Lecture

Classical Equations and Conservation Laws

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In course

ME-469: Nano-scale heat transfer

In this course we study heat transfer (and energy conversion) from a microscopic perspective. First we focus on understanding why classical laws (i.e. Fourier Law) are what they are and what are their limits of validity. Next we discuss emerging opportunit ...

Description

This lecture covers the derivation of classical equations, including Newton's equations of motion and the time-dependent Schrodinger equation, to compute the behavior of particles in various systems. It also discusses the conservation equations for dilute gases, electrons, phonons, and hydrodynamic equations. The presentation delves into the concepts of ensembles, partition functions, and the Fermi-Dirac and Bose-Einstein distributions, providing insights into the behavior of particles in different quantum states.

Instructor

Giulia Tagliabue

Dr. Giulia Tagliabue is an Assistant Professor at the Institute of Mechanical Engineering (IGM). She obtained her B.S. and M.S degrees cum laude in Mechanical Engineering from the University of Udine in Italy. Concurrently she also obtained the diploma from the Scuola Normale Superiore of Udine. In 2015 she obtained her PhD in Mechanical Engineering from ETH Zurich with a thesis on nanophotonic design for light-to-heat and light-to-charge conversion devices. In 2015 Dr. Tagliabue was awarded the Early Mobility Fellowship from the Swiss National Science Foundation and moved to Caltech as a PostDoctoral fellow. In 2017, thanks to the award of an Advanced Mobility Fellowship, she prolonged her stay at Caltech. Here, in collaboration with the Joint Center for Artificial Photosynthesis (JCAP) she investigated coupled light, heat and charge transfer processes in nanophotonic structures and low-dimensional materials for photoelectrochemical and photovoltaic sustainable energy conversion.

Official source

Ontological neighbourhood

Physics

Mechanics: Classical mechanics

Thermodynamics: Statistical mechanics

Related concepts (32)

Equations of motion

In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.

Quantum state

In quantum physics, a quantum state is a mathematical entity that embodies the knowledge of a quantum system. Quantum mechanics specifies the construction, evolution, and measurement of a quantum state. The result is a quantum mechanical prediction for the system represented by the state. Knowledge of the quantum state together with the quantum mechanical rules for the system's evolution in time exhausts all that can be known about a quantum system. Quantum states may be defined in different ways for different kinds of systems or problems.

Schrödinger equation

The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. The equation is named after Erwin Schrödinger, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics.

Computer file

In computing, a computer file is a resource for recording data on a computer storage device, primarily identified by its . Just as words can be written on paper, so can data be written to a computer file. Files can be shared with and transferred between computers and mobile devices via removable media, networks, or the Internet. Different are designed for different purposes. A file may be designed to store an , a written message, a video, a program, or any wide variety of other kinds of data.

Newton's laws of motion

Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force. When a body is acted upon by a force, the time rate of change of its momentum equals the force. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

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