disordered lattice - meaning and definition. What is disordered lattice
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  3. disordered lattice

What (who) is disordered lattice - definition

Sleep-disordered breathing; Sleep disordered breathing
  • A [[sleep apnea]] patient exhibiting a 32s pause in breathing and snoring.

Lattice (order)         
  • '''Pic.&nbsp;6:''' Non-lattice poset: <math>c</math> and <math>d</math> have no common upper bound.
  • '''Pic.&nbsp;10:''' Smallest non-distributive (but modular) lattice M<sub>3</sub>.
  • '''Pic.&nbsp;9:''' Monotonic map <math>f</math> between lattices that preserves neither joins nor meets, since <math>f(u) \vee f(v) = u^{\prime} \vee u^{\prime}= u^{\prime}</math> <math>\neq</math> <math>1^{\prime} = f(1) = f(u \vee v)</math> and <math>f(u) \wedge f(v) = u^{\prime} \wedge u^{\prime} = u^{\prime}</math> <math>\neq</math> <math>0^{\prime} = f(0) = f(u \wedge v).</math>
  • '''Pic.&nbsp;11:''' Smallest non-modular (and hence non-distributive) lattice N<sub>5</sub>. <br>The labelled elements violate the distributivity equation <math>c \wedge (a \vee b) = (c \wedge a) \vee (c \wedge b),</math> but satisfy its dual <math>c \vee (a \wedge b) = (c \vee a) \wedge (c \vee b).</math>
  • '''Pic.&nbsp;7:''' Non-lattice poset: <math>b</math> and <math>c</math> have common upper bounds <math>d, e,</math> and <math>f,</math> but none of them is the [[least upper bound]].
  • '''Pic.&nbsp;8:''' Non-lattice poset: <math>a</math> and <math>b</math> have common lower bounds <math>0, d, g, h,</math> and <math>i,</math> but none of them is the [[greatest lower bound]].
PARTIALLY ORDERED SET THAT ADMITS GREATEST LOWER AND LEAST UPPER BOUNDS
Lattice theory; Bounded lattice; Lattice (algebra); Lattice (order theory); Lattice homomorphism; Lattice Homomorphism; Lattice Automorphism; Lattice automorphism; Lattice Endomorphism; Lattice endomorphism; Lattice Isomorphism; Lattice isomorphism; Sublattice; Lattice order; Conditionally complete lattice; Complement (order theory); Jordan–Dedekind chain condition; Jordan-Dedekind chain condition; Jordan-Dedekind property; Jordan-Dedekind lattice; Jordan-dedekind property; Jordan-dedekind lattice; Jordan–Dedekind lattice; Partial lattice; Join-irreducible; Meet-irreducible; Join-prime; Meet-prime; Separating lattice homomorphism; Complementation (lattice theory); Complement (lattice theory)
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
https://en.wikipedia.org/wiki/Lattice_(order)
Hyperuniformity         
  • Hyperuniformity is defined by the scaling of the variance of the number of points that are within a disk of radius ''R''. For the ideal gas (left), this variance scales like the area of the disk. For a hyperuniform system (center), it scales slower than the area of the disk.<ref name="PRE-68"/> For example, for a crystal (right), it scales like the boundary length of the disk; adapted after Figure 1 of Ref.<ref name=":3"/>
A STATE SIMILAR TO A LIQUID AND A CRYSTAL IN PROPERTIES.
Disordered Hyperuniformity; Disordered hyperuniformity
Hyperuniform materials are mixed-component many-particle systems with unusually low fluctuations in component density at large scales, when compared to the distribution of constituents in common disordered systems, like a mixed ideal gas (air) or typical liquids or amorphous solids: A disordered hyperuniform system is statistically isotropic, like a liquid, but exhibits reduced long-wavelength density fluctuations, similar to crystals.
https://en.wikipedia.org/wiki/Hyperuniformity
Lattice QCD         
QUANTUM CHROMODYNAMICS ON A LATTICE
QCD lattice model; Lattice qcd; Lattice quantum chromodynamics; Lattice Quantum Chromodynamics; Lattice chromodynamics; LQCD
Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on a grid or lattice of points in space and time.
https://en.wikipedia.org/wiki/Lattice_QCD

Wikipedia

Sleep and breathing

When we sleep, our breathing changes due to normal biological processes that affect both our respiratory and muscular systems.

https://en.wikipedia.org/wiki/Sleep and breathing
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