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कैटलॉग का हर समीकरण, हर उत्पाद के लिए एक पंक्ति।

1. Nullwen, the Upper-Limit Herald MugMug \[R = \frac{P(n \mid \mu)}{P(n \mid \mu_{\text{best}})}\]\[P(n \mid \mu) = \frac{(\mu + b)^{n}\, e^{-(\mu + b)}}{n!}\]
2. Nutariel, the Rabi-Flopping Dozer MugMug \[P(t) = \sin^{2}\!\left(\frac{\Omega t}{2}\right)\]
3. Ole Rømer Sticker – Io Isn’t Late. Light Is. | Physics StickerPaper products \[\Delta t = \frac{\Delta d}{c}\]\[\begin{gathered} \frac{2\,\text{AU}}{c} \approx 998\ \text{s} \approx 16.6\ \text{min} \\ (\text{R\o mer's estimate} \approx 22\ \text{min}) \end{gathered}\]\[c = 299\,792\,458\ \text{m/s (exact)}\]
4. Omegoda – The Oh-My-God Particle Physics T-ShirtT-Shirt \[E = (3.2 \pm 0.9) \times 10^{20}\ \text{eV} \approx 51\ \text{J}\]
5. Orbitick – GPS Clock Correction / Gravitational Time Dilation Physics StickerPaper products \[\frac{\Delta f}{f} \approx \frac{\Delta\Phi}{c^2} - \frac{v^2}{2c^2}\]\[\frac{\Delta f}{f} = +4.4647\times10^{-10}\]\[\begin{aligned} f_0 &= 10.23\ \text{MHz} \\ &\quad\times(1 - 4.4647\times10^{-10}) \\ &= 10.229\,999\,995\,43\ \text{MHz} \end{aligned}\]
6. Oscillayne – The Harmonic Pulse / Waveform Resonance Physics T-ShirtT-Shirt \[\ddot x + \gamma\dot x + \omega_0^{2}x = \frac{F_0}{m}\cos\omega t\]\[A(\omega) = \frac{F_0/m}{\sqrt{(\omega_0^{2}-\omega^{2})^{2} + \gamma^{2}\omega^{2}}}\]
7. Paradoxes & Puzzles Pixel Sticker Sheet – 12 Physics StickersPaper products \[k_{\mathrm{eff}} = \tfrac{k}{2}\ (\text{series}) \;\rightarrow\; k_{\mathrm{eff}} = 2k\ (\text{parallel})\]\[\phi = U\left(r + \frac{a^{3}}{2r^{2}}\right)\cos\theta \;\Rightarrow\; F_{\mathrm{drag}} = 0\]\[\frac{\partial p}{\partial r} = \frac{\rho v_\theta^{2}}{r}\]\[L(t) \approx \left[1 + \tfrac{2}{5}\left(1 - \frac{t}{t_\odot}\right)\right]^{-1} L_\odot\]\[p_{\mathrm{Minkowski}} = \frac{n\hbar\omega}{c},\quad p_{\mathrm{Abraham}} = \frac{\hbar\omega}{n c}\]\[R_{\mathrm{Cl}}^{\mathrm{meas}} = 2.56 \pm 0.16 \pm 0.16\ \mathrm{SNU} \quad \text{vs} \quad R_{\mathrm{Cl}}^{\mathrm{pred}} = 7.6^{+1.3}_{-1.1}\ \mathrm{SNU}\]\[z = \frac{\omega^{2} r^{2}}{2g}\]\[\Delta E = \frac{1}{2}\,\frac{C_1 C_2}{C_1 + C_2}\,(V_1 - V_2)^{2}\]\[P \propto \exp\!\left(\frac{\Delta S}{k_B}\right)\]\[P_1 = \cos^{2}\tfrac{\varphi}{2},\ P_2 = \sin^{2}\tfrac{\varphi}{2}\ (\text{with splitter});\quad P_1 = P_2 = \tfrac{1}{2}\ (\text{without})\]\[\mathcal{E} = v B L\]\[r_{\mathrm{fwd}} \propto e^{-\varepsilon/k_B T_1},\ r_{\mathrm{back}} \propto e^{-\varepsilon/k_B T_2} \;\Rightarrow\; T_1 = T_2:\ \langle W\rangle = 0\]
8. Pelletine, the Grain-Counting Clerk MugMug \[S_I = 2qI\]
9. Pendulux – Foucault Pendulum / Earth’s Rotation Physics StickerPaper products \[\omega_{\text{prec}} = \Omega_\oplus \sin\varphi\]\[\Omega_\oplus = \frac{360^\circ}{23.93\ \text{h}}\]\[\Omega_\oplus \approx 15.04^\circ\ \text{per hour}\]
10. Percolia, the Threshold Weaver MugMug \[p_c \approx 0.592746 \quad \text{(site percolation, square lattice)}\]
11. Perturbelle, the First-Order Listener MugMug \[E_n^{(1)} = \langle n | V | n \rangle\]
