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In physics, rigidity theory, or topological constraint theory, is a tool for predicting properties of complex networks (such as glasses) based on their
Rigidity_theory_(physics)
Topics referred to by the same term
Rigidity theory may refer to Study of the concept of rigidity (mathematics) Mathematical theory of structural rigidity Rigidity theory (physics), or topological
Rigidity_theory
grouped into broad areas of physics. Some of the major unsolved problems in physics are theoretical, meaning that existing theories are currently unable to
List of unsolved problems in physics
List_of_unsolved_problems_in_physics
Topics referred to by the same term
referred to as rigidity Structural rigidity, a mathematical theory of the stiffness of ensembles of rigid objects connected by hinges Rigidity (electromagnetism)
Rigidity
Description of physical properties at the atomic and subatomic scale
Quantum mechanics, also known as quantum physics, is the fundamental physical theory that describes the behavior of matter and of light; its unusual characteristics
Quantum_mechanics
Theory of interwoven space and time by Albert Einstein
In physics, the special theory of relativity, or simply special relativity, is a scientific theory of the relationship between space and time. In Albert
Special_relativity
Concept in special relativity, governing a body's dynamics at high speeds
Born rigidity is a concept in special relativity. It is one answer to the question of what, in special relativity, corresponds to the rigid body of non-relativistic
Born_rigidity
Method for load calculation in construction
depends on flexural rigidity. Through the use of calculus, and boundary conditions describing the beam's curvature at its supports, the theory provides a mathematical
Euler–Bernoulli_beam_theory
Scottish physicist and mathematician (1831–1879)
diagrams of forces" (1870) he discussed the rigidity of various designs of lattice. He wrote the textbook Theory of Heat (1871) and the treatise Matter and
James_Clerk_Maxwell
Branch of mathematics that studies dynamical systems
development was motivated by problems of statistical physics. A central concern of ergodic theory is the behavior of a dynamical system when it is allowed
Ergodic_theory
Ratio of shear stress to shear strain
In solid mechanics, the shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material
Shear_modulus
Matrix-valued random variable
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries
Random_matrix
Attributing events to improbable causes
"facts" of conspiracy theories and their connected lies simply reinforces the rigidity of those pathways. Thus, conspiracy theories and dehumanizing lies
Conspiracy_theory
Transparent non-crystalline solid material
as its glass-forming ability. This ability can be predicted by the rigidity theory. Generally, a glass exists in a structurally metastable state with
Glass
American physicist
applies ideas from condensed matter physics including percolation theory, jamming, dislocation avalanches, and rigidity transitions to biological structures
Jennifer_Schwarz
Belief about living organisms
Our theories cannot be both dogmatically held vitalistic constructs and be scientific at the same time. The purposiveness, consciousness and rigidity of
Vitalism
German–British physicist (1882–1970)
Relativitätsprinzips (The Theory of the Rigid Electron in the Kinematics of the Principle of Relativity), which introduced the concept of Born rigidity. On 23 October
Max_Born
Past and present exist while the future does not
the future does not yet exist. Carr proposes this model to reconcile the rigidity of general relativity with the human experience of the passage of time
Growing_block_universe
Threshold of percolation theory models
Yi-Cheng (April 25, 2021). "Percolation on complex networks: Theory and application". Physics Reports. 907: 1–68. arXiv:2101.11761. Bibcode:2021PhR...907
Percolation_threshold
Physical process
Zamponi, Francesco (2010-03-16). "Mean-field theory of hard sphere glasses and jamming". Reviews of Modern Physics. 82 (1): 789–845. arXiv:0802.2180. Bibcode:2010RvMP
Jamming_(physics)
Branch of discrete mathematics
mathematics and physics, including the study of symmetric polynomials and of the symmetric group and in group representation theory in general. Graphs
Combinatorics
Dynamic disturbance in a medium or field
through the American Institute of Physics. ISBN 978-0300022209. Ostrovsky, L.A.; Potapov, A.S. (1999). Modulated Waves, Theory and Applications. Baltimore:
