A DYNAMICAL SYSTEMS APPROACH TO MEMBRANE PHENOMENA UNDERLYING CARDIAC ARRHYTHMIAS

1995 ◽  
Vol 05 (01) ◽  
pp. 75-88 ◽  
Author(s):  
RICHARD P. KLINE ◽  
B. MITCHELL BAKER
Keyword(s):  
Dynamical Systems ◽  
Action Potential ◽  
Systems Approach ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Current Activation ◽  
Patterns Of Behavior ◽  
On Line ◽  
Considerable Detail

A model is constructed for cardiac rhythmic response to stimulation via a family of continuous time dynamical systems. Starting with experimentally observed properties common to the kinetics of both repolarizing membrane currents and cardiac action potential responses to sudden changes in cycle length, extremely elementary dynamical assumptions are made concerning current activation and decay, and repolarization threshold. A two-parameter family of one-dimensional dynamical systems emerges. The resulting systems are analytically tractable in considerable detail generating restitution curves, bifurcation schemes, rhythmic responses and chaotic behavior for a representative cardiac cell. The excellent qualitative and quantitative agreement with experimental data reported for several cardiac preparations is discussed. The two-dimensional analog produces unexpected basin behavior which could be of clinical significance in explaining how a single extra beat or a pause could alter subsequent action potential behavior and cause dispersion of refractoriness across the ventricle increasing the risks for arrhythmias. By having a manageable number of parameters, analytically defined patterns of behavior, and computational ease, this dynamical system has the potential to be used in computer simulations to study the effects of antiarrhythmic drugs on complex two- and three-dimensional reentrant substrates, or used on line by an interactive pacemaker.

scholarly journals A Dynamical Systems Approach to Nonlinear Stellar Pulsations

1993 ◽  
Vol 134 ◽  
pp. 9-31
Author(s):  
J. R. Buchler
Keyword(s):  
Dynamical Systems ◽  
Ad Hoc ◽  
Systems Approach ◽  
Chaotic Behavior ◽  
Theoretical Explanation ◽  
Modal Interactions ◽  
Reduction Techniques ◽  
Numerical Hydrodynamics ◽  
Stellar Pulsations ◽  
The One

AbstractOver the last decade we have seen the application of novel techniques to the old problem of nonlinear stellar pulsations. Together with numerical hydrodynamics this approach provides a more fundamental understanding of the systematics of the pulsational behavior. For weakly nonadiabatic pulsations, whether regular or multi-periodic, dimensional reduction techniques lead to amplitude equations and to a description in terms of modal interactions and resonances. In particular they shed new light on the bump progression in the classical Cepheids. In more dissipative stars numerical hydrodynamical modelling has uncovered the existence of irregular variability, both in radiative and in convective models. An application of modern dynamical systems techniques has shown that this behavior occurs according to well understood routes from regular to chaotic behavior. The mechanism is very robust and represents the first non ad hoc theoretical explanation of irregular stellar variability. Finally, we discuss how a comparison with observations of irregular variability shows the need for more suitable observations, on the one hand, and of better techniques of signal processing, on the other.

A Dynamical Systems Approach to Stability Tracking of Treadmill Running

2008 ◽  
Author(s):  
Christopher S. Adam ◽  
Ian R. Berry ◽  
Kevin M. Short ◽  
Diana I. Saly
Keyword(s):  
Dynamical Systems ◽  
Nearest Neighbor ◽  
Systems Approach ◽  
Three Dimensional ◽  
Low Frequency ◽  
Temporal Variations ◽  
Gait Pattern ◽  
Treadmill Running ◽  
Reference Orbit ◽  
The Mean

Traditional analysis of running gait utilizes averaged biomechanical data from several strides to generate a mean curve. This curve is then used to define the average picture of a runners gait. However, such measures are frequently accompanied by time normalization, which results in a loss of temporal variations in the gait patterns. An examination of stability requires analysis of both time and position, therefore loss of such information makes stability analysis difficult. On the contrary, the use of a dynamical systems approach for gait analysis allows for a better understanding of how variations in gait pattern change over time. In the current study runners ran on a treadmill, with both a flat and uneven surface, at a self selected speed. Three-dimensional position data was captured for 11 different anatomical locations at a frequency of 120 Hz using a Qualysis motion capture system. The data was first shifted to a lumbar coordinate system to account for low frequency drift attributed to the subjects’ drift on the treadmill. Since all of the markers were rigidly connected, via the subject, the movements and variations of certain components of the 33-dimensional measurements were not independent. As a result, it was possible to reduce the dimensionality of the transformed data using singular value decomposition techniques. The primary components were then analyzed using the method of delay embeddings to extract geometric information, revealing the natural structure found in the data as a result of the periodicity of each running stride. A nearest neighbor mean stride orbit was then computed to create a reference orbit, so that deviations from the mean stride orbit can be measured. The expectation was that a more stable running configuration would lead to smaller deviations from the mean stride orbit. On-going work that will be reported includes: (i) analysis of running stability related to the reference stride comparator, (ii) compensation of lumbar centroid dynamics, (iii) reconstructions using one dimension from the lumbar centroid transformed data, and (iv) consideration of transients, fatigue, adaptation, etc.

