scholarly journals Coupled Map Lattices as Musical Instruments

2018 ◽  
Vol 42 (2) ◽  
pp. 22-34 ◽  
Author(s):  
Janko Gravner ◽  
Kyle Johnson
Keyword(s):  
Strange Attractor ◽  
Spatial Organization ◽  
Temporal Evolution ◽  
Musical Instruments ◽  
Initial Configuration ◽  
Coupled Map Lattices ◽  
Uncorrelated Noise ◽  
One Dimensional ◽  
Lattice Size

We use one-dimensional coupled map lattices (CMLs) to generate sounds that reflect their spatial organization and temporal evolution from a random initial configuration corresponding to uncorrelated noise. In many instances, the process approaches an equilibrium, which generates a sustained tone. The pitch of this tone is proportional to the lattice size, so the CML behaves like an instrument that could be tuned. Among exceptional cases, we provide an example with a metastable strange attractor, which produces an evolving sound reminiscent of drone music.

Automatic Texture Based Classification of the Dynamics of One-Dimensional Binary Cellular Automata

2019 ◽  
Vol 8 (4) ◽  
pp. 41-61
Author(s):  
Marcelo Arbori Nogueira ◽  
Pedro Paulo Balbi de Oliveira
Keyword(s):  
Cellular Automata ◽  
Dynamic Behavior ◽  
Temporal Evolution ◽  
Computational Cost ◽  
Great Variability ◽  
Texture Descriptor ◽  
One Dimensional ◽  
Binary Images ◽  
Elementary Cellular Automata

Cellular automata present great variability in their temporal evolutions due to the number of rules and initial configurations. The possibility of automatically classifying its dynamic behavior would be of great value when studying properties of its dynamics. By counting on elementary cellular automata, and considering its temporal evolution as binary images, the authors created a texture descriptor of the images - based on the neighborhood configurations of the cells in temporal evolutions - so that it could be associated to each dynamic behavior class, following the scheme of Wolfram's classic classification. It was then possible to predict the class of rules of a temporal evolution of an elementary rule in a more effective way than others in the literature in terms of precision and computational cost. By applying the classifier to the larger neighborhood space containing 4 cells, accuracy decreased to just over 70%. However, the classifier is still able to provide some information about the dynamics of an unknown larger space with reduced computational cost.

A coupling of finite particle systems

1993 ◽  
Vol 30 (01) ◽  
pp. 258-262 ◽  
Author(s):  
T. S. Mountford
Keyword(s):  
Invariant Measure ◽  
Branching Process ◽  
Interacting Particle Systems ◽  
Particle Systems ◽  
Initial Configuration ◽  
Limit Measure ◽  
One Dimensional ◽  
Interacting Particle ◽  
The One ◽  
Finite Particle

We show that for a large class of one-dimensional interacting particle systems, with a finite initial configuration, any limit measure , for a sequence of times tending to infinity, must be invariant. This result is used to show that the one-dimensional biased annihilating branching process with parameter > 1/3 converges in distribution to the upper invariant measure provided its initial configuration is almost surely finite and non-null.

Map Dynamics Study of the Lorenz Equations

1997 ◽  
Vol 07 (02) ◽  
pp. 373-382 ◽  
Author(s):  
Olivier Michielin ◽  
Paul E. Phillipson
Keyword(s):  
Periodic Orbits ◽  
Symbolic Dynamics ◽  
Strange Attractor ◽  
Good Accuracy ◽  
Simple Solution ◽  
Lorenz Equations ◽  
Computer Solution ◽  
One Dimensional

The Lorenz equations [Lorenz, 1963], in addition to a strange attractor, display sequences of periodic and aperiodic orbits. Approximate one-dimensional map solutions are heuristically constructed, supplementing previous symbolic dynamics studies, which closely reproduce these sequences. A relatively simple solution reproduces the sequence topology to good accuracy. A second more refined solution reproduces to higher accuracy both the topology and scale of the attractor. The second solution is sufficiently accurate to predict periodic orbits not previously observed and difficult to extract directly from computer solution of the Lorenz equations.

FRACTAL EVOLUTION IN DETERMINISTIC AND RANDOM MODELS

1996 ◽  
Vol 06 (11) ◽  
pp. 1977-1995
Author(s):  
SIEGFRIED FUSSY ◽  
GERHARD GRÖSSING ◽  
HERBERT SCHWABL
Keyword(s):  
Order Parameter ◽  
Specific Model ◽  
Coupled Map Lattices ◽  
Normalization Procedure ◽  
Quantum Cellular Automata ◽  
Time Step ◽  
One Dimensional ◽  
Random Models ◽  
Approximate Estimation ◽  
The Stability

One-dimensional coupled map lattices or quantum cellular automata with any additionally implemented temporal feedback operations (involving some memory of the system’s states) and a normalization procedure after each time step exhibit a universal dynamic property called fractal evolution [Fussy & Grössing, 1994]. It is characterized by a power-law behavior of a system’s order parameter with regard to a resolution-like parameter which controls the deviation from an undisturbed (i.e., feedback-less) system’s evolution and provides a dynamically invariant measure for the emerging spatiotemporal patterns. By comparison with another, simpler model without memory, where the patterns are generated randomly, the underlying principles of fractal evolution are studied. It is shown that our system evolving entirely deterministically, exhibits properties occurring usually only in random models, where the global measures, up to a certain degree, are calculable. Other properties like the fractal evolution exponent remain in general computationally irreducible due to the self-referential feedback dynamics. A specific model with an approximate estimation of the fractal evolution exponent is discussed. The stability of fractal evolution with respect to the dependence of pattern formation on the systems variables is also analyzed.