Wave
Austrian American mathematician
dissertation, Planar Rigidity, was supervised by Jack Graver. While still in Austria, Servatius began working on combinatorial group theory, and her first publication
Brigitte_Servatius
French physicist and economist
2006, he gained a PhD in theoretical physics and finance for a thesis on electronic markets titled On the rigidity of amorphous solids. Price fluctuations
Matthieu_Wyart
Time period of seeming infinite density just after the Big Bang
the past. However this classical gravitational theory is expected to be inadequate to describe physics under these conditions. Thus the meaning of this
Initial_singularity
(1997-11-01). "An Algorithm for Two-Dimensional Rigidity Percolation: The Pebble Game". Journal of Computational Physics. 137 (2): 346–365. Bibcode:1997JCoPh.137
Geiringer–Laman_theorem
American mathematician and academic
Vlasov–Poisson system. In addition, his work in general relativity includes proving rigidity results for Kerr black-hole solutions to the Einstein vacuum equations
Alexandru_D._Ionescu
Ocneanu rigidity, which asserts that every fusion ring has finitely many categorifications. A particularly relevant example to condensed matter physics is
Rank-finiteness
Australian-American physicist
administrator specializing in condensed matter theory and statistical mechanics. He is a professor of physics at Michigan State University (MSU), where he
Phillip_Duxbury
Device for measuring or maintaining orientation
an object can experience in any gyroscopic motion are rigidity in space and precession. Rigidity in space describes the principle that a gyroscope remains
Gyroscope
Fictional character in The Big Bang Theory and Young Sheldon
his response is "Oh, no, if only it were that simple!" Because of his rigidity and stubbornness, only his mother and Bernadette, both possessing strong
Sheldon_Cooper
Property of a mass in motion
good example of an almost totally elastic collision, due to their high rigidity, but when bodies come in contact there is always some dissipation. A head-on
Momentum
The following is a timeline of gravitational physics and general relativity. 3rd century B.C. – Aristarchus of Samos proposes the heliocentric model.
Timeline of gravitational physics and relativity
Timeline_of_gravitational_physics_and_relativity
American philosopher
'Pathetic Ethics' (Objectivity in Law and Morals, 2000) 'Rigidity in the Scope of Russell's Theory' (Noûs, 2001) 'A Big, Good Thing' (Noûs, 2004) 'Skepticism
David_Sosa
Group that is also a differentiable manifold with group operations that are smooth
Lie algebra) are especially important. Representation theory is used extensively in particle physics. Groups whose representations are of particular importance
Lie_group
Dutch physicist (1887–1972)
instrument that was sometimes tuned in 31TET. Born rigidity Euler–Fokker genus Geodetic effect Nordström's theory of gravitation Relativistic center of mass "Biography
Adriaan_Fokker
This glossary of physics is a list of definitions of terms and concepts relevant to physics, its sub-disciplines, and related fields, including mechanics
Glossary_of_physics
Australian and American mathematician (born 1975)
differential equations, combinatorics, harmonic analysis, and additive number theory. He is a professor of mathematics at the University of California, Los Angeles
Terence_Tao
coordinates Born probability Born rigidity Born rule Born–Huang approximation Born–Infeld model Born–Infeld theory Born–von Karman boundary condition
Index_of_physics_articles_(B)
Chinese mathematician specializing in number theory
contributions to p-adic Hodge theory, especially his foundational study of relative p-adic Hodge theory and his remarkable work on rigidity and the Riemann-Hilbert
Ruochuan_Liu
American mathematician (born 1954)
exotic R4), and (with Raoul Bott in Bott & Taubes 1989) proved Witten's rigidity theorem on the elliptic genus. In a series of four long papers in the 1990s
Clifford_Taubes
scientific laws List of theories Most of the results below come from pure mathematics, but some are from theoretical physics, economics, and other applied
List_of_theorems
Approach to economics
This approach has often been justified by appealing to rational choice theory. Neoclassical economics is the dominant approach to microeconomics and,
Neoclassical_economics
Testable implication of local hidden-variable theories
In physics, the Clauser–Horne–Shimony–Holt (CHSH) inequality can be used in the proof of Bell's theorem, which states that certain consequences of entanglement
