Fine-structure constant
In physics, the fine-structure constant known as Sommerfeld's constant denoted by α, is a dimensionless physical constant characterizing the strength of the electromagnetic interaction between elementary charged particles. It is related to the elementary charge e, which characterizes the strength of the coupling of an elementary charged particle with the electromagnetic field, by the formula 4πε0ħcα = e2. Being a dimensionless quantity, it has the same numerical value in all systems of units, 1/137; some equivalent definitions of α in terms of other fundamental physical constants are: α = 1 4 π ε 0 e 2 ℏ c = μ 0 4 π e 2 c ℏ = k e e 2 ℏ c = c μ 0 2 R K = e 2 4 π Z 0 ℏ where: e is the elementary charge. The definition reflects the relationship between α and the permeability of free space µ0, which equals µ0 = 2hα/ce2. In the 2019 redefinition of SI base units, 4π × 1.00000000082×10−7 H⋅m−1 is the value for µ0 based upon more accurate measurements of the fine structure constant. In electrostatic cgs units, the unit of electric charge, the statcoulomb, is defined so that the Coulomb constant, ke, or the permittivity factor, 4πε0, is 1 and dimensionless.
The expression of the fine-structure constant, as found in older physics literature, becomes α = e 2 ℏ c. In natural units used in high energy physics, where ε0 = c = ħ = 1, the value of the fine-structure constant is α = e 2 4 π; as such, the fine-structure constant is just another, albeit dimensionless, quantity determining the elementary charge: e = √4πα ≈ 0.30282212 in terms of such a natural unit of charge. In atomic units, the fine structure constant is α = 1 c; the 2014 CODATA recommended value of α is α = e2/4πε0ħc = 0.0072973525664. This has a relative standard uncertainty of 0.23 parts per billion. For reasons of convenience the value of the reciprocal of the fine-structure constant is specified; the 2014 CODATA recommended value is given by α−1 = 137.035999139. While the value of α can be estimated from the values of the constants appearing in any of its definitions, the theory of quantum electrodynamics provides a way to measure α directly using the quantum Hall effect or the anomalous magnetic moment of the electron.
The theory of QED predicts a relationship between the dimensionless magnetic moment of the electron and the fine-structure constant α. The most precise value of α obtained experimentally is based on a measurement of g using a one-electron so-called "quantum cyclotron" apparatus, together with a calculation via the theory of QED that involved 12672 tenth-order Feynman diagrams: α−1 = 137.035999174. This measurement of α has a precision of 0.25 parts per billion. This value and uncertainty are about the same as the latest experimental results; the fine-structure constant, α, has several physical interpretations. Α is: The square of the ratio of the elementary charge to the Planck charge α = 2. The ratio of two energies: the energy needed to overcome the electrostatic repulsion between two electrons a distance of d apart, the energy of a single photon of wavelength λ = 2πd: α = e 2 4 π ε 0 d / h c λ = e 2 4 π ε 0 d × 2 π d h c = e 2 4 π ε 0 d × d ℏ c = e 2 4 π ε
Lorentz force
In physics the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with a velocity v in an electric field E and a magnetic field B experiences a force of F = q E + q v × B. Variations on this basic formula describe the magnetic force on a current-carrying wire, the electromotive force in a wire loop moving through a magnetic field, the force on a charged particle which might be traveling near the speed of light. Historians suggest that the law is implicit in a paper by James Clerk Maxwell, published in 1865. Hendrik Lorentz arrived in a complete derivation in 1895, identifying the contribution of the electric force a few years after Oliver Heaviside identified the contribution of the magnetic force; the force F acting on a particle of electric charge q with instantaneous velocity v, due to an external electric field E and magnetic field B, is given by: where × is the vector cross product. In terms of cartesian components, we have: F x = q, F y = q, F z = q.
In general, the electric and magnetic fields are functions of the time. Therefore, the Lorentz force can be written as: F = q in which r is the position vector of the charged particle, t is time, the overdot is a time derivative. A positively charged particle will be accelerated in the same linear orientation as the E field, but will curve perpendicularly to both the instantaneous velocity vector v and the B field according to the right-hand rule; the term qE is called the electric force. According to some definitions, the term "Lorentz force" refers to the formula for the magnetic force, with the total electromagnetic force given some other name; this article will not follow this nomenclature: In what follows, the term "Lorentz force" will refer to the expression for the total force. The magnetic force component of the Lorentz force manifests itself as the force that acts on a current-carrying wire in a magnetic field. In that context, it is called the Laplace force; the Lorentz force is a force exerted by the electromagnetic field on the charged particle, that is, it is the rate at which linear momentum is transferred from the electromagnetic field to the particle.
