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Heuristic used in simulations of ions passing through solids
In condensed-matter physics, the binary collision approximation (BCA) is a heuristic used to more efficiently simulate the penetration depth and defect
Binary collision approximation
Binary_collision_approximation
Software for simulating ionic interactions with solid matter
implantation, energy loss, and collision cascades in solids using a Monte Carlo implementation of the binary collision approximation. SRIM is widely used in
Stopping and Range of Ions in Matter
Stopping_and_Range_of_Ions_in_Matter
Series of collisions between nearby atoms, initiated by a single energetic atom
kind of cascade can be theoretically well treated using the binary collision approximation (BCA) simulation approach. For instance, H and He ions with
Collision_cascade
System consisting of two black holes in close orbit around each other
A binary black hole (BBH), or black hole binary, is an astronomical object consisting of two black holes in close orbit around each other. Like black
Binary_black_hole
Topics referred to by the same term
concentration of protein in a solution Branched-chain amino acid Binary collision approximation, a heuristic used in simulations of ions passing through solids
BCA
Retarding force acting on charged particles due to interactions with matter
Conventional methods used to calculate ion ranges are based on the binary collision approximation (BCA). In these methods the movement of ions in the implanted
Stopping power (particle radiation)
Stopping_power_(particle_radiation)
Process constraining a charged particle's path through a crystal
The channelling effect was first discovered in pioneering binary collision approximation computer simulations in 1963 in order to explain exponential
Channelling_(physics)
Probabilistic problem-solving algorithm
problem for quantum systems. In radiation materials science, the binary collision approximation for simulating ion implantation is usually based on a Monte
Monte_Carlo_method
Emission of surface atoms through energetic particle bombardment
enough, that collisions occur very close to each other. In this case, the binary collision approximation is no longer valid, and the collisional process should
Sputtering
Binary elastic collision between two charged particles
A Coulomb collision is a binary elastic collision between two charged particles interacting through their own electric field. As with any inverse-square
Coulomb_collision
Method for recursively subdividing a space into two subsets using hyperplanes
multi-resolution fashion (more exactly, as a tree of approximations). Parallels with Huffman codes and probabilistic binary search trees are drawn. Hayder Radha's Ph
Binary_space_partitioning
Term in computer science
by a point is sufficient for the purpose of collision detection with the environment. In this case, binary space partitioning trees provide a viable, efficient
Collision_detection
Use of ions to cause chemical changes
the target is called stopping and can be simulated with the binary collision approximation method. Accelerator systems for ion implantation are generally
Ion_implantation
Energy needed to dislocate an atom within a solid lattice
limitations. The threshold displacement energy is also often used in binary collision approximation computer codes such as SRIM to estimate damage. However, the
Threshold_displacement_energy
Associative array for storing key–value pairs
map. Most hash table designs employ an imperfect hash function. Hash collisions, where the hash function generates the same index for more than one key
Hash_table
Functions for calculating potential energy
~5%–10% from the quantum chemical calculations above 100 eV. In binary collision approximation simulations this kind of potential can be used to describe the
Interatomic_potential
Measure of similarity and diversity between sets
ecology, genomics and other sciences where binary or binarized data are used. Both the exact solution and approximation methods are available for hypothesis
Jaccard_index
Equation of statistical mechanics
"Numerical Solution of the Boltzmann Equation I: Spectrally Accurate Approximation of the Collision Operator". SIAM Journal on Numerical Analysis. 37 (4): 1217–1245
Boltzmann_equation
Physics problem related to laws of motion and gravity
the three-body problem are binary collisions (collisions between two particles at an instant) and triple collisions (collisions between three particles at
