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Mean Field Theory

In physics and probability theory, mean-field theory (aka MFT or rarely self-consistent field theory) studies the behavior of high-dimensional random (stochastic) models by studying a simpler model that approximates the original by averaging over degrees of freedom. Such models consider many individual components that interact with each other. In MFT, the effect of all the other individuals on any given individual is approximated by a single averaged effect, thus reducing a many-body problem to a one-body problem. The main idea of MFT is to replace all interactions to any one body with an average or effective interaction, sometimes called a molecular field. This reduces any multi-body problem into an effective one-body problem. The ease of solving MFT problems means that some insight into the behavior of the system can be obtained at a lower computational cost. MFT has since been applied to a wide range of fields outside of physics, including statistical inference, graphical models, neuroscience, artificial intelligence, epidemic models, queueing theory, computer network performance and game theory, as in the Quantal response equilibrium.

3.0K
03 Nov 2022

Topic Review

Transparent Solar Windows

Many modern glass and window products are based on metal-dielectric coatings, which can control properties such as thermal emissivity, heat gain, colour, and transparency. These can also enable solar energy harvesting through PV integration, if the glazing structure is purpose-designed, to include luminescent materials and special microstructures. Recently, significant progress has been demonstrated in building integrated transparent solar windows, which are expected to add momentum towards the development of smart cities. These window systems are, at present in 2019, the only type of transparent and clear construction materials capable of providing significant energy savings in buildings, simultaneously with renewable energy generation.

3.0K
23 May 2024

Topic Review

Cosmic voids are vast spaces between filaments (the largest-scale structures in the universe), which contain very few or no galaxies. The cosmological evolution of the void regions differs drastically from the evolution of the Universe as a whole: there is a long stage when the curvature term dominates, which prevents the formation of galaxy clusters and massive galaxies. Hence, although even the emptiest regions of voids contain more than ~15% of the average matter density of the Universe, the voids look almost empty for an observer. Voids typically have a diameter of 10 to 100 megaparsecs (30 to 300 million light years); particularly large voids, defined by the absence of rich superclusters, are sometimes called supervoids. They were first discovered in 1978 in a pioneering study by Stephen Gregory and Laird A. Thompson at the Kitt Peak National Observatory. Voids are believed to have been formed by baryon acoustic oscillations in the Big Bang, collapses of mass followed by implosions of the compressed baryonic matter. Starting from initially small anisotropies from quantum fluctuations in the early universe, the anisotropies grew larger in scale over time. Regions of higher density collapsed more rapidly under gravity, eventually resulting in the large-scale, foam-like structure or "cosmic web" of voids and galaxy filaments seen today. Voids located in high-density environments are smaller than voids situated in low-density spaces of the universe. Voids appear to correlate with the observed temperature of the cosmic microwave background (CMB) because of the Sachs–Wolfe effect. Colder regions correlate with voids and hotter regions correlate with filaments because of gravitational redshifting. As the Sachs–Wolfe effect is only significant if the universe is dominated by radiation or dark energy, the existence of voids is significant in providing physical evidence for dark energy.

3.0K
18 Oct 2022

Topic Review Peer Reviewed

The concept of entropy constitutes, together with energy, a cornerstone of contemporary physics and related areas. It was originally introduced by Clausius in 1865 along abstract lines focusing on thermodynamical irreversibility of macroscopic physical processes. In the next decade, Boltzmann made the genius connection—further developed by Gibbs—of the entropy with the microscopic world, which led to the formulation of a new and impressively successful physical theory, thereafter named statistical mechanics. The extension to quantum mechanical systems was formalized by von Neumann in 1927, and the connections with the theory of communications and, more widely, with the theory of information were respectively introduced by Shannon in 1948 and Jaynes in 1957. Since then, over fifty new entropic functionals emerged in the scientific and technological literature. The most popular among them are the additive Renyi one introduced in 1961, and the nonadditive one introduced in 1988 as a basis for the generalization of the Boltzmann–Gibbs and related equilibrium and nonequilibrium theories, focusing on natural, artificial and social complex systems. Along such lines, theoretical, experimental, observational and computational efforts, and their connections to nonlinear dynamical systems and the theory of probabilities, are currently under progress. Illustrative applications, in physics and elsewhere, of these recent developments are briefly described in the present synopsis.