Analysis of chaotic behavior of three-dimensional dynamical systems by a B-spline differential quadrature algorithm

2021 ◽  
pp. 2250077
Author(s):  
Rajni Rohila ◽  
R. C. Mittal
Keyword(s):  
Dynamical Systems ◽  
Prediction Models ◽  
Numerical Solutions ◽  
Chaotic Behavior ◽  
Weather Prediction ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Differential Quadrature ◽  
Lorenz Attractor ◽  
Novel Approach

A novel approach based on cubic [Formula: see text]-spline functions has been developed to find solutions of three-dimensional chaotic dynamical systems. Interesting dynamical behavior has been illustrated in figures. We observed that dynamical systems depend very sensitively on the initial condition and corresponding behavior has been captured in numerical simulations. The Butterfly effect is used in the development of weather prediction models and has been depicted graphically. This paper deals with the numerical solutions of Lorenz attractor, Chen, Genesio and a combination of Lorenz and Rossler attractors. The computed solutions are quite accurate, consistent and confirm that the cubic [Formula: see text]-spline differential quadrature is a very efficient method to portray complex dynamical behaviors of dynamical systems.

Design and calibration of an IVEM for general 3-dimensional imaging of non-diffracting materials

1992 ◽  
Vol 50 (2) ◽  
pp. 1040-1041
Author(s):  
Neil Rowlands ◽  
Jeff Price ◽  
Michael Kersker ◽  
Seichi Suzuki ◽  
Steve Young ◽  
...  
Keyword(s):  
3D Imaging ◽  
Tomographic Reconstruction ◽  
Three Dimensional ◽  
3 Dimensional ◽  
3D Microstructure ◽  
Image Translation ◽  
Digital Correlation ◽  
On Line ◽  
Mechanical Stage ◽  
Projection Angle

Three-dimensional (3D) microstructure visualization on the electron microscope requires that the sample be tilted to different positions to collect a series of projections. This tilting should be performed rapidly for on-line stereo viewing and precisely for off-line tomographic reconstruction. Usually a projection series is collected using mechanical stage tilt alone. The stereo pairs must be viewed off-line and the 60 to 120 tomographic projections must be aligned with fiduciary markers or digital correlation methods. The delay in viewing stereo pairs and the alignment problems in tomographic reconstruction could be eliminated or improved by tilting the beam if such tilt could be accomplished without image translation.A microscope capable of beam tilt with simultaneous image shift to eliminate tilt-induced translation has been investigated for 3D imaging of thick (1 μm) biologic specimens. By tilting the beam above and through the specimen and bringing it back below the specimen, a brightfield image with a projection angle corresponding to the beam tilt angle can be recorded (Fig. 1a).

scholarly journals Lath Martensite Microstructure Modeling: A High-Resolution Crystal Plasticity Simulation Study

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 691
Author(s):  
Francisco-José Gallardo-Basile ◽  
Yannick Naunheim ◽  
Franz Roters ◽  
Martin Diehl
Keyword(s):  
High Resolution ◽  
Mechanical Behavior ◽  
Crystal Plasticity ◽  
Lath Martensite ◽  
Three Dimensional ◽  
Building Blocks ◽  
Quantitative Agreement ◽  
Carbon Steels ◽  
Plastic Behavior ◽  
Austenitic Phase

Lath martensite is a complex hierarchical compound structure that forms during rapid cooling of carbon steels from the austenitic phase. At the smallest, i.e., ‘single crystal’ scale, individual, elongated domains, form the elemental microstructural building blocks: the name-giving laths. Several laths of nearly identical crystallographic orientation are grouped together to blocks, in which–depending on the exact material characteristics–clearly distinguishable subblocks might be observed. Several blocks with the same habit plane together form a packet of which typically three to four together finally make up the former parent austenitic grain. Here, a fully parametrized approach is presented which converts an austenitic polycrystal representation into martensitic microstructures incorporating all these details. Two-dimensional (2D) and three-dimensional (3D) Representative Volume Elements (RVEs) are generated based on prior austenite microstructure reconstructed from a 2D experimental martensitic microstructure. The RVEs are used for high-resolution crystal plasticity simulations with a fast spectral method-based solver and a phenomenological constitutive description. The comparison of the results obtained from the 2D experimental microstructure and the 2D RVEs reveals a high quantitative agreement. The stress and strain distributions and their characteristics change significantly if 3D microstructures are used. Further simulations are conducted to systematically investigate the influence of microstructural parameters, such as lath aspect ratio, lath volume, subblock thickness, orientation scatter, and prior austenitic grain shape on the global and local mechanical behavior. These microstructural features happen to change the local mechanical behavior, whereas the average stress–strain response is not significantly altered. Correlations between the microstructure and the plastic behavior are established.

A DYNAMICAL SYSTEM WITH CHAOTIC BEHAVIOR

1989 ◽  
Vol 03 (15) ◽  
pp. 1185-1188 ◽  
Author(s):  
J. SEIMENIS
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Infinite Number ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Hamiltonian Dynamical Systems

We develop a method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. We apply this method to the system [Formula: see text] We study the case a → 0 and we find that in this case the system has an infinite number of period dubling bifurcations.

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