Three-body_problem
algorithm: an approximation of the square-root of the sum of two squares Methods of computing square roots nth root algorithm Summation: Binary splitting:
List_of_algorithms
Mathematical descriptions of molecular diffusion
since the phenomena described by a lower order approximation is the result of a higher approximation: this problem is solved only by renormalizing the
Fick's_laws_of_diffusion
Electromagnetic radiation due to deceleration of charged particles
logarithm that occurs in other collisional plasma calculations. For y>e−γ the log term is negative, and the approximation is clearly inadequate. Bekefi
Bremsstrahlung
Aspect of relativity in physics
sensitive are supermassive black hole binaries, which form from the collision of galaxies. In addition to individual binary systems, pulsar timing arrays are
Gravitational_wave
Natural number
153rd Markov number 1,099,511,627,776 = 2565 = 1610 = 420 = 240, binary approximation of metric prefix tera- 1,099,511,629,376 : Leyland number using 2
1,000,000,000,000
Sub-area of scientific computing for solving General Relativity equations
In the late 1990s, the Binary Black Hole Grand Challenge Alliance successfully simulated a head-on binary black hole collision. As a post-processing step
Numerical_relativity
Tree data structure that partitions a 2D area
array as an implicit data structure similar to the way a binary heap can store a complete binary tree compactly in an array. Quadtrees may be classified
Quadtree
Mathematical functions
PMID 17954598. Tkachuk, S. A.; Pasnichenko, O. S.; Savchok, L. B. (2021). "Approximation of Growth Indicators and Analysis of Individual Growth Curves by Linear
Hyperbolastic_functions
Infinite binary sequence generated by repeated complementation and concatenation
Binary Sequences of Differences" (PDF). Complex Systems. 13 (4): 381–392. Bugeaud, Yann (2012). Distribution modulo one and Diophantine approximation
Thue–Morse_sequence
Hypothetical types of stars
recorded, may be the head-on collision of two boson stars. In addition, gravitational wave signals from compact binary boson star mergers can be degenerate
Exotic_star
This approximation is very effective if the velocity is very small, but becomes rather inaccurate if v/c becomes larger than about 0.3. For binary systems
Extreme_mass_ratio_inspiral
Field of classical mechanics concerned with the motion of spacecraft
including that which bears his name. Newton's method of successive approximation was formalised into an analytic method by Leonhard Euler in 1744, whose
Orbital_mechanics
Possible dwarf planet
estimate of 866±37 km and 290±21 km for Salacia and Actaea respectively. approximation if Salacia and Actaea were both spherical and had the same albedo This
120347_Salacia
Spectral features due to inelastic interactions
transitions of binary, ternary,... intermolecular complexes, which are (often unjustifyably) neglected in the ideal gas approximation of spectroscopy
Collision-induced absorption and emission
Collision-induced_absorption_and_emission
Measure of the luminosity of celestial objects
luminosity measurements) must be used instead of d, because the Euclidean approximation is invalid for distant objects. Instead, general relativity must be
Absolute_magnitude
Probability distribution
approximation and where infinitely divisible and decomposable distributions are involved, such as Binomial random variables, associated with binary response
Normal_distribution
Connected series of line segments
find a polygonal chain with few segments that serves as an accurate approximation. In graph drawing, polygonal chains are used to represent the edges
Polygonal_chain
particles undergoing binary elastic collisions, the defining difference from the classical Boltzmann equation lies in the collision operator. One common
Quantum_Boltzmann_equation
Equation in stellar astrophysics
The relation for stars with different ranges of mass are, to a good approximation, as the following: LL⊙≈0.23(MM⊙)2.3(M<0.43M⊙)LL⊙=(MM⊙)4(0.43M⊙<M<2M⊙)LL⊙≈1
Mass–luminosity_relation
Alan Hulse, Joseph Hooton Taylor Jr. and others studied the behaviour of binary pulsars experiencing much stronger gravitational fields than those found
Tests_of_general_relativity
Type of star cluster
mass loss on the dynamical evolution of a stellar system – Analytic approximations". Astrophysical Journal. 235 (1): 986–991. Bibcode:1980ApJ...235..986H
Open_cluster
Approximate distinct counting algorithm
