysis of chloroplast signal recognition particle (cpSRP) in chlorophyll biosynthesis

Im ersten Teil dieser Studie habe ich gezeigt, dass die Chaperonaktivität von cpSRP43 für die Stabilität der drei essenziellen TBS-Proteine Glutamyl-tRNA-Reduktase (GluTR), der H-Untereinheit der Magnesium-Chelatase (CHLH) und von Genomes Uncoupled 4 (GUN4 ) wichtig ist. cpSRP43 schützt diese TBS-Proteine effizient vor hitzeinduzierter Aggregatbildung und verbessert ihre Thermostabilität während eines Hitzeschocks. Während die substratbindende Domäne (SBD) von cpSRP43 für die Interaktion mit LHCPs ausreicht, erfordert die Stabilisierung der TBS-Proteine die zusätzliche cpSRP43-Chromodomäne 2 (CD2). Es wurde überraschend gefunden, dass cpSRP54 die Chaperonaktivität von cpSRP43 für LHCPs aktiviert, während es sie für TBS-Proteine vermindern kann. Aber erhöhte Temperatur kann die Bindung von cpSRP43 mit cpSRP54 lösen, aber seine Wechselwirkung mit GluTR, CHLH und GUN4 verstärken, was zu einem verstärkten Schutz von cpSRP43 gegenüber diesen Proteinen unter Hitzeschockbedingungen führt. Im zweiten Teil dieser Studie wurde festgestellt, dass PORB (eines der drei POR Isoformen) ein weiteres Ziel von cpSRP43 ist. Zusammenfassend haben meine Studien einen möglichen Mechanismus von PORB durch konzertierte Aktionen von cpSRP43 und cpSRP54 aufgezeigt. (1) cpSRP43 wirkt als molekulares Chaperon, um PORB vor der Aggregation zu schützen, wodurch die Stabilität des PORB bewahrt wird. (2) cpSRP54 kann PORB bei der Anlagerung an die Thylakoidmembran unterstützen, was vermutlich den Abbau von PORB vermeidet und die Stabilität von PORB verbessert oder den Zugang zum katalytischen Substrat ermöglicht. Zusammenfassend trägt diese Arbeit zum erweiterten Wissen über die voneinander abhängige Chaperonfunktion der beiden Proteine cpSRP43 und cpSRP54 bei der Koordination von Chlorophyllsynthese und LHCP-Biogenese bei.In the first part of this study, I showed that the chaperone activity of cpSRP43 is essential for the stability of the three critical TBS proteins: glutamyl-tRNA reductase (GluTR), the H subunit of magnesium chelatase (CHLH), and GENOMES UNCOUPLED 4 (GUN4). cpSRP43 efficiently protects these TBS clients from heat-induced aggregation and enhances their thermostability during heat shock. Although the substrate-binding domain (SBD) of cpSRP43 is sufficient for the interaction with LHCPs, the stabilization of TBS clients requires the additional chromodomain 2 (CD2). cpSRP54, which activates the chaperone activity of cpSRP43 on LHCPs, was surprisingly found to antagonize this chaperone activity on TBS proteins. The elevated temperature alleviates the binding of cpSRP43 to cpSRP54 but enhances its interaction with GluTR, CHLH and GUN4, resulting in enhanced protection of cpSRP43 to these proteins under heat shock conditions. My study suggests a working model that the temperature sensitivity of the cpSRP43-cpSRP54 complex enables cpSRP43 to serve as an autonomous chaperone for the thermoprotection of TBS proteins. In the second part of this study, PORB (one of the three POR isoforms) was found to be a new target of cpSRP43. My study revealed a potential mechanism of PORB by concerted actions of cpSRP43 and cpSRP54: (1) cpSRP43 acts as a molecular chaperone to protect PORB from aggregation, thereby preserving the stability of PORB. (2) cpSRP54 assists PORB in attachment to the thylakoid membrane, avoids the degradation of PORB and, thus, improves the stability of PORB or enables access to the catalytic substrate. In summary, this thesis contributes to the extended knowledge about the interdependent chaperone function of cpSRP43 and cpSRP54 in coordination of Chl synthesis and LHCP biogenesis

Gait Dynamic Stability Analysis with Wearable Assistive Robots

abstract: Lower-limb wearable assistive robots could alter the users gait kinematics by inputting external power, which can be interpreted as mechanical perturbation to subject normal gait. The change in kinematics may affect the dynamic stability. This work attempts to understand the effects of different physical assistance from these robots on the gait dynamic stability. A knee exoskeleton and ankle assistive device (Robotic Shoe) are developed and used to provide walking assistance. The knee exoskeleton provides personalized knee joint assistive torque during the stance phase. The robotic shoe is a light-weighted mechanism that can store the potential energy at heel strike and release it by using an active locking mechanism at the terminal stance phase to provide push-up ankle torque and assist the toe-off. Lower-limb Kinematic time series data are collected for subjects wearing these devices in the passive and active mode. The changes of kinematics with and without these devices on lower-limb motion are first studied. Orbital stability, as one of the commonly used measure to quantify gait stability through calculating Floquet Multipliers (FM), is employed to asses the effects of these wearable devices on gait stability. It is shown that wearing the passive knee exoskeleton causes less orbitally stable gait for users, while the knee joint active assistance improves the orbital stability compared to passive mode. The robotic shoe only affects the targeted joint (right ankle) kinematics, and wearing the passive mechanism significantly increases the ankle joint FM values, which indicates less walking orbital stability. More analysis is done on a mechanically perturbed walking public data set, to show that orbital stability can quantify the effects of external mechanical perturbation on gait dynamic stability. This method can further be used as a control design tool to ensure gait stability for users of lower-limb assistive devices.Dissertation/ThesisMasters Thesis Mechanical Engineering 201