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See searches and references containing PACKING DENSITY!PACKING DENSITY
Fraction of a space filled by objects packed into that space
A packing density or packing fraction of a packing in some space is the fraction of the space filled by the figures making up the packing. In simplest
Packing_density
Geometrical structure
space filled by the spheres is called the packing density of the arrangement. As the local density of a packing in an infinite space can vary depending
Sphere_packing
Field of geometry closely arranging circles on a plane
circle can be enlarged without creating an overlap. The associated packing density, η, of an arrangement is the proportion of the surface covered by the
Circle_packing
Subpermutation of a longer permutation
is only one nontrivial packing density. Walter Stromquist (unpublished) settled this case by showing that the packing density of 132 is 2√3 − 3, approximately
Permutation_pattern
Two-dimensional packing problem
achieve a packing density greater than any smaller number > 1. (Higher density records all have rattles.) Disk covering problem Square packing in a circle
Circle_packing_in_a_circle
Dense arrangement of congruent spheres in an infinite, regular arrangement
the highest average density – that is, the greatest fraction of space occupied by spheres – that can be achieved by a lattice packing is π 3 2 ≈ 0.74048
Close-packing of equal spheres
Close-packing_of_equal_spheres
Convex polyhedron with 90 rhombic faces
otherwise the optimal packing density of spheres could be surpassed by putting a sphere in each rhombicuboctahedron of the hypothetical packing which surpasses
Rhombic_enneacontahedron
monolayer (SAM) enable variations of desired probe packing density. The density of aptamer packing on the electrode surface is an important parameter
Electrochemical aptamer-based biosensors
Electrochemical_aptamer-based_biosensors
Problems which attempt to find the most efficient way to pack objects into containers
find the configuration that packs a single container with the maximal packing density. More commonly, the aim is to pack all the objects into as few containers
Packing_problems
Shape with seven sides
double lattice packing of the Euclidean plane of packing density approximately 0.89269. This has been conjectured to be the lowest density possible for
Heptagon
Packing method for objects
close-packed density for this particular procedure of packing. The random close packing is the highest possible volume fraction out of all possible packing procedures
Random_close_pack
Mathematical theory
higher the packing density, the less empty space there is in the packing and thus the smaller the volume of the hull (in comparison to other packings with the
Finite_sphere_packing
Three-dimensional packing problem
circle packing in a circle problem in two dimensions. Best packing of m>1 equal spheres in a sphere setting a new density record The best known packings of
Sphere_packing_in_a_sphere
Math theorem about sphere packing
sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density than
Kepler_conjecture
Topics referred to by the same term
Packing fraction may refer to: Packing density, the fraction of the space filled by objects comprising the packing Atomic packing factor, the fraction
Packing_fraction
Law of sediment aggradation
, over time, t {\displaystyle t} , is equal to one over the grain packing density, ε o {\displaystyle \varepsilon _{o}} , times the negative divergence
Exner_equation
Geometry hypothesis
three-dimensional convex body with lower packing density than the sphere? More unsolved problems in mathematics Ulam's packing conjecture, named for Stanisław
Ulam's_packing_conjecture
This number is a measure of the local packing density around a given residue. The influence of local packing density can be assessed by series expansion
Gaussian_network_model
Study of intelligence in birds
head size. Furthermore, bird brains have two-to-four times the neuron packing density of mammal brains, for higher overall efficiency. The visual and auditory
Bird_intelligence
Surgical treatment for aneurysm
aneurysms by limiting blood circulation to the aneurysm space. Clinically, packing density is recommended to be 20-30% or more of the aneurysm's volume, typically
Endovascular_coiling
Curved triangle with constant width
923,} which is the density of one possible double lattice packing for these shapes. The best proven upper bound on the packing density is approximately
Reuleaux_triangle
Concept in three-dimensional geometry
disordered packing at densities exceeding 78%. For a periodic approximant to a quasicrystal with an 82-tetrahedron unit cell, they obtained a packing density as
Tetrahedron_packing
Shape with five sides
any edge-to-edge tiling made by regular polygons: The maximum known packing density of a regular pentagon is ( 5 − 5 ) / 3 ≈ 0.921 {\displaystyle (5-{\sqrt
Pentagon
Mass per unit volume
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ρ (the
Density
Radio-frequency connector for coaxial cable
original specification, they have smaller footprints giving a higher packing density on circuit boards and equipment backplanes. These connectors have true
BNC_connector
Crystallography concept
In crystallography, atomic packing factor (APF), packing efficiency, or packing fraction is the fraction of volume in a crystal structure that is occupied
