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Along a steady axisymmetric ideal-MHD wind, the total specific energyis constant on each magnetic surface. The last term is the electromagnetic energy transported per unit mass flux.

Neighboring magnetic surfaces with different Alfvén speeds carry the same axial waveform at different rates. For a traveling profile $f(R,z+v(R)t)$, differentiation produces the displayed term, so transverse gradients grow even without axial wave steepening. Small magnetic diffusivity or viscosity can eventually act strongly on these gradients. The ideal process redistributes phase rather than directly dissipating wave energy.

The energy of the residual flow and magnetic field in a maintained shear flow has source $S=-a{T}_{xy}$, where $T_{xy}=\rho v_x{v}_y-B_x{B}_y/{\mu }_0$. The kinetic and magnetic stresses can exchange energy with the imposed background. The source vanishes when their off-diagonal contributions cancel.

A magnetohydrodynamic shock is a discontinuity satisfying conservation of mass, momentum, energy, normal magnetic field, and tangential electric field.

For two positive measurements $F_1,F_2$ in the same photometric passband, using the same magnitude zero point, units, and weighting convention, their apparent magnitudes obeyThe logarithm takes a dimensionless ratio. An energy-weighted measurement must be compared with another energy-weighted measurement, and a photon-counting measurement with another consistently calibrated photon-counting measurement. Changing photometric passband or magnitude zero point requires the corresponding calibration, as in a colour index. ^[ref]. ^[ref].

For example, $F_2=100F_1$ gives $\Delta m=-5$: source 2 is brighter. Conversely, $\Delta m=+5$ gives $F_2/F_1=0.01$, and $\Delta m=+1$ gives $F_2/F_1\simeq 0.398107$. Even fractional steps work: $\Delta m=+0.1$ gives $F_2/F_1\simeq 0.912011$, an approximately $8.80\%$ decrease. These are illustrative ratios, independent of any particular star catalogue.

A magnon is one quantum of a spin wave, a collective oscillation of magnetic order. Exchange-coupled spins do not fluctuate independently: a disturbance spreads through the ordered system as a mode with a definite wavevector and energy.

In a simple collinear Heisenberg ferromagnet, a single magnon reduces the total spin projection along the ordered axis by one unit of $\hslash$ while distributing the disturbance across many sites. At low excitation density, magnon modes can be treated approximately as bosonic oscillators, motivating the Holstein–Primakoff transformation and linear spin-wave approximation. Their population contributes to the reduction of magnetization with increasing temperature. Strong interactions, noncollinear order and large excitation densities can require corrections to the simple independent-magnon picture.

The time a star spends with core hydrogen nuclear fusion as its principal energy source. If the usable fuel fraction $f$, conversion efficiency $ϵ$, and composition are comparable, the main-sequence lifetime scales as $M/L$. With a local mass-luminosity relation $L\propto M^{\alpha }$, the lifetime scales as $M^{1-\alpha }$. This is a scaling estimate: convective core size and changing luminosity affect detailed ages.

A Majorana neutrino is its own antiparticle. A corresponding mass term can violate conventional lepton number by two. Observing a wrong-helicity charged-current process is nevertheless suppressed by the very small neutrino mass relative to its energy, rather than having the ordinary charge-conjugate branching fraction.

At fixed angular momentum, rotational energy is minimized by rotation about the largest principal moment of inertia. Indeed, $T={\sum }_i{L}_i^2/(2I_i)\ge {\sum }_i{L}_i^2/(2I_{\max })$. Weak internal dissipation can therefore relax a nearly rigid isolated body towards that axis. A perfectly rigid torque-free body conserves energy and does not settle; both extreme-inertia axes are stable in its ideal dynamics. The maximum-inertia axis need not be the geometrically longest axis.

Malnutrition is impaired nutritional status arising from insufficient, excessive or unbalanced nutrient provision or use. It can concern energy, particular nutrients or both. A person’s body mass alone does not establish whether every nutrient requirement is met.

For incident light with linear polarization, an ideal linear polarizer transmitswhere $I$ is light intensity and $\theta$ is the angle between the incident electric field's line of oscillation and the polarizer's pass axis. The input and output are compared in the same medium. The classical explanation is an orthogonal projection: for a unit vector $\mathbf{u}$ along the pass axis,The dot product reduces the transmitted wave amplitude by $\cos \theta$. For a plane electromagnetic wave in the same medium, light intensity is proportional to squared electric field wave amplitude, giving Malus's law. For example, $\theta =60^{\circ }$ transmits one quarter of the incident light intensity, although the transmitted wave amplitude is one half. ^[ref].

Start with light already in linear polarization along the horizontal $0^{\circ }$ axis and let its light intensity be $I_0$. Two ideal absorbing linear polarizers with pass axes $0^{\circ }$ and $90^{\circ }$ give $I_0{\cos }^2{0}^{\circ }{\cos }^{2}90^{\circ }=0$. Insert a $45^{\circ }$ polarizer between them: the first leaves $I_0$ unchanged, the middle transmits $I_0/2$ with linear polarization along $45^{\circ }$, and the last transmits $I_0/4$ with linear polarization along $90^{\circ }$. Each angle in Malus's law is relative to the preceding output, so the final step uses $90^{\circ }-45^{\circ }=45^{\circ }$:

For these ideal absorbing polarizers, the rejected electric field component transfers energy to the filter. In the three-filter arrangement the middle absorbs the fraction $I_0/2$, and the last absorbs $I_0/4$, leaving $I_0/4$ transmitted. Conservation of energy holds at each step. Inserting the middle polarizer changes the linear polarization arriving at the last one; it does not create light. The effect illustrates why successive orthogonal projections cannot generally be replaced by a single comparison of the first and last axes.

