Character codex

  • Airy Disk Hoodie

    能力
    A circular aperture can't focus light to a point; diffraction turns a point of light into a bright central disk with faint rings.
    方程
    \[I(x) = I_0\left(\frac{2J_1(x)}{x}\right)^2,\qquad x = \frac{\pi D\sin\theta}{\lambda}\]
    年份
    1835
    科学家
    George Biddell Airy
    领域
    Forces & Fields

  • Arnold's Cat

    能力
    Each step stretches the picture in one direction and squeezes it in another, keeping its area, so the cat quickly turns to noise.
    方程
    \[\Gamma:\ (x, y) \mapsto (x + y,\ x + 2y) \bmod 1\]
    年份
    1968
    科学家
    Vladimir Arnold
    领域
    Waves, Chaos & Matter

  • Azurwake

    能力
    A charged particle moving through a medium faster than light travels in that medium emits light in a cone, like a sonic boom.
    方程
    \[\cos\theta = \frac{1}{n\beta}, \qquad \beta > \frac{1}{n}\]
    年份
    1937
    领域
    Forces & Fields

  • Beats Hoodie

    能力
    Two tones with nearly equal frequencies add up to a single tone at their average frequency whose loudness swells and fades.
    方程
    \[x = \cos(2\pi f_1 t)+\cos(2\pi f_2 t) = 2\cos(\pi\Delta f\, t)\cos(2\pi\bar f\, t)\]
    年份
    1863
    领域
    Waves, Chaos & Matter

  • Bifurcation Hoodie

    能力
    The logistic map is a single line of arithmetic, yet as r increases its long-term value splits into 2, 4, 8 values and then becomes chaotic.
    方程
    \[x_{n+1} = r\,x_n(1-x_n)\]
    年份
    1976
    科学家
    Mitchell Feigenbaum
    领域
    Waves, Chaos & Matter

  • Bifurcor

    能力
    A magnetic field that changes with height pushes on an atom's magnetic moment.
    方程
    \[F_z = \mu_z\,\frac{\partial B_z}{\partial z}\]
    年份
    1922
    领域
    Quantum

  • Blackbody Hoodie

    能力
    Planck's law gives how bright a blackbody shines at each wavelength for a given temperature.
    方程
    \[B_\lambda(T) = \frac{2hc^2}{\lambda^5}\,\frac{1}{e^{hc/\lambda k_BT} - 1}\]
    年份
    1901
    科学家
    Max Planck
    领域
    Heat & Entropy

  • Bose-Einstein Condensate 1995 Tee

    能力
    Cool atoms until their quantum waves are as wide as the spaces between them, and thousands of them fall into the same lowest-energy state and act as one.
    方程
    \[\lambda_{\mathrm{dB}} = \frac{h}{\sqrt{2\pi m k_B T}}\]
    年份
    1995
    科学家
    Eric Cornell, Carl Wieman, Wolfgang Ketterle
    领域
    Quantum

  • Brachistochrone Hoodie

    能力
    The fastest slide between two points under gravity is not a straight line but a cycloid, the curve traced by a point on a rolling wheel.
    方程
    \[x = R(\theta - \sin\theta),\qquad y = R(1 - \cos\theta)\]
    年份
    1696
    领域
    Waves, Chaos & Matter

  • Bremsella

    能力
    Any accelerating charge radiates.
    方程
    \[P = \frac{q^2 a^2}{6\pi\varepsilon_0 c^3}\]
    年份
    1897
    领域
    Forces & Fields

  • Brownian Motion Hoodie

    能力
    A pollen grain in water is knocked around by countless molecules, so it wanders randomly with no memory of its previous step.
    方程
    \[\langle r^2\rangle = 4Dt\quad\text{(2D)}\]
    年份
    1905
    科学家
    Albert Einstein
    领域
    Waves, Chaos & Matter, Heat & Entropy

