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definitions are given below. A dissipative operator is called maximally dissipative if it is dissipative and for all λ > 0 the operator λI − A is surjective, meaning
Dissipative_operator
D(A) is dense in X, A is dissipative, and A − λ0I is surjective for some λ0> 0, where I denotes the identity operator. An operator satisfying the last two
Lumer–Phillips_theorem
a positive operator, whereas Δ is a dissipative operator. Using spectral theory, one can define a square root (1 − Δ)1/2 for the operator (1 − Δ). This
Ornstein–Uhlenbeck_operator
Belgian physical chemist (1917–2003)
structures (hence dissipative structures) due to internal self reorganization. In his 1955 text, Prigogine drew connections between dissipative structures and
Ilya_Prigogine
Identity obeyed by many special functions related to the gamma function
marks this as a dissipative system: for a non-dissipative measure-preserving dynamical system, the eigenvalues of the transfer operator lie on the unit
Multiplication_theorem
Reference point in an electrical circuit from which voltages are measured
are two types used in static control: Static Dissipative Mats, and Conductive Mats. A static dissipative mat that rests on a conductive surface (commonly
Ground_(electricity)
Component to protect against excessive heat
component designed to protect an object or a human operator from being burnt or overheated by dissipating, reflecting, and/or absorbing heat. The term is
Heat_shield
Branch of elementary mathematics
Tarasov, Vasily (2008). Quantum Mechanics of Non-Hamiltonian and Dissipative Systems. Elsevier. ISBN 978-0-08-055971-1. Taylor, Joseph L. (2012).
Arithmetic
Markovian quantum master equation for density matrices (mixed states)
\{L_{i}\}_{i}} are a set of jump operators, describing the dissipative part of the dynamics. The shape of the jump operators describes how the environment
Lindbladian
Discrete-time dynamical system
Because the map is dissipative (i.e., volumes shrink under iteration), the determinant must be between -1 and 1. The Hénon map is dissipative for 1. For the
Hénon_map
25(1):365–379, 1995 V. I. Verbitskii and A. N. Gorban, Jointly dissipative operators and their applications, Siberian Mathematical Journal, 33(1):19–23
Autonomous convergence theorem
Autonomous_convergence_theorem
Quantum mechanical theory of spontaneous collapse
small, it is an unpleasant feature for a phenomenological model. The dissipative extensions of the CSL model gives a remedy. One associates to the collapse
Continuous spontaneous localization model
Continuous_spontaneous_localization_model
Russian mathematician
1090/S1061-0022-08-01001-7 with V. V. Peller: Functions of perturbed dissipative operators, Algebra i Analiz, tom 23 (2011), nomer 2. trans. in: St. Petersburg
Alexei_Borisovich_Aleksandrov
In mathematics, a concept that formalizes a certain idea of movement and mixing
system is dissipative. The language of wandering sets can be used to give a precise, mathematical definition to the concept of a dissipative system. The
Wandering_set
Romanian mathematician (1933–2020)
and Basil Nicolaenko: Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations. Springer-Verlag, Applied Mathematical
Ciprian_Foias
Objective collapse theory in quantum mechanics
negligible, this feature of the model is not appealing. For this reason, a dissipative extension of the GRW theory has been investigated. The GRW theory does
Ghirardi–Rimini–Weber_theory
Quantum mechanical system that interacts with a quantum-mechanical environment
and Dissipative Systems. Amsterdam, Boston, London, New York: Elsevier Science. ISBN 978-0-08-055971-1. Weiss, Ulrich (2012). Quantum Dissipative Systems
Open_quantum_system
Ranged incendiary device
harvesting and other land-management tasks. Various forms are designed for an operator to carry, while others are mounted on vehicles. Modern flamethrowers were
Flamethrower
Dissipation in quantum systems
description of the bath will not affect the essential features of the dissipative process, as far as the model contains the minimal ingredients to provide
Quantum_dissipation
Subject of study in ergodic theory
but are no longer invariant; they are in general dissipative and so give insights into dissipative systems and the route to equilibrium. In terms of
Measure-preserving dynamical system
