virial equation of state
hamugeš-e hâlat-e viriyal
Fr.: équation d'état du viriel
Fr.: équilibre du viriel
The condition of a physical system which obeys the → virial theorem.
Fr.: masse du viriel
The mass of a cluster of stars or galaxies in statistical equilibrium derived by using the → virial theorem.
Fr.: paramètre du viriel
A dimensionless parameter that measures the ratio of thermal plus kinetic energies to gravitational energy of a physical system, such as a molecular cloud. The virial parameter is expressed as: αvir = 5σ2R / GM, where R and M are the radius and mass of the cloud respectively, σ is the one-dimensional → velocity dispersion inside the cloud, and G the → gravitational constant. It indicates whether a cloud could be bound or not. For molecular clouds that are confined by their surface pressure and for which self-gravity is unimportant, αvir is much larger than unity, whereas αvir is ~ 1 when the gravitational energy of a clump becomes comparable to its kinetic energy. See, e.g., Bertoldi & McKee, 1992 (ApJ 395, 140). See also → virial theorem.
Fr.: rayon du viriel
The radius centered on a galaxy containing matter at 200 times the → critical density of the Universe.
Fr.: température du viriel
The mean temperature at which a gravitationally → bound system would satisfy the → virial theorem. For a system of mass M and radius R with constant density, the gravitational energy per unit mass is W = GM/R. The kinetic energy per unit mass is E = (3/2)kTvir/μ, where k is → Boltzmann's constant and μ the mean molecular weight. According to the virial theorem, E = W/2, which leads to the virial temperature Tvir = (1/3)(GM/kR).
Fr.: théorème du viriel
A general equation applicable to a gravitationally → bound system of equal mass objects (stars, galaxies, etc.), which is stable against → dynamical disruption. It states that in such a system the average → gravitational potential energy (Wvir) is twice the average → kinetic energy (Kvir) of the system: Wvir = -2Kvir. This general proposition, first derived by Rudolf Clausius (1822-1888), has important applications in a variety of fields ranging from statistical mechanics to astrophysics. See also → virialization, → virial equilibrium, → virialized.
The process whereby a system of gravitationally interacting particles attains stability. The comparable mass components interact with each other, but the whole system does not expand or collapse. Virialization occurs when the → potential energy is twice the negative → kinetic energy: - Wvir = 2 Kvir (→ virial theorem). In the case of a → galaxy cluster, when the cluster is virialized the merging process and the collapse of matter have finished and the formation process of the galaxy cluster is considered to be done. A cluster has formed by → hierarchical clustering. Virialized clusters, in other words finished clusters, can be found by looking at their radius and density. A cluster is virialized when it satisfies the condition: Rvir ~ Rmax/2, where Rvir is the radius when the cluster is virialized and Rmax is the radius when the collapse starts. From this condition it follows that the object is 8 times denser at virialization than when the collapse started.
Verbal noun of → virialize.
To undergo → virialization.
That has undergone → virialization.
Past participle of → virialize.
1) General: Having the efficacy without the material part; unreal but capable
of being considered as real for some purpose.
M.E., from M.L. virtualis, from L. virtus "manliness, excellence, potency, efficacy," from vir "man, human, husband, soldier," cf. Mid.Pers. vīr, wīr "man, hero;" Av. vīra- "man, human;" Skt. vīrá- "man, hero;" Lith. vyras "man, husband;" O.Ir. fer "man;" Goth. wair "man;" O.E. wer "man." In Roman philosophy, virtue became associated with virility and strength of character.
Virâgin from vir "intellect, mind, memory," variants bar, bir (Mid.Pers. vir, varm, vârom "mental faculty, memory, mind;" Av. vārəma, vārəm "according to one's wishes," from var- "to choose") + -âgin a suffix denoting "consisting of, similarity, possession."
Fr.: déplacement virtuel
In → analytical mechanics, any infinitesimal change in the configuration of a material system, consistent with any constraints acting on the system at a given instant. If the constraints are stationary (→ scleronomous), then the actual displacement of the system, in an infinitesimal length of time dt, coincides with one of its virtual displacements. In the case of time-dependent (→ rheonomous) constraints, the actual displacement of the system does not coincide with any of the virtual ones, since the conditions imposed by the constraints vary during the time dt.
Fr.: image virtuelle
Optics: An image formed inside an instrument at the point where diverging rays would cross if they were extended backward into the instrument. Such an image cannot be obtained on a screen placed at its apparent position, since the rays do not pass through that point. → real image.
Fr.: observatoire virtuel
An international initiative by the astronomical community to allow global electronic access to the available astronomical data archives of space and ground-based observatories. It also aims to enable data analysis techniques through a coordinating entity that provides common standards, wide-network bandwidth, and state-of-the-art analysis tools. The Virtual Observatory is also intended for re-using data for scientific objectives different from the original ones, in order to optimize the science return of astronomical observations. The Virtual Observatory's capabilities are enabled through the use of standard protocols for registering the existence and location of data and for requesting data that satisfies the user's interests. These standards are developed on an international basis through the → IVOA. The cornerstone of the Virtual Observatory is → interoperability.
Fr.: particule virtuelle
A subatomic particle that, according to the uncertainty principle, comes into being out of energy fluctuations of the "vacuum" and lasts for extremely short periods of time. An electron-positron pair can exist only about 4 x 10-21 seconds. The lifetime increases as the mass and energy involved decreases. Virtual particles are real and have measurable effects, but cannot be directly observed, according to the uncertainty principle. → vacuum polarization.
Fr.: travail virtuel
virtual work principle
parvaz-e kâr-e virâgin
Fr.: principe du travail virtuel
In → analytical mechanics, a principle whereby it is necessary and sufficient for the equilibrium of any material system with ideal constraints that the sum of the elements of work, performed by the applied forces acting on the system in any virtual displacement, be equal to zero (if all constraints are bilateral) or less than zero (if some of the constraints are unilateral).
An instrument used to measure the → viscosity of a liquid. Same as viscosimeter.
Same as → viscometer.
The property of a → fluid that resists the force tending to cause the fluid to flow. Viscosity may be thought of as the internal → friction of two fluid layers which flow parallel to each other at different speeds. The cause of viscosity is the transport of → momentum by the molecules from one layer to the other. Viscosity is given by η = φ.u.λ.ρ, where φ is a coefficient which depends on the nature of the interaction between the molecules, u is the average velocity of thermal motion of the molecules, λ is the → mean free path, and ρ the → density of the fluid. Also called → dynamic viscosity or → absolute viscosity. See also → kinematic viscosity.