71 research outputs found
Achieving Strong Magnon Blockade through Magnon Squeezing in a Cavity Magnetomechanical System
We propose a scheme to achieve magnon (photon) blockade by using magnon
squeezing within a cavity magnomechanical system under weak pump driving. Under
ideal conditions, we observe a substantial magnon blockade effect, as well as
simultaneous photon blockade. Moreover, both numerical and analytical results
match perfectly, providing robust evidence of consistency. In addition to
calculating optimal parametric gain and detuning values, we can improve the
second-order correlation function. The proposed scheme will be a pioneering
approach towards magnon (photon) blockade in experimental cavity
magnomechanical systems.Comment: 6 page
Shallow water equations for large bathymetry variations
In this study, we propose an improved version of the nonlinear shallow water
(or Saint-Venant) equations. This new model is designed to take into account
the effects resulting from the large spacial and/or temporal variations of the
seabed. The model is derived from a variational principle by choosing the
appropriate shallow water ansatz and imposing suitable constraints. Thus, the
derivation procedure does not explicitly involve any small parameter.Comment: 7 pages. Other author's papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutykh
An optimal scaling to computationally tractable dimensionless models: Study of latex particles morphology formation
In modelling of chemical, physical or biological systems it may occur that the coefficients, multiplying various terms in the equation of interest, differ greatly in magnitude, if a particular system of units is used. Such is, for instance, the case of the Population Balance Equations (PBE) proposed to model the Latex Particles Morphology formation. The obvious way out of this difficulty is the use of dimensionless scaled quantities, although often the scaling procedure is not unique. In this paper, we introduce a conceptually new general approach, called Optimal Scaling (OS). The method is tested on the known examples from classical and quantum mechanics, and applied to the Latex Particles Morphology model, where it allows us to reduce the variation of the relevant coefficients from 49 to just 4 orders of magnitudes. The PBE are then solved by a novel Generalised Method Of Characteristics, and the OS is shown to help reduce numerical error, and avoid unphysical behaviour of the solution. Although inspired by a particular application, the proposed scaling algorithm is expected find application in a wide range of chemical, physical and biological problems
Macroscopic dynamics of incoherent soliton ensembles: soliton-gas kinetics and direct numerical modelling
We undertake a detailed comparison of the results of direct numerical simulations of
the soliton gas dynamics for the Korteweg-de Vries equation with the analytical predictions inferred from the exact solutions of the relevant kinetic equation for solitons. Two model problems are considered: i) the propagation of a “trial” soliton through a one-component “cold” soliton gas consisting of randomly distributed solitons of approximately the same amplitude; and ii) the collision
of two cold soliton gases of different amplitudes (the soliton gas shock tube problem) leading to the formation of an expanding incoherent dispersive shock wave. In both cases excellent agreement is observed between the analytical predictions of the soliton gas kinetics and the direct numerical simulations. Our results confirm the relevance of the kinetic equation for solitons as a quantitatively accurate model for macroscopic non-equilibrium dynamics of incoherent soliton ensembles
Modeling water waves beyond perturbations
In this chapter, we illustrate the advantage of variational principles for
modeling water waves from an elementary practical viewpoint. The method is
based on a `relaxed' variational principle, i.e., on a Lagrangian involving as
many variables as possible, and imposing some suitable subordinate constraints.
This approach allows the construction of approximations without necessarily
relying on a small parameter. This is illustrated via simple examples, namely
the Serre equations in shallow water, a generalization of the Klein-Gordon
equation in deep water and how to unify these equations in arbitrary depth. The
chapter ends with a discussion and caution on how this approach should be used
in practice.Comment: 15 pages, 1 figure, 39 references. This document is a contributed
chapter to an upcoming volume to be published by Springer in Lecture Notes in
Physics Series. Other author's papers can be downloaded at
http://www.denys-dutykh.com
Dispersive wave runup on non-uniform shores
Historically the finite volume methods have been developed for the numerical
integration of conservation laws. In this study we present some recent results
on the application of such schemes to dispersive PDEs. Namely, we solve
numerically a representative of Boussinesq type equations in view of important
applications to the coastal hydrodynamics. Numerical results of the runup of a
moderate wave onto a non-uniform beach are presented along with great lines of
the employed numerical method (see D. Dutykh et al. (2011) for more details).Comment: 8 pages, 6 figures, 18 references. This preprint is submitted to
FVCA6 conference proceedings. Other author papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutykh
Comparison between three-dimensional linear and nonlinear tsunami generation models
The modeling of tsunami generation is an essential phase in understanding
tsunamis. For tsunamis generated by underwater earthquakes, it involves the
modeling of the sea bottom motion as well as the resulting motion of the water
above it. A comparison between various models for three-dimensional water
motion, ranging from linear theory to fully nonlinear theory, is performed. It
is found that for most events the linear theory is sufficient. However, in some
cases, more sophisticated theories are needed. Moreover, it is shown that the
passive approach in which the seafloor deformation is simply translated to the
ocean surface is not always equivalent to the active approach in which the
bottom motion is taken into account, even if the deformation is supposed to be
instantaneous.Comment: 39 pages, 16 figures; Accepted to Theoretical and Computational Fluid
Dynamics. Several references have been adde
Parallel Gaussian Process Optimization with Upper Confidence Bound and Pure Exploration
In this paper, we consider the challenge of maximizing an unknown function f
for which evaluations are noisy and are acquired with high cost. An iterative
procedure uses the previous measures to actively select the next estimation of
f which is predicted to be the most useful. We focus on the case where the
function can be evaluated in parallel with batches of fixed size and analyze
the benefit compared to the purely sequential procedure in terms of cumulative
regret. We introduce the Gaussian Process Upper Confidence Bound and Pure
Exploration algorithm (GP-UCB-PE) which combines the UCB strategy and Pure
Exploration in the same batch of evaluations along the parallel iterations. We
prove theoretical upper bounds on the regret with batches of size K for this
procedure which show the improvement of the order of sqrt{K} for fixed
iteration cost over purely sequential versions. Moreover, the multiplicative
constants involved have the property of being dimension-free. We also confirm
empirically the efficiency of GP-UCB-PE on real and synthetic problems compared
to state-of-the-art competitors
- …