Measure-preserving_dynamical_system
evolution of a density matrix ρ ( t ) {\displaystyle \rho (t)} of quantum dissipative systems. The method can treat system-bath interaction non-perturbatively
Hierarchical equations of motion
Hierarchical_equations_of_motion
Concept in non-equilibrium physics
as O. V. Konstantinov and Vladimir Perel [de]. Extensions to driven-dissipative open quantum systems coupled to Markovian quantum baths were developed
Keldysh_formalism
Scientific law regarding conservation of a physical property
mechanical energy (approximately true for processes close to free of dissipative forces like friction) Conservation of (rest) mass (approximately true
Conservation_law
2022 film by Kyle Edward Ball
the operator he was hurt and feels sick. The operator tells him to stay on the line and that adults are on their way. Kevin informs the operator that
Skinamarink
Matrix used to describe the transitions of a Markov chain
of an ergodic theorem, which is generally true in a wide variety of dissipative dynamical systems: the system evolves, over time, to a stationary state
Stochastic_matrix
Time reversal symmetry in physics
operation of T, but an acceleration does not. Therefore, one models dissipative phenomena through terms that are odd in v. However, delicate experiments
T-symmetry
2014 found footage disaster film by Steven Quale
Karley, a camera operator Jeremy Sumpter as Jacob Hodges, a rookie camera operator Lee Whittaker as Lucas Guerrette, a camera operator Stephanie Koenig
Into_the_Storm_(2014_film)
1997 robbery and shootout in Los Angeles
with another Type 56 rifle from the trunk of the sedan. After LAPD radio operators received the second "officer down" call from police at the shootout, a
North_Hollywood_shootout
Theory in physics and mathematics
stands in contrast to a dissipative system. Roughly speaking, such systems have no friction or other mechanism to dissipate the dynamics, and thus, their
Conservative_system
Mathematical function often applied to matrices
real-valued functional on operators, constructed from either a vector norm or an inner product, or directly from the induced operator norm. It quantifies key
Logarithmic_norm
Property of a mass in motion
into quantum mechanics, where it becomes an operator on a wave function. The momentum and position operators are related by the Heisenberg uncertainty principle
Momentum
Concept in applied mathematics
difference method that optimizes the approximation for the differential operator in the central node of the considered patch and provides numerical solutions
Central_differencing_scheme
Formulation of quantum mechanics
and pre-exponential factor Ao. This form is specifically useful in a dissipative system, in which the systems and surroundings must be modeled together
Path-integral_formulation
campaign that brought him and kept him in power. While a smooth political operator with endless connections, Blowpipe lacks the physical presence and style
List of The Transformers characters
List_of_The_Transformers_characters
Conflict between known physical principles (time symmetry and entropy)
exactly solvable models. Abstract mathematical tools used in the study of dissipative systems include definitions of mixing, wandering sets, and ergodic theory
Loschmidt's_paradox
Large twin-aisle airliner family
February 2018 with the same launch operator. As of July 2026[update], Singapore Airlines is the largest operator with 65 aircraft in its fleet, while
Airbus_A350
Equation describing the evolution of the vorticity of a fluid particle as it flows
}{\rho }}\right)\end{aligned}}} where D/Dt is the material derivative operator, u is the flow velocity, ρ is the local fluid density, p is the local pressure
Vorticity_equation
Structure for controlled release of flows from a dam or levee
features enable a spillway to regulate downstream flow, allowing dam operators to release water in a controlled manner before the reservoir is full,
Spillway
Naval helicopter developed for the USSR
Missile tracking version. Also known as the Ka-25TI and Ka-25IV. Former operators Bulgaria Bulgarian Navy India Indian Naval Air Arm Russia Russian Naval
Kamov_Ka-25
Type of massless subatomic particle
Vitiello taking into account that the brain is an "open" system (the dissipative quantum model of the brain). Applications of spontaneous symmetry breaking
Goldstone_boson