12. Phaselocke, the Lock-In Locksmith MugMug \[V_{\text{out}} = \tfrac{1}{2} V_s V_r \cos\theta\]
13. Physicist Portraits Vol. 1 Pixel Sticker Sheet – 10 Physics StickersPaper products \[Q = \sum_i \frac{\partial L}{\partial \dot q_i}\,\delta q_i\]\[\begin{gathered} E_k = \tfrac{1}{2} m v^{2} \\ (\text{vis viva: } m v^{2}) \end{gathered}\]\[{}^{60}\mathrm{Co} \to {}^{60}\mathrm{Ni}^{*} + e^{-} + \bar\nu_e\]\[d = \tfrac{1}{2}g t^{2}\]\[\vec F = \frac{d\vec p}{dt}\]\[\nabla\cdot\vec E = \frac{\rho}{\varepsilon_0}, \quad \nabla\cdot\vec B = 0\]\[\oint_S \vec E\cdot d\vec A = \frac{Q_{\text{enc}}}{\varepsilon_0}\]\[V(t) = V_0\sin(\omega t)\]\[\frac{d\sigma}{d\Omega} = \left(\frac{zZe^2}{16\pi\varepsilon_0 E}\right)^2\frac{1}{\sin^4(\theta/2)}\]\[\begin{gathered} V(r) = -\frac{g^{2}}{4\pi}\,\frac{e^{-r/R}}{r} \\ R = \frac{\hbar}{m c} \end{gathered}\]
14. Physicist Portraits Vol. 2 Pixel Sticker Sheet – 10 Physics StickersPaper products \[r = v\,\Delta t\]\[Q = \left(M_{\text{initial}} - M_{\text{final}}\right)c^{2}\]\[\begin{gathered} E_N = \hbar\omega\left(N + \tfrac{3}{2}\right) \\ \begin{aligned} g_N &= (N+1)(N+2) \\ &= 2,\,6,\,12,\,\ldots \end{aligned} \\ \Rightarrow\; \text{shells close at } 2,\,8,\,20 \end{gathered}\]\[N(t) = N_0 e^{-\lambda t}\]\[\begin{gathered} h\nu_s = h\nu_0 - h\nu_{\text{vib}} \\ (\text{Stokes}) \end{gathered}\]\[E = h\nu\]\[\begin{gathered} E_n = -\frac{R_\infty hc}{n^{2}} \\ R_\infty hc = 13.605\,693\,122\,990\ \text{eV} \end{gathered}\]\[f(E)=\frac{1}{e^{(E-\mu)/kT}+1}\]\[K(b,a) = \sum_{\text{paths}} e^{iS[x(t)]/\hbar}\]\[\psi(1,2)=\frac1{\sqrt2}\bigl[\phi_a(1)\phi_b(2)-\phi_a(2)\phi_b(1)\bigr]\]
15. Physicist Portraits Vol. 3 Pixel Sticker Sheet – 10 Physics StickersPaper products \[\bar n(\varepsilon) = \frac{1}{e^{(\varepsilon-\mu)/(k_B T)} - 1}\]\[\begin{aligned} \frac{n_{i+1}\,n_e}{n_i} &= \frac{2}{\Lambda^{3}}\,\frac{g_{i+1}}{g_i} \\ &\quad\times\exp\!\left(-\frac{\chi_i}{k_B T}\right) \\ \Lambda &= \frac{h}{\sqrt{2\pi m_e k_B T}} \end{aligned}\]\[\sigma^2 \sim \frac{GM}{R}\]\[f(E)=\frac{1}{e^{(E-\mu)/kT}+1}\]\[\bar\rho \gtrsim \frac{3\pi}{G P^{2}}\]\[\begin{aligned} M_{\text{Ch}} &= \frac{\omega_3^{0}\sqrt{3\pi}}{2}\left(\frac{\hbar c}{G}\right)^{3/2} \\ &\quad\times\frac{1}{(\mu_e m_H)^{2}} \\ &\approx \frac{5.73}{\mu_e^{2}}\,M_\odot \end{aligned}\]\[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]\[v(r)^{2} = \frac{G M(r)}{r}\]\[\Delta t = \frac{\Delta d}{c}\]\[S = k_B \ln W\]
16. Physics Starter Pack Pixel Sticker Sheet – 12 Physics StickersPaper products \[\vec F = \frac{d\vec p}{dt}\]\[K(b,a) = \sum_{\text{paths}} e^{iS[x(t)]/\hbar}\]\[N(t) = N_0 e^{-\lambda t}\]\[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]\[V(t) = V_0\sin(\omega t)\]\[E = h\nu\]\[\begin{gathered} E_n = -\frac{R_\infty hc}{n^{2}} \\ R_\infty hc = 13.605\,693\,122\,990\ \text{eV} \end{gathered}\]\[I_s \propto \frac{1}{\lambda^4}\]\[Q_{\text{erase}} \ge k_B T \ln 2\]\[T(z) = T_0\,(1+z)\]\[\frac{N_0}{N} = 1 - \left(\frac{T}{T_c}\right)^{3/2}\quad(T\le T_c)\]\[r_{L2} \approx R\left(\frac{M_2}{3M_1}\right)^{1/3}\]
