Preliminaries from Nonlinear Dynamics and Statistical Physics

1986 ◽  
pp. 9-76
Author(s):  
John S. Nicolis
Keyword(s):  
Nonlinear Dynamics ◽  
Statistical Physics

DEVELOPMENT OF THERAPEUTIC BRAIN STIMULATION TECHNIQUES WITH METHODS FROM NONLINEAR DYNAMICS AND STATISTICAL PHYSICS

2006 ◽  
Vol 16 (07) ◽  
pp. 1889-1911 ◽  
Author(s):  
PETER A. TASS ◽  
CHRISTIAN HAUPTMANN ◽  
OLEKSANDR V. POPOVYCH
Keyword(s):  
Nonlinear Dynamics ◽  
Parkinson’S Disease ◽  
Parkinson's Disease ◽  
Essential Tremor ◽  
Brain Stimulation ◽  
Brain Function ◽  
Statistical Physics ◽  
Delayed Feedback ◽  
Phase Resetting ◽  
Feedback Mechanisms

Synchronization processes may severely impair brain function, for instance, in Parkinson's disease, essential tremor or epilepsies. We present three different effectively desynchronizing stimulation techniques which have been developed with methods from nonlinear dynamics and statistical physics. These techniques exploit either stochastic phase resetting principles or complex delayed feedback mechanisms. We explain how these methods work and how they can be applied to therapeutic brain stimulation.

scholarly journals New Systematic Solution for Resolving Nonlinear Dynamics Using System Analytical Theory Based on Engineering Science

2021 ◽  
Vol 15 (6) ◽  
pp. 46
Author(s):  
Deok-soo Cha ◽  
Kyoung-il Kim
Keyword(s):  
Nonlinear Dynamics ◽  
Systems Thinking ◽  
Statistical Physics ◽  
Open Loop ◽  
Economic Systems ◽  
Analytic Method ◽  
Engineering Science ◽  
Engineering Systems ◽  
Physical Sciences ◽  
Systematic Solution

There are many nonlinear dynamics in field of non-physical sciences, such as the food chain, economic systems, or engineering systems with the characteristics of closed or open-loop systems. The problems arising from this have been resolved by the outdated chaos theory in statistical physics based on the paradigm of logical thinking. However, it was founded by classical physicists, and it is imperfect and vague, moreover, very difficult for others. Therefore, we require a perfect systematic solution based on systems thinking, such as systems analytical methods in engineering science. Surprisingly, in 2021, a non-physicist, on behalf of a physicist, has successfully resolved the problems and achieved a new solution based on systems thinking through interdisciplinary research; moreover, it has been published. Unfortunately, most physicists do not welcome it because they have no experience and it is disadvantageous to them like the Copernican theory. In addition, they have no ability to evaluate the new solution because they do not know the analytic method. Nevertheless, non-physicists are greatly welcome it, thus, there is no problem in it. Hence, non-physicists will verify it using MATLAB or simulator and apply it to all science, on behalf of physicists. If so, non-physicists will have both a logical solution and a systematic solution for resolving nonlinear dynamics.

scholarly journals Foundations of Complex Systems

2009 ◽  
Vol 17 (2) ◽  
pp. 237-248 ◽  
Author(s):  
Gregoire Nicolis ◽  
Catherine Nicolis
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Data Analysis ◽  
Complex Systems ◽  
Statistical Physics ◽  
Fundamental Science ◽  
The Cross ◽  
Cross Fertilization ◽  
Different Levels

An approach to Complexity from the perspective of fundamental science is outlined, drawing on the cross-fertilization of concepts and tools from nonlinear dynamics, statistical physics, probability and information theories, data analysis and numerical simulation. Emphasis is placed on the intertwining between different levels of description and on the probabilistic dimension of complex systems, in connection with the issue of prediction.

Physical Sciences for Nonphysical Problems

2020 ◽  
pp. 253-268
Author(s):  
Lazaros K. Gallos
Keyword(s):  
Nonlinear Dynamics ◽  
Cardiovascular Diseases ◽  
Control Theory ◽  
Health Outcomes ◽  
Human Disease ◽  
Statistical Physics ◽  
Noncommunicable Diseases ◽  
Physical Sciences ◽  
Complex Population ◽  
And Control

To begin understanding noncommunicable diseases in a population, researchers must understand how people are connected to each other, how they interact with each other, and if there are external influences. Heterogeneity and complexity in human disease suggest new methodological and analytical ways in which the physical sciences can assist research in areas such as obesity, cardiovascular diseases, psychiatric disorders, or cancer. As it is becoming clear that human morbid states are not strictly deterministic diseases, this chapter overviews how statistical physics and nonlinear dynamics (e.g., percolation, cascades, control theory) grounded in stochastic approaches can contribute to the delineation and control of an array of complex population health outcomes.

scholarly journals Cluster-based network modeling—From snapshots to complex dynamical systems

2021 ◽  
Vol 7 (25) ◽  
pp. eabf5006
Author(s):  
Daniel Fernex ◽  
Bernd R. Noack ◽  
Richard Semaan
Keyword(s):  
Nonlinear Dynamics ◽  
Statistical Physics ◽  
Network Modeling ◽  
Network Connectivity ◽  
Dimensional Subspace ◽  
Data Driven ◽  
Lorenz Attractor ◽  
Universal Method ◽  
Time Resolved ◽  
Kolmogorov Flow

We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM describes short- and long-term behavior and is fully automatable, as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict, and control complex systems in all scientific fields.

Nonlinear dynamics and statistical physics of DNA

Nonlinearity ◽  
2004 ◽  
Vol 17 (2) ◽  
pp. R1-R40 ◽  
Author(s):  
Michel Peyrard
Keyword(s):  
Nonlinear Dynamics ◽  
Statistical Physics

scholarly journals Rotating Space Elevators: A New Venue in Space Elevator Physics

2017 ◽  
Vol 9 (1) ◽  
pp. 56
Author(s):  
Leonardo Golubovic ◽  
Steven Knudsen
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotubes ◽  
Statistical Mechanics ◽  
Statistical Physics ◽  
Outer Space ◽  
Rotating System ◽  
The Earth ◽  
Space Objects ◽  
Space Elevators

The physics of Space Elevators connecting the Earth with outer space has recently attracted increased attention, in part due to the discovery of ultra-strong materials such as carbon nanotubes and diamond nano-thread structures. In this article we review a new venue in space elevator physics: Rotating Space Elevators (RSE) [Golubovic, L. & Knudsen, S. (2009). Classical and statistical mechanics of celestial scale spinning strings: Rotating space elevators. Europhysics Letters 86(3), 34001.]. The RSE is a double rotating system of strings reaching outer space. Objects sliding along the RSE string (sliding climbers) do not require internal engines or propulsion to be transported far away from the Earth's surface. The RSE thus solves a major problem in the space elevator technology which is how to supply the energy to the climbers moving along the string. RSE strings exhibit interesting nonlinear dynamics and statistical physics phenomena. Satellites and spacecraft carried by sliding climbers can be released (launched) along RSEs. RSE strings can host space stations and research posts. Sliding climbers can be then used to transport useful loads and humans from the Earth to these outer space locations.

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