Atomic_packing_factor
Technology of indoor and vehicular environmental comfort
air. This depends on the size of the particle or fiber, the filter packing density and depth, and the airflow rate. The HVAC industry includes equipment
Heating, ventilation, and air conditioning
Heating,_ventilation,_and_air_conditioning
Fig. 1) and also the number of cells per volume (Sholl, p. 401, The packing density of perikarya). While methods for estimating the number of cells have
Sholl_analysis
Method of eye examination
eyes. AOSLO has also revealed significant decreases in foveal cone packing density for myopic eyes in comparison to emmetriopic eyes. This difference
Scanning_laser_ophthalmoscopy
Type of concrete mix
stability of the concrete. The reduction in cement content and increase in packing density of materials finer than 80 μm, like fly ash etc. can reduce the water-cement
Self-consolidating_concrete
Distance between the centers of externally tangent objects
of the objects, and its calculation can be difficult. The maximum packing density of hard particles depends on their distance of closest approach. The
Distance_of_closest_approach
Laboratory equipment
commonly used nowadays to create nanoparticle coatings with controlled packing density.[unreliable source?] In early experiments, the trough was first constructed
Langmuir–Blodgett_trough
Chemical compound
chemistry. Barium ferrite is a highly magnetic material, has a high packing density,[clarification needed] and is a metal oxide. Studies of this material
Barium_ferrite
Clarity of vision
[citation needed] Though the resolving power depends on the size and packing density of the photoreceptors, the neural system must interpret the receptors'
Visual_acuity
On tangency patterns of circles
The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible patterns of tangent circles among non-overlapping
Circle_packing_theorem
Three-dimensional packing problem
Sphere packing in a cylinder is a three-dimensional packing problem with the objective of packing a given number of identical spheres inside a cylinder
Sphere_packing_in_a_cylinder
Polish-American mathematician, Auburn U
particular on packing and covering problems. His first paper in this area (1982) showed that the ratio of packing density to covering density of any convex
Włodzimierz_Kuperberg
Storage of electricity within an electrochemical cell
their ion dimensions are able to enter, resulting in larger ionic packing density and increased charge storage. The tailored sizes of pores in nano-structured
Pseudocapacitance
systems for routeing standard cables (without connectors) with a high packing density and split cable entry systems which enable routeing of pre-terminated
Cable_entry_system
particles are compressed into the desired packing density automatically. The coating is done in this packing density with the help of a motorized dipper while
Nanosphere_lithography
lowest maximum packing density of all centrally-symmetric convex plane sets Sphere packing problems, including the density of the densest packing in dimensions
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
The packing constant of a geometric body is the largest average density achieved by packing arrangements of congruent copies of the body. For most bodies
List of shapes with known packing constant
List_of_shapes_with_known_packing_constant
Particle with size less than 100 nm
shapes in a typical powder often lead to non-uniform packing morphologies that result in packing density variations in the powder compact.[citation needed]
Nanoparticle
Two-dimensional packing problem
Circle packing in a square is a packing problem in recreational mathematics where the aim is to pack n unit circles into the smallest possible square.
Circle_packing_in_a_square
Ratio of void volume and total volume of a porous material
cryoporometry). Archie's law Bulk density Coherent diffraction imaging Packing density Particle density (packed density) Petroleum geology Poromechanics
Porosity
Raising fish commercially in enclosures
farms in sheltered coastal waters, therefore supporting higher fish packing density. In Maritime Southeast Asia, traditional fish cages built around an
Fish_farming
Smart fluid whose viscosity increases in a magnetic field
three months. This observation has been attributed to a lower close-packing density due to decreased symmetry of the wires compared to spheres, as well
Magnetorheological_fluid
In biology, any group of fish that stay together for social reasons
where a small packing fraction represents a dilute system like a gas. Integrated conditional density – This parameter measures the density at various length
Shoaling_and_schooling
Type of artillery missile
Inconsistent burn rates, arising from variations in powder composition and packing density, resulted in unpredictable acceleration profiles and contributed significantly
Congreve_rocket
IBM computer family (1964–1977)
much higher data rates, self-threading tape operation and 1600bpi packing density. It remained in the product line until 1979. Punched card devices included
IBM_System/360
Liquid that is attracted by poles of a magnet
addition of surfactants (or any other foreign particles) decreases the packing density of the ferroparticles while in its activated state, thus decreasing