17. Plasma Drift – Ionized Gas / Plasma Physics T-ShirtT-Shirt \[\omega_p = \sqrt{\frac{n_e e^{2}}{\varepsilon_0 m_e}}\]\[\lambda_D = \sqrt{\frac{\varepsilon_0 k_B T_e}{n_e e^{2}}}\]\[\vec v_E = \frac{\vec E \times \vec B}{B^{2}}\]
18. Primordix – Big Bang Nucleosynthesis / Primordial Helium Physics StickerPaper products \[Y_p \simeq \frac{2\,(n/p)}{1 + n/p}\]\[\begin{gathered} \frac{n}{p} \approx \frac{1}{7} \;\Rightarrow \\ Y_p \approx \frac{2/7}{8/7} = 0.25 \end{gathered}\]\[\left.\frac{n}{p}\right|_{\text{freeze}} \approx e^{-Q/k_B T_f}\]\[\begin{aligned} Q &= (m_n - m_p)\,c^2 \\ &= 1.293\ \text{MeV} \end{aligned}\]
19. Puckwarden, the Espresso Pressure Keeper MugMug \[Q = -\frac{k A\, \Delta P}{\mu L}\]
20. QED Vertex Tee: Alpha Near 1/137T-Shirt \[-ie\gamma^{\mu}\]\[\alpha = \frac{e^{2}}{4\pi\varepsilon_0\hbar c},\qquad \alpha^{-1} = 137.035\,999\,177(21)\ \text{(CODATA 2022)}\]\[\alpha^{-1}(m_Z) \approx 128\]
21. Quadrell, the Quadrature Scribe MugMug \[\sigma^{2} = \sum_i \left(\frac{\partial f}{\partial x_i}\right)^{2} \sigma_i^{2}\]
22. Quantum Physics Vol. 1 Pixel Sticker Sheet – 12 Physics StickersPaper products \[\gamma = -\tfrac{1}{2}\,\Omega\]\[L = \frac{2 m_e\,\mu}{g\,e}\]\[R_{\mathrm{Cl}}^{\mathrm{meas}} = 2.56 \pm 0.16 \pm 0.16\ \mathrm{SNU} \quad \text{vs} \quad R_{\mathrm{Cl}}^{\mathrm{pred}} = 7.6^{+1.3}_{-1.1}\ \mathrm{SNU}\]\[h = \frac{\mathbf{s}\cdot\mathbf{p}}{|\mathbf{s}|\,|\mathbf{p}|} = -1\]\[\mathbf{B}_{\text{inside}} = 0\]\[G = \frac{2e^{2}}{h}\sum_n T_n,\quad G_0 = \frac{2e^{2}}{h} \approx 7.748\,091\,729\times10^{-5}\ \mathrm{S}\]\[\Phi_0 = \frac{h}{2e} \approx 2.067\,833\,848\times10^{-15}\ \mathrm{Wb}\]\[\begin{gathered} R_{xy} = \frac{h}{\nu e^2} = \frac{R_K}{\nu} \\ \nu = 1, 2, 3, \ldots \end{gathered}\]\[\alpha = \frac{\mathrm{d}\ln R}{\mathrm{d}\ln T}\]\[t_{\mathrm{echo}} = 2\tau\]\[F_P = \frac{3}{4\pi^{2}}\left(\frac{\lambda}{n}\right)^{3}\frac{Q}{V}\]\[M \propto \Omega\]
23. Quantum Physics Vol. 2 Pixel Sticker Sheet – 12 Physics StickersPaper products \[v = \frac{E}{B}\]\[G = \delta^{N} \;\Rightarrow\; \ln G = N\ln\delta\]\[\mu_B = \frac{e\hbar}{2m_e} = 9.274\,010\,0657(29)\times10^{-24}\ \mathrm{J/T}\]\[I = e f\]\[\Phi_0 = \frac{h}{2e} \approx 2.067\,833\,848\times10^{-15}\ \mathrm{Wb}\]\[p + {}^{7}\mathrm{Li} \rightarrow 2\,\alpha + 17.3\ \mathrm{MeV}\]\[t_{\mathrm{exposure}} \approx 2000\ \mathrm{h}\]\[m_{\bar{X}} = m_X,\quad \tau_{\bar{X}} = \tau_X\]\[I_{\mathrm{peak}} \propto N^{2}\]\[\Delta B \approx \frac{\hbar}{g\,\mu_B\,\tau}\]\[\Delta E = \tfrac{3}{2}\,n\,(n_1 - n_2)\,e\,a_0\,F\]\[E_{KLL} \approx E_K - E_{L} - E_{L}\]
24. Quantum Physics Vol. 3 Pixel Sticker Sheet – 11 Physics StickersPaper products \[\frac{N_0}{N} = 1 - \left(\frac{T}{T_c}\right)^{3/2}\quad(T\le T_c)\]\[a_0 = \frac{4\pi\varepsilon_0\hbar^{2}}{m_e e^{2}} = 5.291\,772\,105\,44(82)\times10^{-11}\ \mathrm{m}\]\[\mu = \frac{m_p}{m_e} = 1836.152\,673\,426(32)\]\[V(\phi) = -\mu^2|\phi|^2 + \lambda|\phi|^4\]\[\sin^{2}\theta_W \approx 0.231\ \ (\overline{\mathrm{MS}},\ \mu = M_Z),\quad e = g\sin\theta_W\]\[d = \frac{\lambda}{2}\]\[\frac{F}{A} = -\frac{\pi^2\hbar c}{240\,d^4}\]\[P_1 = \cos^{2}\tfrac{\varphi}{2},\ P_2 = \sin^{2}\tfrac{\varphi}{2}\ (\text{with splitter});\quad P_1 = P_2 = \tfrac{1}{2}\ (\text{without})\]\[F_z = \mu_z\,\frac{\partial B_z}{\partial z}\]\[\begin{aligned} R(2\pi)\,\psi &= e^{-i\,2\pi\,\hat{n}\cdot\boldsymbol{\sigma}/2}\,\psi \\ &= -\psi \end{aligned}\]
