For a dilute gas with a floor at $z=0$, constant $g$, uniform cross-section and no relevant ceiling, $P(z)=\beta mg{e}^{-\beta mgz}$. Its mean gravitational energy is $k_{B}T$, and $P(z>h)=e^{-\beta mgh}$. A linear potential contributes $k_{B}T$, not the $k_{B}T/2$ of a quadratic degree of freedom.

A stator protein contributing to ion-coupled force generation in proton-driven bacterial flagellar motors.

Together with its stator partners, it couples ion movement to mechanical interaction with the rotor. The surrounding membrane supplies an electrochemical energy source; the flagellar filament is the load rather than the source of that energy. ^[ref]

A stator-associated protein contributing proton-coupling machinery and anchorage to the cell envelope in the familiar proton-driven motor.

A rotor protein involved in stator contact and torque generation. Changes in its organization contribute to directional switching without reversal of ion flow.

A switch-complex protein involved in reception of phosphorylated CheY and control of rotational bias.

Binding of phosphorylated CheY changes the switch’s rotational bias. A change in bias alters the balance of swimming behaviours without requiring the motor to sense external attractant directly. ^[ref]

A switch-complex component participating in organization of the bacterial flagellar rotor's cytoplasmic ring.

Its location in the C ring connects assembly of the cytoplasmic rotor structure to the larger switching machinery. Structural assembly, directional switching and ion-driven torque generation involve interacting but distinct components. ^[ref]

A neutral strange B meson has valence content $\bar{b}s$ in the conventional $B_s^0$ assignment; its antiparticle has $b\bar{s}$. In its charged-current spectator amplitude for $J/\psi \varphi$, $\bar{b}\to \bar{c}{W}^{+}$ and $W^{+}\to c\bar{s}$, while the original strange quark is carried into the final strange pair. This is one Standard-Model contribution, not a complete treatment of mixing, loop amplitudes or hadronization.

Directional cell-to-cell transport of auxin. Transporter abundance, polarity and activity influence local hormone distribution.

Asymmetric localization of transport components can generate tissue-scale patterns from local cell-to-cell transfers. The resulting auxin distribution can guide growth and patterning, while a concentration maximum can reflect transport, synthesis and removal together. ^[ref]

Selective turnover of mitochondria or mitochondrial portions through autophagy. Mitochondrial fragmentation alone is not proof of successful turnover.

An electronically excited atomic-oxygen state that can be quenched collisionally or react with species such as water. Quenching back to the ground state and radical production compete, so the photochemical source rate need not equal the radical source rate.

The timescale on which turbulent optical-path fluctuations decorrelate constrains short-exposure imaging and adaptive-optics control latency. In a frozen-flow approximation it scales as $r_0/v_{\mathrm{eff}}$, with an effective turbulence-weighted wind speed. It is not the temporal coherence time set by the optical bandwidth.^[ref]

Because ice has lower equilibrium vapour pressure than supercooled liquid, a mixed-phase environment can sustain deposition onto ice while liquid droplets evaporate. This is distinct from ice collecting droplets by riming.

Supercooled droplets collide with an ice particle and freeze onto it, increasing its mass. Deposition, riming and ice aggregation are distinct growth mechanisms.

survey completeness is the fraction of a specified true source population recovered by a survey, conditional on properties such as flux, size and sky position. Injecting simulated sources into realistic data and applying the actual detection pipeline measures recovery probability. Completeness differs from purity: recovered objects can include false detections or incorrectly identified sources.