Ferrofluid
Archimedean solid with 26 faces
otherwise the optimal packing density of spheres could be surpassed by putting a sphere in each rhombicuboctahedron of the hypothetical packing which surpasses
Rhombicuboctahedron
Areas of myelinated axons in the brain
regulate myelination in axons. Or, gross changes in the diameter or packing density of the axon might cause the change.[self-published source?] A more
White_matter
Chemical compound
is a mixture of A- and B- unit cells, resulting in an intermediate packing density between the two forms. High-amylose forms of starch make it more resistant
Amylose
Two-dimensional shape
Reinhardt in 1934 and conjectured by him to have the lowest maximum packing density of the plane of all centrally symmetric convex shapes. It was also
Smoothed_octagon
Process from catching to selling fish
before they are transported to reduce their metabolism and increase packing density, and the water can be cooled to further reduce metabolism. Live crustaceans
Fish_processing
Loudspeaker part
coils wound with flattened wire, called ribbon-wire, provide a higher packing density in the magnetic gap than coils with round wire. Some coils are made
Voice_coil
Board to support and connect electronic components
circuits, cordwood construction allowed the highest possible component packing density. The construction method was used with wire-ended components in applications
Printed_circuit_board
Reversible transition in amorphous materials
higher density than ordinary amorphous alloys with high critical cooling rates, it is recommended to have a composition with high packing density for good
Glass_transition
Visible difference in brightness or color
typically about 60 cpd. The high-frequency cut-off is also related to the packing density of the retinal photoreceptor cells: a finer matrix can resolve finer
Contrast_(vision)
American mathematician
In discrete geometry, he settled the Kepler conjecture on the density of sphere packings, the honeycomb conjecture, and the dodecahedral conjecture. In
Thomas_Callister_Hales
Regular tiling of a two-dimensional space
figure is the densest way to arrange circles in two dimensions; its packing density is π 2 3 ≈ 0.907 {\textstyle {\frac {\pi }{2{\sqrt {3}}}}\approx 0
Hexagonal_tiling
Measure of temperature relative to absolute zero
exceed the 74.048% packing density of a closest-packed arrangement. The two regular crystal lattices found in nature that have this density are hexagonal close
Thermodynamic_temperature
Science and technology of creating objects from inorganic, non-metallic materials
shapes in a typical powder often lead to non-uniform packing morphologies that result in packing density variations in the powder compact. Uncontrolled agglomeration
Ceramic_engineering
Angle created by applying the golden ratio to a circle
primordia, with the Fibonacci angle giving the parastichy with optimal packing density. Mathematical modelling of a plausible physical mechanism for floret
Golden_angle
Geometric concept
two-unit-length open intervals) do not overlap in order for there to be a finite packing density. See also Lemma 3.1 in Marathe, M. V.; Breu, H.; Hunt, H. B.; Ravi
Kissing_number
Topics referred to by the same term
called asymptotic density) Dirichlet density Packing density Density (polytope) Density on a manifold Tensor density in differential geometry Dense set
Density_(disambiguation)
Discrete subgroup in geometry
is called a double lattice packing. In many cases the highest known packing density for a body is achieved by a double lattice. Examples include the regular
Double_lattice
Third interstitial nucleus of the anterior hypothalamus
in heterosexual men because homosexual men have a higher neuronal packing density (the number of neurons per cubic millimeter) in the INAH3 than heterosexual
INAH_3
Metric for space taken up by one tonne of cargo in a ship
Ship B is full and no more space is available in the Ship B's holds Packing density Stopford, M. Maritime Economics. Third Edition. Roudledge, 2009. Pages
Stowage_factor
Materials with granular size 1 to 100 nm
nanoparticles in a typical powder often lead to non-uniform packing morphologies that result in packing density variations in the powder compact. Uncontrolled agglomeration
Nanomaterials
Distribution of distances between pairs of particles in a given volume
approximation) and the densely packed (delta function) models, depending on the packing density f {\displaystyle f} . Of special practical importance is the radial
Pair_distribution_function
Concrete breakwater element
and placed in a random attitude to obtain the specified packing density. The proper packing method provides an adequate coverage on breakwater slopes
Accropode
American mathematician
Society and the Mathematical Association of America for his work on packing densities. Barton has taught at various academic Olympiad training programs
Reid_W._Barton
Type IV intermediate filaments found in the cytoplasm of neurons
is determined by the number of neurofilaments in the axon and their packing density. The number of neurofilaments in the axon is thought to be determined
Neurofilament
Regular tiling of the plane
densest possible circle packing. Every circle is in contact with 6 other circles in the packing (kissing number). The packing density is π⁄√12 or 90.69%.
