191 research outputs found
A Regularity Result for the Incompressible Magnetohydrodynamics Equations with Free Surface Boundary
We consider the three-dimensional incompressible magnetohydrodynamics (MHD)
equations in a bounded domain with small volume and free moving surface
boundary. We establish a priori estimate for solutions with minimal regularity
assumptions on the initial data in Lagrangian coordinates. In particular, due
to the lack of the Cauchy invariance for MHD equations, the smallness
assumption on the fluid domain is required to compensate a loss of control of
the flow map. Moreover, we show that the magnetic field has certain
regularizing effect which allows us to control the vorticity of the fluid and
that of the magnetic field. To the best of our knowledge this is the first
result that focuses on the low regularity solution for incompressible
free-boundary MHD equations.Comment: Final version, to appear in Nonlinearit
Compressible Gravity-Capillary Water Waves with Vorticity: Local Well-Posedness, Incompressible and Zero-Surface-Tension Limits
We consider 3D compressible isentropic Euler equations describing the motion
of a liquid in an unbounded initial domain with a moving boundary and a fixed
flat bottom at finite depth. The liquid is under the influence of gravity and
surface tension and it is not assumed to be irrotational. We prove the local
well-posedness by introducing carefully-designed approximate equations which
are asymptotically consistent with the a priori energy estimates. The energy
estimates yield no regularity loss and are uniform in Mach number. Also, they
are uniform in surface tension coefficient if the Rayleigh-Taylor sign
condition holds initially. We can thus simultaneously obtain incompressible and
vanishing-surface-tension limits. The method developed in this paper is a
unified and robust hyperbolic approach to free-boundary problems in
compressible Euler equations. It can be applied to some important complex fluid
models as it relies on neither parabolic regularization nor irrotational
assumption. This paper joined with our previous works [46,47] rigorously proves
the local well-posedness and the incompressible limit for a compressible
gravity water wave with or without surface tension.Comment: 63 page
Calculation of the current noise spectrum in mesoscopic transport: an efficient quantum master equation approach
Based on our recent work on quantum transport [Li et al., Phys. Rev. B 71,
205304 (2005)], where the calculation of transport current by means of quantum
master equation was presented, in this paper we show how an efficient
calculation can be performed for the transport noise spectrum. Compared to the
longstanding classical rate equation or the recently proposed quantum
trajectory method, the approach presented in this paper combines their
respective advantages, i.e., it enables us to tackle both the many-body Coulomb
interactionand quantum coherence on equal footing and under a wide range of
setup circumstances. The practical performance and advantages are illustrated
by a number of examples, where besides the known results and new insights
obtained in a transparent manner, we find that this alternative approach is
much simpler than other well-known full quantum mechanical methods such as the
Landauer-B\"uttiker scattering matrix theory and the nonequilibrium Green's
function technique.Comment: 13 pages, 3 figures, submitted to PR
Zero Surface Tension Limit of the Free-Boundary Problem in Incompressible Magnetohydrodynamics
We show that the solution of the free-boundary incompressible ideal
magnetohydrodynamic (MHD) equations with surface tension converges to that of
the free-boundary incompressible ideal MHD equations without surface tension
given the Rayleigh-Taylor sign condition holds true initially. This result is a
continuation of the authors' previous works [17,32,16]. Our proof is based on
the combination of the techniques developed in our previous works [17,32,16],
Alinhac good unknowns, and a crucial anti-symmetric structure on the boundary.Comment: 35 pages. Final version, accepted by Nonlinearity. We extend the
result to the case of a general diffeomorphis
Full counting statistics of renormalized dynamics in open quantum transport system
The internal dynamics of a double quantum dot system is renormalized due to
coupling respectively with transport electrodes and a dissipative heat bath.
Their essential differences are identified unambiguously in the context of full
counting statistics. The electrode coupling caused level detuning
renormalization gives rise to a fast-to-slow transport mechanism, which is not
resolved at all in the average current, but revealed uniquely by pronounced
super-Poissonian shot noise and skewness. The heat bath coupling introduces an
interdot coupling renormalization, which results in asymmetric Fano factor and
an intriguing change of line shape in the skewness.Comment: 9 pages, 5 figure
Distance-dependent emission spectrum from two qubits in a strong-coupling regime
We study the emission spectrum of two distant qubits strongly coupled to a
waveguide by using the numerical and analytical approaches, which are beyond
the Markovian approximation and the rotating-wave approximation (RWA). The
numerical approach combines the Dirac-Frenkel time-dependent variational
principle with the multiple Davydov ansatz. A transformed RWA (TRWA)
treatment and a standard perturbation (SP) are used to analytically calculate
the emission spectrum. It is found that the variational approach and the TRWA
treatment yield accurate emission spectra of the two distant qubits in certain
strong coupling regimes while the SP breaks down. The emission spectrum is
found to be asymmetric irrespective of the two-qubit distance and exhibits a
single peak, doublet, and multipeaks depending on the two-qubit distance as
well as the initial states. In sharply contrast with the single-qubit case, the
excited-state populations of the two qubits can ultraslowly decay due to the
subradiance even in the presence of a strong qubit-waveguide coupling, which in
turn yields ultranarrow emission line. Our results provide insights into the
emission spectral features of the two distant qubits in the strong light-matter
coupling regime.Comment: 15 pages, 4 figure
Improved Best-of-Both-Worlds Guarantees for Multi-Armed Bandits: FTRL with General Regularizers and Multiple Optimal Arms
We study the problem of designing adaptive multi-armed bandit algorithms that
perform optimally in both the stochastic setting and the adversarial setting
simultaneously (often known as a best-of-both-world guarantee). A line of
recent works shows that when configured and analyzed properly, the
Follow-the-Regularized-Leader (FTRL) algorithm, originally designed for the
adversarial setting, can in fact optimally adapt to the stochastic setting as
well. Such results, however, critically rely on an assumption that there exists
one unique optimal arm. Recently, Ito (2021) took the first step to remove such
an undesirable uniqueness assumption for one particular FTRL algorithm with the
-Tsallis entropy regularizer. In this work, we significantly
improve and generalize this result, showing that uniqueness is unnecessary for
FTRL with a broad family of regularizers and a new learning rate schedule. For
some regularizers, our regret bounds also improve upon prior results even when
uniqueness holds. We further provide an application of our results to the
decoupled exploration and exploitation problem, demonstrating that our
techniques are broadly applicable.Comment: Update the camera-ready version for NeurIPS 202
Local Well-posedness of the Free-Boundary Incompressible Magnetohydrodynamics with Surface Tension
We prove the local well-posedness of the 3D free-boundary incompressible
ideal magnetohydrodynamics (MHD) equations with surface tension, which describe
the motion of a perfect conducting fluid in an electromagnetic field. We adapt
the ideas developed in the remarkable paper [11] by Coutand and Shkoller to
generate an approximate problem with artificial viscosity indexed by
whose solution converges to that of the MHD equations as .
However, the local well-posedness of the MHD equations is no easy consequence
of Euler equations thanks to the strong coupling between the velocity and
magnetic fields. This paper is the continuation of the second and third
authors' previous work [38] in which the a priori energy estimate for
incompressible free-boundary MHD with surface tension is established. But the
existence is not a trivial consequence of the a priori estimate as it cannot be
adapted directly to the approximate problem due to the loss of the symmetric
structure.Comment: 60 page
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