On the Control of Chaos in Extended Structures

1997 ◽  
Vol 119 (4) ◽  
pp. 551-556 ◽  
Author(s):  
C. Barratt
Keyword(s):  
Nearest Neighbor ◽  
Duffing Oscillator ◽  
Vertical Plane ◽  
Small Time ◽  
Time Dependent ◽  
External Forcing ◽  
Control Of Chaos ◽  
Chaotic Vibrations ◽  
Order Of Magnitude ◽  
The Individual

A mechanism is proposed for synchronizing the chaotic vibrations of an externally forced array of oscillators with nearest-neighbor viscoelastic coupling. The proposed mechanism involves the application of small time-dependent perturbations to the individual oscillators. The perturbations required to preserve the coherence are of the order of magnitude of any noise present. The mechanism works with any form of external forcing. A modification of the mechanism is used to control the forced chaotic vibrations of a single Duffing oscillator allowed to vibrate out of the vertical plane.

On the Control of Chaos in Extended Structures

1995 ◽  
Author(s):  
Carl Barratt
Keyword(s):  
Nearest Neighbor ◽  
Duffing Oscillator ◽  
Vertical Plane ◽  
External Forcing ◽  
Control Of Chaos ◽  
Chaotic Vibrations ◽  
Forcing Function ◽  
Control Scheme ◽  
The Individual

Abstract A mechanism is proposed for synchronizing the vibrations of an externally forced array of Duffing oscillators with nearest-neighbor viscoelastic coupling. The parameters of the individual oscillators and the couplings are chosen such that, in the absence of control, the oscillators vibrate chaotically and incoherently. The proposed control scheme brings the elements into synchrony with each other in a few tens of cycles of the external forcing function. It is robust, maintaining the desired state in the presence of noise. It is general in that it works with any form of external forcing. A modification of the mechanism is used to control the forced chaotic vibrations of a single Duffing oscillator allowed to vibrate out of the vertical plane.

scholarly journals Statistical Uncertainty of DNS in Geometries without Homogeneous Directions

2021 ◽  
Vol 11 (4) ◽  
pp. 1399
Author(s):  
Jure Oder ◽  
Cédric Flageul ◽  
Iztok Tiselj
Keyword(s):  
Channel Flow ◽  
A Priori ◽  
Time Integration ◽  
Navier Stokes ◽  
Statistical Uncertainty ◽  
Time Step ◽  
Order Of Magnitude ◽  
Averaging Time ◽  
The Individual ◽  
Time Required

In this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two homogeneous directions and this is usually exploited to speed-up the convergence of the results. As we show, such a procedure reduces statistical uncertainties of the results by up to an order of magnitude. This effect is strongest in the near wall regions. In the case of flow over a confined BFS, there are no such directions and thus very long integration times are required. The individual statistical quantities converge with the square root of time integration so, in order to improve the uncertainty by a factor of two, the simulation has to be prolonged by a factor of four. We provide an estimator that can be used to evaluate a priori the DNS relative statistical uncertainties from results obtained with a Reynolds Averaged Navier Stokes simulation. In the DNS, the estimator can be used to predict the averaging time and with it the simulation time required to achieve a certain relative statistical uncertainty of results. For accurate evaluation of averages and their uncertainties, it is not required to use every time step of the DNS. We observe that statistical uncertainty of the results is uninfluenced by reducing the number of samples to the point where the period between two consecutive samples measured in Courant–Friedrichss–Levy (CFL) condition units is below one. Nevertheless, crossing this limit, the estimates of uncertainties start to exhibit significant growth.

scholarly journals An integrated microfluidic platform for quantifying drug permeation across biomimetic vesicle membranes

2019 ◽  
Author(s):  
Michael Schaich ◽  
Jehangir Cama ◽  
Kareem Al Nahas ◽  
Diana Sobota ◽  
Kevin Jahnke ◽  
...  
Keyword(s):  
Drug Transport ◽  
Membrane Composition ◽  
Drug Permeability ◽  
Bacterial Membranes ◽  
Drug Molecules ◽  
Total Analysis System ◽  
Transport Assay ◽  
Order Of Magnitude ◽  
Analysis System ◽  
The Individual