Triangular_tiling
Tidily securing cables
applications these strain relief plates are also cost-effective because the packing density (meaning the possible number of lines to be fixed on one plate) is
Cable_management
German polymath and scholar (1777–1855)
solving the Kepler conjecture in 1831 with the proof that a greatest packing density of spheres in the three-dimensional space is given when the centres
Carl_Friedrich_Gauss
Heteropolysaccharide found in red algae
agaroses. Hydroxyethylation may reduce the pore size by reducing the packing density of the agarose bundles, therefore LMP gel can also have an effect on
Agarose
Thin layer of material
method uses molecules floating on top of an aqueous subphase. The packing density of molecules is controlled, and the packed monolayer is transferred
Thin_film
Solid metallic material with disordered atomic-scale structure
components has to be significantly different (over 12%), to achieve high packing density and low free volume. The combination of components should have negative
Amorphous_metal
noncompacted data into a smaller space, for example by increasing packing density by transferring images from newsprint to microfilm or by transferring
Data_compaction
Process of attaching nanoparticles to solid surfaces
nanoparticles. The methods differ by their ability to control particle packing density and layer thickness, ability to use different particles and the complexity
Nanoparticle_deposition
German mathematician (1895–1941)
variables, and Reinhardt polygons and the Reinhardt conjecture on packing density. Reinhardt was born on January 27, 1895, in Frankfurt, the descendant
Karl Reinhardt (mathematician)
Karl_Reinhardt_(mathematician)
Relative brain size measure
Dicke (2012), mammals with relatively high cortex volume and neuron packing density (NPD) are more intelligent than mammals with the same brain size. The
Encephalization_quotient
amyloidoidogenic regions Average Packing Density 2006 Web Server-AMYLPRED2 Secondary structure-related Relates average packing density of residues to the formation
Protein aggregation predictors
Protein_aggregation_predictors
High-capacity electrochemical capacitor
unsolvated ions fill the pores (even for large ions), increasing ionic packing density and storage capability by faradaic H 2 intercalation. Activated carbon
Supercapacitor
Method for producing solid materials from small molecules
the unfired body if not relieved. In addition, any fluctuations in packing density in the compact as it is prepared for the kiln are often amplified during
Sol–gel_process
3D printing technique
Sphericity is desired because it guarantees a high flowability and packing density, which translates into fast and reproducible spreading of the powder
Selective_laser_melting
2005 mathematics text
distinguished from sphere packing, which considers higher dimensions (here, everything is two dimensional) and is more focused on packing density than on combinatorial
Introduction to Circle Packing
Introduction_to_Circle_Packing
Particular class of intermetallic phases
close-packed. At this size ratio, the structure has an overall packing volume density of 0.710. Compounds found in Laves phases typically have an atomic
Laves_phase
Field of engineering dealing with extremely low tolerances
functions independent of one another. Achieve greater miniaturization and packing densities. Achieve further advances in technology and the underlying sciences
Precision_engineering
Area of the human brain
the planum temporale on a microscopic level, finding greater cell packing density in females, as well as a reduction of micro-structural asymmetry. Females
Planum_temporale
Filtration by force through a semipermeable membrane
low permeability, high volume hold-up within the membrane and low packing density. This design is conceptually similar to the tubular module with a shell
Ultrafiltration
Gaps between myelin sheaths on the axon of a neuron
constricted in its diameter. The decreased axon size reflects a higher packing density of neurofilaments in this region, which are less heavily phosphorylated
Node_of_Ranvier
Russian mathematician (1935–2017)
cybernetics, Nauka, Moscow, 1974, 207–305. V.I. Levenshtein (1975), "Maximal packing density of n-dimensional Euclidean space with equal balls", Matematicheskie
Vladimir_Levenshtein
Probability distribution
original on January 13, 2012. Dexter, A. R.; Tanner, D. W. (July 1972). "Packing Densities of Mixtures of Spheres with Log-normal Size Distributions". Nature
Log-normal_distribution
1964 mathematics text
Isometric inequalities for polyhedra and problems of packing density and covering density of sphere packings and coverings are also included, and the proofs
Regular_Figures
Structures that connect circuit elements in an integrated circuit
more arbitrary combination of routing options to attain the a higher packing density. In silicon ICs, the most commonly used semiconductor in ICs, the first
Interconnect (integrated circuits)
Interconnect_(integrated_circuits)
States of matter for water as a solid
suppressing long-range density fluctuations and are, therefore, nearly hyperuniform. Classification analysis suggests that low and high density amorphous ices
Phases_of_ice
PACKING DENSITY
PACKING DENSITY
Boy/Male
American, British, English
Son of Parkin
Surname or Lastname
English
English : patronymic from Parkin.Americanized form of one or more like-sounding Jewish names.
