Taken from Experimental Techniques in Modern High-Energy Physics: by Hanagaki, Tanaka, Tomoto, Yamazaki Why? Two basic categories of HEP experiments Find any new particle by converting collision energy to particles Done through finding resonances in the final state Investigate the nature of a particular interaction Done through precise measurements of other physical observables In theory, you work with a small number of states to keep problems tractable. Experimentally, you can get thousands of final states which you have to parse through The number of particles goes as $ln \sqrt{s}$ where s is the square of the center of mass energy of the collision This the angular density to go up, which create “jets” (ie....

Notes adapted from MIT Digital Electronics Lab Also from here Boolean Algebra Theorems Truth Tables Specific Functions 1-Bit Functions 2-bit Functions XOR Overview Verilog Basics Variables Parameters Operators and Loops Enums Syntax Oddities Combinational Logic Continuous Assignment Procedural Assignment Glitches! Gotchas Nesting Modules Combinational Versus Sequential Logic Latches Characteristic Equations Registers Verilog for Sequential Blocks Sequential Always Blocking and Non-Blocking Assignment External Signals (Metastability) FSMs FSM State Encoding Converting to Verilog Clocks PLLS The Treachery of Clocks Skew Jitter Proper usage Timing Timing Parameters Slack Video Black and White TV Color TV VGA HDMI Memory History of Memory Key parameters of memory FPGA SRAM Fabric Case Studies Off FPGA Memory EPROM Family DRAM Buffering DRAM FSM Modularization Pipelining Math Complexity Division CORDIC AXI AXI Signals Signed Number DSP48 CRCs Polynomial Arithmetic Boolean Algebra Theorems Let all variables be boolean in nature (ie....

Notes taken while reading “The Art of Electronics”. I realized that my electronics knowledge is a bit spotty and more theoretically inclined, hence why I’m doing this. The Basics, Because You Have to Start Somewhere Resistors Resistor Rule’s of Thumb Voltage Dividers Thevenin Equivalence Misc Use Cases Capacitors Common Applications RC Time Constants Frequency Filters Differentiators Integrators Inductors Applications Voltage Converters Transformers Diodes Applications Rectifiers Dual Rail Power Supply Voltage Multipliers Biasing Logic Gates Clamps Limiters Logarithm Inductive Kickback Transistors (BJTs) BJTs (Bipolar Junction Transistors) Transistor Switches and Saturation Switching From High Pulse Generator Schmitt Trigger Impedences of Sources and Loads Emitter Follower Emitter Follower Biasing Case Study Canceling Offset Transistor Current Sources Common-emitter Amplifier Unity Gain Phase Splitter Phase Shifter Transconductance Ebers-Moll equation Rules of thumb Emitter Follower Redux Bias Stability Current Mirrors The Basics, Because You Have to Start Somewhere There are two quantities that we care about with circuits: Voltage and Current...

Logistics Principle of “Least” Action Symmetries Gauge Invariance Example Reduce to Quadratures Hamiltonian Mechanics Phase Portraits Poisson Brackets Properties Jacobi Proof Sketch Poisson’s theorem Canonical Transformations Why We Care Liouville’s Theorem Canonical Invariants Entropy Tangent Infinitesimal CTs Hamiltonian Noether’s Theorem Hamilton Jacobi Equation Action Variables Multiperiodic motion Planetary motion Liouville’s Integrability Theorem Cannonical Peturbation Theory Adiabatic Motion Quantum Mach Zender Hilbert Space Linear Algebra Review Time Evolution Heisenberg Formulation Compatible Observables Symmetries Uncertainty Relationship Phase Space Interpretation Entanglement And Mixed States Mixed States Von Neumann Entropy Partial Trace (“Tracing Out”) Infinite Spaces Translation Operator Scattering Probability Current Delta Function Path Integral Free Particle Saddle Point Approximation Path Integral Proof WKB Logistics Matthew Klebon klebon@nyu....

An introduction to databases. Logistics Intro Data Models Database Design Phases Bad Design ER Model Drawing ER Diagrams SQL (Structed Query Language) SQL Schema SQL Query Anatomy SELECT and FROM WHERE AS keyword String Operations LIKE ORDER BY Set Operations UNION INTERSECT EXPECT Null Values Aggregation GROUP BY HAVING Nested Subqueries Subquery tests for WHERE Subquery test for FROM DELETE, INSERT, UPDATE DELETE INSERT UPDATE JOINS Natural/Inner Joins Outer Joins Views Integrity Constraints Authorization Privileges Roles Object-relational Databases Complex Types User Defined Types Inheritance Textual Data Big Data Streaming Data Physical Storage Types Interfaces Magnetic Disks Flash RAID RAID Levels Indexing Ordered Indices B+ Tree Hash Indices Transactions Scheduling Query Processing Parsing Optimization Evaluation Relational Algebra Building Execution graph Query Cost Relational Algebra Implementations Selection Sorting Joins Duplicate elimination Projection Set Operations Implementation Outer Join Aggregations Evaluating Expressions Pipelining Logistics Course link...