be estimated by calculating the maximum number of leading zeros in the binary representation of each number in the set. If the maximum number of leading
HyperLogLog
Phenomenon affecting the orbit of a binary system
the Kozai mechanism is a dynamical phenomenon affecting the orbit of a binary system perturbed by a distant third body under certain conditions. The mechanism
Kozai_mechanism
Velocity of an object as the rate of distance change between the object and a point
astronomy, radial velocity is often measured to the first order of approximation by Doppler spectroscopy. The quantity obtained by this method may be
Radial_velocity
Scientific models assumption of facts
model is applied to make a prediction based on that ideal case. If an approximation is accurate, the model will have high predictive power; for example
Idealization (philosophy of science)
Idealization_(philosophy_of_science)
Algorithmic technique using hashing
search. It differs from conventional hashing techniques in that hash collisions are maximized, not minimized. Alternatively, the technique can be seen
Locality-sensitive_hashing
State of matter
differences: Three factors define an ideal plasma: The plasma approximation: The plasma approximation applies when the plasma parameter Λ, representing the number
Plasma_(physics)
Region in which an astronomical body dominates the attraction of satellites
case, unless the negligible mass of one of the three bodies allows approximation of the system as a two-body problem, known formally as a "restricted
Hill_sphere
Producing images of 3D scenes
camera used to take the photograph must be simulated. The thin lens approximation allows combining perspective projection with depth of field (and bokeh)
Rendering_(computer_graphics)
Probabilistic data structure in computer science
sketch typically has a sublinear number of cells, related to the desired approximation quality of the sketch, while a counting Bloom filter is more typically
Count–min_sketch
Subfield of astronomy
Gaussian fluctuations. Sheth–Tormen approximation – Improves halo mass function predictions. Zeldovich approximation – First-order perturbation for large-scale
Outline_of_astrophysics
Concept in celestial mechanics
much larger than the mass of the orbiting body (m), or M ≫ m. This approximation is standard for planets orbiting the Sun or most moons and greatly simplifies
Standard gravitational parameter
Standard_gravitational_parameter
Computer security technique
in which libraries are loaded. This supplies very little entropy. An approximation of the number of bits of entropy supplied per needed library appears
Address space layout randomization
Address_space_layout_randomization
Measure of a substance's ability to resist or conduct electric current
{\displaystyle \kappa } [clarification needed]. Because the linear approximation is only an approximation, α {\displaystyle \alpha } is different for different reference
Electrical resistivity and conductivity
Electrical_resistivity_and_conductivity
to render the original Arabic pronunciation using English sounds as approximations, and not distinguish that pseudo-Arabic pronunciation from an English
List_of_proper_names_of_stars
Statistical procedure of testing by group
introduction of the generalised binary-splitting algorithm. The generalised binary-splitting algorithm works by performing a binary search on groups that test
Group_testing
Changed position of star vs background
all involve such skinny right triangles, a convenient trigonometric approximation can be used to convert parallaxes (in arcseconds) to distance (in parsecs)
Stellar_parallax
Region of a star
right-hand side and get GM=κL4πc(1−β) Thus the Eddington model is a good approximation in the radiative zone as long as κL/M is approximately constant, which
Radiative_zone
Stars sorted by absolute magnitude
implies an error ~2× as large (thus 20%) in luminosity (see binomial approximation). Stellar distances are only directly measured accurately out to d ~1
List_of_most_luminous_stars
Transport of dissolved species from the highest to the lowest concentration region
Onsager equations, we must take the thermodynamic forces in the linear approximation near equilibrium: X i = ∑ k ≥ 0 ∂ 2 s ( n ) ∂ n i ∂ n k | n = n ∗ ∇
Diffusion
Type of dense exotic matter in physics
gravitational collapse. The term also applies to metals in the Fermi gas approximation. Degenerate matter is usually modelled as an ideal Fermi gas, an ensemble
Degenerate_matter
Hypothetical collection of stable heavy nuclides
