13,179 research outputs found
Aerothermodynamic environment of a Titan aerocapture vehicle
The extent of convective and radiative heating for a Titan aerocapture vehicle is investigated. The flow in the shock layer is assumed to be axisymmetric, steady, viscous, and compressible. It is further assumed that the gas is in chemical and local thermodynamic equilibrium and tangent slab approximation is used for the radiative transport. The effect of the slip boundary conditions on the body surface and at the shock wave are included in the analysis of high-altitude entry conditions. The implicit finite difference techniques is used to solve the viscous shock-layer equations for a 45 degree sphere cone at zero angle of attack. Different compositions for the Titan atmosphere are assumed, and results are obtained for the entry conditions specified by the Jet Propulsion Laboratory
Characteristic matrices for linear periodic delay differential equations
Szalai et al. (SIAM J. on Sci. Comp. 28(4), 2006) gave a general construction
for characteristic matrices for systems of linear delay-differential equations
with periodic coefficients. First, we show that matrices constructed in this
way can have a discrete set of poles in the complex plane, which may possibly
obstruct their use when determining the stability of the linear system. Then we
modify and generalize the original construction such that the poles get pushed
into a small neighborhood of the origin of the complex plane.Comment: 17 pages, 1 figur
Twisted and Nontwisted Bifurcations Induced by Diffusion
We discuss a diffusively perturbed predator-prey system. Freedman and
Wolkowicz showed that the corresponding ODE can have a periodic solution that
bifurcates from a homoclinic loop. When the diffusion coefficients are large,
this solution represents a stable, spatially homogeneous time-periodic solution
of the PDE. We show that when the diffusion coefficients become small, the
spatially homogeneous periodic solution becomes unstable and bifurcates into
spatially nonhomogeneous periodic solutions.
The nature of the bifurcation is determined by the twistedness of an
equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients
decrease. In the nontwisted case two spatially nonhomogeneous simple periodic
solutions of equal period are generated, while in the twisted case a unique
spatially nonhomogeneous double periodic solution is generated through
period-doubling.
Key Words: Reaction-diffusion equations; predator-prey systems; homoclinic
bifurcations; periodic solutions.Comment: 42 pages in a tar.gz file. Use ``latex2e twisted.tex'' on the tex
files. Hard copy of figures available on request from
[email protected]
Anomalous kinetics of attractive reactions
We investigate the kinetics of reaction with the local attractive
interaction between opposite species in one spatial dimension. The attractive
interaction leads to isotropic diffusions inside segregated single species
domains, and accelerates the reactions of opposite species at the domain
boundaries. At equal initial densities of and , we analytically and
numerically show that the density of particles (), the size of domains
(), the distance between the closest neighbor of same species
(), and the distance between adjacent opposite species ()
scale in time as , , and respectively. These dynamical exponents form a new
universality class distinguished from the class of uniformly driven systems of
hard-core particles.Comment: 4 pages, 4 figure
The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions
We show that for two dimensional manifolds M with negative Euler
characteristic there exists subsets of the space of smooth Riemannian metrics
which are invariant and either parabolic or backwards-parabolic for the 2nd
order RG flow. We also show that solutions exists globally on these sets.
Finally, we establish the existence of an eternal solution that has both a UV
and IR limit, and passes through regions where the flow is parabolic and
backwards-parabolic
The Resonance Peak in SrRuO: Signature of Spin Triplet Pairing
We study the dynamical spin susceptibility, , in the
normal and superconducting state of SrRuO. In the normal state, we find
a peak in the vicinity of in agreement with
recent inelastic neutron scattering (INS) experiments. We predict that for spin
triplet pairing in the superconducting state a {\it resonance peak} appears in
the out-of-plane component of , but is absent in the in-plane component.
In contrast, no resonance peak is expected for spin singlet pairing.Comment: 4 pages, 4 figures, final versio
Deterministic Brownian motion generated from differential delay equations
This paper addresses the question of how Brownian-like motion can arise from
the solution of a deterministic differential delay equation. To study this we
analytically study the bifurcation properties of an apparently simple
differential delay equation and then numerically investigate the probabilistic
properties of chaotic solutions of the same equation. Our results show that
solutions of the deterministic equation with randomly selected initial
conditions display a Gaussian-like density for long time, but the densities are
supported on an interval of finite measure. Using these chaotic solutions as
velocities, we are able to produce Brownian-like motions, which show
statistical properties akin to those of a classical Brownian motion over both
short and long time scales. Several conjectures are formulated for the
probabilistic properties of the solution of the differential delay equation.
Numerical studies suggest that these conjectures could be "universal" for
similar types of "chaotic" dynamics, but we have been unable to prove this.Comment: 15 pages, 13 figure
Kundt spacetimes as solutions of topologically massive gravity
We obtain new solutions of topologically massive gravity. We find the general
Kundt solutions, which in three dimensions are spacetimes admitting an
expansion-free null geodesic congruence. The solutions are generically of
algebraic type II, but special cases are types III, N or D. Those of type D are
the known spacelike-squashed AdS_3 solutions, and of type N are the known AdS
pp-waves or new solutions. Those of types II and III are the first known
solutions of these algebraic types. We present explicitly the Kundt solutions
that are CSI spacetimes, for which all scalar polynomial curvature invariants
are constant, whereas for the general case we reduce the field equations to a
series of ordinary differential equations. The CSI solutions of types II and
III are deformations of spacelike-squashed AdS_3 and the round AdS_3,
respectively.Comment: 30 pages. This material has come from splitting v1 of arXiv:0906.3559
into 2 separate papers. v2: minor changes
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