New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here


by: Shanel Lubowitz


Shanel Lubowitz
GPA 3.64


Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Class Notes
25 ?




Popular in Course

Popular in Engineering and Tech

This 7 page Class Notes was uploaded by Shanel Lubowitz on Monday October 26, 2015. The Class Notes belongs to ENGR0011 at University of Pittsburgh taught by Staff in Fall. Since its upload, it has received 29 views. For similar materials see /class/229414/engr0011-university-of-pittsburgh in Engineering and Tech at University of Pittsburgh.




Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/26/15
MONTE CARLO Cainuiations Computer can be used like a simple graphing calculator X 1 x2x3 x Using variables and functions can automate complex calculations e x 2 3 n Must be aware of limitations of precision and accuracy Optimization Developing models of real physical data is a critical aspect in Materials Science calculations 2 leY fxacexpbx c Reducing system to a finite number of parameters 39 Quantitative methods to relate model to data Signai Processing Operations on data to convert into something useful g i Interpolation extrapolation m Frequency domain analysis PSD convolution i L Other statistical methods EVERYTHING UNTIL THIS POINT HAS BEEN GENERAL OR ABSTRACTED NOT SPECIFIC TO MATERIALS SCIENCE New approach to modeling random stochastic processes Uses random numbers to simulate a complex system Software packages exist but are not standard offtheshelf SOFI39WARE 0 Design AI AbInitio First principles Monte Carlo Stochastic Finite elements Diff Eq C 3rd PARTY TODAY Symbolic math Curve fitting optimization 1995 Integration Root finding MATHEMATICAMAPLE 1985 Linear algebra MATLAB Statistics Graphing CALC EXCEL 1975 Arithmetic Atomicmolecular fluctuations and motion determine many materials processes Advances in computation continue to allow more realistic complex simulations Timr39 Lime large scale FEMFD largcescnle plasticity elssneny ncsiimnspm Materials science spans many orders of year E m e magnitude in spatial and temporal scale quot 0 ll l 10 O 10 meiaucn models m mdwmmu We must consider the behaVIor of incliViclual Wmlpiassenyncm atoms as well as their collective macro homogrnization methods behaVIor csow 239 a m m s n s a a a 17 mm consistent models in conjunction 0 3 with advanced constitutive laws w 10 in kirictic mullislate Putts models CC bylk Ginzburg Landau ly pe m diffusion and kinetic phase eld a Warm 7 models microscopic g dimmitln j iicld kinetic models a phase eld 5 o dynamics m dislocation dynamics 2 dislocql39nn 10 7 6 3 dynamics 10 topological network and E molccillax vertex models bounderv g dynamics 5 Debye nequency spring models s 15 quot3 H ms 5 b iimc scale molecular dynamics Debye um MelropolisMomeCarlo 0 14 G s local electron density runcricnol lheorv Figure 12 39 39 A iliv L x A minis scienuel MODELING SIMULATION k 0 0 3 g gt39 6f H a 2 lt lt H X x PLASTICITY GRAIN BOUNDARIES Stress strain dislocation generation 39 Many bOdy problem on atomic scale Can measure properties of system macro Cannot make measurements via experiment scale No analytical expressions are available Don t consider positions of individual atoms or disocations Individual atom positions must be considered ATOMISTIC approach MEANFIELD CONTINUUM approach GLOBAL MODEL GLOBAL CONFIGURATION i A LOCAL CONFIGURATION LOCAL BEHAVIOR GAS LIQUID SOLID U numbu of toms In cube pm length nl39oubc System composed of identical atoms large number 1023 in real systems Each atom has 6 degrees of freedom rx ry rz px py pz Each behaves independently and they simultaneously obey classical ENSEMBLE andlor quantum mechanics laws vibrations F ma wrt Local interactions with neighbors collision mechanics energy exchange bonds Covalenrt ionic metallic hydrogen VDW AN ENSEMBLE 1 E exp Obeys certain statistical mechanics laws R Eexp k for example a IeXpE dr 39 ka Can be described in terms of average PARTITION FUNCTION properties N V T E IL Cp P ARTIFICIAL ENSEMBLE SIMULATION If we set up an ensemble of independently acting atoms in the computer Their collective behavior will mimic or simulate the behavior of a real system 1 rs l 1 Set up ensemble of independent trials or s simple laws pecies gt each obeys 2 Run simulation that applies these laws via RANDOM FLUCTUATIONS many times 3 Statistically sample results to get meaningful global information DETERMINI STIC PROCESS STiOiCHASTIC PROCESS eg Classical mechanics heat flow eg Stock market Brownian motion Analytic form of governing laws No analytic form each step is random Single answer determined completely by Startan Statistical characterization of larger structure conditions This is the essence of Monte Carlo modeling Von Neumann 1944 Diffusion in fissile materials 100 gt X 100 Free motion Gas 100 0 x Lattice sites Solid 1 Single atom placed at center 5050 2 Take n random steps record positions 3 Multiple trials will give statistical behavior Mainm initial conditions loop move atom to new spot end plot results calculate statistics Get new position VK FunctionxNew yNew getNewxym pick random direction xNew m yNew m correct for collision with wall end


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Bentley McCaw University of Florida

"I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Kyle Maynard Purdue

"When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the I made $280 on my first study guide!"

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."


"Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.