The low membrane permeability of candidate drug molecules is a major challenge in drug development and insufficient permeability is one reason for the failure of antibiotic treatment against bacteria. Quantifying drug transport across specific pathways in living systems is challenging since one typically lacks knowledge of the exact lipidome and proteome of the individual cells under investigation. Here, we quantify drug permeability across biomimetic liposome membranes, with comprehensive control over membrane composition. We integrate the microfluidic octanol-assisted liposome assembly platform with an optofluidic transport assay to create a complete microfluidic total analysis system for quantifying drug permeability. Our system enables us to form liposomes with charged lipids mimicking the negative charge of bacterial membranes at physiological salt and pH levels, which proved difficult with previous liposome formation techniques. Furthermore, the microfluidic technique yields an order of magnitude more liposomes per experiment than previous assays. We demonstrate the feasibility of the assay by determining the permeability coefficient of norfloxacin across biomimetic liposomes.

scholarly journals Probing E. coli SSB Protein-DNA topology by reversing DNA backbone polarity

2020 ◽  
Author(s):  
Alexander G. Kozlov ◽  
Timothy M. Lohman
Keyword(s):  
Dna Binding ◽  
Crystal Structures ◽  
Nearest Neighbor ◽  
Genome Maintenance ◽  
Binding Properties ◽  
Ssdna Binding ◽  
E Coli ◽  
Phosphodiester Linkage ◽  
The Individual ◽  
Dna Binding Properties

AbstractE. coli single strand (ss) DNA binding protein (SSB) is an essential protein that binds ssDNA intermediates formed during genome maintenance. SSB homo-tetramers bind ssDNA in two major modes differing in occluded site size and cooperativity. The (SSB)35 mode in which ssDNA wraps on average around two subunits is favored at low [NaCl] and high SSB to DNA ratios and displays high “unlimited”, nearest-neighbor cooperativity forming long protein clusters. The (SSB)65 mode, in which ssDNA wraps completely around four subunits of the tetramer, is favored at higher [NaCl] (> 200 mM) and displays “limited” low cooperativity. Crystal structures of E. coli SSB and P. falciparum SSB show ssDNA bound to the SSB subunits (OB-folds) with opposite polarities of the sugar phosphate backbones. To investigate whether SSB subunits show a polarity preference for binding ssDNA, we examined EcSSB and PfSSB binding to a series of (dT)70 constructs in which the backbone polarity was switched in the middle of the DNA by incorporating a reverse polarity (RP) phosphodiester linkage, either 3’-3’ or 5’-5’. We find only minor effects on the DNA binding properties for these RP constructs, although (dT)70 with a 3’-3’ polarity switch shows decreased affinity for EcSSB in the (SSB)65 mode and lower cooperativity in the (SSB)35 mode. However, (dT)70 in which every phosphodiester linkage is reversed, does not form a completely wrapped (SSB)65 mode, but rather binds EcSSB in the (SSB)35 mode, with little cooperativity. In contrast, PfSSB, which binds ssDNA only in an (SSB)65 mode and with opposite backbone polarity and different topology, shows little effect of backbone polarity on its DNA binding properties. We present structural models suggesting that strict backbone polarity can be maintained for ssDNA binding to the individual OB-folds if there is a change in ssDNA wrapping topology of the RP ssDNA.Statement of SignificanceSingle stranded (ss) DNA binding (SSB) proteins are essential for genome maintenance. Usually homo-tetrameric, bacterial SSBs bind ssDNA in multiple modes, one of which involves wrapping 65 nucleotides of ssDNA around all four subunits. Crystal structures of E. coli and P. falciparum SSB-ssDNA complexes show ssDNA bound with different backbone polarity orientations raising the question of whether these SSBs maintain strict backbone polarity in binding ssDNA. We show that both E. coli and P. falciparum SSBs can still form high affinity fully wrapped complexes with non-natural DNA containing internal reversals of the backbone polarity. These results suggest that both proteins maintain a strict backbone polarity preference, but adopt an alternate ssDNA wrapping topology.

