The Experts below are selected from a list of 25263 Experts worldwide ranked by ideXlab platform
Eric Vandeneijnden - One of the best experts on this subject based on the ideXlab platform.
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averaged equation for energy diffusion on a graph reveals Bifurcation Diagram and thermally assisted reversal times in spin torque driven nanomagnets
Journal of Applied Physics, 2013Co-Authors: Katherine A Newhall, Eric VandeneijndenAbstract:Driving nanomagnets by spin-polarized currents offers exciting prospects in magnetoelectronics, but the response of the magnets to such currents remains poorly understood. We show that an averaged equation describing the diffusion of energy on a graph captures the low-damping dynamics of these systems. From this equation we obtain the Bifurcation Diagram of the magnets, including the critical currents to induce stable precessional states and magnetization switching, as well as the mean times of thermally assisted magnetization reversal in situations where the standard reaction rate theory of Kramers is no longer valid. These results match experimental observations and give a theoretical basis for a Neel-Brown-type formula with an effective energy barrier for the reversal times.
Katherine A Newhall - One of the best experts on this subject based on the ideXlab platform.
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AVERAGED EQUATION FOR ENERGY DIFFUSION ON A GRAPH REVEALS Bifurcation Diagram AND THERMALLY ASSISTED REVERSAL TIMES IN SPIN-TORQUE DRIVEN NANOMAGNETS
2016Co-Authors: Katherine A Newhall, Eric Vanden-eijndenAbstract:Abstract. Driving nanomagnets by spin-polarized currents offers exciting prospects in magnetoelectronics, but the response of the magnets to such currents remains poorly un-derstood. We show that an averaged equation describing the diffusion of energy on a graph captures the low-damping dynamics of these systems. From this equation we obtain the Bifurcation Diagram of the magnets, including the critical currents to induce stable preces-sional states and magnetization switching, as well as the mean times of thermally assisted magnetization reversal in situations where the standard reaction rate theory of Kramers is no longer valid. These results agree with experimental observations and give a theoretical basis for a Néel-Brown-type formula with an effective energy barrier for the reversal times. Manipulating thin-film magnetic elements with spin-polarized currents besides external magnetic fields [12] has generated a lot of recent interest in applications to magnetoelec-tronic devices that offer low power memory storage without the use of moving parts [2]. Understanding the response of the magnet to such currents is nontrivial, however, because they apply a nonconservative force, called spin-transfer torque (STT), on the system. Like other nongradient systems with no Lyapunov function, the phase portrait of nanomagnet
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averaged equation for energy diffusion on a graph reveals Bifurcation Diagram and thermally assisted reversal times in spin torque driven nanomagnets
Journal of Applied Physics, 2013Co-Authors: Katherine A Newhall, Eric VandeneijndenAbstract:Driving nanomagnets by spin-polarized currents offers exciting prospects in magnetoelectronics, but the response of the magnets to such currents remains poorly understood. We show that an averaged equation describing the diffusion of energy on a graph captures the low-damping dynamics of these systems. From this equation we obtain the Bifurcation Diagram of the magnets, including the critical currents to induce stable precessional states and magnetization switching, as well as the mean times of thermally assisted magnetization reversal in situations where the standard reaction rate theory of Kramers is no longer valid. These results match experimental observations and give a theoretical basis for a Neel-Brown-type formula with an effective energy barrier for the reversal times.
Coralie Renault - One of the best experts on this subject based on the ideXlab platform.
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Imperfect Bifurcation for the quasi-geostrophic shallow-water equations
Archive for Rational Mechanics and Analysis, 2019Co-Authors: Taoufik Hmidi, David Dritschel, Coralie RenaultAbstract:We study analytical and numerical aspects of the Bifurcation Diagram of simply-connected rotating vortex patch equilibria for the quasi-geostrophic shallow-water (QGSW) equations. The QGSW equations are a generalisation of the Euler equations and contain an additional parameter, the Rossby deformation length ε −1 , which enters in the relation between streamfunction and (potential) vorticity. The Euler equations are recovered in the limit ε → 0. We prove, close to circular (Rankine) vortices, the persistence of the Bifurcation Diagram for arbitrary Rossby deformation length. However we show that the twofold branch, corresponding to Kirchhoff ellipses for the Euler equations, is never connected even for small values ε, and indeed is split into a countable set of disjoint connected branches. Accurate numerical calculations of the global structure of the Bifurcation Diagram and of the limiting equilibrium states are also presented to complement the mathematical analysis.
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existence of small loops in a Bifurcation Diagram near degenerate eigenvalues
Nonlinearity, 2017Co-Authors: Taoufik Hmidi, Coralie RenaultAbstract:In this paper, we study the global structure of a Bifurcation Diagram for rotating doubly connected patches near a degenerate case for incompressible Euler equations. We show that branches with the same symmetry merge, forming a small loop, provided that they are close enough. This gives an analytical proof for the numerical observations conducted in the recent work by de la Hoz et al (2016 SIAM J. Math. Anal. 48 1892–928).
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EXISTENCE OF SMALL LOOPS IN A Bifurcation Diagram NEAR THE DEGENERATE EIGENVALUES
Nonlinearity, 2017Co-Authors: Taoufik Hmidi, Coralie RenaultAbstract:In this paper we study for the incompressible Euler equations the global structure of the Bifurcation Diagram for the rotating doubly connected patches near the degenerate case. We show that the branches with the same symmetry merge forming a small loop provided that they are close enough. This confirms the numerical observations done in the recent work [10].
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existence of small loops in the Bifurcation Diagram near the degenerate eigenvalues
arXiv: Analysis of PDEs, 2016Co-Authors: Taoufik Hmidi, Coralie RenaultAbstract:In this paper we study for the incompressible Euler equations the global structure of the Bifurcation Diagram for the rotating doubly connected patches near the degenerate case. We show that the branches with the same symmetry merge forming a small loop provided that they are close enough. This confirms the numerical observations done in the recent work [10]
S Residori - One of the best experts on this subject based on the ideXlab platform.
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Local theory of the slanted homoclinic snaking Bifurcation Diagram.
Physical review. E Statistical nonlinear and soft matter physics, 2008Co-Authors: U Bortolozzo, M G Clerc, S ResidoriAbstract:Localized states in out of equilibrium one-dimensional systems are described by the homoclinic snaking associated with the infinite sequence of multibump localized solutions of the corresponding time reversible dynamical system. We show that when the pattern undergoes a saddle-node Bifurcation the homoclinic snaking Bifurcation Diagram becomes slanted and a finite set of localized states continue to exist outside the region of bistability. This generic behavior offers a local theory resolution of the discrepancy between models and experiments.
David T J Liley - One of the best experts on this subject based on the ideXlab platform.
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chaos via shilnikov s saddle node Bifurcation in a theory of the electroencephalogram
Physical Review Letters, 2006Co-Authors: Lennaert Van Veen, David T J LileyAbstract:We study the Bifurcation Diagram of a mesoscopic model of the human cortex. This model is known to exhibit robust chaotic behavior in the space of parameters that model exterior forcing. We show that the Bifurcation Diagram has an unusual degree of organization. In particular, we show that the chaos is spawned by a codimension-one homoclinic Bifurcation that was analyzed by Shilnikov in 1969 but has never before been found in a physical application.