The initially horizontal assumption matters. For unpolarized light of light intensity $I_0$, the first ideal linear polarizer transmits $I_0/2$: averaging ${\cos }^2\theta$ over uniformly distributed incident orientations gives $1/2$. The same $0^{\circ },45^{\circ },90^{\circ }$ sequence then transmits $I_0/8$. This extra first-stage factor does not apply to the already horizontally polarized input in the figure.

The circular timelike orbit with conserved energy equal to rest energy at infinity. Substituting $E/(m{c}^2)=(1-2\mu /r)/\sqrt{1-3\mu /r}$ and solving $E=m{c}^2$ gives $r=4\mu$, with $\mu =GM/c^2$. It is unstable. Strictly bound circular orbits have $r>4\mu$ and $E<m{c}^2$; radial stability requires $r>6\mu$. This limiting orbit is not the smallest radius ever reached by a bound-energy plunging trajectory.

Mario P. Vecchi is an electrical engineer whose work has included semiconductor research, broadband communications and computational optimization. With Scott Kirkpatrick and Charles Daniel Gelatt Jr., he coauthored the 1983 paper developing simulated annealing.^[ref]

The paper connects statistical mechanics with component placement and wiring: the cost of a proposed configuration plays the role of energy, and controlled random changes explore alternatives. His later work also included optical switching and wavelength-division multiplexing in broadband networks, illustrating a career spanning physical devices and communication systems.^[ref]

A Markov reward model assigns a reward or cost rate $r_i$ to each state of a Continuous-time Markov chain and accumulates it with elapsed time:For a finite chain with generator $Q$ and reward column vector $r$, its expected accumulated reward isIntegrating state indicators proves the expectation formula; differentiating the matrix exponential gives the differential equation. Indicator rewards count time in a selected state. If rates represent power consumption, the accumulated reward is energy.

For a two-state chain $0\to 1$ at rate $a>0$ and $1\to 0$ at rate $b>0$, let only state one earn unit reward. Starting at zero,It is the expected duration in state one, obtained by integrating its occupancy probability. With exponential discount $\delta >0$, the infinite-horizon expected reward instead is $(\delta I-Q{)}^{-1}r$, the resolvent applied to $r$. Bounded rewards and positive discount make that integral finite even when the undiscounted cumulative reward grows indefinitely.

Martin Lewis Perl coauthored the evidence that led to identification of the tau lepton. The experiment found electron-muon pairs of opposite electric charges in electron–positron annihilation, with missing energy and momentum and no other detected charged particles or photons. The distributions required additional unseen particles. Studying these unusual final states provided a route to recognizing a new unstable lepton, even though it decayed before leaving a directly visible track.^[ref]

An experimental physicist who led particle searches at SLAC.^[ref]

Martin Rees develops theoretical accounts of cosmic structure. In a 1978 paper with Simon White, he separated the assembly of extended dark haloes from the dissipative concentration of luminous material within them.

Collisionless matter can build a large gravitationally bound halo, while gas can lose energy through radiative cooling and settle into a much denser luminous component. Their two-stage model connected the characteristic sizes and luminosities of galaxies to the cooling of gas inside a hierarchically assembled dark structure. It made the different physical behavior of the components central to the explanation.^[ref]

Coauthor of research on temperature-dependent rotation of the ATP synthase F1 sector. The study connected single-molecule motion with subunit interactions during the catalytic dwell, relating enzyme mechanics to energy conversion.^[ref]

Masatoshi Koshiba helped turn underground neutrino detectors into astronomical instruments. The Kamiokande II report of the 1987 supernova burst described eleven electron-like events over about thirteen seconds. These rare interactions supplied information about the collapsing star through weakly interacting particles rather than only its escaping light. The observation joined the timing and energy measurements of particle detection with a transient event far outside the solar system.^[ref]

A physicist.^[ref]

A maser uses stimulated emission to amplify microwaves. With population inversion and feedback it can sustain a coherent wave field as an oscillator. The name abbreviates "microwave amplification by stimulated emission of radiation".^[ref]

Why make molecules supply an oscillator? Their energy levels offer a reproducible frequency reference, while stimulated emission lets successive molecules reinforce one coherent wave field. In his 1964 lecture, Charles Hard Townes traced his motivation to microwave spectroscopy: resolving molecular structure required useful coherent sources.^[ref] The interesting balance is between molecular amplification and escaping energy: even a beam with population inversion fails to oscillate if cavity losses win. This is the microwave counterpart of laser threshold.

The maser cavity stores a resonant electromagnetic wave so that an arriving molecule encounters a field left by earlier molecules. An output coupling lets part of that stored energy reach a detector. The same coupling also removes energy, so increasing extraction can prevent startup. The cavity provides feedback; the selected molecular beam supplies the useful internal energy.

Let $U$ be stored field energy, $\omega =2\pi {\nu }_0$, and $\kappa ={\kappa }_{\mathrm{int}}+{\kappa }_{\mathrm{out}}$ the total passive energy decay rate. Internal dissipation and output extraction contribute ${\kappa }_{\mathrm{int}}U$ and ${\kappa }_{\mathrm{out}}U$ to lost power. With this energy convention, the loaded quality factor isThe field amplitude decays at $\kappa /2$; confusing amplitude and energy decay introduces a factor of two into a maser oscillation threshold calculation.