CHSH_inequality
Argentine mathematician (born 1973)
powerful tools of rigidity theory, in particular topological and geometric methods". Later, Rodriguez Hertz has researched rigidity theory, which describes
Federico_Rodriguez_Hertz
Israeli mathematician (born 1970)
Fields Medal, for his results on measure rigidity in ergodic theory, and their applications to number theory. Mathematics portal List of second-generation
Elon_Lindenstrauss
Computational problems no algorithm can solve
In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist
List_of_undecidable_problems
Structural engineering theory is the application of physics and mathematics to analyze and design structures to ensure they can withstand loads. Structural
Structural_engineering_theory
positivity results are known. In the context of quasi-local mass definitions, a rigidity result typically refers to the expectation that if the quasi-local energy
Hawking_energy
Force field (chemistry) Force field (physics) Ford viscosity cup Forecasting complexity Form factor (quantum field theory) Form factor (electronics) Form factor
Index_of_physics_articles_(F)
Mathematics award
first female Fields Medalist. With the exception of two PhD holders in physics (Edward Witten and Martin Hairer), only people with a PhD in mathematics
Fields_Medal
Twisting of an object due to an applied torque
of Physics. doi:10.1093/acref/9780198821472.001.0001. ISBN 978-0-19-882147-2. Horner, Joseph Gregory (1960). Dictionary of terms used in the theory and
Torsion_(mechanics)
Material phase change
is based on a rigidity catastrophe caused by the vanishing elastic shear modulus, i.e. when the crystal no longer has sufficient rigidity to mechanically
Melting
Reversible transition in amorphous materials
depends on the composition of the material and can be predicted by the rigidity theory. Below the transition temperature range, the glassy structure does
Glass_transition
American physicist (born 1951)
known for developing KTHNY theory. Nelson graduated from Cornell University Summa cum laude with a double major in physics and mathematics in 1972, and
David_Robert_Nelson
Social science studying goods and services
and optimizing framework of the new classical theory with a new-Keynesian role for nominal rigidities and other market imperfections, such as imperfect
Economics
German mathematician
Bonn. She completed her doctorate in 2014 with the dissertation On Some Rigidity Properties in PDEs supervised by Herbert Koch. After postdoctoral research
Angkana_Rüland
Tannakian categories. There are at least two equivalent definitions of a rigidity. An object X of a monoidal category is called left rigid if there is an
Rigid_category
American mathematician (1938–2017)
diophantine approximation, ergodic theory, and Lie group theory. Ratner, Marina (1990). "Strict measure rigidity for unipotent subgroups of solvable
Marina_Ratner
Condensed matter phenomenon; vortex-like magnetic quasiparticle
In physics, magnetic skyrmions (occasionally described as 'vortices,' or 'vortex-like' configurations) are statically stable solitons which have been
Magnetic_skyrmion
States of matter for water as a solid
January 1933). "A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions". The Journal of Chemical Physics. 1 (8): 515
Phases_of_ice
Properties underlying modern physics
field theory, and with applications in the mathematical formulation of the standard model and condensed matter physics. In general, symmetry in physics, invariance
Symmetry_in_quantum_mechanics
Equation of state
describe matter at ultra-high densities. It is characterized by extreme rigidity and relativistic consistency, in which the pressure is equal to the energy
Zeldovich_equation_of_state
American physicist
semiconductor properties. In 1979, he invented a practical theory of compacted networks, known as rigidity theory, specifically applied first to network glasses,
James_Charles_Phillips
German physicist
Gravitational Physics in Potsdam, Germany. Ehlers' research focused on the foundations of general relativity as well as on the theory's applications to
Jürgen_Ehlers
State similar to a liquid and a crystal
stealthy hyperuniform processes: Maximal rigidity and the bounded holes conjecture". Communications in Mathematical Physics. 363 (1): 97–110. arXiv:1707.04328
Hyperuniformity
Structure that repeats in time; a novel type or phase of non-equilibrium matter
In condensed matter physics, a time crystal is a quantum system of particles whose lowest-energy state is one in which the particles are in repetitive
