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Description of particle density in statistical mechanics
In statistical mechanics, the radial distribution function, (or pair correlation function) g ( r ) {\displaystyle g(r)} in a system of particles (atoms
Radial_distribution_function
Distribution of distances between pairs of particles in a given volume
The pair distribution function describes the distribution of distances between pairs of particles contained within a given volume. Mathematically, if a
Pair_distribution_function
Real function on a Euclidean space whose value depends only on distance from the origin
This characterization of radial functions makes it possible also to define radial distributions. These are distributions S on R n {\displaystyle \mathbb
Radial_function
Measure of a system's order
correlation function in an elemental liquid or a solid (often called a Radial distribution function or a pair correlation function). Correlation functions between
Correlation function (statistical mechanics)
Correlation_function_(statistical_mechanics)
Solution theory
macroscopic information. The radial distribution function (RDF), also termed the pair distribution function or the pair correlation function, is a measure of local
Kirkwood–Buff_solution_theory
Correlation as a function of distance
compressionPages displaying short descriptions of redirect targets Radial distribution function – Description of particle density in statistical mechanics Pal
Correlation_function
for the radial distribution function. The approximation is named after Jerome K. Percus and George J. Yevick. The direct correlation function represents
Percus–Yevick_approximation
Closure relation to solve the Ornstein-Zernike equation
correlation function to the total correlation function. It is commonly used in fluid theory to obtain e.g. expressions for the radial distribution function. It
Hypernetted-chain_equation
Non-crystalline solid
cell. Statistical measures, such as the atomic density function and radial distribution function, are more useful in describing the structure of amorphous
Amorphous_solid
State of matter
on. An equivalent representation of these correlations is the radial distribution function g ( r ) {\displaystyle g(r)} , which is related to the Fourier
Liquid
Resistance of a fluid to shear deformation
below the equilibrium melting temperature either in terms of radial distribution function g(r) or structure factor S(Q) are found to be directly responsible
Viscosity
In chemistry, average force on a particle
to a distance r {\displaystyle r} . It is also related to the radial distribution function of the system, g ( r ) {\displaystyle g(r)} , by: g ( r ) = e
Potential_of_mean_force
Machine learning kernel function
In machine learning, the radial basis function kernel, or RBF kernel, is a popular kernel function used in various kernelized learning algorithms. In
Radial_basis_function_kernel
Equation in statistical mechanics
Thus the pair correlation function only depends on distance, and therefore is also called the radial distribution function. It can be written g ( r 1
Ornstein–Zernike_equation
{\displaystyle I_{2}} are the analytical functions representing the integrals of the radial distribution function in 1st and 2nd order perturbation terms:
PC-SAFT
Topics referred to by the same term
for graphing RDF Schema, its language Radial distribution function, describes how density varies as a function of distance from a reference particle Radio
RDF
Proportionality constant in some physical laws
)\Omega (T)}}} where g ( σ ) {\displaystyle g(\sigma )} is the radial distribution function evaluated at the contact diameter of the particles. For molecules
Mass_diffusivity
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
Physics of many interacting particles
approximate approach is based on reduced distribution functions, in particular the radial distribution function. Molecular dynamics computer simulations
Statistical_mechanics
Alloys with high proportions of several metals
quasirandom structures", designed to most closely approximate the radial distribution function of a random system, combined with the Vienna Ab initio Simulation
High-entropy_alloy
mechanics) Correlation function (quantum field theory) Mutual information Rate distortion theory Radial distribution function Gubner, John A. (2006).
