arXiv subjects

David Llerena

Publications and source records attributed to David Llerena.

6 recordsLinked to original sources

arXiv2026

Wavelength-Selective control of Atomic Scale Au Contacts

We demonstrate wavelength-selective control of atomic motion in a mechanically controllable Au break junction. Excitation at $\lambda_{\mathrm{form}}\simeq 530~{\rm nm}$ drives gap closure and metallic bridge formation, whereas excitation at $\lambda_{\mathrm{rup}}\simeq 407~{\rm nm}$ drives neck thinning, bridge rupture, and subsequent gap opening. Unlike conventional optical switching in metallic contacts, where illumination primarily acts via thermal expansion, the present experiment reveals oppositely directed atomic drift at different wavelengths. Time-resolved conductance traces allow us to distinguish two dynamical regimes. In the tunneling regime, exponential conductance transients measure the drift velocity of the gap coordinate for both gap closure and gap opening. In the metallic regime, the Sharvin relation converts linear $\sqrt{G/G_0}$ transients into radial neck-growth and neck-thinning velocities of comparable magnitude. These results establish optically selected atomic drift as a mechanism for reversible control of metallic nanocontacts and provide a quantitative route to follow plasmon-assisted atomic rearrangements in real time.

cond-mat.mes-hall↗

arXiv2024

Partial regularity and $L^3$-norm concentration effects around possible blow-up points for the micropolar fluid equations

The micropolar fluid system is a model based on the Navier-Stokes equations which considers two coupled variables: the velocity field $\vec u$ and the microrotation field $\vec\omega$. Assuming an additional condition over the variable $\vec u$ we will first prove that weak solutions $(\vec u, \vec\omega)$ of this system are smooth. Then, we will present a concentration effect of the $L^3_x$ norm of the velocity field $\vec u$ near a possible singular time.

math.AP↗

arXiv2023

Some remarks about the stationary Micropolar fluid equations: existence, regularity and uniqueness

We consider here the stationary Micropolar fluid equations which are a particular generalization of the usual Navier-Stokes system where the microrotations of the fluid particles must be taken into account. We thus obtain two coupled equations: one based mainly in the velocity field u and the other one based in the microrotation field $\omega$. We will study in this work some problems related to the existence of weak solutions as well as some regularity and uniqueness properties. Our main result establish, under some suitable decay at infinity conditions for the velocity field only, the uniqueness of the trivial solution.

math.AP↗

arXiv2023

Partial suitable solutions for the micropolar equations and regularity properties

The incompressible Micropolar system is given by two coupled equations: the first equation gives the evolution of the velocity field u while the second equation gives the evolution of the microrotation field $ω$. In this article we will consider regularity problems for weak solutions of this system. For this we will introduce the new notion of partial suitable solutions, which imposes a specific behavior for the velocity field u only, and under some classical hypotheses over the pressure, we will obtain a h{ö}lderian gain for both variables u and $ω$.

math.AP↗

arXiv2022

A crypto-regularity result for the micropolar fluids equations

In the analysis of PDEs, regularity of often measured in terms of Sobolev, H{ö}lder, Besov or Lipschitz spaces, etc. However, sometimes a gain of regularity can also be expressed just in terms of Lebesgue spaces, by passing from a singular setting to a less singular one. In this article we will obtain a gain of integrability for weak solutions of the micropolar fluid equations using as general framework Morrey spaces, which is a very useful language to study regularity in PDEs. An interesting point is that the two variables of the micropolar fluid equations can be studied separately.

math.AP↗

arXiv2021

Interior epsilon-regularity theory for the solutions of the magneto-micropolar equations with a perturbation term

We develop here a particular version of the partial regularity theory for the Magneto-Micropolar equations (MMP) where a perturbation term is added. These equations are used in some special cases, such as in the study of the evolution of liquid cristals or polymers, where the classical Navier-Stokes equations are not an accurate enough model. The incompressible Magneto-Micropolar system is composed of three coupled equations: the first one is based in the Navier-Stokes system, the second one considers mainly the magnetic field while the last equation introduces the microrotation field representing the angular velocity of the rotation of the fluid particles. External forces are considered and a specific perturbation term is added as it is quite useful in some applications.

math.AP↗