25. Quarkbinders – Quantum Chromodynamics / Strong Nuclear Force Physics T-ShirtT-Shirt \[\lvert B\rangle \propto \varepsilon_{ijk}\,\lvert q^{i} q^{j} q^{k}\rangle\]\[\alpha_s(Q^{2}) \approx \frac{12\pi}{(33 - 2n_f)\ln\!\left(Q^{2}/\Lambda_{\text{QCD}}^{2}\right)}\]
26. Quavo & Lia – The Entangled Twins / Quantum Connection Physics T-ShirtT-Shirt \[\lvert\Psi^{-}\rangle = \tfrac{1}{\sqrt{2}}\left(\lvert\uparrow\downarrow\rangle - \lvert\downarrow\uparrow\rangle\right)\]\[\rho_B = \operatorname{Tr}_A\lvert\Psi^{-}\rangle\langle\Psi^{-}\rvert = \tfrac{1}{2}\mathbb{1}\]
27. Quenchard, the Superconducting Duke MugMug \[T < T_c(B): \ \rho = 0, \qquad T_c(\text{NbTi}, B = 0) \approx 9.2\ \text{K}\]\[E = \tfrac{1}{2} L I^{2}\]
28. Radicane, the Square-Root Gambler MugMug \[\sigma_N = \sqrt{N}\]\[\frac{\sigma_N}{N} = \frac{1}{\sqrt{N}}\]
29. Reflexia – The Nonlocal Mirror / Quantum Nonlocality Physics T-ShirtT-Shirt \[S = E(a,b) - E(a,b^{\prime}) + E(a^{\prime},b) + E(a^{\prime},b^{\prime})\]\[\lvert S\rvert \le 2 \ (\text{local}), \qquad \lvert S\rvert \le 2\sqrt{2} \ (\text{quantum})\]\[E(a,b) = -\cos(\theta_a - \theta_b) \ (\text{singlet})\]
30. Refracta – Fermat’s Principle / Snell’s Law Physics StickerPaper products \[\frac{\sin\theta_1}{v_1} = \frac{\sin\theta_2}{v_2}\]\[n_1\sin\theta_1 = n_2\sin\theta_2,\qquad n = c/v\]\[\delta\!\int n\,ds = 0\]
31. Relativity & Cosmos Pixel Sticker Sheet – 11 Physics StickersPaper products \[\mathcal{E} = v B L\]\[\theta \approx \frac{v}{c} \approx 20.5''\]\[L(t) \approx \left[1 + \tfrac{2}{5}\left(1 - \frac{t}{t_\odot}\right)\right]^{-1} L_\odot\]\[h \approx \frac{\Delta L}{L}\]\[Y_p \simeq \frac{2\,(n/p)}{1 + n/p}\]\[T(z) = T_0\,(1+z)\]\[\frac{\Delta f}{f} \approx \frac{\Delta\Phi}{c^2} - \frac{v^2}{2c^2}\]\[\tau = 0\]\[\Delta\alpha = \frac{2\omega D}{c}\]\[\Delta t = \gamma\,\tau, \qquad L = \frac{L_0}{\gamma}\]
32. Relicta – Cosmic Microwave Background / Relic Blackbody Physics StickerPaper products \[T(z) = T_0\,(1+z)\]\[T_0 = 2.72548\ \text{K}\]\[B_\nu(T) = \frac{2h\nu^3}{c^2}\,\frac{1}{e^{h\nu/k_B T}-1}\]\[\nu_{\text{peak}} \approx 160\ \text{GHz}\]
33. Remanenza, the Hysteresis Countess MugMug \[W = \oint H \, dB\]
34. Revolvix – Spinor Rotation / The 720° Return Physics StickerPaper products \[\begin{aligned} R(2\pi)\,\psi &= e^{-i\,2\pi\,\hat{n}\cdot\boldsymbol{\sigma}/2}\,\psi \\ &= -\psi \end{aligned}\]\[R(4\pi)\,\psi = +\psi\]
35. Richard Feynman Sticker – Quantum? It’s Complicated. | Physics StickerPaper products \[K(b,a) = \sum_{\text{paths}} e^{iS[x(t)]/\hbar}\]\[P = \left\lvert\sum_k \phi_k\right\rvert^{2}\]
36. Rimehold, the Supercooled Sentinel MugMug \[J = J_0\, e^{-\Delta G^{*}/k_B T}\]\[\Delta G^{*} = \frac{16\pi\gamma^{3}}{3\,\Delta g_v^{2}}\]