Associated with it is the power, the rate at which energy is transferred from the electromagnetic field to the particle. That power is v ⋅ F = q v ⋅ E. Notice that the magnetic field does not contribute to the power because the magnetic force is always perpendicular to the velocity of the particle. For a continuous charge distribution in motion, the Lorentz force equation becomes: d F = d q where dF is the force on a small piece of the charge distribution with charge dq. If both sides of this equation are divided by the volume of this small piece of the charge distribution dV, the result is: f = ρ where f is the force density and ρ is the charge density. Next, the current density corresponding to the motion of the charge continuum is J = ρ v so the continuous analogue to the equation is The total force is the volume integral over the charge distr
Nobel Prize in Physics
The Nobel Prize in Physics is a yearly award given by the Royal Swedish Academy of Sciences for those who have made the most outstanding contributions for humankind in the field of physics. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the first Nobel Prize in Physics was awarded to physicist Wilhelm Röntgen in recognition of the extraordinary services he rendered by the discovery of the remarkable rays. This award is administered by the Nobel Foundation and regarded as the most prestigious award that a scientist can receive in physics, it is presented in Stockholm at an annual ceremony on 10 December, the anniversary of Nobel's death. Through 2018, a total of 209 individuals have been awarded the prize. Only three women have won the Nobel Prize in Physics: Marie Curie in 1903, Maria Goeppert Mayer in 1963, Donna Strickland in 2018. Alfred Nobel, in his last will and testament, stated that his wealth be used to create a series of prizes for those who confer the "greatest benefit on mankind" in the fields of physics, peace, physiology or medicine, literature.
Though Nobel wrote several wills during his lifetime, the last one was written a year before he died and was signed at the Swedish-Norwegian Club in Paris on 27 November 1895. Nobel bequeathed 94% of his total assets, 31 million Swedish kronor, to establish and endow the five Nobel Prizes. Due to the level of skepticism surrounding the will, it was not until April 26, 1897 that it was approved by the Storting; the executors of his will were Ragnar Sohlman and Rudolf Lilljequist, who formed the Nobel Foundation to take care of Nobel's fortune and organise the prizes. The members of the Norwegian Nobel Committee who were to award the Peace Prize were appointed shortly after the will was approved; the prize-awarding organisations followed: the Karolinska Institutet on June 7, the Swedish Academy on June 9, the Royal Swedish Academy of Sciences on June 11. The Nobel Foundation reached an agreement on guidelines for how the Nobel Prize should be awarded. In 1900, the Nobel Foundation's newly created statutes were promulgated by King Oscar II.
According to Nobel's will, The Royal Swedish Academy of sciences were to award the Prize in Physics. A maximum of three Nobel laureates and two different works may be selected for the Nobel Prize in Physics. Compared with other Nobel Prizes, the nomination and selection process for the prize in Physics is long and rigorous; this is a key reason why it has grown in importance over the years to become the most important prize in Physics. The Nobel laureates are selected by the Nobel Committee for Physics, a Nobel Committee that consists of five members elected by The Royal Swedish Academy of Sciences. In the first stage that begins in September, around 3,000 people – selected university professors, Nobel Laureates in Physics and Chemistry, etc. – are sent confidential forms to nominate candidates. The completed nomination forms arrive at the Nobel Committee no than 31 January of the following year; these nominees are scrutinized and discussed by experts who narrow it to fifteen names. The committee submits a report with recommendations on the final candidates into the Academy, where, in the Physics Class, it is further discussed.
The Academy makes the final selection of the Laureates in Physics through a majority vote. The names of the nominees are never publicly announced, neither are they told that they have been considered for the prize. Nomination records are sealed for fifty years. While posthumous nominations are not permitted, awards can be made if the individual died in the months between the decision of the prize committee and the ceremony in December. Prior to 1974, posthumous awards were permitted; the rules for the Nobel Prize in Physics require that the significance of achievements being recognized has been "tested by time". In practice, it means that the lag between the discovery and the award is on the order of 20 years and can be much longer. For example, half of the 1983 Nobel Prize in Physics was awarded to Subrahmanyan Chandrasekhar for his work on stellar structure and evolution, done during the 1930s; as a downside of this approach, not all scientists live long enough for their work to be recognized.