Certain dynamical systems will eventually return to (or approximate) their initial state
conservative properties on the operator T {\displaystyle T} (leading to Hopf's decomposition into conservative and dissipative parts). For time-independent
Poincaré_recurrence_theorem
decomposition either every St with t ≠ 0 is dissipative or every St with t ≠ 0 is conservative. In the dissipative case, the ergodic flow must be transitive
Ergodic_flow
Speed limit of quantum information
which case the dynamics has a Hamiltonian part and also a dissipative part. The dissipative part is described by terms of Lindblad form, so that the dynamics
Lieb–Robinson_bounds
Study of quantum systems changing with time
often called the "dissipator" or "Lindbladian", describes the irreversible, non-unitary dynamics due to the environment. The operators L k {\displaystyle
Quantum_dynamics
Linearization technique for nonlinear differential systems
Konstantina; Childs, Andrew M. (2021-08-31). "Efficient quantum algorithm for dissipative nonlinear differential equations". Proceedings of the National Academy
Carleman_linearization
Family of assault and attack helicopters
along with five cockpit mock-ups to allow the pilot and weapon station operator positions to be fine-tuned. The Kamov design bureau suggested an army version
Mil_Mi-24
2001 runaway train event in Ohio, US
locomotive's dynamic brake to slow the train to a crawl; dynamic brakes dissipate momentum (kinetic energy) by using the momentum of the train to drive
CSX_8888_incident
Computational model used in machine learning
S2CID 119470636. Hartmann MJ, Carleo G (28 June 2019). "Neural-Network Approach to Dissipative Quantum Many-Body Dynamics". Physical Review Letters. 122 (25) 250502
Neural network (machine learning)
Neural_network_(machine_learning)
1016/0003-4916(78)90279-8. ISSN 0003-4916. Lemos, Nivaldo A. (1980). "Dissipative forces and the algebra of operators in stochastic quantum mechanics". Physics Letters A
Logarithmic Schrödinger equation
Logarithmic_Schrödinger_equation
minor tree damage. It tracked generally east-southeast and struck the Iowa Operator Engineers Training Facility. There, multiple large metal warehouse buildings
List of United States tornadoes from June to August 2019
List_of_United_States_tornadoes_from_June_to_August_2019
2024 film by Lee Isaac Chung
as Ben, a London journalist profiling Tyler Sasha Lane as Lily, a drone operator and member of Tyler's crew Daryl McCormack as Jeb, Kate's boyfriend and
Twisters_(film)
American assault rifle
and M4A1 carbines for United States Special Operations Command (SOCOM) operators in February 1994. Interest in the M4 carbine was accelerated after the
M4_carbine
Mathematical structure that describes the dynamics in a Markovian open quantum system
observables over the degrees of freedom of the environment. To model the dissipative effects due to the interaction with the environment, the Schrödinger
Quantum_Markov_semigroup
2019 historical drama television miniseries
Bryukhanov, and Fomin. Adam Lundgren as Vyacheslav Brazhnik, the senior turbine operator at Chernobyl. Karl Davies as Viktor Proskuryakov, a senior reactor control
Chernobyl_(miniseries)
Amateur radio frequency band
(Europe, Africa, and Russia). The license privileges of amateur radio operators include the use of frequencies within this band for telecommunication
2-meter_band
Mathematical model of the time dependence of a point in space
there are also systems that are typically not integrable systems such as dissipative systems, nonholonomic systems and systems that have a contact manifold
Dynamical_system
Personal computer for mobile use
sink cooling system. Waste heat is usually exhausted away from the device operator towards the rear or sides of the device. Multiple air intake paths are
Laptop
Partial differential equation
(also known as viscous Burgers' equation) in one space dimension is the dissipative system: ∂ u ∂ t + u ∂ u ∂ x = ν ∂ 2 u ∂ x 2 . {\displaystyle {\frac {\partial
Burgers'_equation
2025 video game
skins—unlocked via completing Black Ops 6's main quests—as well as a skin for the operator Samuels, unlocked by reaching Prestige rank 1000 in Black Ops 6, would
Call_of_Duty:_Black_Ops_7
1987 one-shot comic book
handle the situation. Jenny Swensen (Spitfire) – government agent and operator of the M.A.X. Armor, which is used to investigate the scene and try to