37. Rimstain, the Coffee-Ring Mapmaker MugMug \[J(r) \propto (R^{2} - r^{2})^{-\lambda}, \qquad \lambda = \frac{\pi - 2\theta_c}{2\pi - 2\theta_c}\]
38. Ringward, the High-Q Bellkeeper MugMug \[Q = \frac{\omega_0}{\Delta\omega}\]\[E(t) \propto e^{-\omega_0 t / Q}\]
39. Roentgenor – X Marks the Unknown Physics T-ShirtT-Shirt \[E = \frac{hc}{\lambda}\]\[\lambda_{\text{min}} = \frac{hc}{eV}\]
40. Saltara – Hydraulic Jump / Froude Number Physics StickerPaper products \[\mathrm{Fr} = \frac{v}{\sqrt{g h}}\]\[\frac{h_2}{h_1} = \frac{1}{2}\left(\sqrt{1 + 8\,\mathrm{Fr}_1^2} - 1\right)\]
41. Satyendra Nath Bose Sticker – Particle Guy. Major Stats. | Physics StickerPaper products \[\bar n(\varepsilon) = \frac{1}{e^{(\varepsilon-\mu)/(k_B T)} - 1}\]
42. Scatterina – Rayleigh Scattering / Why the Sky Is Blue Physics StickerPaper products \[I_s \propto \frac{1}{\lambda^4}\]\[\frac{I_s(450\,\mathrm{nm})}{I_s(700\,\mathrm{nm})} = \left(\frac{700}{450}\right)^4 \approx 5.9\]
43. Secantha, the Setting-Target Huntress MugMug \[X \approx \sec z \quad (z \lesssim 60^\circ)\]
44. Secundar, the Second Referee MugMug \[\mathbf{A} \to \mathbf{A} + \nabla\chi, \qquad \phi \to \phi - \frac{\partial \chi}{\partial t}\]
45. Siderelle, the Four-Minute Ghost MugMug \[\frac{1}{T_{\text{sid}}} = \frac{1}{T_{\text{sol}}} + \frac{1}{T_{\text{yr}}}\]\[T_{\text{sid}} \approx 23\ \text{h}\ 56\ \text{min}\ 4.09\ \text{s}\]
46. Sigmarel, the Five-Sigma Gatekeeper MugMug \[Z = \Phi^{-1}(1 - p)\]\[Z = 5 \;\Rightarrow\; p \approx 2.87 \times 10^{-7}\]
47. Slithera, the Parallactic Serpent MugMug \[R \approx (n - 1)\tan z\]\[\Delta R = (n_{\lambda_1} - n_{\lambda_2})\tan z\]
48. Sloshwyn, the Coffee-Walker MugMug \[\omega_{mn}^{2} = \frac{g\,\xi_{mn}}{R}\tanh\!\left(\frac{\xi_{mn} H}{R}\right), \qquad \xi_{11} \approx 1.841\]
49. Solitaren, the Mean-Free-Path Hermit MugMug \[\lambda = \frac{k_B T}{\sqrt{2}\,\pi d^{2} p}\]\[\lambda_{\text{air}} \approx \frac{6.6 \times 10^{-3}\ \text{cm}}{p\,[\text{mbar}]}\]
50. Sortex – Maxwell’s Demon / Landauer Erasure Physics StickerPaper products \[Q_{\text{erase}} \ge k_B T \ln 2\]\[k_B T \ln 2 \approx 2.87\times10^{-21}\ \text{J}\]\[(T = 300\ \text{K, per bit})\]
51. Spaghetta – Black Hole Physics / Spaghettification Stretch Physics T-ShirtT-Shirt \[\Delta a \approx \frac{2GM\,L}{r^{3}}\]\[r_s = \frac{2GM}{c^{2}}\]
52. Specklorn, the Pointer-Speckle Phantom MugMug \[C = \frac{\sigma_I}{\langle I \rangle} = 1\]
53. Spinwell – Angular Momentum Physics StickerPaper products \[L = I\omega\]\[I_1\omega_1 = I_2\omega_2\quad(\tau=0)\]
54. Sponara – Hertha Sponer and the Birge–Sponer Method Pixel HoodieHoodie \[G(v) = \omega_e\left(v + \tfrac{1}{2}\right) - \omega_e x_e\left(v + \tfrac{1}{2}\right)^{2}\]\[\Delta G\!\left(v + \tfrac{1}{2}\right) = G(v+1) - G(v) = \omega_e - 2\,\omega_e x_e\,(v + 1)\]\[D_0 = \sum_{v=0}^{v_{\max}} \Delta G\!\left(v + \tfrac{1}{2}\right)\]
55. Stairohm – Quantum Hall Effect / Resistance Plateaus Physics StickerPaper products \[\begin{gathered} R_{xy} = \frac{h}{\nu e^2} = \frac{R_K}{\nu} \\ \nu = 1, 2, 3, \ldots \end{gathered}\]\[\begin{aligned} R_K &= \frac{h}{e^2} \\ &= 25\,812.807\,45\ldots\ \Omega \end{aligned}\]\[R_{xx} = 0\ \text{on a plateau}\]
