Angel de Castro

Breakdown of Smoothness for the Muskat Problem

In this paper we show that there exists analytic initial data in the stable regime for the Muskat problem such that the solution turns to the unstable regime and later breaks down, that is, no longer belongs to C4.

Fully nonlinear long-waves models in presence of vorticity

We study here Green-Naghdi type equations (also called fully nonlinear Boussinesq, or Serre equations) modeling the propagation of large amplitude waves in shallow water without smallness assumption on the amplitude of the waves. The novelty here is that we allow for a general vorticity, hereby allowing complex interactions between surface waves and currents. We show that the a priori 2+1-dimensional dynamics of the vorticity can be reduced to a finite cascade of two-dimensional equations: with a mechanism reminiscent of turbulence theory, vorticity effects contribute to the averaged momentum equation through a Reynolds-like tensor that can be determined by a cascade of equations. Closure is obtained at the precision of the model at the second order of this cascade. We also show how to reconstruct the velocity field in the 2 + 1 dimensional fluid domain from this set of 2-dimensional equations and exhibit transfer mechanisms between the horizontal and vertical components of the vorticity, thus opening perspectives for the study of rip currents for instance.

High Resolution FPGA DPWM Based on Variable Clock Phase Shifting

This letter proposes a very high resolution digital pulsewidth modulator (DPWM) architecture that takes advantage of a field-programmable gate array (FPGA) advanced clock management capability - the fine phase shifting of the clock. This feature is available in almost every FPGA nowadays, thus allowing very small and programmable delays between the input and output clocks. An original use of this fine phase shifting pushes the limits of DPWM resolution. The experimental results show a time resolution of 19.5 ps in a Virtex-5 FPGA.

Universal Digital Controller for Boost CCM Power Factor Correction Stages Based on Current Rebuilding Concept

Continuous conduction mode power factor correction (PFC) without input current measurement is a step forward with respect to previously proposed PFC digital controllers. Inductor volt-second (vsL) measurement in each switching period enables digital estimation of the input current; however, an accurate compensation of the small errors in the measured vsL is required for the estimation to match the actual current. Otherwise, they are accumulated every switching period over the half-line cycle, leading to an appreciable current distortion. A vsL estimation method is proposed, measuring the input (vg) and output voltage (vo). Discontinuous conduction mode (DCM) occurs near input line zero crossings and is detected by measuring the drain-to-source MOSFET voltage vds. Parasitic elements cause a small difference between the estimated voltage across the inductor based on input and output voltage measurements and the actual one, which must be taken into account to estimate the input current in the proposed sensorless PFC digital controller. This paper analyzes the current estimation error caused by errors in the ON-time estimation, voltage measurements, and the parasitic elements. A new digital feedback control with high resolution is also proposed. It cancels the difference between DCM operation time of the real input current, (TDCMg) and the estimated DCM time (TDCMreb). Therefore, the current estimation is calibrated using digital signals during operation in DCM. A fast feedforward coarse time error compensation is carried out with the measured delay of the drive signal, and a fine compensation is achieved with a feedback loop that matches the estimated and real DCM time. The digital controller can be used in universal applications due to the ability of the DCM time feedback loop to autotune based on the operation conditions (power level, input voltage, output voltage...), which improves the operation range in comparison with previous solutions. Experimental results are shown for a 1-kW boost PFC converter over a wide power and voltage range.

Incompressible flow in porous media with fractional diffusion

In this paper we study heat transfer with a general fractional diffusion term of an incompressible fluid in a porous medium governed by Darcys law. We show the formation of singularities with infinite energy, and for infinite energy we obtain existence and uniqueness results of strong solutions for the sub-critical and critical cases. We prove the global existence of weak solutions for different cases. Moreover, we obtain the decay of the solution in Lp, for any p ? 2, and the asymptotic behaviour is shown. Finally, we prove the existence of an attractor in a weak sense and, for the sub-critical dissipative case with ? (1, 2], we obtain the existence of the global attractor for the solutions in the space Hs for any s > (N/2) + 1 ? ?.

Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations

Motivated by the recent work of Hassainia and Hmidi [Z. Hassainia, T. Hmidi - On the {V}-states for the generalized quasi-geostrophic equations,arXiv preprint arXiv:1405.0858], we close the question of the existence of convex global rotating solutions for the generalized surface quasi-geostrophic equation for

Splash singularity for water waves

\alpha \in [1,2)

Single ADC Digital PFC Controller Using Precalculated Duty Cycles

. We also show

Turning waves and breakdown for incompressible flows

C^{\infty}

Finite time singularities for water waves with surface tension

regularity of their boundary for all