Some important scientific discoveries are never considered for a prize, as the discoverers die by the time the impact of their work is appreciated. A Physics Nobel Prize laureate earns a gold medal, a diploma bearing a citation, a sum of money; the Nobel Prize medals, minted by Myntverket in Sweden and the Mint of Norway since 1902, are registered trademarks of the Nobel Foundation. Each medal has an image of Alfred Nobel in left profile on the obverse; the Nobel Prize medals for Physics, Physiology or Medicine, Literature have identical obverses, showing the image of Alfred Nobel and the years of his birth and death. Nobel's portrait appears on the obverse of the Nobel Peace Prize medal and the Medal for the Prize in Economics, but with a different design; the image on the reverse of a medal varies according to the institution awarding the prize. The reverse sides of the Nobel Prize medals for Chemistry and Physics share the same design of Nature, as a Goddess, whose veil is held up by the Genius of Science.
These medals and the ones for Physiology/Medicine and Literature were designed by Erik Lindberg in 1902. Nobel laureates receive a diploma directly from the hands of the
Anderson localization
In condensed matter physics, Anderson localization is the absence of diffusion of waves in a disordered medium. This phenomenon is named after the American physicist P. W. Anderson, the first to suggest that electron localization is possible in a lattice potential, provided that the degree of randomness in the lattice is sufficiently large, as can be realized for example in a semiconductor with impurities or defects. Anderson localization is a general wave phenomenon that applies to the transport of electromagnetic waves, acoustic waves, quantum waves, spin waves, etc; this phenomenon is to be distinguished from weak localization, the precursor effect of Anderson localization, from Mott localization, named after Sir Nevill Mott, where the transition from metallic to insulating behaviour is not due to disorder, but to a strong mutual Coulomb repulsion of electrons. In the original Anderson tight-binding model, the evolution of the wave function ψ on the d-dimensional lattice Zd is given by the Schrödinger equation i ℏ ψ ˙ = H ψ, where the Hamiltonian H is given by = E j ϕ + ∑ k ≠ j V ϕ, with Ej random and independent, potential V falling off as r−2 at infinity.
For example, one may take Ej uniformly distributed in, V = { 1, | r | = 1 0, otherwise. Starting with ψ0 localised at the origin, one is interested in how fast the probability distribution | ψ | 2 diffuses. Anderson's analysis shows the following: if d is 1 or 2 and W is arbitrary, or if d ≥ 3 and W/ħ is sufficiently large the probability distribution remains localized: ∑ n ∈ Z d | ψ | 2 | n | ≤ C uniformly in t; this phenomenon is called Anderson localization.if d ≥ 3 and W/ħ is small, ∑ n ∈ Z d | ψ | 2 | n | ≈ D t, where D is the diffusion constant. The phenomenon of Anderson localization that of weak localization, finds its origin in the wave interference between multiple-scattering paths. In the strong scattering limit, the severe interferences can halt the waves inside the disordered medium. For non-interacting electrons, a successful approach was put forward in 1979 by Abrahams et al; this scaling hypothesis of localization suggests that a disorder-induced metal-insulator transition exists for non-interacting electrons in three dimensions at zero magnetic field and in the absence of spin-orbit coupling.
Much further work has subsequently supported these scaling arguments both analytically and numerically. In 1D and 2D, the same hypothesis shows that there are no extended states and thus no MIT. However, since 2 is the lower critical dimension of the localization problem, the 2D case is in a sense close to 3D: states are only marginally localized for weak disorder and a small spin-orbit coupling can lead to the existence of extended states and thus an MIT; the localization lengths of a 2D system with potential-disorder can be quite large so that in numerical approaches one can always find a localization-delocalization transition when either decreasing system size for fixed disorder or increasing disorder for fixed system size. Most numerical approaches to the localization problem use the standard tight-binding Anderson Hamiltonian with onsite-potential disorder. Characteristics of the electronic eigenstates are investigated by studies of participation numbers obtained by exact diagonalization, multifractal properties, level statistics and many others.
