âmâr-e Fermi-Dirac (#)
Fr.: distribution Fermi-Dirac
Fr.: expérience Fermi-Pasta-Ulam
A computer experiment that was aimed to study the → thermalization process of a → solid. In other words, the goal was to see whether there is an approximate → equipartition of energy in the system, which would mean that the motion is → chaotic. Using computer simulation, Fermi-Pasta-Ulam studied the behavior of a chain of 64 mass particles connected by → nonlinear springs. In fact, they were looking for a theoretical physics problem suitable for an investigation with one of the very first computers, the he MANIAC (Mathematical Analyzer, Numerical Integrator and Computer). They decided to study how a → crystal evolves toward → thermal equilibrium by simulating a chain of particles, linked by a quadratic interaction potential, but also by a weak nonlinear interaction. Fermi-Pasta-Ulam assumed that if the interaction in the chain were nonlinear, then an exchange of energy among the normal modes would occur, and this would bring forth the equipartition of energy, i.e. the thermalization. Contrary to expectations, the energy revealed no tendency toward equipartition. The system had a simple quasi-periodic behavior, and no → chaoticity was observed. This result, known as the Fermi-Pasta-Ulam paradox, shows that → nonlinearity is not enough to guarantee the equipartition of energy (see, e.g., Dauxois et al., 2005, Eur. J. Phys., 26, S3).
E. Fermi, J. Pasta, S. Ulam, 1955, Los Alamos report LA-1940; → problem.
Ferric, from L. ferrum "iron," + → -ic.
Fr.: fer ferrique, fer trivalent
Iron in a plus-3 → oxidation state. Ferric iron needs to share three electrons with an oxygen molecule to make the ion neutral.
Indicating a property of → iron or the presence of iron.
Ferro-, variant ferri-, combining form of L. ferrum "iron."
Âhan-, → iron.
A property observed in certain materials characterized by the presence of a spontaneous electric polarization even in the absence of an external electric field. In the ferroelectric state the center of positive charge of the material does not coincide with the center of negative charge. This phenomenon is explained by spontaneous alignment of these permanent moments along the same direction. The term comes from the similarity with → ferromagnetism, but iron is not a ferroelectric. Ferroelectricity disappears above a critical temperature. Ferroelectric materials have been a fertile field for the study of → phase transitions.
A ferroamagnetic substance, which possesses → ferromagnetism.
Relative to or characterized by → ferromagnetism.
A property of certain substances which are enormously more magnetic than any other known substance. Ferromagnetic substances, such as the chemical elements iron, nickel, cobalt, some of the rare earths, and ceratin alloys, achieve maximum → magnetization at relatively low magnetic field strengths. Their large → magnetic permeabilityies (greater than unity) vary with the strength of the applied field. When the temperature of a ferromagnet is increased the property vanishes gradually due to randomizing effects of thermal agitation. Beyond a definite temperature for each substance ( → Curie temperature) it ceases to behave as a ferromagnet and becomes a → paramagnet. Ferromagnetism is due to the alignment of the → magnetic moments of uncompensated electrons in the crystal lattice. Under the influence of an external magnetizing field, all of the uncompensated electrons line up with their → spins in the direction of the field. In contrast with paramagnetic substances, in which spins interact only with an external magnetic field, in ferromagnets the spins interact with each others, each of them trying to align the others in its own direction. This coupling gives rise to a spontaneous alignment of the moments over macroscopic regions called domains. The domains undergo further alignment when the substance is subjected to an applied field. Ferromagnets retain their magnetisation even when the external magnetic field has been removed. See also → antiferromagnetism ; → diamagnetism; → magnetism.
From L. ferrum "iron," + -ous a suffix forming adjectives that have the general sense "possessing, full of" a given quality.
Fervar, from fer, loan from Fr., + -var adj. suffix.
Fr.: fer ferreux, fer bivalent
Iron in a plus-2 → oxidation state.
M.E., from M.Fr. fertil, from L. fertilis "bearing in abundance, fruitful, productive," from ferre "to bear," from PIE root *bher- "to carry," also "to bear children," cognate with Pers. bordan "to carry, bear," → refer.
Bârvar, literally "fruitful," from bâr "fruit; flower; load; charge" + possession suffix -var, related to bordan "to bear, carry," as above.
Fr.: isotope fertile
An → isotope not itself → fissile but that is converted into a fissile isotope, either directly or after a short → decay process following absorption of a → neutron. Example: U-238 can capture a neutron to give U-239. U-239 then decays to Np-239 which in turn decays to fissile Pu-239. The most important fertile isotope is U-238. This is by far the most abundant isotope of natural uranium, making up 99.28%. The important transformation chain is: 92U238 + 0n1→ 93Np239 + β- (23.5 minutes) → 94Pu239 + β- (2.36 days).
Fr.: diagramme de Feynman
A schematic representation, in quantum electrodynamics and quantum chromodynamics, of the way elementary particles like electrons and protons interact with each other by exchanging photons. Use of Feynman diagrams can greatly reduce the amount of computation involved in calculating a rate or cross section of a physical process.
After the American physicist Richard P. Feynman (1918-1988), Nobel prize 1965; → diagram.
Fr.: étoile FHB
Same as → field horizontal branch star.
From Fr. fibre, from O.Fr. fibre, from L. fibra "a fiber, filament," of uncertain origin, perhaps related to L. filum "thread."
Fibr, loan from Fr., as above.
Fr.: nombre de Fobonacci
One of the numbers in the → Fibonacci sequence.
Fr.: suite de Fibonacci
An infinite sequence of integers, starting with 0 and 1, where each element is the sum of the two previous numbers. For example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... As the sequence develops, the ratio of the consecutive terms converges to the → golden ratio, about 1.618.
Leonardo Pisano Fibonacci (1170-1250), medieval Italian mathematician who wrote Liber abaci (1202; Book of the Abacus), the first European work on Indian and Arabian mathematics, which introduced "Arabic" numerals in Europe; → sequence.