Tectonic and geomorphic controls on the lacustrine deposits of the Neogene Vinchina basin, northwestern Argentina

2020 ◽  
Vol 90 (2) ◽  
pp. 250-267 ◽  
Author(s):  
Sergio A. Marenssi ◽  
Carlos O. Limarino ◽  
Laura J. Schencman ◽  
Patricia L. Ciccioli
Keyword(s):  
Water Depth ◽  
Drainage Basin ◽  
Low Frequency ◽  
Sedimentary Facies ◽  
Coarse Grained ◽  
Lacustrine Deposits ◽  
Facies Associations ◽  
Order Of Magnitude ◽  
Fluvial Sedimentation ◽  
The Individual

ABSTRACT Two episodes of lacustrine sedimentation, separated by an erosional surface and fluvial sedimentation, took place in the southern part of the broken foreland Vinchina basin (NW Argentina) between 11 and 5 Ma. The lacustrine deposits, 768 and 740 meters thick, are recorded in the upper part of the Vinchina Formation (“Vinchina lake”) and the lower part of the Toro Formation (“Toro Negro lake”) respectively. According to sedimentological features, four sedimentary facies associations (FAs) are recognized in the lacustrine deposits: 1) thinly laminated mudstones facies association (FA 1), 2) coarsening- and thickening-upward muddy to sandy cycles (FA 2), 3) medium- to coarse-grained sandstones (FA 3), and 4) mudstones, sandstones, and oolitic limestones (FA 4). Altogether, these facies correspond to ephemeral, shallow, lacustrine systems including saline mudflats. The total thickness of each lacustrine interval, the thickness of the individual cycles and their lithology, and the overall aggradational facies arrangement suggest that both lakes developed during underfilled stages of the basin. The coarsening-upward cycles can be regarded as lacustrine parasequences representing cyclic episodes of expansion and contraction of the lake, but unlike marine parasequences these cycles do not correlate to water depth. The development of lacustrine conditions and continuous base-level rise, together with the coeval southward-directed paleoflow indicators, suggest axial drainages and that the basin was externally closed (endorheic) at that time. The large thicknesses of each lacustrine interval also points to high accommodation in the southern part of the Vinchina basin during these times. Lake filling cycles are one order of magnitude thicker than lake depth, so we postulate that subsidence (tectonic) and rise of the spill point (geomorphology) increased accommodation but not water depth. Thus, unlike marine parasequences, the analyzed coarsening-upward cycles do not correlate to water depth, but rather they are controlled by more complex basinal accommodation processes. We hypothesize that the coeval uplift of the Umango and Espinal basement block to the south, coupled with the initial doming of the Sierra de Los Colorados to the east, may have generated the damming of the southward-directed drainage and a zone of maximum accommodation, then controlling the location of the two lakes and the preservation of their thick sedimentary records. Therefore, localized accommodation was enhanced by a combination of tectonic subsidence and topographic growth. The two lacustrine intervals and the intervening fluvial deposits record changing contributions from axial to transverse drainages and different cycles of closed and open conditions in the basin. A low-frequency, closed to open and back to closed (axial to transverse and return to axial drainage) basin evolution, is envisaged by the development of the two lakes (closed stages) and the erosional surface followed by the interval of fluvial sedimentation that separates them (open stage). In addition, several high-frequency lake fluctuations (expansion–contraction) are represented by the coarsening-upward cycles within each lacustrine interval. The thick lacustrine intervals and their intermediate incision surfaces record cyclic filling and re-excavation stages and localized episodes of increased subsidence in the Vinchina basin, which seem to be a common feature of tectonically active broken foreland basins.