The_Pitt_(comics)
German-Finnish Internet entrepreneur (born 1974)
February 2020. Sandoval, Greg (20 January 2012). "FBI charges Megaupload operators with piracy crimes". CNET News. Archived from the original on 21 January
Kim_Dotcom
Formulation of classical mechanics in terms of Hilbert spaces
Koopman–von Neumann (KvN) theory is a description of classical mechanics as an operatorial theory similar to quantum mechanics, based on a Hilbert space of complex
Koopman–von Neumann classical mechanics
Koopman–von_Neumann_classical_mechanics
US military truck
range on its 50 U.S. gallons (190 L; 42 imp gal) single fuel tank. Most operators experience an average of 10 mpg‑US (24 L/100 km; 12 mpg‑imp) for an unladen
M35 series 2½-ton 6×6 cargo truck
M35_series_2½-ton_6×6_cargo_truck
Connection between brain and computer
When the subject became drowsy, the phone sent arousing feedback to the operator to rouse them. In 2011, researchers reported a cellular based BCI that
Brain–computer_interface
Type of calculus problem
(2001). Infinite-dimensional dynamical systems: An introduction to dissipative parabolic PDEs and the theory of global attractors. Cambridge: Cambridge
Initial_value_problem
Naturally occurring combustible liquid
Alsace; a discovery made more than a century ago. What a Pennsylvania operator saw abroad, primitive methods of obtaining oil, the process similar to
Petroleum
Type of adjustable-speed drive
main sub-systems: AC motor, main drive controller assembly, and drive/operator interface. The AC electric motor used in a VFD system is usually a three-phase
Variable-frequency_drive
Parameter describing physics near critical points
theory. Critical exponents also exist for self organized criticality for dissipative systems. Universality class for the numerical values of critical exponents
Critical_exponent
Type of nuclear fission reactor
compared to large light-water reactors, as well as allow data center operators to draw power exclusively from a behind-the-meter SMR without purchasing
Small_modular_reactor
Series of military utility transport helicopters
Pave Hawk, and HH-60 Jayhawk for operators of military H-60/S-70 variants; see Sikorsky S-70 for non-military operators of other H-60/S-70 family helicopters
Sikorsky_UH-60_Black_Hawk
Scientific theory
; Mountain, Raymond D. (1999-03-01). "Velocity Verlet algorithm for dissipative-particle-dynamics-based models of suspensions". Physical Review E. 59
Langevin_dynamics
Dam in Ticino, Switzerland
after GoldenEye was released, to a commercial bungee jump operator. According to the operator, over 10,000 people have jumped the 220 m (720 ft) from the
Contra_Dam
Aerodynamic condition related to helicopter flight
Multirotors that do not have altitude hold are also more likely to succumb to operator error, where the pilot drops the craft too fast resulting in the upwash
Vortex_ring_state
Attacks on vessels circumventing sanctions
Black Sea and prompted some commercial shipping firms, including Turkish operator Besiktas Shipping, to suspend operations related to Russian trade due to
Ukrainian attacks on the Russian shadow fleet
Ukrainian_attacks_on_the_Russian_shadow_fleet
Field of mathematics and science based on non-linear systems and initial conditions
certain parameter values. Zhang and Heidel showed that, at least for dissipative and conservative quadratic systems, three-dimensional quadratic systems
Chaos_theory
Asymmetry of classical and quantum action
symmetry-breaking parameter goes to zero. Perhaps the first known anomaly was the dissipative anomaly in turbulence: time-reversibility remains broken (and energy
Anomaly_(physics)
Business laptops and tablets series from Lenovo
with the text "Think" printed on an aluminum plate was placed atop the operator's console. For decades, IBM had also distributed small notepads with the
ThinkPad
1930s French flying boat
payload and endurance. It was introduced to passenger service by national operator Air France, which was able to launch several previously unattainable long-distance
Latécoère_521
Water current moving away from shore
just beyond the zone of the breaking waves, at which point the current dissipates and releases everything it is carrying. A rip current forms because wind
Rip_current
Vertical or steeply inclined set of rungs or steps
