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Nonlinear Dynamics of Classical Magnetic Systems, Nov 2017, India

Posted By: Dr. Y. Rameshwar
Date:Tue, 19 Sep 2017, 1:40 p.m.


India, November 11, 2017

The course cover problems concerning systems far from
equilibrium where there is a competition between injection
and dissipation of energy. The prototypes models will be
based on contemporary magnetic systems at nanometer scales.
Theoretical and numerical approaches will be treated. The
course will focus on different aspect of parametric
instabilities in magnetic systems, at zero-, one- and two-
spatial dimensions.

Description:

 

The balance between injection and dissipation of a physical
quantity leads a system to behave in a complicated manner,
producing a rich variety of spatiotemporal structures.
Commonly, systems far from equilibrium are described by
nonlinear differential equations (NDEs) or coupled maps. In
general, it is not possible to obtain analytic solutions
for these NDEs.
Nevertheless, in the last decades an extensive variety of
general techniques have been developed to obtain
approximate solutions close to the onset of the
instabilities. In a determinist system, different type of
states can be found varying the parameters and the initial
conditions. By changing one parameter in the system, it can
pass from one state to another. For instance, in an
extended system a homogeneous state can become a pattern.
This type of bifurcation is called spatial instability.
The pattern can be regular or chaotic. The latter term
means that pattern’s behavior in a long time window is
aperiodic and sensible to the initial conditions. One type
of physical systems that presents a variety of complex
phenomena is the magnetic systems, especially when a
parametric driven forcing is acting over the system. In
fact, in low dimensional magnetic system chaotic behaviors
may appear when the magnetic field is a time dependent
function. On the hand, extended systems can exhibit
dissipative Solitons or Faraday waves depending on the
amplitude and frequency of the driven forcing.
The course pretends to cover problems concerning systems
far from equilibrium where there is a competition
between injection and dissipation of energy. The prototypes
models will be based on contemporary magnetic systems at
nanometer scales. Theoretical and numerical approaches will
be treated. These problems are interesting from both
physical and mathematical point of view. The first goal of
the course is to motivate students to solve complex
problems. The course will focus on different aspect of
parametric instabilities in magnetic systems, at zero-,
one- and two- spatial dimensions. The different types of
dimensions have a practical significance because they can
be used to model particles, wires, stripes as well as
spin-valve oscillator devices, which are central part of
nanoscience and have potential technological applications.
The second goal is to show the intrinsic correspondence
between the physics and mathematics of the magnetic
systems. The derivation of the spatiotemporal evolution
equations will be performed and some features of them will
be analyzed. The final goal is to show how several branches
of mathematics are indispensable to characterize the
dynamical behavior of such systems. In particular,
different methods based on bifurcation analysis,
perturbation methods, and the normal form theory will be
introduced. In addition, numerical simulations techniques
will be examined. In particular, the Lyapunov exponents
method will be shown.
The course will benefit the students of graduate and post
graduate levels, and academicians of mathematics and
physics to acquire a new experience to apply mathematical
methods in modern physical problems.
Modules Foundations of magnetism, Magnetization dynamics ,
Non-autonomous dynamics , Simulations
Conservative systems, 1D, 2D systems out of equilibrium,
Spintronics


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