Time_crystal
Local and global geometry of the universe
completely understood. Those of finite volume can be understood via the Mostow rigidity theorem. For hyperbolic local geometry, many of the possible three-dimensional
Shape_of_the_universe
documentaries or commemorations of SR during the World Year of Physics 2005; new, untested theories modifying SR like Doubly special relativity or Variable speed
Timeline of special relativity and the speed of light
Timeline_of_special_relativity_and_the_speed_of_light
manifold is determined by its fundamental group, up to homeomorphism. It is a rigidity conjecture, asserting that a weak, algebraic notion of equivalence (namely
Borel_conjecture
Public research institute in Mumbai, India
for his work on rigidity. The School of Natural Sciences is further split into seven departments working in several areas of physics, chemistry and biology
Tata Institute of Fundamental Research
Tata_Institute_of_Fundamental_Research
Split of materials or structures under stress
under the action of stress. The science of fracture is a field of study in physics and engineering. The fracture of a solid usually occurs due to the development
Fracture
theoretical in origin and some of them concern the inability of orthodox economic theory to explain an empirical observation. Cambridge capital controversy: The
List of unsolved problems in economics
List_of_unsolved_problems_in_economics
Paradox in special relativity
disc in the theory of relativity. In its original 1909 formulation as presented by Paul Ehrenfest in relation to the concept of Born rigidity within special
Ehrenfest_paradox
Research apparatus for particle physics
research in particle physics. Accelerators are also used as synchrotron light sources for the study of condensed matter physics. Smaller particle accelerators
Particle_accelerator
Concept from evolutionary biology
Y. B. (1944). Theory of Combustion and Detonation of Gases. Selected Works of Yakov Borisovich Zeldovich, Volume I: Chemical Physics and Hydrodynamics
Turing_pattern
Parameters describing a planet's rigidity
Love numbers (h, k, and l) are dimensionless parameters that measure the rigidity of a planetary body or other gravitating object, and the susceptibility
Love_number
Study of complex manifolds and several complex variables
significant applications to theoretical physics, where it is essential in understanding conformal field theory, string theory, and mirror symmetry. It is often
Complex_geometry
Measure of a material's resistance to localized plastic deformation
topological constraints acting between the atoms of the network. Hence, the rigidity theory has allowed predicting hardness values with respect to composition
Hardness
Contraction of length in the direction of propagation in Minkowski space
edu. E M Lifshitz, L D Landau (1980). The classical theory of ields. Course of Theoretical Physics. Vol. 2 (Fourth ed.). Oxford UK: Butterworth-Heinemann
Length_contraction
Quantum mechanics principle
of magnitude larger than that of diamond. However, even this enormous rigidity can be overcome by the gravitational field of a neutron star mass exceeding
Pauli_exclusion_principle
Science behind the motion of bicycles and motorcycles
components, due to the forces acting on them. Dynamics falls under a branch of physics known as classical mechanics. Bike motions of interest include balancing
Bicycle and motorcycle dynamics
Bicycle_and_motorcycle_dynamics
of rigidity by Elon Lindenstrauss in ergodic theory, and their applications to number theory. A proof of Szemerédi's theorem using ergodic theory, by
List of Israeli inventions and discoveries
List_of_Israeli_inventions_and_discoveries
started to appear. This was mitigated by adding considerable torsional rigidity to the wings, and was wholly cured when the Mk.XIV was introduced. The
History_of_aerodynamics
American mathematician (born 1951)
topology, operator algebras, K-theory and representation theory, with applications to string theory (especially dualities) in physics. Rosenberg received his
Jonathan Rosenberg (mathematician)
Jonathan_Rosenberg_(mathematician)
Danish chemist and physicist (1904–1980)
contributions to the theory of relativity, theory of gravitation and quantum chemistry. He is known for Møller–Plesset perturbation theory and Møller scattering
Christian_Møller
American physicist (born 1980)
(2017). "A geometrically controlled rigidity transition in a model for confluent 3D tissues". New Journal of Physics. 20 (2): 022002. arXiv:1706.02656.