56. Stellar Core – Nuclear Fusion Physics T-ShirtT-Shirt \[4\,{}^{1}\mathrm{H} \to {}^{4}\mathrm{He} + 2e^{+} + 2\nu_e\]\[Q = \left(4m_p + 2m_e - m_\alpha\right)c^{2} \approx 26.73\ \text{MeV}\]
57. Stephen Hawking Sticker – Black Holes? Been There, Bent That. | Physics StickerPaper products \[T_H = \frac{\hbar c^{3}}{8\pi G M k_B}\]\[S_{BH} = \frac{k_B c^{3} A}{4G\hbar}\]
58. Stratalat, the Layered Latte Sage MugMug \[\rho = \rho_0\,(1 - \alpha\,\Delta T + \beta\,\Delta S)\]\[R_\rho = \frac{\alpha\,\Delta T}{\beta\,\Delta S}\]
59. Streakwin, the Cosmic-Ray Interloper MugMug \[I \approx 1\ \text{cm}^{-2}\,\text{min}^{-1} \quad \text{(horizontal detector, sea level)}\]\[I(\theta) \propto \cos^{2}\theta, \qquad I_v \approx 70\ \text{m}^{-2}\,\text{s}^{-1}\,\text{sr}^{-1}\]
60. Sublimora, the Freeze-Dry Mage MugMug \[p < p_{\text{tp}} = 611.657\ \text{Pa} \;\Rightarrow\; \text{ice} \to \text{vapour}\]
61. Subrahmanyan Chandrasekhar Sticker – No Seconds. | Physics StickerPaper products \[\begin{aligned} M_{\text{Ch}} &= \frac{\omega_3^{0}\sqrt{3\pi}}{2}\left(\frac{\hbar c}{G}\right)^{3/2} \\ &\quad\times\frac{1}{(\mu_e m_H)^{2}} \\ &\approx \frac{5.73}{\mu_e^{2}}\,M_\odot \end{aligned}\]\[\begin{gathered} \mu_e = 2\ (\text{carbon/oxygen}) \\ \Rightarrow\; M_{\text{Ch}} \approx 1.43\,M_\odot \\ (\text{usually quoted as } 1.44) \end{gathered}\]\[\begin{gathered} \mu_e = 2.5\ (\text{assumed in 1931}) \\ \Rightarrow\; M_{\text{Ch}} \approx 0.91\,M_\odot \end{gathered}\]
62. Summitbrew, the High-Altitude Brewer MugMug \[\frac{dp}{dT} = \frac{L}{T\,\Delta v} \approx \frac{L\,p}{R_w T^{2}}\]\[p \approx 61\ \text{kPa} \;\Rightarrow\; T_{\text{sat}} \approx 86\ ^\circ\text{C}\]
63. Superfluid – Quantum Fluid at Near Absolute Zero Physics T-ShirtT-Shirt \[v_c = \min_{p}\frac{\varepsilon(p)}{p}\]\[\oint \vec v_s\cdot d\vec\ell = n\,\frac{h}{m_4}\]
64. Superlumen, the Phase-Velocity Courier MugMug \[v_p = \frac{\omega}{k} = \frac{c}{n}\]\[v_g = \frac{d\omega}{dk} = \frac{c}{n + \omega\,\dfrac{dn}{d\omega}}\]
65. Surgelle, the Full-Moon Thief MugMug \[B(g) = \frac{B_0}{1 + \tan(g/2)/h}\]
66. Tallywick, the Dark-Count Lamplighter MugMug \[J = A T^{2} e^{-W/kT}\]
67. Taulock, the Critical-Point Sleeper MugMug \[\tau \propto \xi^{z}\]
68. Tepidora, the Zeroth-Law Ghost MugMug \[T_A = T_C \ \wedge\ T_B = T_C \;\Rightarrow\; T_A = T_B\]
69. Terminara – Terminal Velocity Physics StickerPaper products \[m\frac{dv}{dt} = mg - \tfrac12\rho C_d A\,v^2\]\[v_t = \sqrt{\frac{2mg}{\rho C_d A}}\]\[v(t) = v_t\tanh\!\left(\frac{g t}{v_t}\right)\]
70. The Silence Beyond – Cosmic Horizon / Observable Limit Physics T-ShirtT-Shirt \[d_{p}(t_0) = a(t_0)\int_{0}^{t_0}\frac{c\,dt}{a(t)}\]
71. The Spark Herald – Electromagnetism / Lightning Command Physics T-ShirtT-Shirt \[\nabla\cdot\vec E = \frac{\rho}{\varepsilon_0}\]\[\nabla\cdot\vec B = 0\]\[\nabla\times\vec E = -\frac{\partial\vec B}{\partial t}\]\[\nabla\times\vec B = \mu_0\vec J + \mu_0\varepsilon_0\frac{\partial\vec E}{\partial t}\]\[c = \frac{1}{\sqrt{\mu_0\varepsilon_0}}\]\[\vec S = \frac{1}{\mu_0}\,\vec E\times\vec B\]
