Investigation of the Buttiker-Thomas momentum balance equation from the Heisenberg equation of motion for Bloch electrons

1995 ◽  
Vol 7 (32) ◽  
pp. L429-L434 ◽  
Author(s):  
X L Lei
Author(s):  
I. Campos ◽  
J.L. Jiménez ◽  
M.A. López-Mariño

We present a momentum balance equation derived directly from Maxwell's equations. This equation contains a force density, which we call Maxwell's force density, which generalizes the Lorentz force density, now including total fields rather than only external fields, and arbitrary charge and current distributions. As a test for this balance equation we derive for gases the electrostatic and magnetostatic Helmholtz force densities. This deduction will be useful for advanced undergraduates and graduate students, as well as for specialists interested in the conceptual aspects of electromagnetism.


1991 ◽  
Vol 15 ◽  
pp. 63-72
Author(s):  
Robert S. Pritchard

The mechanical energy balance of sea ice provides information about ice dynamic behavior, driving forces and the constitutive law. The energy balance equation, formed as the product of ice velocity with the ice momentum balance equation, describes changes to the kinetic and potential energy densities as power is input to the ice by wind and current. The momentum balance equation may also be used to describe the ice-stress divergence, air stress, and water stress, but the scalar form of the energy balance is simpler to understand. This paper provides new interpretations of several terms in the energy balance equation, in particular power input by air and water stress and by sea-surface tilt. Barometric pressure fields and drifting buoys deployed on the Chukchi Sea ice cover during 1982 provide wind, ice motion and current measurements that allow each term in the energy balance equation to be evaluated as a function of time. Magnitudes of power input by wind and current show how the energy balance is decomposed and help describe the relative importance of these driving forces. In the nearshore Chukchi Sea during February, March and April 1982, both wind and current provided significant forcing of the ice. Ice stress was also important and, at times, dominated other terms in the mechanical energy balance.


1986 ◽  
Vol 1 (20) ◽  
pp. 73 ◽  
Author(s):  
Steven K. Baum ◽  
David R. Basco

A numerical model is developed which calculates the longshore current profile for an arbitrary bottom profile. The basis of the model is the use of radiation stress theory in a longshore momentum balance equation which includes a driving stress, a bottom stress, and a lateral mixing stress. Each of the stresses is derived from previously developed formulations, rederiving them to take into account separate cross shore variations in the wave height and the water depth, as well as the wave approach angle. This is done to dispense with the constant wave breaking index assumption used to model wave decay in the surf zone, which is rejected as unrealistic for natural beaches. A numerical model is used to calculate distributions of the wave height and water depth across the surf zone for arbitrary, yet realistic, bottom profiles. A numerical model of the theoretically derived longshore momentum balance equation is developed and solved using the distributions obtained from the wave decay model. The profiles calculated are compared to previous theoretical models and to laboratory and field measurements.


1991 ◽  
Vol 15 ◽  
pp. 63-72
Author(s):  
Robert S. Pritchard

The mechanical energy balance of sea ice provides information about ice dynamic behavior, driving forces and the constitutive law. The energy balance equation, formed as the product of ice velocity with the ice momentum balance equation, describes changes to the kinetic and potential energy densities as power is input to the ice by wind and current. The momentum balance equation may also be used to describe the ice-stress divergence, air stress, and water stress, but the scalar form of the energy balance is simpler to understand. This paper provides new interpretations of several terms in the energy balance equation, in particular power input by air and water stress and by sea-surface tilt. Barometric pressure fields and drifting buoys deployed on the Chukchi Sea ice cover during 1982 provide wind, ice motion and current measurements that allow each term in the energy balance equation to be evaluated as a function of time. Magnitudes of power input by wind and current show how the energy balance is decomposed and help describe the relative importance of these driving forces. In the nearshore Chukchi Sea during February, March and April 1982, both wind and current provided significant forcing of the ice. Ice stress was also important and, at times, dominated other terms in the mechanical energy balance.


2009 ◽  
Vol 2009.58 (0) ◽  
pp. 231-232
Author(s):  
Takaaki NISHIZUKA ◽  
Yoshihiro INOUE ◽  
Shintaro YAMASHITA ◽  
Haruhisa YANO

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