M._Lisa_Manning
Tool from special relativity
this rigidity property holds at larger scales. This is truly a remarkable rigidity property, given the well-known fact that in relativistic physics, no
Rindler_coordinates
Cosmic rays inside the heliosphere
Nicola; Bertucci, Bruna; Fiandrini, Emanuele (2022). "Temporal evolution and rigidity dependence of the solar modulation lag of Galactic cosmic rays". Physical
Anomalous_cosmic_ray
Physical property that measures stiffness of material
referred to simply as the elastic modulus. The shear modulus or modulus of rigidity (G or μ {\displaystyle \mu \,} Lamé second parameter) describes an object's
Elastic_modulus
South Korean mathematician (born 1963)
Institute for Advanced Study. He was in 2006 an invited speaker with talk Rigidity of rational homogeneous spaces at the International Congress of Mathematicians
Jun-Muk_Hwang
Nobel prize winning physicist
of experimental work: In reality, a theory in natural science cannot be without experimental foundations; physics, in particular, comes from experimental
Samuel_C._C._Ting
Swedish economist (1851–1926)
the University of Uppsala in 1869 to study mathematics, astronomy and physics. He received his first degree in two years, and he engaged in graduate
Knut_Wicksell
Intensive property in mechanics
In mechanics, the flexural modulus, bending modulus, or modulus of rigidity is an intensive property that is computed as the ratio of stress to strain
Flexural_modulus
Hypothetical device in theoretical physics
Treatment of Born's Definition of Rigidity II]. Physikalische Zeitschrift. 12: 412–413. David Bohm, The Special Theory of Relativity, New York: W.A. Benjamin
Tachyonic_antitelephone
Aristotle's teaching of physics, introducing the theory of impetus. The theory of impetus was an auxiliary or secondary theory of Aristotelian dynamics
History_of_science
American mathematician
Bishop, Christopher J.; Steeger, Thomas (1993). "Representation theoretic rigidity in PSL(2, R)". Acta Mathematica. 170 (1): 121–149. doi:10.1007/BF02392456
Christopher_J._Bishop
Group type in algebra
manifolds have finite fundamental group (see Myers' theorem). Mostow's rigidity theorem: for compact hyperbolic manifolds of dimension at least 3, an isomorphism
Finitely_generated_group
Italian-born American mathematician (1923–2023)
Margulis, who established their global rigidity results out of attempts to understand infinitesimal rigidity results such as Calabi and Vesentini's,
Eugenio_Calabi
Study of mathematical algorithms for optimization problems
and an infinite number of designs that are some compromise of weight and rigidity. The set of trade-off designs that improve upon one criterion at the expense
Mathematical_optimization
RIGIDITY THEORY-PHYSICS
RIGIDITY THEORY-PHYSICS
Surname or Lastname
English and Scandinavian
English and Scandinavian : variant of Thor.French (Thoré) : nickname for a strong or violent individual, from Old French t(h)or(el) ‘bull’. Compare Spanish Toro.French (Thoré) : from a reduced pet form of the personal name Maturin.
Female
Greek
(ΘήÏα) Greek name THERA means "lustrous." In mythology, this is the name of one of Amphion's seven daughters. Compare with another form of Thera.
Female
Scandinavian
Variant spelling of Scandinavian Tora, THORA means "Thor" or "thunder."
Female
Spanish
 Pet form of Spanish Theresa, THERA means "harvester." Compare with another form of Thera.
Female
English
Variant spelling of English Cherie, SHERRY means "darling."
Male
English
Compare with feminine Terry. English form of Norman French Thierri, TERRY means "first of the people; king of nations." Pet form of English Terence, possibly meaning "rub, turn, twist."Â
Male
Greek
(ΘήÏων) Greek name THERON means "hunter."
Girl/Female
American, Australian, British, Christian, English, French, Hindu, Indian, Jamaican, Latin
Fruit; Cherry Fruit; Dear; Beloved; Form of Cheryl; Brotherly Love; Name of a Fruit; Darling; Cherry
Surname or Lastname
English and Danish
English and Danish : topographic name for someone who lived by a thorn bush or hedge (Old English, Old Norse þorn). The name is also found in Sweden.English : habitational name from a place named with Old English, Old Norse þorn ‘thorn bush’ (see 1), for example Thorne in Kent, Somerset, and South Yorkshire.North German and Danish : topographic name for someone who lived near a tower, from Middle Low German torn ‘tower’.German : habitational name from the city of Thorn (Toruń in Poland), which was named with Middle High German torn ‘tower’.
Male
Swedish
Swedish and Norwegian form of Old Norse Þórr, THOR means "thunder."Â
Female
English
Variant spelling of English Terrie, TERRY means "harvester." Compare with masculine Terry.