72. Thermal Mirage – Heat Refraction / Optical Distortion Physics T-ShirtT-Shirt \[n\cos\alpha = \text{constant}\quad\text{(stratified air)}\]\[n - 1 = K\rho \propto \frac{p}{T},\qquad n - 1 \approx 2.9\times10^{-4}\ \text{at STP}\]\[\alpha_{\max} \approx \sqrt{2\,\Delta n} \approx 0.4^{\circ}\ \text{for}\ \Delta T \approx 30\ \mathrm{K}\]
73. Thermican, the Slow Bolometer Monk MugMug \[\tau = \frac{C}{G}\]\[\Delta T = \Delta T_0\, e^{-t/\tau}\]
74. Thermodynamics Pixel Sticker Sheet – 12 Physics StickersPaper products \[x_3(T \to 0) \approx 6.4\text{–}6.6\,\%\]\[P \propto \exp\!\left(\frac{\Delta S}{k_B}\right)\]\[\langle V^{2}\rangle = 4 k_B T R\,\Delta f\]\[V = S\,\Delta T\]\[\frac{1}{T} = \frac{\partial S}{\partial E} < 0\]\[W = J\,Q\]\[r_{\mathrm{fwd}} \propto e^{-\varepsilon/k_B T_1},\ r_{\mathrm{back}} \propto e^{-\varepsilon/k_B T_2} \;\Rightarrow\; T_1 = T_2:\ \langle W\rangle = 0\]\[\gamma = \frac{4\pi^{2} m V}{A^{2} p\,T^{2}}\]\[Q_{\text{erase}} \ge k_B T \ln 2\]\[\rho_{\mathrm{N_2}}^{\mathrm{air}} \approx 1.005\,\rho_{\mathrm{N_2}}^{\mathrm{chem}}\]\[c^{2} = \frac{\gamma k_B T}{m}\]
75. Theta Warden – Strong CP Problem Physics T-ShirtT-Shirt \[\mathcal{L}_\theta = \bar\theta\,\frac{g_s^{2}}{32\pi^{2}}\,G^{a}_{\mu\nu}\tilde G^{a\,\mu\nu}\]\[\bar\theta = \theta - \arg\det M_q\]\[d_n \sim 10^{-16}\,\bar\theta\ e\,\text{cm}\]
76. Trialsworn, the Look-Elsewhere Seer MugMug \[p_{\text{global}} \approx p_{\text{local}} + \langle N(c_0) \rangle\, e^{-(c - c_0)/2}\]
77. Truncalis, the Divergent-Series Oracle MugMug \[n_{\text{opt}} \sim \frac{1}{\alpha} \approx 137\]
78. Turbulorn, the Seeing Wraith MugMug \[r_0 \propto \lambda^{6/5}\]
79. Twinkelle, the Point-Source Dancer MugMug \[\sigma_I^{2} = \frac{\langle I^{2} \rangle}{\langle I \rangle^{2}} - 1\]
80. Unruh Effect TeeT-Shirt \[T = \frac{\hbar a}{2\pi c k_B} \approx 4.06\times10^{-21}\ \mathrm{K}\times\frac{a}{1\ \mathrm{m\,s^{-2}}}\]\[x^{2} - c^{2}t^{2} = \left(\frac{c^{2}}{a}\right)^{2}\]
81. Vaporelle, the Latent Spirit MugMug \[Q = m c \,\Delta T\]\[Q = m L_v\]
82. Vera Rubin Sticker – Galaxy Rotation? She Saw the Dark Side. | Physics StickerPaper products \[v(r)^{2} = \frac{G M(r)}{r}\]\[v(r) \approx \text{const} \;\Rightarrow\; M(r) \propto r\]
83. Vevette – Higgs Field / Vacuum Expectation Value Physics StickerPaper products \[V(\phi) = -\mu^2|\phi|^2 + \lambda|\phi|^4\]\[\begin{gathered} \langle\phi\rangle = \frac{v}{\sqrt{2}} \\ v = (\sqrt{2}\,G_F)^{-1/2} \end{gathered}\]\[v \approx 246\ \text{GeV}\]\[m_f = \frac{y_f\,v}{\sqrt{2}}\]
84. Vitressa, the Arrested Glassblower MugMug \[\tau = \tau_0\, e^{B/(T - T_0)}\]
85. Void Whisperer – Dark Energy Expansion Physics T-ShirtT-Shirt \[\rho_\Lambda = \frac{\Lambda c^{2}}{8\pi G} \approx 6\times10^{-27}\ \mathrm{kg\,m^{-3}} \approx (2.2\ \mathrm{meV})^{4}\quad(\hbar = c = 1)\]\[\Lambda = \frac{3\,\Omega_\Lambda H_0^{2}}{c^{2}} \approx 1.1\times10^{-52}\ \mathrm{m^{-2}},\qquad w = \frac{p}{\rho c^{2}} = -1\]\[\rho_{\mathrm{vac}}^{\mathrm{naive}} \sim \bar M_{\mathrm{Pl}}^{4} \sim 10^{73}\ \mathrm{GeV^{4}}\quad\text{vs}\quad \rho_\Lambda \sim 10^{-47}\ \mathrm{GeV^{4}}\]
