Length scale in the context of "Classical electrodynamics"

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⭐ Core Definition: Length scale

In physics, length scale is a particular length or distance determined with the precision of at most a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales are said to decouple, i.e. they can be separated and studied independently. In other words, the decoupling of different length scales makes it possible to have a self-consistent theory that only describes the relevant length scales for a given problem. Scientific reductionism says that the physical laws on the shortest length scales can be used to derive the effective description at larger length scales. The idea that one can derive descriptions of physics at different length scales from one another can be quantified with the renormalization group.

In quantum mechanics the length scale of a given phenomenon is related to its de Broglie wavelength = ħ/p, where ħ is the reduced Planck constant and p is the momentum that is being probed. In relativistic mechanics time and length scales are related by the speed of light. In relativistic quantum mechanics or relativistic quantum field theory, length scales are related to momentum, time and energy scales through the Planck constant and the speed of light. Often in high energy physics natural units are used where length, time, energy and momentum scales are described in the same units (usually with units of energy such as GeV).

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👉 Length scale in the context of Classical electrodynamics

Classical electromagnetism or classical electrodynamics is a branch of physics focused on the study of interactions between electric charges and currents using an extension of the classical Newtonian model. It is, therefore, a classical field theory. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics which is a quantum field theory.

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Length scale in the context of Microscopic scale

The microscopic scale (from Ancient Greek μικρός (mikrós) 'small' and σκοπέω (skopéō) 'to look (at); examine, inspect') is the scale of objects and events smaller than those that can easily be seen by the naked eye, requiring a lens or microscope to see them clearly. In physics, the microscopic scale is sometimes regarded as the scale between the macroscopic scale and the quantum scale. Microscopic units and measurements are used to classify and describe very small objects. One common microscopic length scale unit is the micrometre (also called a micron) (symbol: μm), which is one millionth of a metre.

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Length scale in the context of Macroscopic scale

The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic.

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Length scale in the context of Synoptic scale meteorology

In meteorology, the synoptic scale (also called the large scale or cyclonic scale) is a horizontal length scale of the order of 1,000 km (620 mi) or more. This corresponds to a horizontal scale typical of mid-latitude depressions (e.g. extratropical cyclones). Most high- and low-pressure areas seen on weather maps (such as surface weather analyses) are synoptic-scale systems, driven by the location of Rossby waves in their respective hemisphere. Low-pressure areas and their related frontal zones occur on the leading edge of a trough within the Rossby wave pattern, while high-pressure areas form on the back edge of the trough. Most precipitation areas occur near frontal zones. The word synoptic is derived from the Ancient Greek word συνοπτικός (sunoptikós), meaning "seen together".

The Navier–Stokes equations applied to atmospheric motion can be simplified by scale analysis in the synoptic scale. It can be shown that the main terms in horizontal equations are Coriolis force and pressure gradient terms; therefore, one can use geostrophic approximation. In vertical coordinates, the momentum equation simplifies to the hydrostatic equilibrium equation.

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Length scale in the context of Protein dynamics

In molecular biology, proteins are generally thought to adopt unique structures determined by their amino acid sequences. However, proteins are not strictly static objects, but rather populate ensembles of (sometimes similar) conformations. Transitions between these states occur on a variety of length scales (tenths of angstroms to nm) and time scales (ns to s),and have been linked to functionally relevant phenomena such as allosteric signaling and enzyme catalysis.

The study of protein dynamics is most directly concerned with the transitions between these states, but can also involve the nature and equilibrium populations of the states themselves.These two perspectives—kinetics and thermodynamics, respectively—can be conceptually synthesized in an "energy landscape" paradigm:highly populated states and the kinetics of transitions between them can be described by the depths of energy wells and the heights of energy barriers, respectively.

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