  • Catenary Hoodie

    能力
    A chain hanging freely under its own weight takes the shape of a hyperbolic cosine, the catenary.
    方程
    \[y = a\cosh(x/a)\]
    年份
    1691
    领域
    Waves, Chaos & Matter

  • Caustic Hoodie

    能力
    Light reflecting off the inside of a cup gathers along a bright curve, a caustic, where many reflected rays bunch together.
    方程
    \[x = \tfrac{R}{4}\left(3\cos t-\cos 3t\right)\]
    领域
    Forces & Fields

  • Chandrasekhar Limit Tee: 1.4 M☉

    能力
    In a white dwarf, electrons refuse to share quantum states and push back, holding the star up.
    方程
    \[M_{\mathrm{Ch}} = \frac{\omega_3^{0}\sqrt{3\pi}}{2}\left(\frac{\hbar c}{G}\right)^{3/2}\frac{1}{(\mu_e m_H)^{2}} \approx \frac{5.8\,M_\odot}{\mu_e^{2}}\]
    年份
    1931
    科学家
    Subrahmanyan Chandrasekhar
    领域
    Relativity & Cosmos

  • Condensa

    能力
    Below a critical temperature, a gas of bosons starts collecting in its lowest quantum state.
    方程
    \[\frac{N_0}{N} = 1 - \left(\frac{T}{T_c}\right)^{3/2}\quad(T\le T_c)\]
    年份
    1925
    领域
    Quantum

  • Corekeeper

    能力
    Yukawa proposed that nucleons attract by exchanging a massive particle.
    方程
    \[V(r) = -\frac{g^{2}}{4\pi}\frac{e^{-r/\lambda}}{r}, \qquad \lambda = \frac{\hbar}{m_\pi c}\]
    年份
    1935
    科学家
    Murray Gell-Mann, Richard Feynman
    领域
    Forces & Fields

  • Coriolix

    能力
    In a rotating frame, moving objects appear to be pushed sideways by the Coriolis term, −2Ω × v.
    方程
    \[\mathbf{a}' = -2\,\boldsymbol{\Omega}\times\mathbf{v}' - \boldsymbol{\Omega}\times(\boldsymbol{\Omega}\times\mathbf{r}')\]
    年份
    1835
    领域
    Waves, Chaos & Matter

  • Cryo Fault

    能力
    Griffith showed that a crack grows when the elastic energy it releases is enough to pay for the new surface it creates.
    方程
    \[\sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}}\]
    年份
    1921
    科学家
    Alan Arnold Griffith
    领域
    Waves, Chaos & Matter, Heat & Entropy

  • Dark Matter Host

    能力
    When two galaxy clusters collided in the Bullet Cluster, their hot gas slammed together and stalled, but bent background light shows most of the mass sailed on with the galaxies.
    方程
    \[v(r)^{2} = \frac{G M(r)}{r} \;\Rightarrow\; M(r) = \frac{v^{2} r}{G}\]
    年份
    1937
    科学家
    Albert Einstein, Isaac Newton, Vera Rubin
    领域
    Relativity & Cosmos

  • Decay Dancer

    能力
    A free neutron decays into a proton, an electron and an antineutrino, because one down quark turns into an up quark by emitting a W boson.
    方程
    \[n \to p + e^{-} + \bar\nu_e\]
    年份
    1934
    科学家
    Enrico Fermi
    领域
    Forces & Fields

  • Decoherex

    能力
    The off-diagonal terms in a density matrix carry the ability to interfere.
    方程
    \[\rho_{01}(t) = \rho_{01}(0)\,e^{-t/\tau_D}\]
    年份
    1970
    科学家
    Wojciech Zurek
    领域
    Quantum

  • Diagonix

    能力
    A polarizer passes the fraction cos²θ of already-polarized light.
    方程
    \[I = I_0\cos^2\theta\]
    年份
    1809
    领域
    Forces & Fields

