All ETDs from UAB

Advisory Committee Chair

Ryoichi Kawai

Advisory Committee Members

Renato Camata

Gary Cheng

Joseph Harrison

James Patterson

Document Type

Dissertation

Date of Award

2015

Degree Name by School

Doctor of Philosophy (PhD) College of Arts and Sciences

Abstract

When a mesoscopic object (Brownian object) is inserted into a fluid, it is subject to frequent collisions with fluid molecules (environment). Through these collisions, energy is exchanged between the environment and the Brownian object. When the Brownian particle and its environment are in thermal equilibrium, the net energy exchange will be zero due to the detailed balance and fluctuation-dissipation theorem, and the Brownian object will diffuse without net drift. However, when the environment is in non-equilibrium, the detailed balance no longer holds and the Brownian object can undergo drift. The mechanism responsible for its drift is not well understood. In this thesis, the adiabatic piston and several Brownian motors are investigated which exhibit drift when the environment is in non-equilibrium. These models are theoretically investigated using the concept of Momentum Deficit due to Dissipation (MDD), and with molecular dynamics simulation. When the Brownian object is simultaneously in contact with two heat baths at the different temperatures. This heat exchange can be explained at the level of Langevin theory and stochastic energetics, but there is a class of non-equilibrium phenomona, including the adiabatic piston and Brownian motors, which cannot be explained by Langevin theory. In recent work by Fruleux, Kawai, and Sekimoto [Phys. Rev. Lett. 108 (2012), 160601] a force that acts on a Brownian object in a non-equilibrium environment was discovered. This force, whose magnitude is proportional to heat flux, is due to a momentum deficit associated with dissipation. This concept unambiguously explains the motion of the adiabatic piston and Brownian motors. It is the goal of the present thesis to test the validity of the concept of MDD through investigation of several simple models including the adiabatic piston and Brownian motors. We introduce a new setting for the adiabatic piston where thermal baths are included in the system without the use of an artificial thermostat. This new model also keeps the fluid pressure constant to ensure that the hydrodynamic effects are correctly taken into account. Results show that as heat flows from the hot bath to the cold, through a Brownian object, momentum also flows, but in the opposite direction.

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