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Examples
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I think that the dimension of turbulence as a chaotic dynamical-system, again measured by the Kolmogorov scales, is much too large to be a candidate for interpretation as a low-dimensional chaotic system.
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The role of the statistician is somewhat trivial in such cases; she simply calculates the projection of the high-dimensional data onto the low-dimensional subspace the “model”.
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The low-dimensional noncritical string theories are not controversial in the way the supercritical ones are.
News From The Front, II cjohnson 2005
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Studies of superlattices and quantum wells were rapidly promoted in the West and afterwards in this country soon resulted in coming into being of a new area of the quantum physics of solid: the physics of low-dimensional electron systems.
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Apart from fundamental results that were quite new and important efficient one-side injection, the "superinjection" effect, diagonal tunneling, electron and optical confinement in a double heterostructure (which in a short while became the main element in studying the low-dimensional electron gas in semiconductors), we succeeded in employing principal benefits of heterostructure applications in devices, i.e., lasers, LEDs, solar cells, dynistors and transistors.
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"One should not forget the value in science getting access to novel types of materials and to studying previously unavailable low-dimensional physics," Samuelson said.
Honey, Who Shrank the Circuits? Lakshmi Sandhana 2002
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The first break led to a curious result about the embeddability being realizable in surprisingly low-dimensional ambient spaces provided that one would accept that the embedding would have only limited smoothness.
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Monte-Carlo simulations were used to validate these initial findings We examined the changes over time of four well-known low-dimensional chaotic systems: Lorenz,
PLoS ONE Alerts: New Articles Michel Laurent et al. 2010
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Therefore, we used the same analytical method to analyze the oscillations of four well-known, low-dimensional, chaotic oscillators, originally designed in diverse settings and all possibly well-adapted to model the fluctuations of cell populations: the Lorenz, Rössler, Verhulst and Duffing oscillators.
PLoS ONE Alerts: New Articles Michel Laurent et al. 2010
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Therefore, we used the same analytical method to analyze the oscillations of four well-known, low-dimensional, chaotic oscillators, originally designed in diverse settings and all possibly well-adapted to model the fluctuations of cell populations: the Lorenz, Rössler, Verhulst and Duffing oscillators.
PLoS ONE Alerts: New Articles Michel Laurent et al. 2010
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