GLOBAL KNOWLEDGE ARK

Reference library

Foundations

Explore concepts, laws, equations and methods, with clear explanations of their use and sources. Choose an area of study or find a specific entry.

More filters

Reference entries

Showing 751–780 of 1709 reference entries

Earth & cosmosGravitational cloud collapse and protostars

Cold dense regions of molecular clouds can contract gravitationally when support is insufficient.

Model
Earth & cosmosPlanetary material classes and interior inference

Terrestrial planets are dominated by rock and metal; giant planets contain larger proportions of light gases and volatile-rich material.

Model
Earth & cosmosComparative planetary atmospheres and energy balance

Atmospheric mass, composition and opacity affect a planet's surface conditions.

Model
Earth & cosmosAsteroid and comet material evidence

Asteroids include bodies with differing rocky, carbon-rich and metallic material signatures; meteorites and spacecraft observations test interpretations of their histories.

Model
Earth & cosmosGas phases of the interstellar medium

The interstellar medium contains ionized, atomic and molecular gas alongside dust.

Definition
Earth & cosmosGalactic components and stellar populations

The Milky Way contains disk, bulge and halo components with differing distributions, motions and stellar populations.

Model
Earth & cosmosGalaxy morphology and physical populations

Spiral galaxies commonly contain a disk, bulge and spiral patterns with gas and ongoing star formation.

Definition
Earth & cosmosGravitational lens geometry and image multiplicity

A thin gravitational lens relates a source's unlensed angular position to observed image positions through a mass-dependent deflection.

Model
Earth & cosmosCosmological redshift and expansion

In an FLRW expansion model, light emitted and observed by comoving observers is stretched by the ratio of their scale factors.

Model
Earth & cosmosEarly-universe nuclei and photon decoupling

The hot expanding universe passed through changing particle and radiation conditions.

Model
Earth & cosmosCosmic structure growth and dark-matter modelling

In the standard cosmological model, small density variations grow gravitationally and dark-matter structures help concentrate baryonic matter after photon coupling becomes less effective.

Model
Biology · Physics · ChemistryIon equilibrium potentials and membrane current balance

An ion's equilibrium potential balances its chemical and electrical driving terms.

Model
BiologyUbiquitin, proteasomes and lysosomal turnover

Eukaryotic protein abundance depends on synthesis and degradation.

Model
BiologyCaspases and mitochondrial/death-receptor apoptosis

In representative animal apoptosis pathways, activated initiator caspases promote an execution cascade that cleaves cellular targets.

Model
BiologyBase excision versus nucleotide excision repair

Base-excision repair begins when a glycosylase removes a recognized damaged base, leaving a site that is processed and restored by DNA synthesis and ligation.

Model
BiologyNonhomologous DNA end joining

End joining can restore continuity of a double-strand-broken DNA molecule without using a long homologous donor template.

Model
BiologySensory transduction and graded receptor potentials

Sensory receptors convert appropriate physical or chemical stimuli into changes in cellular electrical signalling.

Model
BiologyExperimental units and biological inference

The experimental unit is the entity independently assigned to a treatment in a specified design.

Method
BiologyNephron transport and the concentrating gradient

In the mammalian nephron model, selective tubular transport modifies filtered fluid.

Model
BiologyVasopressin and renal sodium-water control

Vasopressin released from the posterior pituitary can increase collecting-duct water permeability through aquaporin insertion.

Model
BiologyEndocrine axes and negative feedback

In the vertebrate thyroid-axis example, hypothalamic signals stimulate pituitary hormone release, which stimulates the thyroid.

Model
BiologyHormonal coordination of glucose storage and release

In the mammalian model, pancreatic insulin and glucagon coordinate nutrient use and storage with blood-glucose availability.

Model
BiologyRespiratory partial pressures and oxygen transport

Gases diffuse across respiratory surfaces down their own partial-pressure gradients.

Model
BiologyVentilation, pressure and alveolar surface tension

Mammalian ventilation moves air when respiratory-muscle action changes thoracic volume and pressure.

Model
BiologyMammalian cardiac conduction and blood flow

Coordinated electrical activation drives atrial and ventricular contractions.

Model
BiologyActin–myosin cycling and contraction control

Myosin interaction with actin converts ATP-dependent molecular cycling into force.

Model
BiologyNeural and hormonal coordination of digestion

In the vertebrate digestive example, signals coordinate secretion, motility and delivery of material between compartments.

Model
BiologyAntigen presentation and lymphocyte specificity

In jawed-vertebrate adaptive immunity, B-cell receptors recognize suitable antigen structures, while T-cell receptors recognize antigen presented with appropriate MHC molecules.

Model
BiologyOperons and integrated bacterial transcription control

In the E. coli lac example, a repressor and a cAMP-linked activator integrate lactose-related and glucose-related conditions to regulate transcription.

Model
BiologyPost-transcriptional RNA stability and silencing

RNA-binding proteins, RNA processing and degradation influence how long a transcript remains available for translation.

Model
ModelSource checked

Gravitational lens geometry and image multiplicity

Earth & cosmos

A thin gravitational lens relates a source's unlensed angular position to observed image positions through a mass-dependent deflection.

Key knowledge

A thin gravitational lens relates a source's unlensed angular position to observed image positions through a mass-dependent deflection. Nonlinearity can produce multiple images. Lens-to-source and observer distances are angular-diameter distances; cosmological lens–source distance is not generally their simple difference.

Values and equations

β = θ − (Dls/Ds) α̂(θ)

β
unlensed source angle rad
θ
image angle rad
α̂
physical deflection angle rad
Dls
lens-to-source angular-diameter distance m
Ds
observer-to-source angular-diameter distance m

Conditions and scope

  • Assumes small angular deflections and a thin lens; strong lensing refers to image multiplicity, not necessarily strong-field gravity.
  • Image shapes or positions constrain projected mass through a model and can retain degeneracies.
Sources · 1

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. Section 7.2.2: The Lens EquationStéphane Courteau and collaborators — Galaxy Masses review (2014), NASA/IPAC Extragalactic Database archiveTextbook chapterned.ipac.caltech.eduRead source

Evidence and review

Read scalar geometry θDs=βDs+αDds, angular-diameter distance distinction and multiple-image paragraph; did not reproduce the source's dimensionally incomplete printed mass-inside-ring sentence.

2026-10-10 · Independent AI editorial review: All26 Life-authored Cosmos compact statements, conditions, displayed equations and all56 origin semantic links read. Entire26-entry author statement/source matrix and explicit exclusions assessed. Targeted independent primary sections are listed below; this does not claim every referenced source body or proof was independently re-read. This is scoped AI reference-content review, not human disciplinary certification or whole-field completion. Receipt: cosmos-life-independent-content-review.1.

Entry detailsPermanent link to this entry ↗
Record identity
uni-cosmos-thin-lens
Revision
core.1
Structured reference record
University core expansion