Boy/Male
Arabic, Muslim, Sindhi
Walking
Girl/Female
Tamil
Making
Surname or Lastname
English and German
English and German : patronymic from the personal name Paul.
Girl/Female
Arabic, Muslim
Abstinent; Lacking Mundane Ambitions
Surname or Lastname
English
English : from Old English LÄ“ofecing, a patronymic from LÄ“ofeca (see Levick 2), or possibly, as Reaney suggests, a late derivative of Lovekin (see Lucken).
Surname or Lastname
English
English : from a diminutive of Middle English cok ‘cock’ (see Cocke).
Boy/Male
American, Anglo, Australian, British, English
Little Rock; Little Peter
Boy/Male
Muslim/Islamic
Walking
Surname or Lastname
English
English : from a pet form of Paul.Altered form, in the New Netherland Dutch community, of Paling. Compare Paulding.
Surname or Lastname
English
English : variant of Markin.
Surname or Lastname
English (Staffordshire)
English (Staffordshire) : from the Welsh personal name Pasgen, a derivative of Latin Pascentius.
Girl/Female
Gujarati, Indian
Sweet Eyes
Surname or Lastname
English (chiefly Devon)
English (chiefly Devon) : from a Middle English pet form of the Old English personal name Hocca.Dutch : patronymic from Hock 4.
Girl/Female
Hindu
Making
Boy/Male
English
Little rock.
Surname or Lastname
English (Lancashire)
English (Lancashire) : habitational name from Hacking in Lancashire, the name of which is of uncertain origin. Early forms appear with the definite article, and the name may represent an Old English term for a fish weir, a derivative of hæcc ‘hatch’, ‘low gate’, or haca ‘hook’.
Surname or Lastname
English (mainly Yorkshire)
English (mainly Yorkshire) : from the Middle English personal name Perkin, Parkin, a pet form of Peter with the diminutive suffix -kin. (The change from -er- to -ar- was a characteristic phonetic development in Old French and Middle English.)
Surname or Lastname
English
English : possibly from Middle English Old French personal name Pic (see Pike 6) + the diminutive suffix -in.
PACKING DENSITY
PACKING DENSITY
Boy/Male
Hindu
Kingdom
Girl/Female
Irish
Joy. The name of an early queen of Connaught.
Boy/Male
Armenian, Australian
Fighter
Boy/Male
Muslim
Symbol, Prince, Honored, Respected
Boy/Male
English
From the elfs home.
Boy/Male
Indian
Lovely Angel
Surname or Lastname
German
German : from Middle High German kit(t)el ‘smock’, ‘shirt-like garment’, hence a metonymic occupational name for a maker of such garments or a nickname for someone who habitually wore one.English : variant of Kettle.
Boy/Male
Hindu
Boy/Male
Greek American Slavic Russian
Earth-lover. Of Demeter. Demeter is the mythological Greek goddess of corn and harvest. She...
Girl/Female
Indian, Punjabi, Sikh
Pass through
PACKING DENSITY
PACKING DENSITY
PACKING DENSITY
PACKING DENSITY
PACKING DENSITY
n.
Same as Filling.
n.
A substance or piece used to make a joint impervious
n.
A trick; collusion.
n.
The act of one who, or that which, marks; the mark or marks made; arrangement or disposition of marks or coloring; as, the marking of a bird's plumage.
p. pr. & vb. n.
of Tack
n.
Any material used to pack, fill up, or make close.
n.
A yielding ring, as of metal, which surrounds a piston and maintains a tight fit, as inside a cylinder, etc.
n.
A thin layer, or sheet, of yielding or elastic material inserted between the surfaces of a flange joint.
n.pl.
Packing of hemp.
n.
Stout, coarse cloth of which sacks, bags, etc., are made.
n.
The act or process of one who packs.
v. t.
Small coal produced in making the nicking.
n.
The substance in a stuffing box, through which a piston rod slides.
a.
Done or made as with a pointed tool; as, a picking sound.
n.
A union of securities given at different times, all of which must be redeemed before an intermediate purchaser can interpose his claim.
n.
Spun yarn used in racking ropes.
p. pr. & vb. n.
of Sack
a.
Distressing; worrying; perplexing; corroding; as, carking cares.
p. pr. & vb. n.
of Pack
n.
A coarse woolen fabric, used for floor cloths, to cover carpets, etc.; -- so called from the town of Bocking, in England, where it was first made.