Cross-correlation_matrix
Model particles in statistical mechanics
^{3}}{{\left(1-\eta \right)}^{3}}}.} One can also obtain the value of the radial distribution function, g ( r ) {\displaystyle g(r)} , evaluated at the surface of a
Hard_spheres
Computational quantum mechanical modelling method to investigate electronic structure
_{s})}}=(-1)^{s}n_{s}(\mathbf {r} _{1},\dots ,\mathbf {r} _{s}).} The radial distribution function with s = 2 measures the change in the density at a given point
Density_functional_theory
Number of atoms, molecules or ions bonded to a molecule or crystal
defined. The first coordination number can be defined using the radial distribution function g(r): n 1 = 4 π ∫ r 0 r 1 r 2 g ( r ) ρ d r , {\displaystyle
Coordination_number
Atomic-scale non-crystalline structure of liquids and glasses
Fourier transformed to provide a corresponding radial distribution function (or pair correlation function), denoted in this article as g(r). For an isotropic
Structure of liquids and glasses
Structure_of_liquids_and_glasses
Probability distribution on a hyper-sphere of arbitrary dimension
p=2} the distribution reduces to the von Mises distribution on the circle. The probability density function of the von Mises–Fisher distribution for the
Von_Mises–Fisher_distribution
Properties and behavior of hydrated cations in aqueous solution
is short-range order. X-ray diffraction on solutions yields a radial distribution function from which the coordination number of the metal ion and metal-oxygen
Metal ions in aqueous solution
Metal_ions_in_aqueous_solution
Property of glass forming liquids
for example, intensification of Ni-P and Cu-P peaks in the radial distribution function close to the glass-transition, and liquid fragility. The physical
Fragility_(glass_physics)
Final stage of electricity delivery to individual consumers in a power grid
following functions: Circuit breakers and switches enable the substation to be disconnected from the transmission grid or for distribution lines to be
Electric_power_distribution
Method in computational chemistry
h(r;\Theta )} is the total correlation function, g ( r ; Θ ) {\displaystyle g(r;\Theta )} is the radial distribution function accounting for the direct effects
Solvent_model
Multivariable generalization of the Student's t-distribution
-1}}={\frac {p}{\nu -2}}} . Given the Beta-prime distribution, the radial cumulative distribution function of y {\displaystyle y} is known: F Y ( y ) ∼ I
Multivariate_t-distribution
Approximation in mathematics
PMID 20364982. S2CID 22763509. Banetta, L.; Zaccone, A. (2019). "Radial distribution function of Lennard-Jones fluids in shear flows from intermediate asymptotics"
Method of matched asymptotic expansions
Method_of_matched_asymptotic_expansions
Mathematical function
patterns in the feature space. Bell-shaped function Cauchy distribution Normal distribution Radial basis function kernel Squires, G. L. (2001-08-30). Practical
Gaussian_function
Equation which relates the isothermal compressibility to the structure of the liquid
where ρ {\displaystyle \rho } is the number density, g(r) is the radial distribution function and k T ( ∂ ρ ∂ p ) {\displaystyle kT\left({\frac {\partial \rho
Compressibility_equation
Response if an optical system to a point source of light
lens axis, r is radial distance in the image plane, and wavenumber k = 2π/λ where λ = wavelength, then the argument of the function is: kr tan(Θmax)
Point_spread_function
American physicist (1925–2020)
liquid-solid phase transition for hard sphere and the velocity autocorrelations function decay in liquids. Alder, along with Teller, was one of the founders of
Berni_Alder
Class of thermodynamic models
{\displaystyle {\bar {m}}} is the mole-average chain length, g(β) is the radial distribution function (RDF) evaluated at contact, and β is the reduced volume. The
Cubic_equations_of_state
Artificial neural network node function
common activation functions can be divided into three categories: ridge functions, radial functions and fold functions. An activation function f {\displaystyle
Activation_function
Technique for the characterisation of crystalline materials
number of benefits such as higher quality and better resolved radial distribution functions than in typical traditional geometries, improved dynamic range
Rietveld_refinement
Technique in physical chemistry
1724013. B.H. Zimm (1948). "The Scattering of Light and the Radial Distribution Function of High Polymer Solutions". J. Chem. Phys. 16 (12): 1093. Bibcode:1948JChPh
Static_light_scattering
Bending of electron beams due to electrostatic interactions with matter
Kassier, G. H.; Miller, R. J. D. (2020-11-21). "Determining the radial distribution function of water using electron scattering: A key to solution phase chemistry"
Electron_diffraction
Central atom with four substituents located at the corners of a tetrahedron
""Tetrahedrality" and the Relationship between Collective Structure and Radial Distribution Functions in Liquid Water". J. Phys. Chem. B. 111 (20): 5669–5679. doi:10
Tetrahedral molecular geometry
Tetrahedral_molecular_geometry
Theorem in classical statistical mechanics
the gas by a spherically symmetric distribution. It is then customary to introduce a radial distribution function g(r) such that the probability density
Equipartition_theorem
Mathematical description in crystallography
expression for S ( q ) {\displaystyle S(q)} in terms of the radial distribution function g ( r ) {\displaystyle g(r)} : In the limiting case of no interaction
Structure_factor
Chemical reaction between oppositely-charged ions in solution
bridge (protein and supramolecular) Noncovalent interactions Radial distribution function Davies, C. W. (1962). Ion Association. London: Butterworths.