this star type. Whether they do may be verified by detecting binary compact stellar collisions via gravitational waves. Holdom, Bob; Ren, Jing; Zhang, Chen
Continent_of_stability
Data structure for approximate set membership
over other data structures for representing sets, such as self-balancing binary search trees, tries, hash tables, or simple arrays or linked lists of the
Bloom_filter
Natural phenomenon due to which tidal locking occurs
orbital velocity and a shorter and shorter orbital period, until a final collision with the primary. The naming is somewhat confusing, because the average
Tidal_acceleration
Hypothetical vacuum, less stable than true vacuum
S2CID 53978709. Mukhanov, V. F.; Sorin, A. S. (2022), "Instantons: Thick-wall approximation", Journal of High Energy Physics, 2022 (7): 147, arXiv:2206.13994, Bibcode:2022JHEP
False_vacuum
Nucleosynthesis pathway
sometimes approximated over a small mass region using the so-called "local approximation", by which the ratio of abundances is inversely proportional to the
S-process
is the case, collective electrostatic interactions dominate over binary collisions, and the plasma particles can be treated as if they only interact
Plasma_parameter
Study of oscillations in stars
perturbation to the gravitational potential is negligible (the Cowling approximation) and that the star's structure varies more slowly with radius than the
Asteroseismology
Randomly determined process
randomly chosen points and averages the results to obtain a better approximation. It is essentially an application of the Monte Carlo method to 3D computer
Stochastic
Subset of evolutionary computation
computational complexity is due to fitness function evaluation. Fitness approximation is one of the solutions to overcome this difficulty. However, seemingly
Evolutionary_algorithm
Mathematics used in Ancient China
numeral system (binary and decimal), algebra, geometry, number theory and trigonometry. Since the Han dynasty, as diophantine approximation being a prominent
Chinese_mathematics
Problem in physics and celestial mechanics
treating interactions among the planets as perturbations. Perturbative approximation works well as long as there are no orbital resonances in the system
N-body_problem
Overview of titanium's biocompatible properties
protein), and F is the Faraday constant in C⋅mol−1. The equation for collision frequency is as follows: v c = 2 π D c d N A {\displaystyle v_{\text{c}}={2\pi
Titanium_biocompatibility
Fictional character in The Big Bang Theory and Young Sheldon
CBS. "The Einstein Approximation". The Big Bang Theory. Season 3. Episode 14. February 1, 2010. CBS. "The Large Hadron Collision". The Big Bang Theory
Sheldon_Cooper
Long-term future of planet Earth
There is a remote chance that Earth will instead be captured by a passing binary star system, allowing the planet's biosphere to remain intact. The odds
Future_of_Earth
Process of energy release of a contracting star or planet
the known luminosity of the Sun (note that this will involve another approximation, as the power output of the Sun has not always been constant): U r L
Kelvin–Helmholtz_mechanism
Continuous band of stars that appears on plots of stellar color versus brightness
luminosity depends only on a star's mass, at least to zeroth-order approximation, as long as it is fusing hydrogen at its core—and that is what almost
Main_sequence
Equilibrium points near two orbiting bodies
of Lagrange points—John C. Baez Locations of Lagrange points, with approximations—David Peter Stern Astronomy Cast—Ep. 76: "Lagrange Points" by Fraser
Lagrange_point
Belgian scientist and Catholic priest (1894–1966)
L'approximation des fonctions de plusieurs variables réelles ("The approximation of functions of several real variables"), written under the direction
Georges_Lemaître
Branch of astrophysics
surfaces, the dense plasma or gas particles collide very frequently, and collisions result in equipartition and perhaps viscosity under magnetic field. We
Stellar_dynamics
Chemically peculiar stars of spectral types A and B
In most cases a field which is modelled as a simple dipole is a good approximation and provides an explanation as to why there is an apparent periodic
Magnetic chemically peculiar star
Magnetic_chemically_peculiar_star
Equation used in relativistic physics
Mirco (2017). "Lorentz invariant relative velocity and relativistic binary collisions". International Journal of Modern Physics A. 32 (2n03): 1730002. arXiv:1605
Velocity-addition_formula
Periodic table of the elements with eight or more periods
