58,011 research outputs found
Longitudinal control effectiveness and entry dynamics of a single-stage-to-orbit vehicle
The classical theory of flight dynamics for airplane longitudinal stability and control analysis was extended to the case of a hypervelocity reentry vehicle. This includes the elements inherent in supersonic and hypersonic flight such as the influence of the Mach number on aerodynamic characteristics, and the effect of the reaction control system and aerodynamic controls on the trim condition through a wide range of speed. Phugoid motion and angle of attack oscillation for typical cases of cruising flight, ballistic entry, and glide entry are investigated. In each case, closed form solutions for the variations in altitude, flight path angle, speed and angle of attack are obtained. The solutions explicitly display the influence of different regions design parameters and trajectory variables on the stability of the motion
Well-posedness of the Ericksen-Leslie system
In this paper, we prove the local well-posedness of the Ericksen-Leslie
system, and the global well-posednss for small initial data under the physical
constrain condition on the Leslie coefficients, which ensures that the energy
of the system is dissipated. Instead of the Ginzburg-Landau approximation, we
construct an approximate system with the dissipated energy based on a new
formulation of the system.Comment: 16 page
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
Phase Separation of Bismuth Ferrite into Magnetite under Voltage Stressing
Micro-Raman studies show that under ~700 kV/cm of d.c. voltage stressing for
a few seconds, thin-film bismuth ferrite BiFeO3 phase separates into magnetite
Fe3O4. No evidence is found spectroscopically of hemite alpha-Fe2O3, maghemite
gamma-Fe2O3, or of Bi2O3. This relates to the controversy regarding the
magnitude of magnetization in BiFeO3.Comment: 9 pages and 2 figure
Combinatorial Formulae for Vassiliev Invariants from Chern-Simons Gauge Theory
We analyse the perturbative series expansion of the vacuum expectation value
of a Wilson loop in Chern-Simons gauge theory in the temporal gauge. From the
analysis emerges the notion of the kernel of a Vassiliev invariant. The kernel
of a Vassiliev invariant of order n is not a knot invariant, since it depends
on the regular knot projection chosen, but it differs from a Vassiliev
invariant by terms that vanish on knots with n singular crossings. We
conjecture that Vassiliev invariants can be reconstructed from their kernels.
We present the general form of the kernel of a Vassiliev invariant and we
describe the reconstruction of the full primitive Vassiliev invariants at
orders two, three and four. At orders two and three we recover known
combinatorial expressions for these invariants. At order four we present new
combinatorial expressions for the two primitive Vassiliev invariants present at
this order.Comment: 73 pages, latex, epsf, 18 figures, 2 table
Bose-Einstein supersolid phase for a novel type of momentum dependent interaction
A novel class of non-local interactions between bosons is found to favor a
crystalline Bose-Einstein condensation ground state. By using both low energy
effective field theory and variational wavefunction method, we compare this
state not only with the homogeneous superfluid, as has been done previously,
but also with the normal (non-superfluid) crystalline phase and obtain the
phase diagram. The key characters are: the interaction potential displays a
negative minimum at finite momentum which determines the wavevector of this
supersolid phase; and the wavelength corresponding to the momentum minimum
needs to be greater than the mean inter-boson distance.Comment: 4 pages 3 figures, fig 1 and fig 2 update
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