Mechanical Waves

Waves.  The wave speed v=\lambda f, \lambda – the wavelength, f – the frequency.

Wave functions and wave dynamics.  The displacement of individual particles in the medium
y(x,t)=A\cos[\omega(\frac xv-t)] (or, more intuitively, y(x,t)=A\cos[\omega(t-\frac xv)])
y(x,t)=A\cos2\pi(\frac x\lambda-\frac tT)
y(x,t)=A\cos(kx-\omega t), where k=\frac{2\pi}\lambda and \omega=2\pi f=vk
Wave function: \frac{\partial^2y(x,t)}{\partial x^2}=\frac1{v^2}\frac{\partial^2y(x,t)}{\partial t^2}


How to Remove Git History

  1. Checkout
    git checkout --orphan latest_branch
  2. Add all the files
    git add -A
  3. Commit the changes
    git commit -am "commit message"
  4. Delete the branch
    git branch -D master
  5. Rename the current branch to master
    git branch -m master
  6. Finally, force update your repository
    git push -f origin master

From here:

Alternating Current

Voltage, current, and phase angle.  In general, the instantaneous voltage v=V\cos(\omega t+\phi) between two points in an ac circuit is not in phase with the instantaneous current i=I\cos\omega t passing through those points.

Resistance and reactance.  The voltage across a resistor is in phase with the current, V_R=IR.  The voltage across an inductor leads the the current by \frac\pi 2, V_L=IX_L, inductive reactance X_L=\omega L.  The voltage across a capacitor lags the the current by \frac\pi 2, V_C=IX_C, capacitive reactance X_C=\frac1{\omega C}.

Impedance and the L-R-C series circuit.  In general ac circuit, the voltage and current amplitutes are related by the circuit impedance Z, V=IZ.  In an L-R-C series circuit, Z=\sqrt{R^2+(\omega L-\frac1{\omega C})^2}, \tan\phi=\frac{\omega L-\frac1{\omega C}}R.

Power in ac circuits.  The average power input to an ac circuit: P_{av}=\frac12VI\cos\phi=V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\phi, where \phi is the phase angle of the voltage relative to the current.  The factor \cos\phi is called the power factor of the circuit.

Resonance angular frequencey.  \omega_0=\frac1{\sqrt{LC}}.

Transformers.  \frac{V_2}{V_1}=\frac{N_2}{N_1}, V_1I_1=V_2I_2.

Mutual Inductance

Mutual inductance.  When a changing current i_1 in one circuit causes a changing magnetic flux in a second circuit, an emf \mathcal{E}_2 is induced in the second circuit.  \mathcal{E}_2=-M\frac{di_1}{dt} and \mathcal{E}_1=-M\frac{di_2}{dt}, M=\frac{N_2\Phi_{B2}}{i_1}=\frac{N_1\Phi_{B1}}{i_2} – mutual inductance, N_1 – number of turns of coil of the first circuit, \Phi_1 – average magnetic flux through each turn of coil 1.

Self-inductance.  A changing current i in any circuit causes a self-induced emf \mathcal{E}=-L\frac{di}{dt}L=\frac{N\Phi_B}i – depends on the geometry of the circuit and the material surrounding it.

Magnetic field energy.  An inductor with inductance L carrying current I has energy U associated with the inductor’s magnetic field: U=\frac12LI^2.  Magnetic energy density: u=\frac{B^2}{2\mu}.

R-L circuits.  In an R-L circuit the growth and decay of current are exponential with time constant \tau=\frac LR.

L-C circuits.  An L-C circuit undergoes electrical oscillations with an angular frequency \omega=\sqrt{\frac1{LC}}.

L-R-C circuits.  The frequency of damped oscillations \omega'=\sqrt{\frac1{LC}-\frac{R^2}{4L^2}}.

Uncharted 4: A Thief’s End

Surprisingly awesome!

No proverbial zombies or substances this time.  Deeper and more likeable characters, who you actually care about – nothing like “The Last of Us” with its intrusive “emotional bond development” crap.  Way better from moral standpoint.  A lot (a lot!) of details.  Very impressive facial expressions.  A real treat for vehicle driving fans.  Incredibly small number of bugs.  I didn’t feel irritated with the gamepad while shooting (like I did playing Uncharted 1-3).

The biggest con I can think of is the traditional (for the Uncharted series) total lack of (perceived) cooperation among opposing NPCs.  Of course, if one of the NPCs sees you, a bunch of others will attack you as well, but they won’t say anything – as if they just communicate telepathically.  Probably a design choice, because there’s already a lot of comments and remarks going on between the player and his allies.

Also, I didn’t particularly like the two ending scenes.  The thing is, all the three Drakes – who we meet in the game (Elena is somehow sill Fischer) – lie to each other, to Elena, and to others, at one point of the game or another.  And only Nathan has to pay for it, and only a little.  And the only guy in the whole game who is actively, seriously not happy about lying is… the villain!  Who dies in a deus-ex-machina way – as usual in the Uncharted series.

P.S. How come Rafe didn’t see Sam at Rossi???

P.P.S. Actually, that’s not the only curious thing about the game.