  • Diffraction Hoodie

    能力
    X-rays reflecting from successive planes of atoms in a crystal add up only when the extra path between planes is a whole number of wavelengths.
    方程
    \[n\lambda = 2d\sin\theta\]
    年份
    1913
    科学家
    William Lawrence Bragg
    领域
    Waves, Chaos & Matter

  • Double Pendulum Hoodie

    能力
    Two pendulums hinged together follow exactly from one Lagrangian with no randomness at all.
    方程
    \[L = ml^2\left[\dot\theta_1^2 + \tfrac12\dot\theta_2^2 + \dot\theta_1\dot\theta_2\cos(\theta_1-\theta_2)\right] + mgl\left(2\cos\theta_1 + \cos\theta_2\right)\]
    年份
    1788
    科学家
    Joseph-Louis Lagrange
    领域
    Waves, Chaos & Matter, Forces & Fields

  • Double Slit Hoodie

    能力
    Light from two slits interferes, giving bright stripes wherever the path difference is a whole number of wavelengths.
    方程
    \[I(\theta) = I_0\cos^2\!\left(\frac{\pi d\sin\theta}{\lambda}\right)\mathrm{sinc}^2\!\left(\frac{\pi a\sin\theta}{\lambda}\right)\]
    年份
    1804
    科学家
    Thomas Young
    领域
    Quantum

  • Drum Mode Hoodie

    能力
    A drumhead fixed at its rim can only vibrate in certain shapes, each a Bessel function in radius times a cosine in angle.
    方程
    \[\nabla^2 u = \frac{1}{c^2}\frac{\partial^2 u}{\partial t^2}\]
    年份
    1829
    科学家
    Siméon Denis Poisson
    领域
    Waves, Chaos & Matter

  • Einstein Ring Hoodie

    能力
    A mass lying exactly between us and a distant source bends the source's light into a ring.
    方程
    \[\beta = \theta - \frac{\theta_E^2}{\theta}\]
    年份
    1936
    科学家
    Albert Einstein
    领域
    Relativity & Cosmos

  • Eventide Prophet

    能力
    Hawking showed that black holes glow faintly, with a temperature that goes down as their mass goes up.
    方程
    \[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]
    年份
    1975
    科学家
    Jacob Bekenstein, Stephen Hawking
    领域
    Relativity & Cosmos

  • Exclusor

    能力
    Electrons are fermions, so their joint wavefunction must change sign when two are swapped.
    方程
    \[\psi(x_1,x_2) = \frac{1}{\sqrt{2}}\begin{vmatrix} \phi_a(x_1) & \phi_b(x_1) \\ \phi_a(x_2) & \phi_b(x_2) \end{vmatrix}\]
    年份
    1925
    科学家
    Wolfgang Pauli
    领域
    Quantum

  • Expulsieur

    能力
    A superconductor expels magnetic field from its interior, which a merely perfect conductor would not do.
    方程
    \[\mathbf{B}_{\text{inside}} = 0\]
    年份
    1935
    领域
    Quantum

  • Feynman Diagram Hoodie

    能力
    When an electron and positron annihilate into a muon pair through a virtual photon, quantum electrodynamics gives the angular pattern 1 + cos²θ.
    方程
    \[\frac{d\sigma}{d\Omega} = \frac{\alpha^2}{4s}\left(1+\cos^2\theta\right)\]
    年份
    1949
    科学家
    Richard Feynman
    领域
    Forces & Fields, Quantum

  • Field Lines Hoodie

    能力
    Every electric charge produces a field pointing away from it if positive, or toward it if negative, weakening as one over distance squared.
    方程
    \[\nabla\cdot\mathbf{E} = \frac{\rho}{\varepsilon_0}\]
    年份
    1785
    科学家
    Charles-Augustin de Coulomb
    领域
    Forces & Fields

  • ForceShift

    能力
    A quantum particle facing a barrier higher than its energy has a small chance of appearing on the other side.
    方程
    \[T \approx e^{-2\kappa L}, \qquad \kappa = \frac{\sqrt{2m(V_0 - E)}}{\hbar}\]
    年份
    1928
    科学家
    George Gamow
    领域
    Quantum