An introduction to solid state physics. Logistics Heat Capacity of Solids Einstein Model of Heat Capacity of Solids Debye Model of Heat Capacity of Solids Electrical Properties (Drude Model) Constant E&M Force Thermal Conductivity Sommerfield Model Fermi-Dirac Statistics Sommerfield Model (cont.) LCAO (Linear Combination of Atomic Orbitals)/ Tight Binding Theory Chemistry Review Shell Theory Ionic Bonds Covalent Bonds LCAO Basics Vibrations 2 Types of Springs Crystal Structure Reciprocal Space Logistics Location: 307 Pupin Time: 2:40-3:55 PM Tuesdays and Thursdays Textbook: The Oxford Solid State Basics Grading Scheme 30% problem sets (5 in total....

An introduction to plasma physics. Logistics Grading Scheme MHD Equillibrium Consequences of MHD Equillibrium Theta Pinch Z Pinch Screw Pinch Toroidal Geometry Definitions Forces Grad Shafranov Equation Stream Functions Grad Shafranov Derivation Sketch Aspect Ratio Expansion Logistics Location: Mudd 825 Time: 1:10-2:40 Book: MHD Stability of Tokamaks by Zohm Grading Scheme Projects: 60% Homework: 40% MHD Equillibrium Suprisingly useful since particles in plasma undergo gyration, which enhances number of collisions and causes discrete particle to behave more fluid-like Setting time derivatives in MHD equations to zero This is a good assumption, since deviations from this result in motion with timescales on the order of microseconds (called the Alfven time $\tau_{A}$) Hence, if you are physically observe the plasma, good chance it is in EQ $\vec{v} = 0$ is the magneto-static limit (or that $v« v_{a}$) where $v_{a}$ is the Alfven speed (which in turn is defined as size of detector divided by $\tau_{a}$) In space, the magneto-static approximation is normally not valid Define the plasma beta as $\beta = \frac{p}{\frac{B^{2}}{2\mu}}$ or the thermal energy divided by the magnetic field energy Equation of state $P = n_{e}T_{e}+n_{i}T_{i}$ Momentum equation: $\rho(\frac{\partial}{\partial t}\vec{v}+\vec{v}\nabla\cdot \vec{v}) = \vec{J}\times B =\nabla P$ Maxwell’s equations $\nabla \times \vec{B} = \mu_{0}\vec{J}$ $\nabla \cdot B = 0$ $v \times B +E =0 \rightarrow E = 0$ $\frac{\partial }{\partial t} B = -\nabla \times E \rightarrow \frac{\partial }{\partial t} B =0$ Continuity $\frac{\partial}{\partial t}\rho + \nabla \cdot v = 0$ 0=0 Energy $\frac{\partial}{\partial t}P+\vec{v}\cdot\nabla p -c_{s}^{2}(\frac{\partial}{\partial t}\rho + \vec{v}\cdot \nabla \rho) = 0$ To Summarize, for MHD equilibrium, we have that...

Logistics Conventions Newtonian Gravity The Two Body Problem Kepler’s Second Law Kepler’s Third Law From Kepler To Newton The Equivalence Principle Gravitational Redshift Light falls Differential Geometry Definitions/Basics Crash Course Example 2-Sphere Special Relativity Minkowski Spacetime Diagrams Metric Useful Tricks 4-Vectors 4-velocity Dual Vectors 4-momentum Inverse Metric Variational Approach Moving to GR Christoffel Symbols We haven’t done GR yet. Let’s do that Qausi-Stationary Curved or not Curved Tensors General Covariance Useful facts Scalar Field Transformation Vector Field Transformation Dual Vector Transformation Stress-Energy Tensor $T^{\mu\nu}$ Dust Covariant Derivatives Properties of Covariant Derivatives Tidal Forces of Curvature Newtonian GR version Directional Covariant Derivative Reimannian tensor Reimannian Tensor properties Parallel Transport Stress Energy Tensor Conservation EM Force Law Einstein’s Equation What the Heck is $\kappa$?...

Ohm’s Law Drude Model Flux Maxwell’s Equations Mutual Inductance Self Inductance Energy in Fields Maxwell’s Equation in Matter Electric Magnetic Boundary Conditions Continuity Equations Charge Energy Momentum Angular Momentum Waves Basic Waves Polarization EM Waves Reflection and Transmission Absorption and Dispersion Absorption Dispersion Wave Guides Potentials Gauge Freedom Coulomb Gauge Lorenz gauge Leinard-Weichart Potentials Radiation Dipoles Point Charges Ohm’s Law $\vec{J} = \sigma (\vec{E}+v\times \vec{B}) \approx \sigma \vec{E}$ $J$ is the current density $\sigma$ is the conductivity $\vec{E}$ is the electric field Microscopic description typically, the velocities are so slow that we can drop the magnetic field term $\vec{I} = \int \vec{J}\cdot \vec{dA}$...

Grading Breakdown Heat Equation Steady state solutions Time Dependent Solution Seperation of Variables Laplace Equation Polar Coordinates Mean Value Property Maximum Principle Fourier Series Convergence Term by Term Differentiation Solving Inhomogeneous Equations Wave Equation Strum Liouville Theory SL properties Green’s Identity Minimization Principle Parseval’s Identity Bessel’s Identity Multi-Dimensional PDEs Green’s Identity (Higher Dimensions) Polar Coordinates Bessel’s equation Fourier Transforms Green’s Functions Heat Equation Case Study Dirac Delta Green’s Function via Differential Equation Nonhomogeneous BCs Green’s Function via Eigenvalue Expansion Fredholm Alternative Grading Breakdown HW: 40% Assigned on Monday weekly....