Boy/Male
American, Australian, British, English
Town of Thorns; Thornton Variant; Surname; From the Thorny Thicket
Girl/Female
Greek
Watcher.
Surname or Lastname
English and Irish
English and Irish : from the common Norman personal name, T(h)erry (Old French Thierri), composed of the unattested Germanic element þeudo- ‘people’, ‘race’ + rÄ«c ‘power’. Theodoric was the name of the Ostrogothic leader (c. 454–526) who invaded Italy in 488 and established his capital at Ravenna in 493. His name was often taken as a derivative of Greek TheodÅros (see Theodore). There was an Anglo-Norman family of this name in County Cork.Irish : Anglicized (‘translated’) form of Gaelic Mac Toirdhealbhaigh (see Turley).Southern French : occupational name for a potter, from Occitan terrin ‘earthenware vase’ (a diminutive of terre ‘earth’, Latin terra).
Male
French
Variant spelling of Norman French Thierri, THIERRY means "first of the people; king of nations."
Male
English
Short form of English Theodore, THEO means "gift of God," and other names beginning with Theo-.
Male
English
English form of French Henri, HENRY means "home-ruler."
Girl/Female
Australian, Greek
Watcher
Biblical
there they are; their riches
Girl/Female
Biblical
There they are, their riches.
RIGIDITY THEORY-PHYSICS
RIGIDITY THEORY-PHYSICS
Boy/Male
Hindu, Indian, Sanskrit
In the Heart
Boy/Male
Australian, Biblical
The Lord is Good; God is Good
Boy/Male
Arabic, Indian, Kannada, Muslim, Tamil
Old Arabic Name
Boy/Male
Tamil
A part of divine
Girl/Female
American, Australian, British, English, French, Greek, Latin
Resurrection; Fruitful; Shall be Reborn; Form of Anastasia; Giving Fruit
Girl/Female
American, German
Strong as Man; Free Woman
Boy/Male
Hindu
Lord Shiva
Surname or Lastname
English
English : from a medieval personal name, originally an Old English patronymic from a personal name or byname Tippa, for which there is evidence in place names such as Tiptree, but which is of uncertain origin.
Girl/Female
Tamil
Parinitha | பரிணீதா
Expert
Girl/Female
Indian
Friendly, Of good company
RIGIDITY THEORY-PHYSICS
RIGIDITY THEORY-PHYSICS
RIGIDITY THEORY-PHYSICS
RIGIDITY THEORY-PHYSICS
RIGIDITY THEORY-PHYSICS
n.
Rigidity; stiffness.
n.
An exposition of the general or abstract principles of any science; as, the theory of music.
n.
Want of heat or vigor; as, the frigidity of old age.
n.
The quality or state of being rapid; swiftness; celerity; velocity; as, the rapidity of a current; rapidity of speech; rapidity of growth or improvement.
n.
Stiffness of appearance or manner; want of ease or elegance.
n.
Want of ardor, animation, vivacity, etc.; coldness of affection or of manner; dullness; stiffness and formality; as, frigidity of a reception, of a bow, etc.
n.
The philosophical explanation of phenomena, either physical or moral; as, Lavoisier's theory of combustion; Adam Smith's theory of moral sentiments.
a.
Rapidity.
superl.
Full of thorns or spines; rough with thorns; spiny; as, a thorny wood; a thorny tree; a thorny crown.
n.
The wild cherry; as, Prunus serotina (wild black cherry), valued for its timber; P. Virginiana (choke cherry), an American shrub which bears astringent fruit; P. avium and P. Padus, European trees (bird cherry).
n.
Speculation; theory.
v. t.
To formulate into a theorem.
a.
Relating to, or skilled in, theory; theoretically skilled.
a.
After death; as, post-mortem rigidity.
n.
Severity; rigor.
n.
The quality or state of being rigid; want of pliability; the quality of resisting change of form; the amount of resistance with which a body opposes change of form; -- opposed to flexibility, ductility, malleability, and softness.
pron. & a.
The possessive case of the personal pronoun they; as, their houses; their country.
n.
The science, as distinguished from the art; as, the theory and practice of medicine.
n.
The timber of the cherry tree, esp. of the black cherry, used in cabinetmaking, etc.
a.
Like a red cherry in color; ruddy; blooming; as, a cherry lip; cherry cheeks.