Lateral Dynamics of Walking-Like Mechanical Systems and Their Chaotic Behavior

2019 ◽  
Vol 29 (09) ◽  
pp. 1930024
Author(s):  
Sergej Čelikovský ◽  
Volodymyr Lynnyk
Keyword(s):  
Stability Region ◽  
Inverted Pendulum ◽  
Chaotic Behavior ◽  
Mechanical Systems ◽  
Small Time ◽  
Time Varying ◽  
External Forcing ◽  
Double Support ◽  
Lateral Dynamics ◽  
Detailed Mathematical Analysis

A detailed mathematical analysis of the two-dimensional hybrid model for the lateral dynamics of walking-like mechanical systems (the so-called hybrid inverted pendulum) is presented in this article. The chaotic behavior, when being externally harmonically perturbed, is demonstrated. Two rather exceptional features are analyzed. Firstly, the unperturbed undamped hybrid inverted pendulum behaves inside a certain stability region periodically and its respective frequencies range from zero (close to the boundary of that stability region) to infinity (close to its double support equilibrium). Secondly, the constant lateral forcing less than a certain threshold does not affect the periodic behavior of the hybrid inverted pendulum and preserves its equilibrium at the origin. The latter is due to the hybrid nature of the equilibrium at the origin, which exists only in the Filippov sense. It is actually a trivial example of the so-called pseudo-equilibrium [Kuznetsov et al., 2003]. Nevertheless, such an observation holds only for constant external forcing and even arbitrary small time-varying external forcing may destabilize the origin. As a matter of fact, one can observe many, possibly even infinitely many, distinct chaotic attractors for a single system when the forcing amplitude does not exceed the mentioned threshold. Moreover, some general properties of the hybrid inverted pendulum are characterized through its topological equivalence to the classical pendulum. Extensive numerical experiments demonstrate the chaotic behavior of the harmonically perturbed hybrid inverted pendulum.

Unsteady convective diffusion with interphase mass transfer

1973 ◽  
Vol 333 (1592) ◽  
pp. 115-132 ◽  
Keyword(s):  
Dispersion Model ◽  
Reaction Rates ◽  
The Other ◽  
Time Dependent ◽  
Transport Systems ◽  
Exchange Coefficient ◽  
Dispersion Coefficients ◽  
Interfacial Transport ◽  
Order Of Magnitude ◽  
Proper Values

The theory of miscible dispersion is extended to interphase transport systems. As a specific example miscible dispersion in laminar flow in a tube in the presence of interfacial transport due to an irreversible first-order reaction at the wall is analysed by an exact procedure. A new exact dispersion model which accounts for dispersion with interphase transport is derived from first principles. The new concept of an ‘exchange coefficient’ arises naturally. This coefficient depends strongly on the rate of interfacial transport. Such transport also affects the convection and dispersion coefficients significantly. A general expression is derived which shows clearly the time-dependent nature of the coefficients in the dispersion model. The complete time-dependent expression for the exchange coefficient is obtained explicitly and is independent of the velocity distribution in the flow; however, it does depend on the initial solute distribution. Because of the complexity of the problem only asymptotic large-time evaluations are made for the convection and dispersion coefficients, but these are sufficient to give useful physical insight into the nature of the problem. When the rate of the wall reaction approaches zero the exchange coefficient also approaches zero and the other two coefficients approach their proper values in the absence of interfacial transport. At the other extreme of rapid wall reaction rates, the convection coefficient is more than 50 % larger than its value in the absence of interfacial transport and the dispersion coefficient is an order of magnitude smaller than that for zero interphase transport.

scholarly journals Conformity in the collective: differences in hunger affect individual and group behavior in a shoaling fish

2019 ◽  
Vol 30 (4) ◽  
pp. 968-974 ◽  
Author(s):  
Alexander D M Wilson ◽  
Alicia L J Burns ◽  
Emanuele Crosato ◽  
Joseph Lizier ◽  
Mikhail Prokopenko ◽  
...  
Keyword(s):  
Collective Behavior ◽  
Nearest Neighbor ◽  
Collective Motion ◽  
Internal State ◽  
Group Behavior ◽  
Fundamental Interest ◽  
Individual Level ◽  
Group Members ◽  
The Individual ◽  
Nearest Neighbor Distances

