arXiv subjects

Luis Bonilla

Publications and source records attributed to Luis Bonilla.

4 recordsLinked to original sources

arXiv2022

The statistical theory of the angiogenesis equations

Angiogenesis is a multiscale process by which a primary blood vessel issues secondary vessel sprouts that reach regions lacking oxygen. Angiogenesis can be a natural process of organ growth and development or a pathological induced by a cancerous tumor. A mean field approximation for a stochastic model of angiogenesis consists of partial differential equation (PDE) for the density of active tip vessels. Addition of Gaussian and jump noise terms to this equation produces a stochastic PDE that defines an infinite dimensional L\'evy process and is the basis of a statistical theory of angiogenesis. The associated functional equation has been solved and the invariant measure obtained. The results are compared to a direct numerical simulation of the stochastic model of angiogenesis and invariant measure multiplied by an exponentially decaying factor. The results of this theory are compared to direct numerical simulations of the underlying angiogenesis model. The invariant measure and the moments are functions of the Korteweg-de Vries soliton which approximates the deterministic density of active vessel tips.

math.AP↗

arXiv2019

Large-scale critical behavior of the rippling phase transition for graphene membranes

We analyze the spontaneous rippling of graphene membranes as function of the coupling between lattice deformations and electrons. We numerically study a model of an elastic membrane coupled to Dirac fermions. We identify a phase transition from a flat to a rippled configuration of the membrane when increasing the coupling and propose a scaling procedure that allows us to effectively reach arbitrary large system sizes. We find that the critical value of the coupling rapidly decays as the system increases its size, in agreement with the experimental observation of an unavoidable stable rippled state for suspended graphene membranes. This decay turns out to be controlled by a power law with a critical exponent $\sim 1/2$.

cond-mat.soft↗

arXiv2019

A numerical study of the rippling instability driven by electron-phonon coupling in graphene

Suspended graphene exhibits ripples of size ranging from 50 to 100 {\AA} and height $\sim$10{\AA}, however, their origin remains undetermined. Previous theoretical works have proposed that rippling in graphene might be generated by the coupling between the bending modes and the density of electrons. These studies theoretically proposed that in the thermodynamic limit a membrane of single layer graphene displays a lattice instability for large enough electron-phonon coupling, undergoing a phase transition from a flat phase to a rippled one. In this work we solve the elasticity equations for a finite membrane of graphene coupled to the charge distribution, modeled in the tight-binding approximation, we find that the electron-phonon coupling controls a transition from a stable flat configuration to a stable rippled phase.

cond-mat.mes-hall↗

arXiv2017

Parameter dependence of high-frequency nonlinear oscillations and intrinsic chaos in short GaAs/(Al,Ga)As superlattices

We explore the design parameter space of short (5--25 period), n-doped, Ga/(Al,Ga)As semiconductor superlattices (SSLs) in the sequential resonant tunneling regime. We consider SSLs at cool (77K) and warm (295K) temperatures, simulating the electronic response to variations in (a) the number of SSL periods, (b) the contact conductivity, and (c) the strength of disorder (aperiodicities). Our analysis shows that the chaotic dynamical phases exist on a number of sub-manifolds of codimension zero within the design parameter space. This result provides an encouraging guide towards the experimental observation of high-frequency intrinsic dynamical chaos in shorter SSLs.

cond-mat.mes-hall↗