  • Foucault Hoodie

    能力
    The swing plane of a Foucault pendulum appears to turn because the floor rotates with the Earth underneath it.
    方程
    \[\Omega = \omega_\oplus\sin\phi\]
    年份
    1851
    领域
    Waves, Chaos & Matter

  • Graviton Whisper

    能力
    Far from strong sources, Einstein's equations reduce to a wave equation: moving masses send out ripples in spacetime that travel at the speed of light.
    方程
    \[\Box\,\bar h_{\mu\nu} = -\frac{16\pi G}{c^{4}}\,T_{\mu\nu}\]
    年份
    1916
    科学家
    Matvei Bronstein, Richard Feynman
    领域
    Relativity & Cosmos

  • Gyrolla

    能力
    A magnetic field bends a charged particle into a circle without changing its speed.
    方程
    \[q v B = \frac{m v^2}{r} \;\Rightarrow\; r = \frac{m v}{q B}\]
    年份
    1932
    领域
    Forces & Fields

  • Hadron Brawler

    能力
    The Cornell potential describes the force between a heavy quark and antiquark: Coulomb-like at short range, with an extra term that grows steadily with distance.
    方程
    \[V(r) = -\frac{4}{3}\frac{\alpha_s \hbar c}{r} + \sigma r\]
    年份
    1975
    科学家
    Murray Gell-Mann
    领域
    Forces & Fields

  • I Twist Space Itself

    能力
    Mass curves spacetime, so a ray of light passing the Sun follows a bent path.
    方程
    \[\alpha = \frac{4GM}{c^{2}b}\]
    年份
    1916
    科学家
    Albert Einstein
    领域
    Relativity & Cosmos

  • Interfera

    能力
    When a particle can reach the screen by two paths, you add the amplitudes before squaring them, and the cross term creates bright and dark fringes.
    方程
    \[P = \lvert\psi_1 + \psi_2\rvert^{2} = \lvert\psi_1\rvert^{2} + \lvert\psi_2\rvert^{2} + 2\,\mathrm{Re}\!\left(\psi_1^{*}\psi_2\right)\]
    年份
    1976
    科学家
    Richard Feynman, Thomas Young
    领域
    Quantum

  • Invertia

    能力
    Temperature is defined by how entropy changes when you add energy.
    方程
    \[\frac{1}{T} = \frac{\partial S}{\partial E} < 0\]
    年份
    1951
    领域
    Heat & Entropy

  • Ising Model Hoodie

    能力
    In the Ising model each spin points up or down and prefers to match its neighbours, while heat tries to scramble them.
    方程
    \[H = -J\sum_{\langle ij\rangle} s_is_j,\qquad s_i = \pm1\]
    年份
    1944
    科学家
    Lars Onsager
    领域
    Waves, Chaos & Matter, Heat & Entropy

  • Kepler Orbit Hoodie

    能力
    A planet sweeps out equal areas in equal times, which is angular momentum conservation, so it moves fastest when it is closest to the Sun.
    方程
    \[\frac{dA}{dt} = \frac{L}{2m} = \text{const}\]
    年份
    1609
    科学家
    Johannes Kepler
    领域
    Waves, Chaos & Matter, Forces & Fields

  • Lagrange Points Hoodie

    能力
    In a frame rotating with two orbiting bodies, gravity and the centrifugal effect combine into one effective potential.
    方程
    \[U = -\frac{1-\mu}{r_1} - \frac{\mu}{r_2} - \frac{x^2+y^2}{2}\]
    年份
    1772
    科学家
    Joseph-Louis Lagrange
    领域
    Waves, Chaos & Matter, Forces & Fields

  • Lenzor

    能力
    A changing magnetic flux induces a voltage, and the induced current always flows so as to oppose the change.
    方程
    \[\mathcal{E} = -\frac{d\Phi_B}{dt}\]
    年份
    1834
    领域
    Forces & Fields

