22,048 research outputs found
In Situ Formation and Dynamical Evolution of Hot Jupiter Systems
Hot Jupiters, giant extrasolar planets with orbital periods shorter than ~10
days, have long been thought to form at large radial distances, only to
subsequently experience long-range inward migration. Here, we propose that in
contrast with this picture, a substantial fraction of the hot Jupiter
population formed in situ via the core accretion process. We show that under
conditions appropriate to the inner regions of protoplanetary disks, rapid gas
accretion can be initiated by Super-Earth type planets, comprising 10-20 Earth
masses of refractory composition material. An in situ formation scenario leads
to testable consequences, including the expectation that hot Jupiters should
frequently be accompanied by additional low-mass planets with periods shorter
than ~100 days. Our calculations further demonstrate that dynamical
interactions during the early stages of planetary systems' lifetimes should
increase the inclinations of such companions, rendering transits rare.
High-precision radial velocity monitoring provides the best prospect for their
detection.Comment: 19 pages, 10 figures, accepted to Ap
Soft-pulse dynamical decoupling in a cavity
Dynamical decoupling is a coherent control technique where the intrinsic and
extrinsic couplings of a quantum system are effectively averaged out by
application of specially designed driving fields (refocusing pulse sequences).
This entails pumping energy into the system, which can be especially dangerous
when it has sharp spectral features like a cavity mode close to resonance. In
this work we show that such an effect can be avoided with properly constructed
refocusing sequences. To this end we construct the average Hamiltonian
expansion for the system evolution operator associated with a single ``soft''
pi-pulse. To second order in the pulse duration, we characterize a symmetric
pulse shape by three parameters, two of which can be turned to zero by shaping.
We express the effective Hamiltonians for several pulse sequences in terms of
these parameters, and use the results to analyze the structure of error
operators for controlled Jaynes-Cummings Hamiltonian. When errors are cancelled
to second order, numerical simulations show excellent qubit fidelity with
strongly-suppressed oscillator heating.Comment: 9pages, 5eps figure
Theoretical studies of the kinetics of mechanical unfolding of cross-linked polymer chains and their implications for single molecule pulling experiments
We have used kinetic Monte Carlo simulations to study the kinetics of
unfolding of cross-linked polymer chains under mechanical loading. As the ends
of a chain are pulled apart, the force transmitted by each crosslink increases
until it ruptures. The stochastic crosslink rupture process is assumed to be
governed by first order kinetics with a rate that depends exponentially on the
transmitted force. We have performed random searches to identify optimal
crosslink configurations whose unfolding requires a large applied force
(measure of strength) and/or large dissipated energy (measure of toughness). We
found that such optimal chains always involve cross-links arranged to form
parallel strands. The location of those optimal strands generally depends on
the loading rate. Optimal chains with a small number of cross-links were found
to be almost as strong and tough as optimal chains with a large number of
cross-links. Furthermore, optimality of chains with a small number of
cross-links can be easily destroyed by adding cross-links at random. The
present findings are relevant for the interpretation of single molecule force
probe spectroscopy studies of the mechanical unfolding of load-bearing
proteins, whose native topology often involves parallel strand arrangements
similar to the optimal configurations identified in the study
Curvature Corrections to Dynamics of Domain Walls
The most usual procedure for deriving curvature corrections to effective
actions for topological defects is subjected to a critical reappraisal. A
logically unjustified step (leading to overdetermination) is identified and
rectified, taking the standard domain wall case as an illustrative example.
Using the appropriately corrected procedure, we obtain a new exact (analytic)
expression for the corresponding effective action contribution of quadratic
order in the wall width, in terms of the intrinsic Ricci scalar and the
extrinsic curvature scalar . The result is proportional to with the
coefficient given by . The resulting form of the ensuing dynamical
equations is obtained in terms of the second fundamental form and the
Dalembertian of its trace, K. It is argued that this does not invalidate the
physical conclusions obtained from the "zero rigidity" ansatz used in
previous work.Comment: 19 pages plain TeX, 2 figures include
Time-stepping approach for solving upper-bound problems: Application to two-dimensional Rayleigh-Benard convection
An alternative computational procedure for numerically solving a class of variational problems arising from rigorous upper-bound analysis of forced-dissipative infinite-dimensional nonlinear dynamical systems, including the Navier-Stokes and Oberbeck-Boussinesq equations, is analyzed and applied to Rayleigh-Benard convection. A proof that the only steady state to which this numerical algorithm can converge is the required global optimal of the relevant variational problem is given for three canonical flow configurations. In contrast with most other numerical schemes for computing the optimal bounds on transported quantities (e.g., heat or momentum) within the "background field" variational framework, which employ variants of Newton's method and hence require very accurate initial iterates, the new computational method is easy to implement and, crucially, does not require numerical continuation. The algorithm is used to determine the optimal background-method bound on the heat transport enhancement factor, i.e., the Nusselt number (Nu), as a function of the Rayleigh number (Ra), Prandtl number (Pr), and domain aspect ratio L in two-dimensional Rayleigh-Benard convection between stress-free isothermal boundaries (Rayleigh's original 1916 model of convection). The result of the computation is significant because analyses, laboratory experiments, and numerical simulations have suggested a range of exponents alpha and beta in the presumed Nu similar to (PrRa beta)-Ra-alpha scaling relation. The computations clearly show that for Ra <= 10(10) at fixed L = 2 root 2, Nu <= 0.106Pr(0)Ra(5/12), which indicates that molecular transport cannot generally be neglected in the "ultimate" high-Ra regime.NSF DMS-0928098 DMS-1515161 DMS-0927587 PHY-1205219Simons FoundationNSFONRInstitute for Computational Engineering and Sciences (ICES
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