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The model solid approximation is a method used for determining the extrema of energy bands in semiconductors. The method was first proposed for silicon-germanium
Model_solid_approximation
Set of principles for modeling solid geometry
Solid modeling (or solid modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes (solids). Solid
Solid_modeling
Physical model of solid metals as electron gases
the crystal lattice of a solid. The model is closely related to the more conceptual empty lattice approximation. The model enables understanding and
Nearly_free_electron_model
Describes the range of energies of an electron within the solid
theoretical solid state physics. In addition to the models mentioned above, other models include the following: Empty lattice approximation: the "band
Electronic_band_structure
The quasi-harmonic approximation is a phonon-based model of solid-state physics used to describe volume-dependent thermal effects, such as the thermal
Quasi-harmonic_approximation
Branch of physics focused on matter in the solid state
Bloch's theorem is only an approximation, but it has proven to be a tremendously valuable approximation, without which most solid-state physics analysis would
Solid-state_physics
Method in physics
In thermodynamics and solid-state physics, the Debye model is a method developed by Peter Debye in 1912 to estimate phonon contribution to the specific
Debye_model
Model of electrical conduction
obstructions to the flow of electrons. The model is an application of kinetic theory. It assumes that when electrons in a solid are exposed to the electric field
Drude_model
Approximation in many-body systems
The GW approximation is a method used to calculate the self-energy of a many-body system of electrons. The approximation is that the expansion of the
GW_approximation
Simplification of a physical system into a network of discrete components
represented to a first-order approximation by lumped elements. To account for leakage in capacitors for example, we can model the non-ideal capacitor as
Lumped-element_model
Simplified model in condensed matter physics
magnetism, and charge density waves. The Hubbard model is based on the tight-binding approximation from solid-state physics, which describes particles moving
Hubbard_model
Model of electrons within a metallic solid
In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed
Free_electron_model
Any mathematical model describing semiconductor diodes
segments (i.e. resistive behaviour). In a relatively good approximation a diode is modelled by the single-exponential Shockley diode law. This nonlinearity
Diode_modelling
Any of the five regular polyhedra
{3-\varphi }}.} Among the Platonic solids, either the dodecahedron or the icosahedron may be seen as the best approximation to the sphere. The icosahedron
Platonic_solid
Model describing the adsorption of a mono-layer of gas molecules on an ideal flat surface
a homogeneous flat solid surface is the conceptual basis for this adsorption model. In 1916, Irving Langmuir presented his model for the adsorption of
Langmuir_adsorption_model
Theoretical electronic band structure model in which the potential is periodic and weak
The empty lattice approximation is a theoretical electronic band structure model in which the potential is periodic and weak (close to constant). One may
Empty_lattice_approximation
Method of approximating the properties of a composite material
science, effective medium approximations (EMA) or effective medium theory (EMT) pertain to analytical or theoretical modeling that describes the macroscopic
Effective medium approximations
Effective_medium_approximations
Light scattering by small particles
the light is typically treated by the Mie theory, the discrete dipole approximation and other computational techniques. Rayleigh scattering applies to particles
Rayleigh_scattering
Model of electronic band structures of solids
In solid-state physics, the tight-binding model (or TB model) is an approach to the calculation of electronic band structure using an approximate set
Tight_binding
Computational quantum mechanical modelling method to investigate electronic structure
quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation interactions
Density_functional_theory
Approximations in density functional theory
realistic systems (molecules and solids). In general, for a spin-unpolarized system, a local-density approximation for the exchange-correlation energy
Local-density_approximation
Damping of electric fields
pseudopotential models. The screening effect leads to the independent electron approximation, which explains the predictive power of introductory models of solids like
Electric-field_screening
The coherent potential approximation (CPA) is a method, in theoretical physics, of finding the averaged Green's function of an inhomogeneous (or disordered)
Coherent potential approximation
Coherent_potential_approximation
Model of electronic circuits involving transistors
capacitances and other parasitic elements. The hybrid-pi model is a linearized two-port network approximation to the BJT using the small-signal base-emitter voltage
Hybrid-pi_model
Primitive quantum mechanical model of electronic structure
functional theory. The Thomas–Fermi model is correct only in the limit of an infinite nuclear charge. Using the approximation for realistic systems yields poor
