Keywords: Phase Transitions (6)

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Atomistic Computer Modeling of Materials (SMA 5107), Spring 2005

Atomistic Computer Modeling of Materials (SMA 5107), Spring 2005

This course uses the theory and application of atomistic computer simulations to ... (more)

This course uses the theory and application of atomistic computer simulations to model, understand, and predict the properties of real materials. Specific topics include: energy models from classical potentials to first-principles approaches; density functional theory and the total-energy pseudopotential method; errors and accuracy of quantitative predictions: thermodynamic ensembles, Monte Carlo sampling and molecular dynamics simulations; free energy and phase transitions; fluctuations and transport properties; and coarse-graining approaches and mesoscale models. The course employs case studies from industrial applications of advanced materials to nanotechnology. Several laboratories will give students direct experience with simulations of classical force fields, electronic-structure approaches, molecular dynamics, and Monte Carlo. (less)

Subject:
Science and Technology
Material Type:
Activities and Labs
Case Study
Full Course
Lecture Notes
Syllabi
Video Lectures
Collection:
MIT OpenCourseWare
Provider:
M.I.T.
Author:
Ceder, Gerbrand
Marzari, Nicola
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Materials at Equilibrium (SMA 5111), Fall 2003

Materials at Equilibrium (SMA 5111), Fall 2003

Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical ... (more)

Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical systems, solutions, and phase diagrams. Computation of phase diagrams. Statistical thermodynamics and relation between microscopic and macroscopic properties, including ensembles, gases, crystal lattices, phase transitions. Applications to phase stability and properties of mixtures. Computational modeling. Interfaces. (less)

Subject:
Science and Technology
Material Type:
Activities and Labs
Assessments
Full Course
Homework and Assignments
Syllabi
Collection:
MIT OpenCourseWare
Provider:
M.I.T.
Author:
Ceder, Gerbrand
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Networks, Fall 2009

Networks, Fall 2009

" Networks are ubiquitous in our modern society. The World Wide Web ... (more)

" Networks are ubiquitous in our modern society. The World Wide Web that links us to and enables information flows with the rest of the world is the most visible example. It is, however, only one of many networks within which we are situated. Our social life is organized around networks of friends and colleagues. These networks determine our information, influence our opinions, and shape our political attitudes. They also link us, often through important but weak ties, to everybody else in the United States and in the world. Economic and financial markets also look much more like networks than anonymous marketplaces. Firms interact with the same suppliers and customers and use Web-like supply chains. Financial linkages, both among banks and between consumers, companies and banks, also form a network over which funds flow and risks are shared. Systemic risk in financial markets often results from the counterparty risks created within this financial network. Food chains, interacting biological systems and the spread and containment of epidemics are some of the other natural and social phenomena that exhibit a marked networked structure. This course will introduce the tools for the study of networks. It will show how certain common principles permeate the functioning of these diverse networks and how the same issues related to robustness, fragility, and interlinkages arise in several different types of networks." (less)

Subject:
Science and Technology
Social Sciences
Material Type:
Activities and Labs
Assessments
Full Course
Homework and Assignments
Lecture Notes
Collection:
MIT OpenCourseWare
Provider:
M.I.T.
Author:
Acemoglu, Daron
Ozdaglar, Asu
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Phase Transitions in the Earth's Interior, Spring 2005

Phase Transitions in the Earth's Interior, Spring 2005

This course discusses phase transitions in Earth's interior. Phase transitions in Earth ... (more)

This course discusses phase transitions in Earth's interior. Phase transitions in Earth materials at high pressures and temperatures cause the seismic discontinuities and affect the convections in the Earth's interior. On the other hand, they enable us to constrain temperature and chemical compositions in the Earth's interior. However, among many known phase transitions in mineral physics, only a few have been investigated in seismology and geodynamics. This course reviews important papers about phase transitions in mantle and core materials. (less)

Subject:
Science and Technology
Material Type:
Full Course
Homework and Assignments
Syllabi
Collection:
MIT OpenCourseWare
Provider:
M.I.T.
Author:
Shim, Sang-heon
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Statistical Mechanics II:  Statistical Physics of Fields, Spring 2008

Statistical Mechanics II: Statistical Physics of Fields, Spring 2008

A two-semester course on statistical mechanics. Basic principles are examined in 8.333: ... (more)

A two-semester course on statistical mechanics. Basic principles are examined in 8.333: the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Postulates of classical statistical mechanics, microcanonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose systems. Interacting systems: cluster expansions, van der Waal's gas, and mean-field theory. Topics from modern statistical mechanics are explored in 8.334: the hydrodynamic limit and classical field theories. Phase transitions and broken symmetries: universality, correlation functions, and scaling theory. The renormalization approach to collective phenomena. Dynamic critical behavior. Random systems. (less)

Subject:
Science and Technology
Material Type:
Activities and Labs
Assessments
Full Course
Homework and Assignments
Lecture Notes
Syllabi
Collection:
MIT OpenCourseWare
Provider:
M.I.T.
Author:
Kardar, Mehran
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Symmetry Breaking on a Rotating Hoop

Symmetry Breaking on a Rotating Hoop

The Rotating Hoop Launcher package shows the dynamics of a mass that ... (more)

The Rotating Hoop Launcher package shows the dynamics of a mass that is constrained to move on a rotating hoop. The rotating hoop model is an excellent mechanical model of first- and second-order phase transitions. Although the minimum of the potential energy curve corresponds to the bottom of the hoop at low rotation frequency, a spontaneous symmetry breaking (cusp catastrophe) occurs as the frequency is increased. This package presents the theory, a demonstration, and an Easy Java Simulation (EJS) of this experiment. The package was presented at the NC Section of the AAPT Spring 2008 meeting. (less)

Subject:
Science and Technology
Material Type:
Activities and Labs
Simulations
Collection:
Open Source Physics
Provider:
comPADRE
Read the Fine Print
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Subject:
Science and Technology
Material Type:
Assessments
Full Course
Homework and Assignments
Lecture Notes
Syllabi
Collection:
MIT OpenCourseWare
Provider:
M.I.T.
Author:
George Kocur
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