Foundations

An inverse-square force models attraction between point masses.

Homogeneity and isotropy reduce gravitational expansion to two balances.

A bound nucleus has less rest mass than its separated nucleons.

A fixed decay probability per time gives a population timescale.

Nuclear rearrangement can release or require energy.

Pure phases coexist at common T and p when their molar Gibbs energies are equal.

Thermal radiation in a vacuum cavity at temperature T has spectral energy density per angular frequency u_ω=ħω³/[π²c³(exp(ħω/(k_BT))−1)].

For a light source and observer receding directly from each other at relative speed v, f_obs=f_source√[(1−v/c)/(1+v/c)].

For a frame rotating at constant Ω about a common inertial origin, a_inertial=a_rot+2Ω×v_rot+Ω×(Ω×r).

For a smooth inviscid, nonconducting fixed-composition fluid, D_ts=0 and ρD_te=−P∇·v, where e and s are internal energy and entropy per mass.

An isolated Newtonian gravitational binary has relative semimajor axis a=a₁+a₂ and period T satisfying T²=4π²a³/[G(m₁+m₂)].

Independent constant decay channels have total rate λ=Σ_iλ_i and branching fractions b_i=λ_i/λ.

In a dilute nondegenerate gas of independently distributed reacting nuclei at common temperature T, reaction events per volume/time are R_ab=n_an_b⟨σv⟩/(1+δ_ab), where δ_ab=1 for the same species and 0 otherwise.

For repulsively charged nuclei with κ=Z_aZ_be²/(4πε₀)>0 and relative speed v, the Sommerfeld parameter is η=κ/(ħv) and the leading low-energy Coulomb penetration exponential is exp(−2πη)=exp[−√(E_G/E)], E_G=2μ(πκ/ħ)².

The Calvin–Benson cycle carboxylates ribulose-1,5-bisphosphate through RuBisCO, reduces the resulting carbon compounds using ATP and NADPH, and regenerates the acceptor.

Nitrogen fixation converts N₂ toward biologically usable reduced nitrogen; ammonification, nitrification and denitrification transform nitrogen among distinct chemical pools.

Stress and strain need a loading geometry and a constitutive range.