Ion_association
Concept within complex analysis
of distributions f such that M f is in Lp(T). The function F defined on the unit disk by F(reiθ) = (f ∗ Pr)(eiθ) is harmonic, and M f is the radial maximal
Hardy_space
For liquids, the potential of mean force is related to the radial distribution function g ( r ) {\displaystyle g(r)} , which is given by: g ( r ) = P
Statistical_potential
Protons hopping across hydrogen bonds between hydronium ions and water molecules
candidate of the two. By use of conditional and time-dependent radial distribution functions (RDF), it was shown that the hydronium RDF can be decomposed
Grotthuss_mechanism
Function used in signal processing
two-dimensional window function is shared by its two-dimensional Fourier transform. The difference between the separable and radial forms is akin to the
Window_function
Smooth and compactly supported function
supported smooth function. Such functions are important examples of test functions, especially in distribution theory, but the terms "bump function" and "test
Bump_function
Policy maker, scholar, and advocate for people with developmental disabilities
at the Wayback Machine New York Times Obituary, January 30, 1996 The Radial Distribution Function in Liquids, Journal of Chemical Physics, June 1, 1942
Elizabeth_Monroe_Boggs
Probability distribution
distribution over directions that describes the radial projection of a random variable with n-variate normal distribution over the unit (n-1)-sphere. Given a random
Projected_normal_distribution
Astronomic function
the masses of the components. The binary mass function follows from Kepler's third law when the radial velocity of one binary component is known. Kepler's
Binary_mass_function
Aspect of computational chemistry
"tetrahedral" water structure that better reproduces the experimental radial distribution functions from neutron diffraction, and the temperature of maximal density
Water_model
Chinese-born electrical engineering professor (born 1931)
the mean deviation of the atomic coordinates obtained from the radial distribution function (RDF). In 1972, Tsu organized a group and was invited by the
Raphael_Tsu
Canadian chemist
Azim, Gunther Kassier, and R. J. Dwayne Miller. Determining the radial distribution function of water using electron scattering: A key to solution phase chemistry
R._J._Dwayne_Miller
New Zealand mathematician and academic physicist (1919–2012)
Edinburgh to do a PhD under Max Born. His thesis was entitled The radial distribution function and its application to the properties of fluids. McLellan returned
Alister_McLellan
Method for simulating ion transport
the charge on ions from other ions but also modulates the ion radial distribution function causing the formation of peaks and troughs. The average minimum
Biology_Monte_Carlo_method
Rabi cycle Rabi frequency Rabi problem Radial distribution function Radial motion Radial polarization Radial velocity Radian per second Radian per second
Index_of_physics_articles_(R)
Radio antenna feature
engineering, radial has three distinct meanings, all referring to lines which radiate from (or intersect at) a radio antenna. Ground system radial wires When
Radial_(radio)
British biologist
London where he was awarded a PhD in 1976 for research on the Radial distribution function and electron density in metals. Cusack was elected a Fellow of
Stephen_Cusack_(biologist)
fluid Radial distribution function J.M.J. van Leeuwen; J. Groenveld; J. de Boer (1959). "New method for the calculation of the pair correlation function I"
Classical-map hypernetted-chain method
Classical-map_hypernetted-chain_method
Family of solutions to related differential equations
to represent the Laplace distribution as an Exponential-scale mixture of normal distributions. The modified Bessel function of the second kind has also
Bessel_function
Functional relationship between two quantities
looser sense, a power-law probability distribution is a distribution whose density function (or mass function in the discrete case) has the form, for
Power_law
Indian academic, researcher (1964–2016)
Water (2004), Estimating the entropy of liquids from atom-atom radial distribution functions: silica, beryllium fluoride and water (2008), and Excess entropy