Thomas–Fermi_model
Model of a crystalline solid
The Einstein solid is a model of a crystalline solid that contains a large number of independent three-dimensional quantum harmonic oscillators of the
Einstein_solid
Open source software
functional theory approximations can be used, including the local-density approximation (LDA), the generalized gradient approximation (GGA), or hybrid
Qbox
Model in quantum optics
mode of an optical cavity (or a bosonic field). The model assumes the rotating-wave approximation, neglects dissipation initially, and treats only a single
Jaynes–Cummings_model
structure in solids. The approximation was proposed by John C. Slater. Augmented plane wave method (APW) is a method which uses muffin-tin approximation. It is
Muffin-tin_approximation
Atomic model introduced by Niels Bohr in 1913
In atomic physics, the Bohr model or Rutherford–Bohr model is an obsolete model of the atom that incorporated some early quantum concepts. Developed from
Bohr_model
Condition for ferromagnetism
simplified model of a solid. It is named after Edmund Clifton Stoner. Ferromagnetism ultimately stems from Pauli exclusion. The simplified model of a solid which
Stoner_criterion
Topics referred to by the same term
the electron beam Independent electron approximation Lone pair or free electron pair Nearly free electron model Orbital angular momentum of free electrons
Free_electron
Subtractive color model
still a model used in artistic environments, causing confusion about primary and complementary colors. It can be considered an approximation of the CMY
RYB_color_model
Software for simulating ionic interactions with solid matter
(TRIM), models ion implantation, energy loss, and collision cascades in solids using a Monte Carlo implementation of the binary collision approximation. SRIM
Stopping and Range of Ions in Matter
Stopping_and_Range_of_Ions_in_Matter
Solid-state physics model
According to quantum mechanics (in the single-electron approximation), the quasi-free electrons in any solid are characterized by wavefunctions which are eigenstates
K·p_perturbation_theory
Mode-stirred chamber Mode volume Model building (particle physics) Model photosphere Model solid approximation Modelling and Simulation in Materials Science
Index_of_physics_articles_(M)
Relation in crystallography
The Cauchy–Born rule or Cauchy–Born approximation is a basic hypothesis used in the mathematical formulation of solid mechanics which relates the movement
Cauchy–Born_rule
American 3D graphics software company
Solid Modeling Solutions (SMS) was a software company that specialized in 3D computer graphics geometry software. SMS was acquired by Nvidia Corporation
Solid_Modeling_Solutions
Thermodynamic concept imporant in astrophysics
to model rocky planets. The reason is that n = 0 polytrope has constant density, i.e., incompressible interior. This is a zero order approximation for
Polytrope
Generalized version of classical Green's function
; Ipatova, I. (1971). Theory of lattice dynamics in the harmonic approximation. Solid State Physics. Vol. Supplement 3 (Second ed.). New York: Academic
Multiscale_Green's_function
Force resisting sliding motion
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding or grinding against each other. Types
Friction
Physical model of non-interacting fermions
sections, in the macroscopic limit we may use a continuous approximation (Thomas–Fermi approximation) to convert this sum to an integral: Ω ( T , V , μ ) =
Fermi_gas
Model to simulate Li-ion cells electrical dynamics
(2004-11-30). "Modeling of lithium ion cells—A simple equivalent-circuit model approach". Solid State Ionics. Fourteenth International Conference on Solid State
Equivalent circuit model for Li-ion cells
Equivalent_circuit_model_for_Li-ion_cells
Model of interacting spinless bosons on a lattice
in solid-state physics as an approximate description of superconducting systems and the motion of electrons between the atoms of a crystalline solid. The
Bose–Hubbard_model
Computer graphics shading and rendering technique
function of other geometry in the scene. However, it is a very crude approximation to full global illumination. The appearance achieved by ambient occlusion
Ambient_occlusion
Method in computational chemistry
Born approximation. The Generalized Born (GB) model is an approximation to the exact (linearized) Poisson-Boltzmann equation. It is based on modeling the
Implicit_solvation
Mathematical formalism used in quantum field theory
The random phase approximation (RPA) is an approximation method in condensed matter physics and nuclear physics. It was first introduced by David Bohm
Random_phase_approximation
American materials physicist at UC Santa Barbara
Belgian Known for First-principles calculations for materials Model solid approximation Awards Aneesur Rahman Prize (2025) Medard W. Welch Award (2013)
Chris_G._Van_de_Walle
Description of a system using mathematical concepts and language
some amount of variance into the model. It is therefore usually appropriate to make some approximations to reduce the model to a sensible size. Engineers
Mathematical_model
Function describing an electron in an atom
validations of the atomic orbital model. The atomic orbital model is nevertheless an approximation to the full quantum theory, which only recognizes many electron
Atomic_orbital
Approximation for practical capacitors and inductors