One-dimensional dynamics for traveling fronts in coupled map lattices

2000 ◽  
Vol 61 (2) ◽  
pp. 1329-1336 ◽  
Author(s):  
R. Carretero-González ◽  
D. K. Arrowsmith ◽  
F. Vivaldi
Keyword(s):  
Coupled Map Lattices ◽  
One Dimensional ◽  
Traveling Fronts

Spatio-temporal evolution of thin Alfven resonance layer

2010 ◽  
Vol 76 (5) ◽  
pp. 709-734
Author(s):  
I. S. DMITRIENKO
Keyword(s):  
Large Scale ◽  
Temporal Evolution ◽  
Spatial Structures ◽  
One Dimensional ◽  
Resonance Detuning ◽  
Different Types ◽  
Temporal Structures ◽  
Spatio Temporal ◽  
Over Time ◽  
Resonance Equation

AbstractWe describe the spatio-temporal evolution of one-dimensional Alfven resonance disturbance in the presence of various factors of resonance detuning: dispersion and absorption of Alfven disturbance, nonstationarity of large-scale wave generating resonant disturbance. Using analytical solutions to the resonance equation, we determine conditions for forming qualitatively different spatial and temporal structures of resonant Alfven disturbances. We also present analytical descriptions of quasi-stationary and non-stationary spatial structures formed in the resonant layer, and their evolution over time for cases of drivers of different types corresponding to large-scale waves localized in the direction of inhomogeneity and to nonlocalized large-scale waves.

Dynamics of bead formation, filament thinning and breakup in weakly viscoelastic jets

2010 ◽  
Vol 665 ◽  
pp. 46-56 ◽  
Author(s):  
A. M. ARDEKANI ◽  
V. SHARMA ◽  
G. H. McKINLEY
Keyword(s):  
Temporal Evolution ◽  
Relative Magnitude ◽  
Ohnesorge Number ◽  
Physical Processes ◽  
Spatiotemporal Evolution ◽  
One Dimensional ◽  
Elastic Stresses ◽  
Low Viscosity ◽  
String Structure ◽  
Nonlinear Free Surface

The spatiotemporal evolution of a viscoelastic jet depends on the relative magnitude of capillary, viscous, inertial and elastic stresses. The interplay of capillary and elastic stresses leads to the formation of very thin and stable filaments between drops, or to ‘beads-on-a-string’ structure. In this paper, we show that by understanding the physical processes that control different stages of the jet evolution it is possible to extract transient extensional viscosity information even for very low viscosity and weakly elastic liquids, which is a particular challenge in using traditional rheometers. The parameter space at which a forced jet can be used as an extensional rheometer is numerically investigated by using a one-dimensional nonlinear free-surface theory for Oldroyd-B and Giesekus fluids. The results show that even when the ratio of viscous to inertio-capillary time scales (or Ohnesorge number) is as low as Oh ~ 0.02, the temporal evolution of the jet can be used to obtain elongational properties of the liquid.

scholarly journals Analysis of Lattice Size, Energy Density and Denaturation for a One-Dimensional DNA Model

2012 ◽  
Vol 02 (02) ◽  
pp. 84-89
Author(s):  
Gabriel Gouvea Slade ◽  
Natalia Favaro Ribeiro ◽  
Elso Drigo Filho ◽  
Jose Roberto Ruggiero
Keyword(s):  
Energy Density ◽  
One Dimensional ◽  
Lattice Size

Periodic solutions in one-dimensional coupled map lattices

2003 ◽  
Vol 24 (5) ◽  
pp. 521-526
Author(s):  
Zheng Yong-ai ◽  
Liu Zeng-rong
Keyword(s):  
Periodic Solutions ◽  
Coupled Map Lattices ◽  
One Dimensional

Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 2. Stationary solution and evolution of initial distributions

1991 ◽  
Vol 46 (2) ◽  
pp. 219-229 ◽  
Author(s):  
Victor S. Krivitsky ◽  
Sergey V. Vladimirov
Keyword(s):  
Distribution Function ◽  
Particle Acceleration ◽  
Nonlinear Interaction ◽  
Particle Distribution ◽  
Temporal Evolution ◽  
Linear Interaction ◽  
One Dimensional ◽  
The One ◽  
Initial Distributions ◽  
Stochastic Particle

The evolution of the distribution function due to the simultaneous nonlinear interaction of plasma particles with resonant and non-resonant waves is studied. A stationary particle distribution resulting from a balance of the quasi-linear interaction and the nonlinear one is found. The temporal evolution of an initial δ-function-shaped distribution (like a ‘beam’) is examined in the one-dimensional case. General formulae are obtained for stochastic particle acceleration (taking account of the nonlinear interaction studied here).

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