31 research outputs found
-Strands
A -strand is a map for a Lie
group that follows from Hamilton's principle for a certain class of
-invariant Lagrangians. The SO(3)-strand is the -strand version of the
rigid body equation and it may be regarded physically as a continuous spin
chain. Here, -strand dynamics for ellipsoidal rotations is derived as
an Euler-Poincar\'e system for a certain class of variations and recast as a
Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as
for a perfect complex fluid. For a special Hamiltonian, the -strand is
mapped into a completely integrable generalization of the classical chiral
model for the SO(3)-strand. Analogous results are obtained for the
-strand. The -strand is the -strand version of the
Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical
sorting. Numerical solutions show nonlinear interactions of coherent wave-like
solutions in both cases. -strand equations on the
diffeomorphism group are also introduced and shown
to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc
On the Evolution Equation for Magnetic Geodesics
In this paper we prove the existence of long time solutions for the parabolic
equation for closed magnetic geodesics.Comment: In this paper we prove the existence of long time solutions for the
parabolic equation for closed magnetic geodesic
Phase Change Materials in Energy: Current State of Research and Potential Applications
© 2020, Springer Science+Business Media, LLC, part of Springer Nature. Recent research on phase change materials promising to reduce energy losses in industrial and domestic heating/air-conditioning systems is reviewed. In particular, the challenges q fphase change material applications such as an encapsulation strategy for active ingredients, the stability of the obtained phase change materials, and emerging corrosion complications are discussed. Moreover, phase change materials could be employed in refrigerators to increase the efficiency and in storage facilities to reduce evaporative losses of fuels and industrial liquid products. Promising areas for using these materials are highlighted. Ways of solving possible problems are outlined