8,573 research outputs found
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
which includes in particular the energy space H^{1/2}(\RR^2). The
main tools that enable to reach 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 . In order to take into account Dirichlet boundary conditions
which are not compatible with the Dirac Hamiltonian , we propose a
different model built on a modified Hamiltonian displaying the same energy band
diagram as near the Dirac points. The well-posedness of the system in
this case is proved in , the domain of the fractional order Dirichlet
Laplacian operator, for
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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
Modeling the global positioning system signal propagation through the ionosphere
Based on realistic modeling of the electron density of the ionosphere and using a dipole moment approximation for the Earth's magnetic field, one is able to estimate the effect of the ionosphere on the Global Positioning System (GPS) signal for a ground user. The lowest order effect, which is on the order of 0.1-100 m of group delay, is subtracted out by forming a linear combination of the dual frequencies of the GPS signal. One is left with second- and third-order effects that are estimated typically to be approximately 0-2 cm and approximately 0-2 mm at zenith, respectively, depending on the geographical location, the time of day, the time of year, the solar cycle, and the relative geometry of the magnetic field and the line of sight. Given the total electron content along a line of sight, the authors derive an approximation to the second-order term which is accurate to approximately 90 percent within the magnetic dipole moment model; this approximation can be used to reduce the second-order term to the millimeter level, thus potentially improving precise positioning in space and on the ground. The induced group delay, or phase advance, due to second- and third-order effects is examined for two ground receivers located at equatorial and mid-latitude regions tracking several GPS satellites
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