Fruitful is the transfer-matrix method which allows a direct computation of the localization lengths and further validates the scaling hypothesis by a numerical proof of the existence of a one-parameter scaling function. Direct numerical solution of Maxwell equations to demonstrate Anderson localization of light has been implemented. Recent work has shown that a non-interacting Anderson localized system can become many-body localized in the presence of weak interactions; this result has been rigorously proven in 1D, while perturbative arguments exist for two and three dimensions. Two reports of Anderson localization of light in 3D random media exist up to date though absorption complicates interpretati
Klaus von Klitzing
Klaus von Klitzing is a German physicist, known for discovery of the integer quantum Hall effect, for which he was awarded the 1985 Nobel Prize in Physics. In 1962, Klitzing passed the Abitur at the Artland Gymnasium in Quakenbrück, before studying physics at the Braunschweig University of Technology, where he received his diploma in 1969, he continued his studies at the University of Würzburg at the chair of Gottfried Landwehr, completing his PhD thesis entitled Galvanomagnetic Properties of Tellurium in Strong Magnetic Fields in 1972, gaining habilitation in 1978. During his career Klitzing has worked at the Clarendon Laboratory at the University of Oxford and the Grenoble High Magnetic Field Laboratory in France, where he continued to work until becoming a professor at the Technical University of Munich in 1980, he has been a director of the Max Planck Institute for Solid State Research in Stuttgart since 1985. The von Klitzing constant, RK = h/e2 = 25812.8074555 Ω, is named in honor of Klaus von Klitzing's discovery of the quantum Hall effect, is listed in the National Institute of Standards and Technology Reference on Constants and Uncertainty.
The inverse of the constant is equal to half the value of the conductance quantum. More Klitzing's research focuses on the properties of low-dimensional electronic systems in low temperatures and in high magnetic fields. Von Klitzing has won numerous awards and honours including
Self-similarity
In mathematics, a self-similar object is or similar to a part of itself. Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. Self-similarity is a typical property of artificial fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object, similar to the whole. For instance, a side of the Koch snowflake is both scale-invariant; the non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a straight line may resemble the whole, further detail is not revealed. A time developing phenomenon is said to exhibit self-similarity if the numerical value of certain observable quantity f measured at different times are different but the corresponding dimensionless quantity at given value of x / t z remain invariant, it happens. The idea is just an extension of the idea of similarity of two triangles.
Note that two triangles are similar if the numerical values of their sides are different however the corresponding dimensionless quantities, such as their angles, coincide. In mathematics, self-affinity is a feature of a fractal whose pieces are scaled by different amounts in the x- and y-directions; this means that to appreciate the self similarity of these fractal objects, they have to be rescaled using an anisotropic affine transformation. A compact topological space X is self-similar if there exists a finite set S indexing a set of non-surjective homeomorphisms for which X = ⋃ s ∈ S f s If X ⊂ Y, we call X self-similar if it is the only non-empty subset of Y such that the equation above holds for. We call L = a self-similar structure; the homeomorphisms may be iterated. The composition of functions creates the algebraic structure of a monoid; when the set S has only two elements, the monoid is known as the dyadic monoid. The dyadic monoid can be visualized as an infinite binary tree; the automorphisms of the dyadic monoid is the modular group.
A more general notion than self-similarity is Self-affinity. The Mandelbrot set is self-similar around Misiurewicz points. Self-similarity has important consequences for the design of computer networks, as typical network traffic has self-similar properties. For example, in teletraffic engineering, packet switched data traffic patterns seem to be statistically self-similar; this property means that simple models using a Poisson distribution are inaccurate, networks designed without taking self-similarity into account are to function in unexpected ways. Stock market movements are described as displaying self-affinity, i.e. they appear self-similar when transformed via an appropriate affine transformation for the level of detail being shown. Andrew Lo describes stock market log return self-similarity in econometrics. Finite subdivision rules are a powerful technique for building self-similar sets, including the Cantor set and the Sierpinski triangle; the Viable System Model of Stafford Beer is an organizational model with an affine self-similar hierarchy, where a given viable system is one element of the System One of a viable system one recursive level higher up, for whom the elements of its System One are viable systems one recursive level lower down.
Self-similarity can be found in nature, as well. To the right is a mathematically generated self-similar image of a fern, which bears a marked resemblance to natural ferns. Other plants, such as Romanesco broccoli, exhibit strong self-similarity. Strict canons display various amounts of self-similarity, as do sections of fugues. A Shepard tone is self-similar in the wavelength domains; the Danish composer Per Nørgård has made use of a self-similar integer sequence named the'infinity series' in much of his music. In the research field of music information retrieval, self-similarity refers to the fact that music consists of parts that are repeated in time. In other words, music is self-similar under temporal translation, rather than under scaling. "Copperplate Chevrons" — a self-similar fractal zoom movie "Self-Similarity" — New articles about Self-Similarity. Waltz Algorithm Mandelbrot, Benoit B.. "Self-affinity and fractal dimension". Physica Scripta. 32: 257–260. Bibcode:1985PhyS...32..257M. Doi:10.1088/0031-8949/32/4/001.
Sapozhnikov, Victor.