2.9K
07 May 2022

Topic Review

Coherent States

In physics, specifically in quantum mechanics, a coherent state is the specific quantum state of the quantum harmonic oscillator, often described as a state which has dynamics most closely resembling the oscillatory behavior of a classical harmonic oscillator. It was the first example of quantum dynamics when Erwin Schrödinger derived it in 1926, while searching for solutions of the Schrödinger equation that satisfy the correspondence principle. The quantum harmonic oscillator and hence, the coherent states arise in the quantum theory of a wide range of physical systems. For instance, a coherent state describes the oscillating motion of a particle confined in a quadratic potential well (for an early reference, see e.g. Schiff's textbook). The coherent state describes a state in a system for which the ground-state wavepacket is displaced from the origin of the system. This state can be related to classical solutions by a particle oscillating with an amplitude equivalent to the displacement. These states, expressed as eigenvectors of the lowering operator and forming an overcomplete family, were introduced in the early papers of John R. Klauder, e.g. . In the quantum theory of light (quantum electrodynamics) and other bosonic quantum field theories, coherent states were introduced by the work of Roy J. Glauber in 1963. The concept of coherent states has been considerably abstracted; it has become a major topic in mathematical physics and in applied mathematics, with applications ranging from quantization to signal processing and image processing (see Coherent states in mathematical physics). For this reason, the coherent states associated to the quantum harmonic oscillator are sometimes referred to as canonical coherent states (CCS), standard coherent states, Gaussian states, or oscillator states.

3.0K
20 Oct 2022

Topic Review

A solar tree is a structure incorporating solar energy technology on a single pillar, like a tree trunk. It may be a solar artwork or a functional power generator.

2.9K
17 Oct 2022

Topic Review

In cognitive psychology and neuroscience, spatial memory is a form of memory responsible for the recording of information about one's environment and spatial orientation. For example, a person's spatial memory is required in order to navigate around a familiar city, just as a rat's spatial memory is needed to learn the location of food at the end of a maze. It is often argued that in both humans and animals, spatial memories are summarized as a cognitive map. Spatial memory has representations within working, short-term memory and long-term memory. Research indicates that there are specific areas of the brain associated with spatial memory. Many methods are used for measuring spatial memory in children, adults, and animals.

2.9K
04 Nov 2022

Topic Review

Yield (Engineering)

In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed, some fraction of the deformation will be permanent and non-reversible and is known as plastic deformation. The yield strength or yield stress is a material property and is the stress corresponding to the yield point at which the material begins to deform plastically. The yield strength is often used to determine the maximum allowable load in a mechanical component, since it represents the upper limit to forces that can be applied without producing permanent deformation. In some materials, such as aluminium, there is a gradual onset of non-linear behavior, making the precise yield point difficult to determine. In such a case, the offset yield point (or proof stress) is taken as the stress at which 0.2% plastic deformation occurs. Yielding is a gradual failure mode which is normally not catastrophic, unlike ultimate failure. In solid mechanics, the yield point can be specified in terms of the three-dimensional principal stresses ([math]\displaystyle{ \sigma_1, \sigma_2 , \sigma_3 }[/math]) with a yield surface or a yield criterion. A variety of yield criteria have been developed for different materials.

2.9K
17 Oct 2022

Topic Review

Transactinide Element

In chemistry, transactinide elements (also, transactinides, or super-heavy elements) are the chemical elements with atomic numbers from 104 to 120. Their atomic numbers are immediately greater than those of the actinides, the heaviest of which is lawrencium (atomic number 103). Glenn T. Seaborg first proposed the actinide concept, which led to the acceptance of the actinide series. He also proposed the transactinide series ranging from element 104 to 121 and the superactinide series approximately spanning elements 122 to 153. The transactinide seaborgium was named in his honor. By definition, transactinide elements are also transuranic elements, i.e. have an atomic number greater than uranium (92). The transactinide elements all have electrons in the 6d subshell in their ground state. Except for rutherfordium and dubnium, even the longest-lasting isotopes of transactinide elements have extremely short half-lives, measured in seconds, or smaller units. The element naming controversy involved the first five or six transactinide elements. These elements thus used systematic names for many years after their discovery had been confirmed. (Usually the systematic names are replaced with permanent names proposed by the discoverers relatively shortly after a discovery has been confirmed.) Transactinides are radioactive and have only been obtained synthetically in laboratories. None of these elements has ever been collected in a macroscopic sample. Transactinide elements are all named after physicists and chemists or important locations involved in the synthesis of the elements. IUPAC defines an element to exist if its lifetime is longer than 10−14 seconds, which is the time it takes for the nucleus to form an electron cloud.

2.9K
01 Dec 2022

Topic Review

Holika (Sanskrit: होलिका) was a demoness in Hindu Vedic scriptures, who was burnt to death with the help of God Vishnu. She was the sister of King Hiranyakashipu and aunt of Prahlad. The story of Holika Dahan (Holika's death) signifies the triumph of good over evil. Holika is associated with the annual bonfire on the night before Holi, the Hindu festival of colors.

2.9K
29 Nov 2022

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