inductance. However, they can be treated, to a very good degree of approximation, as being ideal capacitors and inductors in series with a resistance;
Equivalent_series_resistance
Mass of a particle when interacting with other particles
within the range of validity of the approximation above. As a result, the electron mass in models such as the Drude model must be replaced with the effective
Effective mass (solid-state physics)
Effective_mass_(solid-state_physics)
Model of intermolecular interactions
molecular models of complex molecules, e.g. alkanes or water. The Lennard-Jones potential can also be used to model the adsorption interactions at solid–fluid
Lennard-Jones_potential
Function of four real variables that defines how light is reflected at an opaque surface
data. Lebedev model for analytical-grid BRDF approximation. ABC-like model for accurate and efficient rendering of glossy surfaces. ABg model K-correlation
Bidirectional reflectance distribution function
Bidirectional_reflectance_distribution_function
Chinese physicist (1919–2005)
early theory of polaritons, the Born–Huang approximation, the Huang–Rhys factor [de] and the Huang–Zhu model. He was awarded the State Preeminent Science
Huang_Kun
Concept in quantum mechanics
H(t)} during the evolution with a change of phase only. Often a solid crystal is modeled as a set of independent valence electrons moving in a mean perfectly
Adiabatic_theorem
Use of both classical and quantum physics to analyze a system
In physics, the semiclassical approximation divides a system into two parts, one to be described quantum-mechanically, and the other to be treated classically
Semiclassical_physics
Form of computer-aided engineering
in various fields and differences in types of approximations between the model and reality. Shell models must be manifold (having no holes or cracks in
3D_modeling
diffraction and imperfections. This can be modeled with a point spread function (PSF) weighted within a solid angle larger than the pixel. From a signal
Cone_tracing
Speed of sound wave through elastic medium
sound travels most slowly in gases, faster in liquids, and fastest in solids. For example, while sound travels at 343 m/s in air, it travels in fresh
Speed_of_sound
Model of phase equilibrium in statistical thermodynamics
coefficient model used in description of phase equilibria. The model is a so-called lattice model and has been derived from a first order approximation of interacting
UNIQUAC
Approximation method in quantum physics
the Hartree–Fock wave function and energy of the system. Hartree–Fock approximation is an instance of mean-field theory, where neglecting higher-order fluctuations
Hartree–Fock_method
Probabilistic problem-solving algorithm
strongly coupled solids, and cellular structures, e.g. cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases.[citation
Monte_Carlo_method
Scientific activity that produces models
to execute the model, it needs to be implemented as a computer simulation. This requires more choices, such as numerical approximations or the use of heuristics
Scientific_modelling
Numerical method for solving physical or engineering problems
equations are often partial differential equations (PDEs). To explain the approximation of this process, FEM is commonly introduced as a special case of the
Finite_element_method
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
Concept in partial differential equations
protection systems, self-similar solutions can be found for semi-infinite solids. The governing equation when heat conduction is the primary heat transfer
Self-similar_solution
Numerical simulations of physical problems via computers
numerical approximations are required. Computational physics is the subject that deals with these numerical approximations: the approximation of the solution
Computational_physics
Projection of data onto lower-dimensional manifolds
includes a quality of data approximation and some penalty terms for the bending of the manifold. The popular initial approximations are generated by linear
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
First modern model of the atom
to a liquid rather than a solid since he thought the electrons moved around in it. Thomson's model was the first atomic model to describe an internal structure
Plum_pudding_model
Swedish physicist (1930–2002)
Atoms, Molecules and Solids" on 30 October 1965. Hedin had developed a model in 1965 which later became known as the GW approximation, where G is the many-body
Lars_Hedin
Excess energy at the surface of a material relative to its interior
While this is only strictly true for amorphous solids (glass) and liquids, isotropy is a good approximation for many other materials. In particular, if the
Surface_energy
Non-destructive spectroscopy
Parameter-Free Model for Interpreting the Measured Positron Annihilation Spectra of Materials Using a Generalized Gradient Approximation". Physical Review
Positron annihilation spectroscopy
Positron_annihilation_spectroscopy
Personality model consisting of five broad dimensions
personality trait model or five-factor model (FFM), sometimes called by the mnemonic acronym OCEAN or CANOE, is a scientific model for measuring and describing
Big_Five_personality_traits
Equation for two-body bound states
of a ladder (or rainbow), hence the name of this approximation. While in QED the ladder approximation caused problems with crossing symmetry and gauge
Bethe–Salpeter_equation
