40,390 research outputs found
Thermal stability and topological protection of skyrmions in nanotracks
Magnetic skyrmions are hailed as a potential technology for data storage and
other data processing devices. However, their stability against thermal
fluctuations is an open question that must be answered before skyrmion-based
devices can be designed. In this work, we study paths in the energy landscape
via which the transition between the skyrmion and the uniform state can occur
in interfacial Dzyaloshinskii-Moriya finite-sized systems. We find three
mechanisms the system can take in the process of skyrmion nucleation or
destruction and identify that the transition facilitated by the boundary has a
significantly lower energy barrier than the other energy paths. This clearly
demonstrates the lack of the skyrmion topological protection in finite-sized
magnetic systems. Overall, the energy barriers of the system under
investigation are too small for storage applications at room temperature, but
research into device materials, geometry and design may be able to address
this
Vortex motion around a circular cylinder above a plane
The study of vortex flows around solid obstacles is of considerable interest
from both a theoretical and practical perspective. One geometry that has
attracted renewed attention recently is that of vortex flows past a circular
cylinder placed above a plane wall, where a stationary recirculating eddy can
form in front of the cylinder, in contradistinction to the usual case (without
the plane boundary) for which a vortex pair appears behind the cylinder. Here
we analyze the problem of vortex flows past a cylinder near a wall through the
lenses of the point-vortex model. By conformally mapping the fluid domain onto
an annular region in an auxiliary complex plane, we compute the vortex
Hamiltonian analytically in terms of certain special functions related to
elliptic theta functions. A detailed analysis of the equilibria of the model is
then presented. The location of the equilibrium in front of the cylinder is
shown to be in qualitative agreement with the experimental findings. We also
show that a topological transition occurs in phase space as the parameters of
the systems are variedComment: 17 pages, 8 figure
Lyapunov Functions in Piecewise Linear Systems: From Fixed Point to Limit Cycle
This paper provides a first example of constructing Lyapunov functions in a
class of piecewise linear systems with limit cycles. The method of construction
helps analyze and control complex oscillating systems through novel geometric
means. Special attention is stressed upon a problem not formerly solved: to
impose consistent boundary conditions on the Lyapunov function in each linear
region. By successfully solving the problem, the authors construct continuous
Lyapunov functions in the whole state space. It is further demonstrated that
the Lyapunov functions constructed explain for the different bifurcations
leading to the emergence of limit cycle oscillation
Smooth Hamiltonian systems with soft impacts
In a Hamiltonian system with impacts (or "billiard with potential"), a point
particle moves about the interior of a bounded domain according to a background
potential, and undergoes elastic collisions at the boundaries. When the
background potential is identically zero, this is the hard-wall billiard model.
Previous results on smooth billiard models (where the hard-wall boundary is
replaced by a steep smooth billiard-like potential) have clarified how the
approximation of a smooth billiard with a hard-wall billiard may be utilized
rigorously. These results are extended here to models with smooth background
potential satisfying some natural conditions. This generalization is then
applied to geometric models of collinear triatomic chemical reactions (the
models are far from integrable -degree of freedom systems with ).
The application demonstrates that the simpler analytical calculations for the
hard-wall system may be used to obtain qualitative information with regard to
the solution structure of the smooth system and to quantitatively assist in
finding solutions of the soft impact system by continuation methods. In
particular, stable periodic triatomic configurations are easily located for the
smooth highly-nonlinear two and three degree of freedom geometric models.Comment: 33 pages, 8 figure
Modelling of a dynamic multiphase flash: the positive flash. Application to the calculation of ternary diagrams
A general and polyvalent model for the dynamic simulation of a vapor, liquid, liquid-liquid, vapor-liquid or vapor-liquid-liquid stage is proposed. This model is based on the -method introduced as a minimization problem by Han & Rangaiah (1998) for steady-state simulation. They suggested modifying the mole fraction summation such that the same set of governing equations becomes valid for all phase regions. Thanks to judicious additional switch equations, the -formulation is extended to dynamic simulation and the minimization problem is transformed into a set of differential algebraic equations (DAE). Validation of the model consists in testing its capacity to overcome phase number changes and to be able to solve several problems with the same set of equations: calculation of heterogeneous residue curves, azeotropic points and distillation boundaries in ternary diagrams
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