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2.57 Midterm Exam No. 1
November 2, 2004 * Mass of one proton : 1.67 10-27 kg. You should remember other constants needed. 1. Answer the following ten short questions. Briefly explain your answer (60 Points). (1) Estimate the average velocity of h
2.57 Nano-to-Macro Transport Processes Fall 2004 Lecture 24 In the last lecture, we have talked about Einstein's work on the Brownian motion.
Stoke's flow P(x) P(x+dx)
F = 3 Du
In the left figure above, pressure difference exists in the fluid. For one par
2.57 Nano-to-Macro Transport Processes Fall 2004 Lecture 23 In the last lecture, we talked about the energy flux along a thin film as 1 qx = fvx
= . V k x k y k z
y vy vy v vx v vx
d
x
vz
Temperature Gradient Or Electrical Field
(a)
(b)
Now let us cons
2.57 Nano-to-Macro Transport Processes Fall 2004 Lecture 8 In the last lecture, we have talked about the primitive unit cell. There is only one lattice point (equivalently speaking) per primitive unit cell. The smallest space formed by all the bisecting p
2.57 Nano-to-Macro Transport Processes Fall 2004 Lecture 7 In the last lecture, we have talked about atoms in a one-dimensional chain. We find the solution as u j = A exp[-i(t - kja)],
where the frequency is = 2
K ka sin . m 2
Na
(j-1)a ja (j+1)a
Note: Wh
2.57 Nano-to-Macro Transport Processes Fall 2004 Lecture 6 Quick review of Lecture 5 In the last lecture, we approximate the potential field as rectangular wells in the crystal. From periodicity, the Bloch theorem gives additional equations [ x + (a + b)n
2.57 Nano-to-Macro Transport Processes Fall 2004 Lecture 5 Quick review of Lecture 4 1. Free particles The energy can be any values determined by the wavelength. (h / ) 2 = 2
k 2 = E = p 2 / 2m = ; k = 2 / , = = h / 2
2m 2m
2. Quantum well ENERGY AND WAV
2.57 Nano-to-Macro Transport Processes Fall 2004 Lecture 4 Quick review of Lecture 3 Photon: E = h , p = h / . Assuming t(r,t)=(r)Y(t), we use separation of variables to solve the Schrdinger equation 2 t - 2 t + Ut = i . 2m t The solutions are E Y = C1 ex
2.57 Nano-to-Macro Transport Processes Fall 2004 Lecture 3 8. Micro & Nanoscale Phenomena 8.1 Classical size effects In section 7, the characteristic length of the box is much longer than the mean free path . Therefore, the collisions between molecules an
2.57 Nano-to-Macro Transport Processes Fall 2004 Lecture 2 5.1 Heat conduction
Th
Tc
In last lecture, we describe electrons as free electron gas and lattice vibrations as phonon gas. Basically they are both gases in a box. 5.2 Convection 1) Typically elec
2.57 Nano-to-Macro Transport Processes Fall 2004 Lecture 1 1. Overview for nano sciences 1.1 Length scale 1.2 Examples in microtechnology 1.3 Examples in nanotechnology 1.4 Nano for energy (phonon, phonon, electron; wavelength, mean free path) 1.5 Nanosca
2.57 HOMEWORK 9 Due: 2:30 pm, Wednesday November 17, 2004
Problem 1. Read the following paper and write a one page report. Hicks, L.D. and Dresselhaus, M.S., 1993, "Effect of Quantum-Well Structures on the Thermoelectric Figure of Merit," Physical Review
2.57 HOMEWORK 8 Due: 2:30 pm, Wednesday November 10, 2004
Problem 1. Read one of the following two papers and write a one page report. Schwab, K., Henriksen, E.A., Worlock, J.M., and Roukes, M.L., "Measurement of the Quantum of Thermal Conductance," Natur
2.57 HOMEWORK 7 Due: 2:30 pm, Wednesday October 27, 2004
Problem 1. Read the following paper and write a one page report. Little, W.A., "The Transport of Heat between Dissimilar Solids at Low Temperatures," Canadian Journal of Physics, Vol. 37, pp. 334-34
2.57 HOMEWORK 6 Due: 2:30 pm, Wednesday October 20, 2004
Problem 1. Read one out of the following two papers and write a one page report. 1. Lin, M.F., Shung, W.W.K., "Electronic Specific Heat of Single-Walled Carbon Nanotubes," Physical Review B, Vol. 54
2.57 HOMEWORK 5 Due: 2:30 pm, Wednesday October 13, 2004
Problem 1. Read and write a one page report on the following paper. R. Saito, M. Fujita, G. Dresselhaus, and M.S. Dresselhaus, "Electronic Structure of Chiral Graphene Tubules," Applied Physics Lett
2.57 HOMEWORK 4 Due: 2:30 pm, Wednesday October 6, 2004
Problem 1. Read and write a one page report on the following paper. Yablonovitch, E., "Inihibited Spontaneous Emission in Solid-State Physics and Electronics," Physics Review Letters, Vol. 58, pp. 20
2.57 HOMEWORK 3 Due: 2:30 pm, Wednesday September 29, 2004
Problem 1. Read and write a one page report on the following paper (this paper is often considered as the starting point for artificial quantum structures). L. Esaki and R. Tsu, "Superlattice and
2.57 HOMEWORK 2 Due: 2:30 pm, Wednesday September 15, 2004
Problem 1. Read and write a one page report on Einstein's paper. I am interested in reading your comments on Einstein's thought process. "On a Heuristic Point of View Concerning the Production and
Unusual Photon Tunneling Caused by Negative Refraction Qing Hao Department of Mechanical Engineering Massachusetts Institute of Technology Abstract In recent years, tremendous efforts have been devoted to a class of novel metamaterials, left-handed materi
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2.57 Midterm Exam No. 2 Fall, 2004
Take Home Exam Distributed: Friday, November 19, 7:00 pm Due: November 24, 2:30 pm Four questions, each counts for 25 points Rules: (1) You are required to finish these problems independently, without consultatio
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2.57 Midterm Exam No. 1 Fall, 2002
1. Answer the following ten short questions. Briefly explain your answer (60 Points). (1) Diamond has an fcc structure with a lattice constant (conventional unit cell) of 3.57 , calculate the density of diamond.
2.57 Project Report
December 10 2004
Modeling Transport Mechanism in Nanofluids
Jacob Eapen Department of Nuclear Engineering, MIT
Abstract Nanofluid connotes a colloidal suspension with dispersed nano-sized particles. Experiments in the past decade revea
Journal of Nano-to-Macro Energy Transport (JNET), December 2004
Modeling a MEMS Thermal Conductivity Pressure Sensor for the Evaluation of Glass Frit Vacuum Packaging
Kerry Cheung Department of Electrical Engineering and Computer Science Massachusetts Ins