Arrangement of steering linkages
turned, the inner wheel turns farther than the outer wheel. A simple approximation to perfect Ackermann steering geometry may be generated by moving the
Ackermann_steering_geometry
Probability distribution
bounds and approximations would be similarly scaled by θ. K. P. Choi found the first five terms in a Laurent series asymptotic approximation of the median
Gamma_distribution
Concept in fluid dynamics
and gradual failure of the continuum approximation. The first-order expression, which is often used to model fluid slip in sufficiently rarefied flows
No-slip_condition
Transport of dissolved species from the highest to the lowest concentration region
{\displaystyle c_{0}} . Various versions of these jump models are also suitable for simple diffusion mechanisms in solids. For diffusion in porous media the basic equations
Diffusion
Branch of physics
1900 proposed the first theoretical model for a classical electron moving through a metallic solid. Drude's model described properties of metals in terms
Condensed_matter_physics
Mathematical model of ferromagnetism in statistical mechanics
approximation improves as the dimension becomes larger. A deeper understanding of how the Ising model behaves, going beyond mean-field approximations
Ising_model
Molecular interface between a surface and a fluid
surface of an object when it is exposed to a fluid. The object might be a solid particle, a gas bubble, a liquid droplet, or a porous body. The DL refers
Double layer (surface science)
Double_layer_(surface_science)
Model particles in statistical mechanics
In statistical mechanics, hard spheres are widely used as model particles in fluids and solids. They are defined simply as impenetrable spheres that cannot
Hard_spheres
Predecessor to modern quantum mechanics (1900–1925)
mechanics. The theory has come to be understood as the semi-classical approximation to modern quantum mechanics. The main and final accomplishments of the
Old_quantum_theory
Effective field theory of nucleons
Jona-Lasinio The model is much inspired by the different field of solid state theory, particularly from the BCS breakthrough of 1957. The model was introduced
Nambu–Jona-Lasinio_model
Cohesive force between species
multipoles (see the qualitative description above). Additionally, an approximation, named after Albrecht Unsöld, must be introduced in order to obtain
London_dispersion_force
French physicist (1889–1969)
contributions to quantum mechanics, radio wave propagation in the atmosphere, solid-state physics, and information theory. Brillouin was born in Sèvres, near
Léon_Brillouin
Theory of laser diodes
high number of particles involved. Various approximations can be made: Free carrier model: In simple models, many-particle interactions are often neglected
Semiconductor_laser_theory
Quantity in solid state thermodynamics
The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted
Fermi_level
Model of electrical resistance
In solid-state physics, the t-J model is a model first derived by Józef Spałek and Andrzej M. Oleś to explain antiferromagnetic properties of Mott insulators
T-J_model
Lattice model of statistical mechanics
XY model (sometimes also called classical rotor (rotator) model or O(2) model) is a lattice model of statistical mechanics. In general, the XY model can
Classical_XY_model
Form of causal modeling that fit networks of constructs to data
parameters in the statistical model, and L is the maximized value of the likelihood of the model. Root Mean Square Error of Approximation (RMSEA) Fit index where
Structural_equation_modeling
Physical model of solid metals as electron gases
homogeneous electron gas (HEG), is a quantum mechanical model of interacting free electrons in a solid where the complementary positive charges are not atomic
Jellium
Thermal engineering discipline concerning transfer of heat in physical systems
only valid for idealized model systems. Practical applications are generally investigated using numerical methods, approximation techniques, or empirical
Heat_transfer
Measure of positive and negative charges
a non-zero divergence equal to the bound charge density (as modeled in this approximation). It may be noted that this approach can be extended to include
Electric_dipole_moment
Mathematical model
related to a specific phase or crystallographic orientation. This model is mostly used for solid-state phase transformations where multiple grains evolve (e
Phase-field_model
Chemical reaction between a fuel and oxygen
Symplified Kinetics Modelling. Berlin: Springer. Valorani, M.; Goussis, D.; Najm, H.N. (2005). "Higher order corrections in the approximation of low-dimensional
Combustion
File format for 3D printing and scanning
begins with the line: solid name where name is an optional string (though if name is omitted there must still be a space after solid, for compatibility with
STL_(file_format)
Arruda–Boyce model reduces to the Gaussian network based neo-Hookean solid model. It can be shown that the Gent model is a simple and accurate approximation of
Arruda–Boyce_model
Study of the deformation of solids that touch each other
Contact mechanics is the study of the deformation of solids that touch each other at one or more points. A central distinction in contact mechanics is
Contact_mechanics
MODEL SOLID-APPROXIMATION
MODEL SOLID-APPROXIMATION
Boy/Male
Arabic, Muslim
Model; Example
Boy/Male
Indian
Solid
Boy/Male
Latin
Swarthy.
