Oscillations in Simple Systems

In comparison to many other fields of ultrastructural research in Cell Biology, the successful exploration of genes and gene activity with the electron microscope in higher organisms is a late conquest. Nucleic acid molecules of Prokaryotes could be successfully visualized already since the early sixties, thanks to the Kleinschmidt spreading technique - and much basic information was obtained concerning the shape, length, molecular weight of viral, mitochondrial and chloroplast nucleic acid. Later, additonal methods revealed denaturation profiles, distinction between single and double strandedness and the use of heteroduplexes-led to gene mapping of relatively simple systems carried out in close connection with other methods of molecular genetics.

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Simple Systems

10.1093/oso/9780199595068.003.0004 ◽

2017 ◽

Author(s):

Jochen Rau

Keyword(s):

Magnetic Field ◽

Low Temperatures ◽

General Framework ◽

Gibbs State ◽

Macroscopic System ◽

Basic Model ◽

System A ◽

Paramagnetic Salt ◽

High And Low Temperatures ◽

Simple Systems

Even though the general framework of statistical mechanics is ultimately targeted at the description of macroscopic systems, it is illustrative to apply it first to some simple systems: a harmonic oscillator, a rotor, and a spin in a magnetic field. These applications serve to illustrate how a key function associated with the Gibbs state, the so-called partition function, is calculated in practice, how the entropy function is obtained via a Legendre transformation, and how such systems behave in the limits of high and low temperatures. After discussing these simple systems, this chapter considers a first example where multiple constituents are assembled into a macroscopic system: a basic model of a paramagnetic salt. It also investigates the size of energy fluctuations and how—in the case of the paramagnet—these fluctuations scale with the number of constituents.

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ChemInform Abstract: THEORY OF ION-NEUTRAL INTERACTIONS: APPLICATION OF TRANSITION STATE THEORY CONCEPTS TO BOTH COLLISIONAL AND REACTIVE PROPERTIES OF SIMPLE SYSTEMS

Chemischer Informationsdienst ◽

10.1002/chin.198310389 ◽

1983 ◽

Vol 14 (10) ◽

Author(s):

W. J. CHESNAVICH ◽

M. T. BOWERS

Keyword(s):

Transition State ◽

Transition State Theory ◽

State Theory ◽

Abstract Theory ◽

Simple Systems ◽

Reactive Properties

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A New Category of Three-Dimensional Chaotic Flows with Identical Eigenvalues

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127420500261 ◽

2020 ◽

Vol 30 (02) ◽

pp. 2050026 ◽

Cited By ~ 1

Author(s):

Zahra Faghani ◽

Fahimeh Nazarimehr ◽

Sajad Jafari ◽

Julien C. Sprott

Keyword(s):

Chaotic Systems ◽

Autonomous Systems ◽

Three Dimensional ◽

Special Property ◽

Computer Search ◽

Chaotic Flows ◽

Stable Equilibria ◽

Dynamical Properties ◽

Simple Systems ◽

First Time

In this paper, some new three-dimensional chaotic systems are proposed. The special property of these autonomous systems is their identical eigenvalues. The systems are designed based on the general form of quadratic jerk systems with 10 terms, and some systems with stable equilibria. Using a systematic computer search, 12 simple chaotic systems with identical eigenvalues were found. We believe that systems with identical eigenvalues are described here for the first time. These simple systems are listed in this paper, and their dynamical properties are investigated.

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