13,719 research outputs found
A model for Faraday pilot waves over variable topography
Couder and Fort discovered that droplets walking on a vibrating bath possess
certain features previously thought to be exclusive to quantum systems. These
millimetric droplets synchronize with their Faraday wavefield, creating a
macroscopic pilot-wave system. In this paper we exploit the fact that the waves
generated are nearly monochromatic and propose a hydrodynamic model capable of
quantitatively capturing the interaction between bouncing drops and a variable
topography. We show that our reduced model is able to reproduce some important
experiments involving the drop-topography interaction, such as non-specular
reflection and single-slit diffraction
Asymptotic behaviour for a class of non-monotone delay differential systems with applications
The paper concerns a class of -dimensional non-autonomous delay
differential equations obtained by adding a non-monotone delayed perturbation
to a linear homogeneous cooperative system of ordinary differential equations.
This family covers a wide set of models used in structured population dynamics.
By exploiting the stability and the monotone character of the linear ODE, we
establish sufficient conditions for both the extinction of all the populations
and the permanence of the system. In the case of DDEs with autonomous
coefficients (but possible time-varying delays), sharp results are obtained,
even in the case of a reducible community matrix. As a sub-product, our results
improve some criteria for autonomous systems published in recent literature. As
an important illustration, the extinction, persistence and permanence of a
non-autonomous Nicholson system with patch structure and multiple
time-dependent delays are analysed.Comment: 26 pages, J Dyn Diff Equat (2017
Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D
We present an effective harmonic density interpolation method for the
numerical evaluation of singular and nearly singular Laplace boundary integral
operators and layer potentials in two and three spatial dimensions. The method
relies on the use of Green's third identity and local Taylor-like
interpolations of density functions in terms of harmonic polynomials. The
proposed technique effectively regularizes the singularities present in
boundary integral operators and layer potentials, and recasts the latter in
terms of integrands that are bounded or even more regular, depending on the
order of the density interpolation. The resulting boundary integrals can then
be easily, accurately, and inexpensively evaluated by means of standard
quadrature rules. A variety of numerical examples demonstrate the effectiveness
of the technique when used in conjunction with the classical trapezoidal rule
(to integrate over smooth curves) in two-dimensions, and with a Chebyshev-type
quadrature rule (to integrate over surfaces given as unions of non-overlapping
quadrilateral patches) in three-dimensions
Parametric Competition in non-autonomous Hamiltonian Systems
In this work we use the formalism of chord functions (\emph{i.e.}
characteristic functions) to analytically solve quadratic non-autonomous
Hamiltonians coupled to a reservoir composed by an infinity set of oscillators,
with Gaussian initial state. We analytically obtain a solution for the
characteristic function under dissipation, and therefore for the determinant of
the covariance matrix and the von Neumann entropy, where the latter is the
physical quantity of interest. We study in details two examples that are known
to show dynamical squeezing and instability effects: the inverted harmonic
oscillator and an oscillator with time dependent frequency. We show that it
will appear in both cases a clear competition between instability and
dissipation. If the dissipation is small when compared to the instability, the
squeezing generation is dominant and one can see an increasing in the von
Neumann entropy. When the dissipation is large enough, the dynamical squeezing
generation in one of the quadratures is retained, thence the growth in the von
Neumann entropy is contained
Theory of weakly nonlinear self sustained detonations
We propose a theory of weakly nonlinear multi-dimensional self sustained
detonations based on asymptotic analysis of the reactive compressible
Navier-Stokes equations. We show that these equations can be reduced to a model
consisting of a forced, unsteady, small disturbance, transonic equation and a
rate equation for the heat release. In one spatial dimension, the model
simplifies to a forced Burgers equation. Through analysis, numerical
calculations and comparison with the reactive Euler equations, the model is
demonstrated to capture such essential dynamical characteristics of detonations
as the steady-state structure, the linear stability spectrum, the
period-doubling sequence of bifurcations and chaos in one-dimensional
detonations and cellular structures in multi- dimensional detonations
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