Boy/Male
Muslim
Solid
Boy/Male
Arabic, Muslim
Solid
Girl/Female
Hebrew
From the tower.
Girl/Female
Christian & English(British/American/Australian)
Model or Pattern
Boy/Male
Arabic, Muslim
Sample; Model; Paragon
Female
Yiddish
(×”Ö¸×דֶעל) Pet form of Yiddish Hode, HODEL means "myrtle tree."
Boy/Male
Australian, French
Famous Ruler
Girl/Female
Arabic, Muslim
Example; Model; Demo
Girl/Female
Hindu, Indian, Traditional
Model; Idea
Boy/Male
Muslim
Sample, Model, Paragon
Boy/Male
Muslim/Islamic
Solid
Boy/Male
Muslim
Model, Example
Surname or Lastname
English
English : from an Old German personal name, Godilo, Godila.German (Gödel) : from a pet form of a compound personal name beginning with the element gÅd ‘good’ or god, got ‘god’.Variant of Godl or Gödl, South German variants of Gote, from Middle High German got(t)e, gö(t)te ‘godfather’.Jewish (Ashkenazic) : from the Yiddish male personal name Godl, a pet form of God, a variant of biblical Gad.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Marathi
Enjoyment
Boy/Male
Egyptian
To model.
Male
Yiddish
Pet form of Yiddish Mordche, MOTEL means "devotee of Marduk."Â
Girl/Female
British, English, German, Russian
Supper
MODEL SOLID-APPROXIMATION
MODEL SOLID-APPROXIMATION
Girl/Female
Indian, Sikh
Sky of the World
Girl/Female
Indian
Practical Girl
Boy/Male
Gaelic Irish
Free man.
Boy/Male
Arabic, Muslim
Great King
Girl/Female
Arabic, Muslim
Thanks; Gratitude; Gratefulness
Surname or Lastname
English
English : variant of Pinnock.
Boy/Male
Bengali, Hindu, Indian
Algea; Lord; Raper
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi, Telugu
Spellbound; Innocent; Innocent Young; Spell Bound; Peace
Boy/Male
Indian
The Visible Glory of God
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi
Lord Shiva
MODEL SOLID-APPROXIMATION
MODEL SOLID-APPROXIMATION
MODEL SOLID-APPROXIMATION
MODEL SOLID-APPROXIMATION
MODEL SOLID-APPROXIMATION
a.
Suitable to be taken as a model or pattern; as, a model house; a model husband.
a.
Indicating, or pertaining to, some mode of conceiving existence, or of expressing thought.
v. t.
To model.
n.
Prevailing popular custom; fashion, especially in the phrase the mode.
v. i.
To make a copy or a pattern; to design or imitate forms; as, to model in wax.
n.
Anything which serves, or may serve, as an example for imitation; as, a government formed on the model of the American constitution; a model of eloquence, virtue, or behavior.
a.
Of or pertaining to a mode or mood; consisting in mode or form only; relating to form; having the form without the essence or reality.
n.
Something intended to serve, or that may serve, as a pattern of something to be made; a material representation or embodiment of an ideal; sometimes, a drawing; a plan; as, the clay model of a sculpture; the inventor's model of a machine.
a.
Not hollow; full of matter; as, a solid globe or cone, as distinguished from a hollow one; not spongy; dense; hence, sometimes, heavy.
p. pr. & vb. n.
of Model
n.
The scale as affected by the various positions in it of the minor intervals; as, the Dorian mode, the Ionic mode, etc., of ancient Greek music.
a.
United; without division; unanimous; as, the delegation is solid for a candidate.
v. t.
To plan or form after a pattern; to form in model; to form a model or pattern for; to shape; to mold; to fashion; as, to model a house or a government; to model an edifice according to the plan delineated.
a.
Sound; not weakly; as, a solid constitution of body.
n.
Manner of doing or being; method; form; fashion; custom; way; style; as, the mode of speaking; the mode of dressing.
a.
Firm; compact; strong; stable; unyielding; as, a solid pier; a solid pile; a solid wall.
a.
Having all the geometrical dimensions; cubic; as, a solid foot contains 1,728 solid inches.