86. Voidcask, the Vacuum-Flask Guardian MugMug \[q = \frac{\sigma\,(T_h^{4} - T_c^{4})}{1/\varepsilon_1 + 1/\varepsilon_2 - 1}\]
87. Vortessa – Kármán Vortex Street / Strouhal Shedding Physics StickerPaper products \[f = \mathrm{St}\,\frac{U}{D}, \qquad \mathrm{St} \approx 0.2\]\[\mathrm{Re} = \frac{U D}{\nu}\]\[\frac{h}{a} \approx 0.281\]
88. W-ZED – Weak Nuclear Force / Boson Carrier Physics T-ShirtT-Shirt \[M_W = M_Z\cos\theta_W \quad (\text{tree level})\]\[\frac{G_F}{\sqrt{2}} = \frac{g^{2}}{8M_W^{2}} \quad (\hbar = c = 1)\]\[R \sim \frac{\hbar}{M_W c} \approx 2.5\times10^{-18}\ \text{m}\]
89. Waistwyn, the Gaussian Archer MugMug \[z_R = \frac{\pi w_0^{2}}{\lambda}\]\[w(z_R) = \sqrt{2}\, w_0\]
90. Weird Quantum Pixel Sticker Sheet – 12 Physics StickersPaper products \[\begin{aligned} R(2\pi)\,\psi &= e^{-i\,2\pi\,\hat{n}\cdot\boldsymbol{\sigma}/2}\,\psi \\ &= -\psi \end{aligned}\]\[F_z = \mu_z\,\frac{\partial B_z}{\partial z}\]\[\frac{F}{A} = -\frac{\pi^2\hbar c}{240\,d^4}\]\[P_1 = \cos^{2}\tfrac{\varphi}{2},\ P_2 = \sin^{2}\tfrac{\varphi}{2}\ (\text{with splitter});\quad P_1 = P_2 = \tfrac{1}{2}\ (\text{without})\]\[d = \frac{\lambda}{2}\]\[t_{\mathrm{exposure}} \approx 2000\ \mathrm{h}\]\[\frac{N_0}{N} = 1 - \left(\frac{T}{T_c}\right)^{3/2}\quad(T\le T_c)\]\[\frac{1}{T} = \frac{\partial S}{\partial E} < 0\]\[\mathbf{B}_{\text{inside}} = 0\]\[\gamma = -\tfrac{1}{2}\,\Omega\]\[I_{\mathrm{peak}} \propto N^{2}\]\[\psi(1,2)=\frac1{\sqrt2}\bigl[\phi_a(1)\phi_b(2)-\phi_a(2)\phi_b(1)\bigr]\]
91. Wolfgang Pauli Sticker – One Per State | Physics StickerPaper products \[\psi(1,2)=\frac1{\sqrt2}\bigl[\phi_a(1)\phi_b(2)-\phi_a(2)\phi_b(1)\bigr]\]\[\psi\equiv 0\quad\text{when }a=b\]
92. Women in Physics Pixel Sticker Sheet – 9 Physics StickersPaper products \[Q = \left(M_{\text{initial}} - M_{\text{final}}\right)c^{2}\]\[N(t) = N_0 e^{-\lambda t}\]\[{}^{60}\mathrm{Co} \to {}^{60}\mathrm{Ni}^{*} + e^{-} + \bar\nu_e\]\[\bar\rho \gtrsim \frac{3\pi}{G P^{2}}\]\[v(r)^{2} = \frac{G M(r)}{r}\]\[Q = \sum_i \frac{\partial L}{\partial \dot q_i}\,\delta q_i\]\[\begin{aligned} \frac{n_{i+1}\,n_e}{n_i} &= \frac{2}{\Lambda^{3}}\,\frac{g_{i+1}}{g_i} \\ &\quad\times\exp\!\left(-\frac{\chi_i}{k_B T}\right) \\ \Lambda &= \frac{h}{\sqrt{2\pi m_e k_B T}} \end{aligned}\]\[\begin{gathered} E_k = \tfrac{1}{2} m v^{2} \\ (\text{vis viva: } m v^{2}) \end{gathered}\]\[\begin{gathered} E_N = \hbar\omega\left(N + \tfrac{3}{2}\right) \\ \begin{aligned} g_N &= (N+1)(N+2) \\ &= 2,\,6,\,12,\,\ldots \end{aligned} \\ \Rightarrow\; \text{shells close at } 2,\,8,\,20 \end{gathered}\]
93. Zeno – Quantum Zeno Effect / The Observer Physics T-ShirtT-Shirt \[P_{\text{stay}}(t) \approx 1 - \left(\frac{t}{\tau_Z}\right)^{2}, \qquad \tau_Z = \frac{\hbar}{\Delta H}\]\[P_{1\to 2}(n) = \tfrac{1}{2}\left[1 - \cos^{n}\!\left(\tfrac{\pi}{n}\right)\right]\]
94. Δ-X – The Heisenberg Runner / Uncertainty Principle Physics T-ShirtT-Shirt \[\sigma_x\,\sigma_k \ge \tfrac{1}{2}, \qquad p = \hbar k \;\Rightarrow\; \sigma_x\sigma_p \ge \tfrac{\hbar}{2}\]