A rechargeable cell transferring lithium ions between host electrodes during charging and discharge. Host chemical potentials determine voltage; an exposed lithium-metal electrode is a distinct design.

A rechargeable aqueous sulfuric-acid cell using lead and lead dioxide electrodes. Discharge converts both active materials to lead sulfate; charging reverses that conversion subject to corrosion, gas evolution and morphology limitations.

A metal-air cell that oxidizes zinc while reducing oxygen at a gas-accessible positive electrode. Primary and electrically rechargeable designs exist; reversible zinc morphology and durable oxygen-evolution catalysis are major requirements for the latter.

Electrical charge delivered per unit mass, commonly expressed in ampere-hours per gram. For an ideal active material transferring $n$ electrons per formula unit, $q=nF/(3600M)$ when $M$ is in grams per mole.

A battery designed to recover usable chemical energy by electrical charging that reverses its discharge reactions. Reversibility, cycle life and parasitic reactions distinguish a practical secondary cell from a merely thermodynamically reversible equation.

A miniature battery, often fabricated as a thin film or patterned three-dimensional structure for small devices. The term concerns size and construction; primary or rechargeable chemistry can be used.

A battery using lithium oxidation and oxygen reduction, often producing lithium peroxide in a nonaqueous discharge. Specific-energy claims depend strongly on whether oxygen, electrolyte and inactive components are included in the mass.

A beam fixed at one end and free at the other. A transverse end force $F$ gives bending moment $M(x)=F(L-x)$ and, for a rectangular section, maximum bending stress $6FL/(w{h}^2)$ at the fixed end. Longitudinal tension and compression are greatest on opposite outer fibres.

The planar equilibrium of an inextensible slender beam can have large tangent angle while retaining small elastic strain across its thickness. For constant horizontal compressive force $F$, moment balance and curvature ${\theta }^{\prime }=d\theta /ds$ give the displayed nonlinear equation. Multiplication by ${\theta }^{\prime }$ gives the first integral $EI{\theta }^{\prime 2}/2-F\cos \theta =C$. A tensile load has $F<0$ in this convention.

For a shared quantum entanglement resource, one party's choice of measurement can prepare different conditional ensembles for the distant party. Discarding the outcome leaves the same distant reduced density matrix, so steering does not itself permit signalling. Demonstrating steering against a local hidden-state model is stronger than merely observing a change in a postselected description.

Universal metric coupling and local special-relativistic nongravitational physics do not select a unique dynamical metric action. Additional assumptions are needed to obtain the Einstein field equations. A local freely falling coordinate choice can remove connection coefficients at a point but cannot remove curvature or tidal effects over a finite region. Tests of redshift, free fall and self-gravitating dynamics therefore address related but distinct claims.

If a classical monatomic gas re-equilibrates by collisions while losing atoms by effusion, the escaping atoms carry mean kinetic energy $2k_{B}T$. Without wall heating, conservation of energy gives $d(3N{k}_{B}T/2)=2k_{B}TdN$ and therefore $T\propto N^{1/3}$. This assumes a fixed container volume and a small aperture in the molecular-flow regime.

During collisionless effusion, selective loss changes the distribution of surviving particle velocities without collision-driven relaxation to a new Maxwell-Boltzmann distribution. The loss law depends on flight paths and on the wall-reflection rule. Speed-dependent depletion and, for specular walls, directional structure can remain.

For an isotropic two-dimensional velocity distribution, a straight opening of width $w$ in a region of number per area $n_2$ loses particles at the displayed rate. The angular integral is ${\int }_{-\pi /2}^{\pi /2}\cos \theta d\theta /(2\pi )=1/\pi$. At fixed equilibrium kinetic energy the speed distribution scales as $m^{-1/2}$, so the rate has the same scaling. A fixed second moment alone does not determine the first moment without a distribution assumption.

An equilibrium Maxwell-Boltzmann gas has number flux $n\overline{v}/4$ onto a plane. Molecules crossing the plane are weighted by their positive normal velocity, so their mean translational kinetic energy is $2k_{B}T$, rather than the bulk value $3k_{B}T/2$. The translational energy flux is therefore $F_E=n\overline{v}{k}_{B}T/2$. Internal degrees of freedom contribute their mean energy per crossing molecule when independent of translational velocity.

A dimensionless weight in effective dose; the weights over the reference tissues sum to one.

Differences between arrival times of nearby earthquakes at a common station largely cancel common propagation errors. Comparing observed and predicted differences constrains relative source separation and origin-time differences. Closely similar waveforms permit precise differential picks by cross-correlation. Absolute position still needs an accurate model or external anchor.

An earthquake origin time is the estimated onset time of rupture. Predicted arrivals add this time to a propagation travel time; an uncertain origin time therefore couples to uncertain source depth in some station geometries.