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Toda oscillator

Index Toda oscillator

In physics, the Toda oscillator is a special kind of nonlinear oscillator. [1]

28 relations: Acceleration, Approximation error, Communications in Mathematical Physics, Derivative, Dynamical system, Evolution, Exponential growth, Frequency, Friction, Journal of Physics A, Korteweg–de Vries equation, Laser science, Logarithm, Morikazu Toda, Optical cavity, Optical table, Oscillation, Physics, Physics Reports, Self-pulsation, Significant figures, Solid-state laser, Time, Toda field theory, Toda lattice, Translational symmetry, Velocity, Zeitschrift für Physik.

Acceleration

In physics, acceleration is the rate of change of velocity of an object with respect to time.

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Approximation error

The approximation error in some data is the discrepancy between an exact value and some approximation to it.

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Communications in Mathematical Physics

Communications in Mathematical Physics is a peer-reviewed academic journal published by Springer.

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Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

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Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.

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Evolution

Evolution is change in the heritable characteristics of biological populations over successive generations.

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Exponential growth

Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.

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Frequency

Frequency is the number of occurrences of a repeating event per unit of time.

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Friction

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.

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Journal of Physics A

The Journal of Physics A: Mathematical and Theoretical is a peer-reviewed scientific journal published by IOP Publishing.

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Korteweg–de Vries equation

In mathematics, the Korteweg–de Vries equation (KdV equation for short) is a mathematical model of waves on shallow water surfaces.

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Laser science

Laser science or laser physics is a branch of optics that describes the theory and practice of lasers.

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Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

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Morikazu Toda

was a Japanese physicist, best known for the discovery of the Toda lattice.

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Optical cavity

An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors that forms a standing wave cavity resonator for light waves.

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Optical table

An optical table is a vibration control platform that is used to support systems used for laser- and optics-related experiments, engineering and manufacturing.

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Oscillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states.

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Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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Physics Reports

Physics Reports is a peer-reviewed scientific journal, a review section of Physics Letters that has been published by Elsevier since 1971.

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Self-pulsation

Self-pulsation is a transient phenomenon in continuous-wave lasers.

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Significant figures

The significant figures (also known as the significant digits) of a number are digits that carry meaning contributing to its measurement resolution.

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Solid-state laser

A solid-state laser is a laser that uses a gain medium that is a solid, rather than a liquid such as in dye lasers or a gas as in gas lasers.

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Time

Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.

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Toda field theory

In the study of field theory and partial differential equations, a Toda field theory (named after Morikazu Toda) is derived from the following Lagrangian: Here x and t are spacetime coordinates, is the Killing form of a real r-dimensional Cartan algebra \mathfrak of a Kac–Moody algebra over \mathfrak, αi is the ith simple root in some root basis, ni is the Coxeter number, m is the mass (or bare mass in the quantum field theory version) and β is the coupling constant.

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Toda lattice

The Toda lattice, introduced by, is a simple model for a one-dimensional crystal in solid state physics.

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Translational symmetry

In geometry, a translation "slides" a thing by a: Ta(p).

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Velocity

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.

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Zeitschrift für Physik

Zeitschrift für Physik (English: Journal for physics) is a defunct series of German peer-reviewed German scientific journal of physics established in 1920 by Springer Berlin Heidelberg.

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Redirects here:

Oscillator Toda.

References

[1] https://en.wikipedia.org/wiki/Toda_oscillator

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