  • Libratrix

    能力
    Two bodies orbiting each other have five points where a small third body can keep pace with them.
    方程
    \[r_{L2} \approx R\left(\frac{M_2}{3M_1}\right)^{1/3}\]
    年份
    1772
    领域
    Waves, Chaos & Matter, Forces & Fields

  • Light Cone Hoodie

    能力
    In spacetime, light travels along a cone that separates events you could reach or be reached from (past and future) from those you can't (elsewhere).
    方程
    \[ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2\]
    年份
    1909
    科学家
    Hermann Minkowski
    领域
    Relativity & Cosmos

  • Lissajous Hoodie

    能力
    Plotting one oscillation against another at right angles traces a Lissajous figure.
    方程
    \[x = A\sin(3\omega t),\qquad y = B\sin(2\omega t + \pi/2)\]
    年份
    1857
    领域
    Waves, Chaos & Matter

  • Mach Cone Hoodie

    能力
    An object moving faster than sound outruns its own sound waves, and they pile up into a cone.
    方程
    \[\sin\mu = \frac{c}{v} = \frac{1}{M}\]
    年份
    1887
    科学家
    Ernst Mach
    领域
    Waves, Chaos & Matter

  • Magnara

    能力
    A spinning ball moving through air is pushed sideways, toward the side where its surface moves with the airflow.
    方程
    \[\mathbf{F}_M = \alpha\,\boldsymbol{\omega}\times\mathbf{v}\]
    年份
    1853
    领域
    Waves, Chaos & Matter

  • Magnetic Dipole Hoodie

    能力
    Magnetic field lines never start or stop, because there are no magnetic charges.
    方程
    \[\nabla\cdot\mathbf{B} = 0\]
    年份
    1865
    科学家
    James Clerk Maxwell
    领域
    Forces & Fields

  • Magnetron Twins

    能力
    The energy of two small magnets depends on both their distance and how they are oriented relative to the line joining them.
    方程
    \[U = -\frac{\mu_0}{4\pi r^{3}}\left[3(\vec m_1\cdot\hat r)(\vec m_2\cdot\hat r) - \vec m_1\cdot\vec m_2\right]\]
    年份
    1873
    科学家
    James Clerk Maxwell
    领域
    Forces & Fields

  • Moderon

    能力
    A neutron loses the largest share of its energy when it hits a nucleus of about its own mass.
    方程
    \[\alpha = \left(\frac{A-1}{A+1}\right)^2\]
    年份
    1935
    领域
    Forces & Fields

  • Muonaut

    能力
    Muons made high in the atmosphere live only about two microseconds, too short to cross the atmosphere at face value.
    方程
    \[\Delta t = \gamma\,\tau, \qquad L = \frac{L_0}{\gamma}\]
    年份
    1941
    领域
    Relativity & Cosmos

  • Neutrina Fade

    能力
    A charged particle moving through water faster than light moves in water gives off a cone of blue Cherenkov light, at an angle set by its speed and the refractive index.
    方程
    \[\cos\theta_C = \frac{1}{n\beta}\]
    年份
    1937
    科学家
    Enrico Fermi, Wolfgang Pauli
    领域
    Forces & Fields

  • Nodal Lines Hoodie

    能力
    A vibrating plate obeys an equation in which its bending stiffness balances its inertia.
    方程
    \[D\,\nabla^4 w = \rho h\,\omega^2 w,\qquad D = \frac{E h^3}{12(1-\nu^2)}\]
    年份
    1850
    科学家
    Ernst Chladni
    领域
    Waves, Chaos & Matter

  • Null Beacon

    能力
    In a universe whose expansion is speeding up, there is a largest distance from which light sent today can ever reach us: about 16.7 billion light-years.
    方程
    \[d_{\text{EH}}(t) = a(t)\int_{t}^{\infty} \frac{c\,dt^{\prime}}{a(t^{\prime})}\]
    年份
    1956
    领域
    Relativity & Cosmos