A region of lithosphere approximated as rigid on the spatial and temporal scale of a plate-kinematic model. Its instantaneous motion on a sphere is a rotation; deformation within boundary zones limits the rigid-plate approximation.

The direction of the instantaneous angular-velocity vector describing relative rigid-plate motion on a sphere. At position $\mathbf{r}$, the relative velocity is $\mathbf{\omega }\times \mathbf{r}$. The antipodal pole represents the same physical rotation if the angular-velocity sign is reversed.

A plate boundary at which relative motion is tangential to the boundary. It neither creates nor consumes lithosphere in the ideal kinematic model. The admissible junction velocities form a line parallel to the fault through either adjacent plate velocity in velocity space.

An accreting divergent plate boundary. In the symmetric normal-spreading model, its normal velocity equals the mean normal velocity of the adjoining plates; motion parallel to the ridge does not change that normal compatibility condition.

A point where three plate boundaries meet. Kinematic stability means that one instantaneous junction velocity is compatible with all three moving boundaries, so a connected junction can persist. It is not a guarantee of dynamical stability for arbitrary future plate motion.

A geological fault is a fracture or fracture zone across which rock has undergone relative displacement. Its local geometry is described by a fault plane, fault strike, fault dip and fault rake. A locked fault can store elastic strain while surrounding rock deforms; some faults also accommodate displacement by slow creep.

A planet transfers angular momentum to disk material through its spiral wakes, tending to push gas away from its orbital annulus. A persistent deep gap requires this clearing to compete with pressure and disk transport. A gap can reduce local supply without completely shutting off gas streams or fixing the final planet mass.

Orbital migration of a low-mass embedded planet driven by its interaction with disk gas, without a deep gap. Spiral wave torques and corotation-region torques exchange orbital angular momentum. The sign depends on the disk gradients and thermodynamics; this regime is not restricted to inward migration.

Fix two attachments a distance $2a$ apart on a straight line and a simple fence of length $2l$ in one half-plane, with $a<l<\pi a/2$. There is a unique $\theta \in (0,\pi /2)$ satisfying $l/a=\theta /\sin \theta$: its derivative has numerator $\sin \theta -\theta \cos \theta >0$, since that numerator starts at zero and has derivative $\theta \sin \theta >0$. A radius-$R$ minor circular arc with half-angle $\theta$ then has the required chord and length. Its graph is $y=\sqrt{R^2-x^2}-\sqrt{R^2-a^2}$, for $-a\le x\le a$, and sector-minus-triangle geometry gives the displayed area.

To prove global maximality, attach the complementary major arc of this circle, lying in the opposite half-plane, to any competing fence. The resulting closed curve has perimeter $2l+(2\pi R-2l)=2\pi R$. Its enclosed area is the competitor's area plus a fixed major-segment area. The planar isoperimetric inequality bounds the total by $\pi R^2$, with equality only for a circle. Subtracting that fixed added area proves the minor arc is the unique maximizing shape on the chosen side. The same arc follows from the Beltrami identity for the area-minus-length functional.

A genomic source of piRNA precursor transcripts, often containing fragments of transposable elements. Cluster-derived guides can recognize related active elements elsewhere in the genome.

Reciprocal guide-directed cleavage produces new piRNA ends from complementary precursor or target RNAs. A 10-nucleotide overlap of opposite-strand 5′ ends supports this mechanism but does not prove amplification in every piRNA pathway.

A class of approximately 21-nucleotide Caenorhabditis elegans piRNAs associated with PRG-1. They are not generated by the standard fly ping-pong system.

A ceramic material used for piezoelectricity, often offering large charge response and electromechanical coupling with comparatively high stiffness. Brittle fracture, mechanical impedance matching and mounting conditions can limit a vibration harvester. A high charge coefficient alone is not a device power ranking.

A polymer exhibiting piezoelectricity. A compliant, low-density film can accept larger bending or strain than a brittle ceramic, while low permittivity can yield a large voltage coefficient despite a modest charge coefficient. Extractable energy still depends on mechanical input, capacitance and electrical loading.

An Arabidopsis transcription factor linking environmental and hormonal inputs to growth. DELLA binding can restrict its DNA-binding activity.

A reaction-center protein of photosystem II, encoded by psbA messenger RNA in chloroplast expression systems. Damage creates demand for replacement during photosystem II repair.

Processes replacing damaged photosystem II components and restoring functional complexes. Regulated D1 protein synthesis is one part of this cycle.

PsbS participates in rapid proton-dependent regulation of photosynthetic antenna quenching in plants. Loss of PsbS-dependent quenching can be separated experimentally from loss of light-harvesting capacity.

LHCII is a major light-harvesting antenna complex in plants. A regulated mobile fraction participates in photosynthetic state transitions; antenna redistribution is distinct from simply dissipating excitation.

The manganese–calcium-containing catalytic machinery that extracts electrons from water in oxygenic photosynthesis. Four oxidizing equivalents permit formation of one oxygen molecule from two water molecules.