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Energy Matters, November/December 1999
Energy Matters is an Office of Industrial Technologies bimonthly publication on energy efficiency opportunities. This issue's focus is on the future of industrial energy efficiency. The issue also contains articles on seven companies that are to receive cost-shared funding for plant-wide, energy efficiency assessments; submitting proposals to assess energy flow and steam system opportunities; partnering to save energy and money; and root cause failure analysis on AC induction motors. Also a special feature by Don Casada ''Lights that Shine Forever.'
Thermodynamical Consistent Modeling and Analysis of Nematic Liquid Crystal Flows
The general Ericksen-Leslie system for the flow of nematic liquid crystals is
reconsidered in the non-isothermal case aiming for thermodynamically consistent
models. The non-isothermal model is then investigated analytically. A fairly
complete dynamic theory is developed by analyzing these systems as quasilinear
parabolic evolution equations in an -setting. First, the existence of
a unique, local strong solution is proved. It is then shown that this solution
extends to a global strong solution provided the initial data are close to an
equilibrium or the solution is eventually bounded in the natural norm of the
underlying state space. In these cases, the solution converges exponentially to
an equilibrium in the natural state manifold
Covariant Balance Laws in Continua with Microstructure
The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of
energy method to continua with microstructure. The key idea is to replace the
group of Galilean transformations with the group of diffeomorphisms of the
ambient space. A key advantage is that one obtains in a natural way all the
needed balance laws on both the macro and micro levels along with two
Doyle-Erickson formulas
Two-phase densification of cohesive granular aggregates
When poured into a container, cohesive granular materials form low-density,
open granular aggregates. If pressed upon with a ram, these aggregates densify
by particle rearrangement. Here we introduce experimental evidence to the
effect that particle rearrangement is a spatially heterogeneous phenomenon,
which occurs in the form of a phase transformation between two configurational
phases of the granular aggregate. We then show that the energy landscape
associated with particle rearrangement is consistent with our interpretation of
the experimental results. Besides affording insight into the physics of the
granular state, our conclusions are relevant to many engineering processes and
natural phenomena.Comment: 7 pages, 3 figure
Global Weak Solutions to a General Liquid Crystals System
We prove the global existence of finite energy weak solutions to the general
liquid crystals system. The problem is studied in bounded domain of with
Dirichlet boundary conditions and the whole space
Asymptotic Behavior for a Nematic Liquid Crystal Model with Different Kinematic Transport Properties
We study the asymptotic behavior of global solutions to hydrodynamical
systems modeling the nematic liquid crystal flows under kinematic transports
for molecules of different shapes. The coupling system consists of
Navier-Stokes equations and kinematic transport equations for the molecular
orientations. We prove the convergence of global strong solutions to single
steady states as time tends to infinity as well as estimates on the convergence
rate both in 2D for arbitrary regular initial data and in 3D for certain
particular cases
Blow up criterion for compressible nematic liquid crystal flows in dimension three
In this paper, we consider the short time strong solution to a simplified
hydrodynamic flow modeling the compressible, nematic liquid crystal materials
in dimension three. We establish a criterion for possible breakdown of such
solutions at finite time in terms of the temporal integral of both the maximum
norm of the deformation tensor of velocity gradient and the square of maximum
norm of gradient of liquid crystal director field.Comment: 22 page
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