Flexible ladders are also sometimes used as swim ladders on boats. Dissipative ladders are portable ladders built to ESD (Electrostatic Discharge) standard
Ladder
Fictional character from Succession
have that killer instinct. He's not a ruthless person; he's not an amoral operator the way his father is." Regardless, he added that the only future for Kendall
Kendall_Roy
Square root of the mean square
electric current equals the value of constant direct current that would dissipate the same power in a resistive load. A special case of RMS of waveform
Root_mean_square
Statistical physics theorem
the fluctuation of the particle at rest has the same origin as the dissipative frictional force one must do work against, if one tries to perturb the
Fluctuation–dissipation theorem
Fluctuation–dissipation_theorem
manifolds are concerned with the long term behavior of the solutions of dissipative dynamical systems. Inertial manifolds are finite-dimensional, smooth
Inertial_manifold
High-capacity public transport
transit operators now use these technologies to present information to their users. In addition to online maps and timetables, some transit operators now
Rapid_transit
1996 aviation accident in the Atlantic Ocean
indicated that residues of the type of explosives found on the wreckage would dissipate completely after two days of immersion in seawater (nearly all recovered
TWA_Flight_800
1939 bomber aircraft family by Consolidated Aircraft
radio/radar operator sat behind the pilots, facing sideways and sometimes doubled as a waist gunner. The flight engineer sat adjacent to the radio operator behind
Consolidated_B-24_Liberator
Mathematical description of mixing substances
this way, the system is a conservative system, placed in contrast to a dissipative system, where some subsets A {\displaystyle A} wander away, never to
Mixing_(mathematics)
American observer plane
The exhaust gases are then moved through an acoustical fairing into a dissipating and resonating muffler continuing to the aft end of the fuselage. Nine
Lockheed_YO-3_Quiet_Star
Energy rationing and rolling blackouts were implemented by the main operators across several regions on 30 June. The highest daytime temperatures during
2026_European_heatwaves
Possible solution to the measurement problem
mesoscopic scale. Recently, the model has been generalized by including dissipative and non-Markovian effects. It is well known that general relativity and
Diósi–Penrose_model
Model compatible with special relativity
implication of the hyperbolic equation is that by switching from a parabolic (dissipative) to a hyperbolic (includes a conservative term) partial differential
Relativistic_heat_conduction
American physicist of quantum computing (1930–2022)
physics. II," Journal of Mathematical Physics, Vol. 12, 1971, pp. 360–376. "Operator valued measures in quantum mechanics: finite and infinite processes," Journal
Paul_Benioff
Equation known for chaotic behavior
Kopelevich, D. I. (1993). "Laminarizing effects of dispersion in an active-dissipative nonlinear medium". Physica D: Nonlinear Phenomena. 63 (3–4): 299–320
Kuramoto–Sivashinsky_equation
Lowest possible energy of a quantum system or field
FDT being that the vacuum could be treated as a heat bath coupled to a dissipative force and as such energy could, in part, be extracted from the vacuum
Zero-point_energy
Passive electronic component providing electrical resistance
electronic noise, particularly in the first stage of amplification. As a dissipative element, even an ideal resistor naturally produces a randomly fluctuating
Resistor
2026 crewed flyby of the Moon
spacecraft would briefly dip into the upper atmosphere to generate lift, dissipate energy, and improve landing precision. However, this was replaced with
Artemis_II
Law of electrical current and voltage
that the ratio (V1 − V2)/(I1 − I2) is also a constant equal to R. The operator "delta" (Δ) is used to represent a difference in a quantity, so we can
Ohm's_law
Mathematics
y = 0 , {\displaystyle \nabla ^{2}y+y=0,} where ∇2 denotes the Laplace operator, the Neumann boundary conditions on a domain Ω ⊂ Rn take the form ∂ y ∂
Neumann_boundary_condition
Topological quantum error correcting code
model with Rydberg atoms, in which the Hamiltonian and the effects of dissipative noise can be demonstrated. Experiments in Rydberg atom arrays have also
Surface_code
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