Charusita_Chakravarty
Mathematical transform that expresses a function of time as a function of frequency
Loukas; Teschl, Gerald (2013), "On Fourier transforms of radial functions and distributions", J. Fourier Anal. Appl., 19 (1): 167–179, arXiv:1112.5469
Fourier_transform
Function of propagation delay and Doppler frequency
communication systems. An ambiguity function plane can be viewed as a combination of an infinite number of radial lines. Each radial line can be viewed as the fractional
Ambiguity_function
Statistical model
those (infinitely many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g. time or space. The concept of
Gaussian_process
Type of probability distribution
normal distribution is a circular distribution representing the direction of a random variable with multivariate normal distribution, obtained by radial projection
Circular_distribution
Coordinates comprising two distances and an angle
perpendicular to the longitudinal axis are called radial lines. The distance from the axis may be called the radial distance or radius, while the angular coordinate
Cylindrical_coordinate_system
Concept in probability theory
the univariate case, the distribution is defined in terms of its characteristic function. The multivariate stable distribution can also be thought as an
Multivariate stable distribution
Multivariate_stable_distribution
Electrical wiring technique
The topology contrasts with the typical radial circuit configuration, in which nodes and the distribution point at the protective device are connected
Ring_circuit
functions Structure Radial distribution functions coordination numbers spatial density maps Thermodynamics Kinetic and potential energy distributions
MDANSE
Reference point in an electrical circuit from which voltages are measured
such long radials, they can in many cases be adequately replaced by a greater number of shorter radials, or a smaller number of longer radials. In transmitting
Ground_(electricity)
Directional planes
another. For a spinning earth, the plumb line deviates from the radial orientation as a function of latitude. Only on the equator and at the North and South
Vertical_and_horizontal
Mathematical description of quantum state
measurements, to the wave function ψ and calculate the statistical distributions for measurable quantities. Wave functions can be functions of variables other
Wave_function
American physicist (1922–2011)
the PY is a foundational closure approximation for computing radial distribution functions and related thermodynamic properties of dense fluids. Yevick
George_Yevick
Differential operator in mathematics
density distribution is a constant multiple of that density distribution. Solutions of Laplace's equation Δf = 0 are called harmonic functions and represent
Laplace_operator
Aspect of probability theory
two distinct distributions can both have the same characteristic function, so the distribution of X + Y must be just this normal distribution. For independent
Sum of normally distributed random variables
Sum_of_normally_distributed_random_variables
[0,2\pi ]} , while the density function for the radial coordinate r is chosen according to the probability distribution ρ {\displaystyle \rho } : ρ ( r
Hyperbolic_geometric_graph
Theorem of analytic continuations
can be solved locally in such a way that the radial limits of G and F tend locally to the same function in a higher Sobolev space. For k large enough
Edge-of-the-wedge_theorem
Distribution within a group of stars of the ratio of iron to hydrogen in a star
The metallicity distribution function is an important concept in stellar and galactic evolution. It is a curve of what proportion of stars have a particular
Metallicity distribution function
Metallicity_distribution_function
Tool in multivariate statistical analysis
{\displaystyle \nu } is an integer, limiting values should be taken (see ). Radial basis function Genton, Marc G. (1 March 2002). "Classes of kernels for machine
Matérn_covariance_function
Physical anomaly involving extra fingers or toes
be a complete functioning digit. The extra digit is most common on the ulnar (little finger) side of the hand, less common on the radial (thumb) side,
