Taken from here Why Parallelism? A parallel computer is a collection of compute modules which work together to perform a task efficiently In principle, more processors means more power However, a major bottleneck is communication speed Think of a room of people working together on a calculation. Information needs to travel between them for them to cooperate efficiently. Better communication == faster results If communication takes longer than the task at hand, then the upsides of parallelism go away Some processors might have easier tasks than others, or are more efficient than other nodes....

Symmetries Of Hamiltonians Imagine we have some Hamiltonian Symmetries which preserve the inner product are Unitary and Anti-Unitary Time-reversal Reverses momenta/spins and keeps position the same $TQT^{-1} = Q$ $TPT^{-1} = P$ $U_{T}^{\dag} H^{*} U_{T} = H$ Think of this as a conjugation operator K, then some unitary operator $T = U_{T}K$ Ie. it’s anti-unitary Quick proof: Assume T is unitary. $i\hbar = i\hbar T T^{-1} = T i\hbar T^{-1} = T(QP-PQ)T^{-1} = -i\hbar$ If T is a symmetry of the system, then by Wigner’s theorem, T must be anti-unitary $T^{2} = \pm 1$ Follows from Kramer Degeneracy (even number of fermions +, odd number -) Particle/hole (charge conjugation): $U_{c}^{\dag} H^{*} U_{c} = -H$ $C^{2} = \pm 1$ Sub-lattice/chiral symmetry: $U_{S}^{\dag} H U_{S} = -H$ Think of this as some function of time-reversal and charge conjugation symmetries $U_{S} = U_{C} U_{T}^{*}$ $S^{2} = 1$ This is still a distinct symmetry of the system Standard unitary symmetry: $U^{\dag} H U = H$ Assuming that you have some unitary symmetry U This implies that the structure of the Hamiltonian takes some block diagonal form What the symmetry U is applied, there is no “mixing” between the blocks For much of this class, we will go down to some “irreducible representation” (ie....

Should have written this 2 days ago, but arrived very late back from my folk’s place and forgot to write this up. My bad. I keep punting finishing the Gray-Scott simulation. I found the numpy equivalent library and started chipping away at the PDE solver. I have finals that I need to study for, a 3D general-relativistic hydro code that I need to get done by the semester’s End, and a presentation I have to gets done, but I will manage....

Midterms are happening, so I’ve been pretty swamped recently. Enjoying learning new things, but still swamped. I made a little progress on the Gray-Scott sim (Got the UI down, researched efficient Laplacian algorithms). I have stalled on getting through Baumann and Preskill in light of prioritizing my classes and research. I got a NAS to backup some VMs, sites and photo albums that I have. In terms of extracurriculars, it’s been a slow month, but that’s the way it goes sometimes…

A lot of side projects got put on hold since classes started up again and I have teaching responsibilities, but that’s the way it goes. I’m taking General Relativity (covering exterior calculus and it’s applications to general relativity), High energy astrophysics (talking about how various astrophysical sources are able to produce these high energy photons that all the space missions are observing), and Biophysics (fluid dynamics and statistical mechanics applied to biological systems)....

Cell Overview Plasma Membrane Outer shell of the cell responsible for seperating the cell from the enviornment Regulates transport of nutrients and waste of the cell Consists of a phospholipic bilayer (seperates hydrophobic materials on the interior of the membrane from the aqeous enviornment The heads are hydrophilic, while the tails are hydrophobic Lots of things are embedded in and pierce the bilayer (peripheral proteins, protein channels, Alpha-Helix proteins etc.) The proteins which pierce the membrane can be asymetric (re: inside has one structure, outside has a different structure) Cytoplasm refers to the intracellular content 80% of interior is water consists of cytosol (intracellular fluid) and organelles (internal structures) cytosol is a non-newtonian fluid and is colorless Cytoskeleton Protein filaments in the cytoplasm Holds cellular structure, aids in migration, signalling, and chromosome segregation during cytokinesis There are more specialized cytoskeleton structures: flagella, cilia, filopodia, lammelipodia etc....

Scales Black holes are described by 3 parameters: Mass, spin, and charge In practice, astrophysical black holes have no charge, since they are embedded in a plasma which “shorts out” the hole We can define some characteristic scales of black holes $R_{s} = \frac{2GM}{c^{2}}$ is the Schwartzchild radius $\Delta t_{LC} = \frac{R_{s}}{c}$ is the light crossing time (roughly the time needed to cross the black hole, up to a scale factor) How bright can be a black hole be?...

Following Misner, Wheeler and Thorne. Foundations of General Relativity All laws of physics can be expressed geometrically Local reference frames are flat gravitational mass is equivalent to inertial mass All reference frames are equivalent (re: there is no preferred reference frame) Minimal coupling: work in SR to find physical laws , then go to general frame to include gravity Basic Definitions and Math Things Take naturalized units (c=G=1) when working with GR Events: Things that happen at a particular point in spacetime....

This was a slow month. I was overly ambitious in how quickly I could read Baumann’s Cosmology. Luckily, there is no rush; I’ll try and finish it before the semester ends. I’ll also try and finish Preskill’s notes, but this is less urgent. I tried bumping up the resolution of the camera experiment by storing the raw pixel data in some off-chip DRAM via a gearbox FIFO system. I need to write a testbench, since it’s buggy on the fabric....