Zinc
Zinc is a chemical element with symbol Zn and atomic number 30. It is the first element in group 12 of the periodic table. In some respects zinc is chemically similar to magnesium: both elements exhibit only one normal oxidation state, the Zn2+ and Mg2+ ions are of similar size. Zinc has five stable isotopes; the most common zinc ore is sphalerite, a zinc sulfide mineral. The largest workable lodes are in Australia and the United States. Zinc is refined by froth flotation of the ore and final extraction using electricity. Brass, an alloy of copper and zinc in various proportions, was used as early as the third millennium BC in the Aegean, the United Arab Emirates, Kalmykia and Georgia, the second millennium BC in West India, Iran, Syria and Israel/Palestine. Zinc metal was not produced on a large scale until the 12th century in India, though it was known to the ancient Romans and Greeks; the mines of Rajasthan have given definite evidence of zinc production going back to the 6th century BC. To date, the oldest evidence of pure zinc comes from Zawar, in Rajasthan, as early as the 9th century AD when a distillation process was employed to make pure zinc.
Alchemists burned zinc in air to form what they called "philosopher's wool" or "white snow". The element was named by the alchemist Paracelsus after the German word Zinke. German chemist Andreas Sigismund Marggraf is credited with discovering pure metallic zinc in 1746. Work by Luigi Galvani and Alessandro Volta uncovered the electrochemical properties of zinc by 1800. Corrosion-resistant zinc plating of iron is the major application for zinc. Other applications are in electrical batteries, small non-structural castings, alloys such as brass. A variety of zinc compounds are used, such as zinc carbonate and zinc gluconate, zinc chloride, zinc pyrithione, zinc sulfide, dimethylzinc or diethylzinc in the organic laboratory. Zinc is an essential mineral, including to postnatal development. Zinc deficiency affects about two billion people in the developing world and is associated with many diseases. In children, deficiency causes growth retardation, delayed sexual maturation, infection susceptibility, diarrhea.
Enzymes with a zinc atom in the reactive center are widespread in biochemistry, such as alcohol dehydrogenase in humans. Consumption of excess zinc may cause ataxia and copper deficiency. Zinc is a bluish-white, diamagnetic metal, though most common commercial grades of the metal have a dull finish, it is somewhat less dense than iron and has a hexagonal crystal structure, with a distorted form of hexagonal close packing, in which each atom has six nearest neighbors in its own plane and six others at a greater distance of 290.6 pm. The metal is hard and brittle at most temperatures but becomes malleable between 100 and 150 °C. Above 210 °C, the metal can be pulverized by beating. Zinc is a fair conductor of electricity. For a metal, zinc has low melting and boiling points; the melting point is the lowest of all the d-block metals aside from cadmium. Many alloys contain zinc, including brass. Other metals long known to form binary alloys with zinc are aluminium, bismuth, iron, mercury, tin, cobalt, nickel and sodium.
Although neither zinc nor zirconium are ferromagnetic, their alloy ZrZn2 exhibits ferromagnetism below 35 K. A bar of zinc generates a characteristic sound when bent, similar to tin cry. Zinc makes up about 75 ppm of Earth's crust. Soil contains zinc in 5–770 ppm with an average 64 ppm. Seawater has only 30 ppb and the atmosphere, 0.1–4 µg/m3. The element is found in association with other base metals such as copper and lead in ores. Zinc is a chalcophile, meaning the element is more to be found in minerals together with sulfur and other heavy chalcogens, rather than with the light chalcogen oxygen or with non-chalcogen electronegative elements such as the halogens. Sulfides formed as the crust solidified under the reducing conditions of the early Earth's atmosphere. Sphalerite, a form of zinc sulfide, is the most mined zinc-containing ore because its concentrate contains 60–62% zinc. Other source minerals for zinc include smithsonite, hemimorphite and sometimes hydrozincite. With the exception of wurtzite, all these other minerals were formed by weathering of the primordial zinc sulfides.
Identified world zinc resources total about 1.9–2.8 billion tonnes. Large deposits are in Australia and the United States, with the largest reserves in Iran; the most recent estimate of reserve base for zinc was made in 2009 and calculated to be 480 Mt. Zinc reserves, on the other hand, are geologically identified ore bodies whose suitability for recovery is economically based at the time of determination. Since exploration and mine development is an ongoing process, the amount of zinc reserves is not a fixed number and sustainability of zinc ore supplies cannot be judged by extrapolating the combined mine life of today's zinc mines; this concept is well supported by data from the United States Geol