Polydactyly
last piece of the power distribution infrastructure, finally delivering generated power to where it will be consumed. Radial A circuit where the conductors
Electrical wiring in the United Kingdom
Electrical_wiring_in_the_United_Kingdom
American physical chemist (1920–1985)
interests included sea shells and horticulture. J. Donohue. Radial Distribution Functions of Some Structures of the Polypeptide Chain. Proc. Natl. Acad
Jerry_Donohue
Geometric symmetry in living beings
a few types of symmetry which are possible in body plans. These include radial (cylindrical) symmetry, bilateral, biradial and spherical symmetry. Additionally
Symmetry_in_biology
Distribution of crystallographic orientations in a polycrystalline material
set of different Euler angles, the distribution of which is described by the ODF. The orientation distribution function, ODF, cannot be measured directly
Crystallographic_texture
Statistical model used in machine learning
and minimized as the loss function. Additionally, novel samples can be generated by sampling from the initial distribution, and applying the flow transformation
Flow-based_generative_model
{\displaystyle k} K ( x , x k ) {\displaystyle K(x,x_{k})} is the Radial basis function kernel (Gaussian kernel) as formulated below. K ( x , x k ) = e
General regression neural network
General_regression_neural_network
Lowest possible mass of the celestial object
extrasolar planets detected by the radial velocity method or Doppler spectroscopy, and is determined using the binary mass function. This method reveals planets
Minimum_mass
Observed discrepancy in galactic angular momenta
the orbital speeds of visible stars or gas in that galaxy versus their radial distance from that galaxy's centre. It is typically rendered graphically
Galaxy_rotation_curve
Function describing an electron in an atom
is a function describing the location and wave-like behavior of an electron in an atom. This function describes an electron's charge distribution around
Atomic_orbital
Mathematical function used to approximate atomic orbitals in quantum chemistry
chemistry and physics, a 1s Slater-type function is a simple mathematical function used to approximate the distribution of a single electron in its lowest
1s_Slater-type_function
Process of calculating the causal factors that produced a set of observations
monitoring of the object into a 2D image of the emission (as a function of the radial velocity and of the phase in the periodic rotation movement) of
Inverse_problem
Continuous probability distribution
represented by κ-Gaussian distributions. In astrophysics, stellar-residual-radial-velocity data have a Gaussian-type statistical distribution, in which the K index
Kaniadakis Gaussian distribution
Kaniadakis_Gaussian_distribution
Limit of sequence of smooth functions
a distribution function. Just as in the formulation of distribution theory, it is in practice regarded as a limit of a sequence of smooth functions; one
Laplacian_of_the_indicator
British physicist (1942–2010)
developed a powerful electron diffraction technique for determining radial distribution functions from small areas of amorphous materials, collecting only elastically
David_Cockayne
Measure of the fluid slip in the impeller of a compressor or a turbine
outlet flow in the same direction), slip is a very important phenomenon in radial impellers and is useful in determining the accurate estimation of work input
Slip_factor
Management system for electrical power distribution
state of the distribution network indicating radial mode, loops and parallels in the network. In territories such as the UK a core function of a DMS has
Distribution management system
Distribution_management_system
RADIAL DISTRIBUTION-FUNCTION
RADIAL DISTRIBUTION-FUNCTION
Girl/Female
Arabic
Distributor
Boy/Male
Muslim
Greenery
Surname or Lastname
English
English : habitational name from various places, for example either of the places named Radway (in Devon and Warwickshire), Reddaway or Roadway (both in Devon), all named from Old English rÄ“ad ‘red’ + waye ‘road’, ‘way’, or from Rodway in Somerset, in which the first element is from Old English rÄd ‘road’, ‘track’.
