Search results for "Nonlinear"
showing 10 items of 3684 documents
A blow-up result for a nonlinear wave equation on manifolds: the critical case
2021
We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (Formula presented.) of dimension (Formula presented.), without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when (Formula presented.), our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.
Modelling of rotations by using matrix solutions of nonlinear wave equations
2007
A family of matrix solutions of nonlinear wave equations is extended and its application to modelling is given. It is shown that a similarity transformation, induced by the matrix solution, is equivalent to the rotation. Matrix solutions are used for modelling helical motions and vortex rings, simultaneous rotations and particles collision, mapping contraction and pulsating spheres. Geometrical interpretation of the doubling of rotation angle in each step of sequential mapping contraction is given. First Published Online: 14 Oct 2010
An operatorial approach to stock markets
2009
We propose and discuss some toy models of stock markets using the same operatorial approach adopted in quantum mechanics. Our models are suggested by the discrete nature of the number of shares and of the cash which are exchanged in a real market, and by the existence of conserved quantities, like the total number of shares or some linear combination of cash and shares. The same framework as the one used in the description of a gas of interacting bosons is adopted.
Information-theoretic assessment of cardiovascular-brain networks during sleep
2015
This study was aimed at detecting the structure of the physiological network underlying the regulation of the cardiovascular and brain systems during normal sleep. To this end, we measured from the polysomnographic recordings of 10 healthy subjects the normalized spectral power of heart rate variability in the high frequency band (HF) and the EEG power in the δ, θ, α, σ, and β bands. Then, the causal statistical dependencies within and between these six time series were assessed in terms of internal information (conditional self entropy, CSE) and information transfer (transfer entropy, TE) computed via a linear method exploiting multiple regression models and a nonlinear method combining ne…
A hybrid stimulation strategy for suppression of spiral waves in cardiac tissue
2011
International audience; Atrial fibrillation (AF) is the most common cardiac arrhythmia whose mechanisms are thought to be mainly due to the self perpetuation of spiral waves (SW). To date, available treatment strategies (antiarrhythmic drugs, radiofrequency ablation of the substrate, electrical cardioversion) to restore and to maintain a normal sinus rhythm have limitations and are associated with AF recurrences. The aim of this study was to assess a way of suppressing SW by applying multifocal electrical stimulations in a simulated cardiac tissue using a 2D FitzHugh-Nagumo model specially convenient for AF investigations. We identified stimulation parameters for successful termination of S…
A score model for the continuous grading of early allograft dysfunction severity
2014
Early allograft dysfunction (EAD) dramatically influences graft and patient outcomes. A lack of consensus on an EAD definition hinders comparisons of liver transplant outcomes and management of recipients among and within centers. We sought to develop a model for the quantitative assessment of early allograft function [Model for Early Allograft Function Scoring (MEAF)] after transplantation. A retrospective study including 1026 consecutive liver transplants was performed for MEAF score development. Multivariate data analysis was used to select a small number of postoperative variables that adequately describe EAD. Then, the distribution of these variables was mathematically modeled to assig…
Recurrence quantification analysis as a tool for complex fractionated atrial electrogram discrimination
2012
International audience; Atrial fibrillation is the most encountered pathology of the heart rate. The reasons of its occurrence and its particular characteristics remain unknown, resulting from complex phenomena interaction. From these interactions emerges Complex Fractionated Atrial Electrograms (CFAE) which are useful for the ablation procedure. This study presents a method based on nonlinear data analysis, the Recurrence Quantification Analysis (RQA) applied on intracardiac atrial electrograms to detect CFAE particularities. The results obtained on areas previously tagged by a cardilogist show a good sensitivity to CFAE. Combination of RQA features offers a larger discrimination potential…
Synchronization index for quantifying nonlinear causal coupling between RR interval and systolic arterial pressure after myocardial infarction
2002
The analysis of nonlinear couplings among cardiovascular variability series can improve the knowledge of the cardioregulatory mechanism and help to understand how it can be affected by pathologies. In this study, the influences of acute myocardial infarction (AMI) on the causal relationships between the heart period and the arterial pressure were investigated by a nonlinear dynamic approach based on the corrected cross-conditional entropy. Whereas the global synchronization index did not differentiate the post-AMI patients from the young and old control groups, the causal indexes evidenced the impairment of the baroreflex control and showed an increase of the mechanical driving of the RR in…
Second order nonlinear optics in AlGaAs metasurfaces
2023
Recently, nonlinear optics at the nanoscale level has emerged as a promising branch of nanophotonics. In this work, we focus our attention on Aluminum Gallium Arsenide (AlGaAs) nanoantennas and metasurfaces for efficient and controlled second harmonic photon emission. After a brief introduction concerning the main studies in this field, we present the latest results achieved in AlGaAs platforms both in the lossless and absorption regimes.
Silicon metasurfaces with tunable electromagnetic resonances for nonlinear optical conversion
2021
Dielectric metasurfaces sustain electromagnetic modes which can be exploited to enhance nonlinear frequency-conversion processes such as third-harmonic generation. In this work we employ electron-beam lithography to fabricate silicon metasurfaces supporting electromagnetic resonances with different quality factors (Q), ruled by the geometry. This allows to investigate the trade-off between resonant enhancement and matching the spectral bandwidth of the ultrafast excitation source. Both experiments and simulations indicate that higher values of Q do not a priori bring about a stronger third-harmonic generation, which correlates to the spectral overlap between the metasurface resonance and th…