Abstract Animal groups are often composed of individuals that vary according to behavioral, morphological, and internal state parameters. Understanding the importance of such individual-level heterogeneity to the establishment and maintenance of coherent group responses is of fundamental interest in collective behavior. We examined the influence of hunger on the individual and collective behavior of groups of shoaling fish, x-ray tetras (Pristella maxillaris). Fish were assigned to one of two nutritional states, satiated or hungry, and then allocated to 5 treatments that represented different ratios of satiated to hungry individuals (8 hungry, 8 satiated, 4:4 hungry:satiated, 2:6 hungry:satiated, 6:2 hungry:satiated). Our data show that groups with a greater proportion of hungry fish swam faster and exhibited greater nearest neighbor distances. Within groups, however, there was no difference in the swimming speeds of hungry versus well-fed fish, suggesting that group members conform and adapt their swimming speed according to the overall composition of the group. We also found significant differences in mean group transfer entropy, suggesting stronger patterns of information flow in groups comprising all, or a majority of, hungry individuals. In contrast, we did not observe differences in polarization, a measure of group alignment, within groups across treatments. Taken together these results demonstrate that the nutritional state of animals within social groups impacts both individual and group behavior, and that members of heterogenous groups can adapt their behavior to facilitate coherent collective motion.

Markov-modulated traffic with nearly complete decomposability characteristics and associated fluid queueing models

1995 ◽  
Vol 27 (04) ◽  
pp. 1144-1185
Author(s):  
Kimon P. Kontovasilis ◽  
Nikolas M. Mitrou
Keyword(s):  
State Space ◽  
Time Scales ◽  
Structural Characteristics ◽  
Queueing Systems ◽  
Queuing Models ◽  
Aggregation Techniques ◽  
Phase Perturbation ◽  
Order Of Magnitude ◽  
Markov Modulated ◽  
The Individual

This paper considers fluid queuing models of Markov-modulated traffic that, due to large differences in the time-scales of events, possess structural characteristics that yield a nearly completely decomposable (NCD) state-space. Extension of domain decomposition and aggregation techniques that apply to approximating the eigensystem of Markov chains permits the approximate subdivision of the full system to a number of small, independent subsystems (decomposition phase), plus an ‘aggregative' system featuring a state-space that distinguishes only one index per subsystem (aggregation phase). Perturbation analysis reveals that the error incurred by the approximation is of an order of magnitude equal to the weak coupling of the NCD Markov chain. The study in this paper is then extended to the structure of NCD fluid models describing source superposition (multiplexing). It is shown that efficient spectral factorization techniques that arise from the Kronecker sum form of the global matrices can be applied through and combined with the decomposition and aggregation procedures. All structural characteristics and system parameters are expressible in terms of the individual sources multiplexed together, rendering the construction of the global system unnecessary. Finally, besides providing efficient computational algorithms, the work in this paper can be recast as a conceptual framework for the better understanding of queueing systems under the presence of events happening in widely differing time-scales.

Influence sampling of trailing variables of dynamical systems

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Paul Krause
Keyword(s):  
Data Assimilation ◽  
Numerical Models ◽  
Discrete Control ◽  
Dynamical Instability ◽  
Lorenz Equations ◽  
Control Scheme ◽  
Insertion Method ◽  
Order Of Magnitude ◽  
Large Systems ◽  
The Individual

AbstractFor dealing with dynamical instability in predictions, numerical models should be provided with accurate initial values on the attractor of the dynamical system they generate. A discrete control scheme is presented to this end for trailing variables of an evolutive system of ordinary differential equations. The Influence Sampling (IS) scheme adapts sample values of the trailing variables to input values of the determining variables in the attractor. The optimal IS scheme has affordable cost for large systems. In discrete data assimilation runs conducted with the Lorenz 1963 equations and a nonautonomous perturbation of the Lorenz equations whose dynamics shows on-off intermittency the optimal IS was compared to the straightforward insertion method and the Ensemble Kalman Filter (EnKF). With these unstable systems the optimal IS increases by one order of magnitude the maximum spacing between insertion times that the insertion method can handle and performs comparably to the EnKF when the EnKF converges. While the EnKF converges for sample sizes greater than or equal to 10, the optimal IS scheme does so fromsample size 1. This occurs because the optimal IS scheme stabilizes the individual paths of the Lorenz 1963 equations within data assimilation processes.

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