Girl/Female
Arabic, French
Satisfied; Content
Boy/Male
Indian
Distributor, Divider
Male
English
Variant spelling of English Gaddiel, GADIEL means "God is my fortune."Â
Boy/Male
Muslim
Distributor, Divider
Boy/Male
Hindu, Indian
God's Kindness
Female
Serbian
(Радмила) Feminine form of Serbian Radmilo, RADMILA means "happy favor."
Male
English
Medieval form of English Randolf, RANDAL means "shield-wolf."
Girl/Female
Indian
Content, Satisfied
Boy/Male
Muslim/Islamic
Divider distributor
Girl/Female
Muslim
Honesty, Just, Upright, Justice
Boy/Male
Muslim
Distributor, Divider
Boy/Male
Indian
Distributor, Divider
Girl/Female
Indian, Sikh
Distributing Happiness
Girl/Female
Muslim
Content, Satisfied
Girl/Female
Indian
Honesty, Just, Upright, Justice
Boy/Male
Hindu, Indian
Wife of Lord Krishna
Boy/Male
Arabic, British, Islamic, Malaysian, Muslim, Pakistani, Tamil, Urdu
Distribution
RADIAL DISTRIBUTION-FUNCTION
RADIAL DISTRIBUTION-FUNCTION
Girl/Female
Irish
Sad.
Girl/Female
American, Australian, British, English
Soft-napped Fabric
Girl/Female
Indian, Sanskrit
Born from the Water; Lotus
Girl/Female
American, Christian, Gujarati, Hindu, Indian, Japanese, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Telugu
Water; Toy
Boy/Male
Muslim
Great
Biblical
measure of God
Male
English
Anglicized form of Hebrew Uwthay, UTHAI means "whom Jehovah helps." In the bible, this is the name of a son of Ammihud and a son of Bigvai.Â
Boy/Male
Tamil
Passion
Boy/Male
English American
and Zachary.
Boy/Male
Indian
A narrator of Hadith
RADIAL DISTRIBUTION-FUNCTION
RADIAL DISTRIBUTION-FUNCTION
RADIAL DISTRIBUTION-FUNCTION
RADIAL DISTRIBUTION-FUNCTION
RADIAL DISTRIBUTION-FUNCTION
n.
A radical quantity. See under Radical, a.
a.
A radical vessel. See under Radical, a.
n.
A radiate.
a.
Belonging to, or proceeding from, the root of a plant; as, radical tubers or hairs.
a.
Of or pertaining to a radius or ray; consisting of, or like, radii or rays; radiated; as, (Bot.) radial projections; (Zool.) radial vessels or canals; (Anat.) the radial artery.
a.
Expressing separation; denoting a taking singly, not collectively; as, a distributive adjective or pronoun, such as each, either, every; a distributive numeral, as (Latin) bini (two by two).
a.
Of or pertaining to a race or family of men; as, the racial complexion.
a.
Relating, or belonging, to the root, or ultimate source of derivation; as, a radical verbal form.
adv.
By distribution; singly; not collectively; in a distributive manner.
n.
Radial plates in the calyx of a crinoid.
a.
Hence: Of or pertaining to the root or origin; reaching to the center, to the foundation, to the ultimate sources, to the principles, or the like; original; fundamental; thorough-going; unsparing; extreme; as, radical evils; radical reform; a radical party.
a.
Of or pertaining to a radix or root; as, a radical quantity; a radical sign. See below.
a.
Of or pertaining to distribution.
a.
Situated around the radii, or radial tubes, of a radiate.
a.
See Predial.
pl.
of Radiale
n.
The act of distributing or dispensing; the act of dividing or apportioning among several or many; apportionment; as, the distribution of an estate among heirs or children.
adv.
In a radial manner.
n.
A distributive adjective or pronoun; also, a distributive numeral.