Abstract: The reactive-wetting process, e.g. spreading of a liquid droplet on a reactive substrate is known as a complex, non-linear process with high sensitivity to minor fluctuations. The dynamics and geometry of the interface (triple line) between the materials is supposed to shed light on the main mechanisms of the process. We recently studied a room temperature reactive-wetting system of a...

We investigate the question of how well points on a nondegenerate k-dimensional submanifold M ⊆ Rd can be approximated by rationals also lying on M , establishing an upper bound on the “intrinsic Dirichlet exponent” for M . We show that relative to this exponent, the set of badly intrinsically approximable points is of full dimension and the set of very well intrinsically approximable points is...

A compilation of 54 sets of geoacoustic measurements of marine sediments was reviewed in order to bound estimates of parameters for use in Buckingham's grain shearing (GS) theory of acoustic propagation. These data, for unconsolidated sands (siliciclastic and carbonate) with grain sizes between 0.0156 mm and 0.57 mm, were all made in shallow water (maximum depth of 60 m) sites at diverse locale...

A one-dimensional tight-binding Hamiltonian describes the evolution of a single impurity interacting locally with N electrons. The impurity spectral function has a power-law singularity A(ω) ∝| ω− ω0 |−1+β with the same exponent β that characterizes the logarithmic decay of the quasiparticle weight Z with the number of electrons N , Z ∝ N−β. The exponent β is computed by (1) perturbation theory...

We study the asymptotic expansions with respect to h of

We study the fractional diffusion in a Gaussian noisy environment as described by the fractional order stochastic heat equations of the following form: D t u(t, x) = Bu + u · Ẇ , where D t is the Caputo fractional derivative of order α ∈ (0, 1) with respect to the time variable t, B is a second order elliptic operator with respect to the space variable x ∈ R and Ẇ a time homogeneous fractional ...

In this Letter, we address the relationship between the statistical fluctuations of grain displacements for a full quasistatic plane shear experiment, and the corresponding anomalous diffusion exponent α. We experimentally validate a particular case of the Tsallis-Bukman scaling law, α=2/(3-q), where q is obtained by fitting the probability density function (PDF) of the displacement fluctuation...

The dependence of the Lyapunov exponent on the closeness parameter, ǫ, in tangent bifurcation systems is investigated. We study and illustrate two averaging procedures for defining Lyapunov exponents in such systems. First, we develop theoretical expressions for an isolated tangency channel in which the Lyapunov exponent is defined on single channel passes. Numerical simulations were done to co...

The existence of stochastic processes is discussed, describing turbulent solutions of the full Navier-Stokes equation, driven by unidirectional flow, in dimensions one, two and three. These solutions turn out to have a finite velocity and velocity gradient but they are not smooth instead the velocity is Hölder continuous with a Hölder exponent depending on the dimension. They scale with the Kol...