been synthesized or discovered in nature. According to the orbital approximation in quantum mechanical descriptions of atomic structure, the g-block
Extended_periodic_table
Structure of stars
"sees" below itself is always hotter than the temperature above, this approximation is normally excellent because the photon mean free path, λ {\displaystyle
Stellar_structure
Computer hardware technology that uses quantum mechanics
computing. Unlike a classical bit, which can be in one of two states (a binary), a qubit can exist in a linear combination of states known as a quantum
Quantum_computing
Speed of electromagnetic waves
1 billion kilometres per hour; 700 million miles per hour. For other approximations of c, valid for various units and size scales see the infobox. The shorter
Speed_of_light
Spectroscopic technique
Fermi's Golden Rule uses the approximation that the perturbation acts on the system for an infinite time. This approximation is valid when the time that
X-ray photoelectron spectroscopy
X-ray_photoelectron_spectroscopy
Algorithm to be run on quantum computers
takes inspiration from quantum annealing, performing a discretized approximation of quantum annealing using a quantum circuit. It can be used to solve
Quantum_algorithm
Uses of the constant
Many of these formulae can be found in the article Pi, or the article Approximations of π. π = C d = C 2 r {\displaystyle \pi ={\frac {C}{d}}={\frac {C}{2r}}}
List_of_formulae_involving_π
Light emitted by the Sun
orbit by using the day number of the year (dn), is given to a good approximation by Eext=Esc⋅(1+0.033412⋅cos(2πdn−3365)), where dn=1 on January 1; dn=32
Sunlight
Resistance of a fluid to shear deformation
from cohesive molecular forces, while in gases it results from molecular collisions. Except for the case of superfluidity, there is no fluid with zero viscosity
Viscosity
The Moon's circuit around Earth
own axes. The properties of the orbit described in this section are approximations. The Moon's orbit around Earth has many variations (perturbations) due
Orbit_of_the_Moon
Regular and periodic mutual gravitational influence of orbiting bodies
integers. Most commonly, this relationship is found between a pair of objects (binary resonance). The physical principle behind orbital resonance is similar in
Orbital_resonance
Gas equation of state which accounts for non-ideal gas behavior
accurate for only a few substances. Most simple fluids are only a valuable approximation. The ideal gas law follows from the van der Waals equation whenever
Van_der_Waals_equation
Executing several computations during overlapping time periods
denotation denoted by a closed system S is constructed increasingly better approximations from an initial behavior called ⊥S using a behavior approximating function
Concurrent_computing
Algorithms and methods of plotting the Mandelbrot set on a computing device
"Distance Estimated 3D Fractals (V): The Mandelbulb & Different DE Approximations". Archived from the original on 13 May 2021. Retrieved 10 May 2021.
Plotting algorithms for the Mandelbrot set
Plotting_algorithms_for_the_Mandelbrot_set
Natural satellite orbiting Earth
07.006. Alexander, M.E. (1973). "The Weak Friction Approximation and Tidal Evolution in Close Binary Systems". Astrophysics and Space Science. 23 (2):
Moon
Hungarian and American mathematician and physicist (1903–1957)
Strzelecki, Michał (2022). "Approximation, Gelfand, and Kolmogorov numbers of Schatten class embeddings". Journal of Approximation Theory. 277 105736. arXiv:2103
John_von_Neumann
Method by which atoms of a planet's atmosphere are ejected into space
the escape of heavier atoms of a planetary atmosphere through numerous collisions with lighter atoms, typically hydrogen. This mechanism may explain why
Hydrodynamic_escape
Type of Linux installation
Compiler Collection (rated at 11 SBUs). The unit must be interpreted as an approximation; various factors influence the actual time required to build a package
Linux_from_Scratch
Curved path of an object around a point
although it may also refer to a non-repeating trajectory. To a close approximation, planets, and satellites follow elliptic orbits, with the center of
Orbit
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BINARY COLLISION-APPROXIMATION
BINARY COLLISION-APPROXIMATION
BINARY COLLISION-APPROXIMATION
BINARY COLLISION-APPROXIMATION
BINARY COLLISION-APPROXIMATION
BINARY COLLISION-APPROXIMATION
BINARY COLLISION-APPROXIMATION
BINARY COLLISION-APPROXIMATION
BINARY COLLISION-APPROXIMATION
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