Global continuous solutions to diagonalizable hyperbolic systems with large and monotone data

In this paper, we study diagonalizable hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and nondecreasing initial data. Moreover, we show in particular cases some uniqueness results. We also remark that these results cover the case of systems which are hyperbolic but not strictly hyperbolic. Physically, this kind of diagonalizable hyperbolic systems appears naturally in the modelling of the dynamics of dislocation densities

Analysis of models for quantum transport of electrons in graphene layers

We present and analyze two mathematical models for the self consistent quantum transport of electrons in a graphene layer. We treat two situations. First, when the particles can move in all the plane \RR^2, the model takes the form of a system of massless Dirac equations coupled together by a selfconsistent potential, which is the trace in the plane of the graphene of the 3D Poisson potential associated to surface densities. In this case, we prove local in time existence and uniqueness of a solution in H^s(\RR^2), for $s > 3/8$ which includes in particular the energy space H^{1/2}(\RR^2). The main tools that enable to reach $s\in (3/8,1/2)$ are the dispersive Strichartz estimates that we generalized here for mixed quantum states. Second, we consider a situation where the particles are constrained in a regular bounded domain $\Omega$. In order to take into account Dirichlet boundary conditions which are not compatible with the Dirac Hamiltonian $H_{0}$, we propose a different model built on a modified Hamiltonian displaying the same energy band diagram as $H_{0}$ near the Dirac points. The well-posedness of the system in this case is proved in $H^s_{A}$, the domain of the fractional order Dirichlet Laplacian operator, for $1/2\leq s<5/2$

Golgotha, Beirut: A Feminist Memoir of the Port Blast

This partly biographical narrative recounts its narrator’s first-hand, ground-zero experience of the Beirut Port explosion, one of the largest and most destructive in living memory. As the narrator recollects her mother’s distress over the possibility of losing her children post-divorce and her joy at finally obtaining—after a seven-year legal battle—the annulment of an abusive marriage, Beirut Port explodes. The focus shifts to a memorable encounter with another anguished mother who, on the heels of the blast, is hysterical but then completely transformed once reunited with her children. The writer of the memoir culled its material through a number of interviews with the narrator who consented to have her story shared in narrative format, so that the resulting creative nonfiction may contribute to the nascent corpus of gendered writing exploring and interrogating, not only the August 4, 2020 national tragedy in Lebanon, but also the patriarchal system facilitating this calamity

A review of machine learning techniques in photoplethysmography for the non-invasive cuff-less measurement of blood pressure

Hypertension or high blood pressure is a leading cause of death throughout the world and a critical factor for increasing the risk of serious diseases, including cardiovascular diseases such as stroke and heart failure. Blood pressure is a primary vital sign that must be monitored regularly for the early detection, prevention and treatment of cardiovascular diseases. Traditional blood pressure measurement techniques are either invasive or cuff-based, which are impractical, intermittent, and uncomfortable for patients. Over the past few decades, several indirect approaches using photoplethysmogram (PPG) have been investigated, namely, pulse transit time, pulse wave velocity, pulse arrival time and pulse wave analysis, in an effort to utilise PPG for estimating blood pressure. Recent advancements in signal processing techniques, including machine learning and artificial intelligence, have also opened up exciting new horizons for PPG-based cuff less and continuous monitoring of blood pressure. Such a device will have a significant and transformative impact in monitoring patients’ vital signs, especially those at risk of cardiovascular disease. This paper provides a comprehensive review for non-invasive cuff-less blood pressure estimation using the PPG approach along with their challenges and limitations

Derivation and study of dynamical models of dislocation densities

In this paper, starting from the microscopic dynamics of isolated dislocations, we explain how to derive formally mean field models for the dynamics of dislocation densities. Essentially these models are tranport equations, coupled with the equations of elasticity. Rigorous results of existence of solutions are presented for some of these models and the main ideas of the proofs are given

Short time existence and uniqueness in Hölder spaces for the 2D dynamics of dislocation densities

In this paper, we study the model of Groma and Balogh describing the dynamics of dislocation densities. This is a two-dimensional model where the dislocation densities satisfy a system of two transport equations. The velocity vector field is the shear stress in the material solving the equations of elasticity. This shear stress can be related to Riesz transforms of the dislocation densities. Basing on some commutator estimates type, we show thatthis model has a unique local-in-time solution corresponding to any initial datum in the space $C^r(\R^2)\cap L^p(\R^2)$ for $r>1$ and $

incestuous: A Childhood Memoir in Verse

Childhood sexual abuse, including incest, is underreported and often unreported in the staunchly patriarchal Lebanese setting. The revolutionary spirit that accompanied the country’s October 2019 uprising instigated hope that Lebanese patriarchy, and its concomitant juggernaut of warlords and/or formidable father figures—social, political, cultural, religious, and familial—were not immune to opprobrium in public and private spheres alike. It is within this context that this poem’s protagonist, a friend and fellow demonstrator, managed to share her memories of traumas lived in 1980s Beirut. Written not only with the permission but also at the request of the subject in the story, this childhood memory in verse retells its female narrator’s experiences of child sex abuse in Lebanon, a topic largely shrouded in debilitating silence