The systematic gravitational drag experienced by a massive body interacting with a population of lighter bodies. In a planetesimal swarm, it tends to damp a massive embryo's random motion while transferring random kinetic energy to the smaller bodies. Its detailed strength depends on the background velocity distribution and geometry.

Growth of solid aggregates through collisions and sticking in a protoplanetary disk. Relative motion can arise from Brownian motion, settling, turbulence and differential radial drift. Bouncing and fragmentation can interrupt growth; collision frequency alone does not determine whether an encounter increases aggregate mass.

A growing solid protoplanet dynamically important compared with the surrounding smaller planetesimals. The term identifies a formation stage, rather than a single sharply specified mass.

A concentrated thin layer of solids can become self-gravitating if particle random velocities and stellar shear do not support it. Gas turbulence, drag and settling change both concentration and velocity dispersion. Collapse into solid planetesimals supplies seeds for core accretion and is distinct from direct fragmentation of a gaseous disk patch.

A plane tree with a distinguished root and root corner, equivalently a rooted tree with a linear order on the children at each vertex. Trees with $n$ edges are counted by the Catalan number $C_n$.

For a unidirectional incompressible flow between stationary plates a distance $H>0$ apart, removing the driving pressure gradient leaves $u_t=\nu u_{yy}$ when the kinematic viscosity $\nu >0$ is constant. The no-slip boundary condition gives $u(0,t)=u(H,t)=0$. For an initial profile $g$ in L2 space, separation of variables and the Fourier sine series give the displayed solution, withEach normal mode decays at a rate proportional to $n^2$. The lowest mode present dominates at late times; when $b_1\ne 0$, its time constant is $H^2/(\nu {\pi }^2)$, consistent with the viscous diffusion time. The solution approaches the initial data in L2 space; compatible smooth profiles also give the familiar pointwise initial condition. This is a heat equation for momentum diffusion, rather than temperature.

A Drosophila Piwi-family protein participating in germline piRNA-mediated regulation, including ping-pong amplification.

It binds selected small RNAs and participates in transcript recognition and cleavage within a germline defence network. Its relationship with AGO3 helps amplify appropriate guide molecular populations, linking molecular specificity to transposon control. ^[ref]

A Drosophila Piwi-family protein that participates with Aubergine in piRNA ping-pong amplification.

Complementary cleavage relationships between small-RNA molecular populations can reinforce production of transposon-targeting guides. The resulting signature links sequence recognition to amplification rather than simply accumulating every small RNA indiscriminately. ^[ref]

A mouse Piwi-family protein participating in germ-cell piRNA biogenesis and transposon control.

Its associated guide RNAs contribute sequence information for recognition of transposon-related material. Repression can involve both RNA-level and chromatin-associated outputs, depending on developmental stage and partner factors. ^[ref]

A mouse Piwi-family protein associated with fetal male germ-cell transposon repression and de novo DNA methylation.

The Caenorhabditis elegans Piwi-family protein associated with 21U piRNAs and germline surveillance of RNA expression.

Recognition by its associated small RNAs helps distinguish transcripts for germline surveillance. Establishing a persistent silenced state additionally involves downstream pathways, so initial recognition and long-term maintenance are different stages. ^[ref]

A photosystem involved in water oxidation during oxygenic photosynthesis. Its reaction-center components include D1 protein.

Photosystem I is a light-driven reaction-centre complex in oxygenic photosynthesis. Excitation supports electron transfer to acceptors including ferredoxin; the balance between linear and cyclic routes affects reductant and ATP supply.

The critical modulation for a photoresist is the smallest aerial-image modulation that permits a common exposure time to clear bright regions while retaining full thickness in dark regions. Consider a positive photoresist with retention exposure dose $D_0>0$ and clearing exposure dose $D_c>D_0$. Write the extreme image intensities asFor exposure time $t$, the requirements are $t{I}_{\max }\ge D_c$ and $t{I}_{\min }\le D_0$. A feasible $t$ exists exactly whenwith $M=1$ handled directly since the dark-region exposure dose is zero. Rearrangement givesThis derivation assumes exposure dose is intensity times exposure time and uses fixed retention and clearing thresholds. In the idealized linear contrast-curve model of photoresist contrast, $D_c/D_0=10^{1/\gamma }$, soFor example, $D_c=4D_0$ gives $M_c=3/5$. Greater photoresist contrast lowers the required aerial-image modulation in this model.^[ref]

A vertebrate retinal photoreceptor class important in photopic vision and colour discrimination.

A frequency interval without bulk propagating electromagnetic modes in the specified directions and polarizations. A complete gap excludes all directions and polarizations; a one-dimensional stop band need not do so.