18,174 research outputs found
A discrete methodology for controlling the sign of curvature and torsion for NURBS
This paper develops a discrete methodology for approximating the so-called convex domain of a NURBS curve, namely the domain in the ambient space, where a user-specified control point is free to move so that the curvature and torsion retains its sign along the NURBS parametric domain of definition. The methodology provides a monotonic sequence of convex polyhedra, converging from the interior to the convex domain. If the latter is non-empty, a simple algorithm is proposed, that yields a sequence of polytopes converging uniformly to the restriction of the convex domain to any user-specified bounding box. The algorithm is illustrated for a pair of planar and a spatial Bézier configuration
Information geometric methods for complexity
Research on the use of information geometry (IG) in modern physics has
witnessed significant advances recently. In this review article, we report on
the utilization of IG methods to define measures of complexity in both
classical and, whenever available, quantum physical settings. A paradigmatic
example of a dramatic change in complexity is given by phase transitions (PTs).
Hence we review both global and local aspects of PTs described in terms of the
scalar curvature of the parameter manifold and the components of the metric
tensor, respectively. We also report on the behavior of geodesic paths on the
parameter manifold used to gain insight into the dynamics of PTs. Going
further, we survey measures of complexity arising in the geometric framework.
In particular, we quantify complexity of networks in terms of the Riemannian
volume of the parameter space of a statistical manifold associated with a given
network. We are also concerned with complexity measures that account for the
interactions of a given number of parts of a system that cannot be described in
terms of a smaller number of parts of the system. Finally, we investigate
complexity measures of entropic motion on curved statistical manifolds that
arise from a probabilistic description of physical systems in the presence of
limited information. The Kullback-Leibler divergence, the distance to an
exponential family and volumes of curved parameter manifolds, are examples of
essential IG notions exploited in our discussion of complexity. We conclude by
discussing strengths, limits, and possible future applications of IG methods to
the physics of complexity.Comment: review article, 60 pages, no figure
Dirac nodal line metal for topological antiferromagnetic spintronics
Topological antiferromagnetic (AFM) spintronics is an emerging field of
research, which exploits the N\'eel vector to control the topological
electronic states and the associated spin-dependent transport properties. A
recently discovered N\'eel spin-orbit torque has been proposed to electrically
manipulate Dirac band crossings in antiferromagnets; however, a reliable AFM
material to realize these properties in practice is missing. Here, we predict
that room temperature AFM metal MnPd allows the electrical control of the
Dirac nodal line by the N\'eel spin-orbit torque. Based on first-principles
density functional theory calculations, we show that reorientation of the
N\'eel vector leads to switching between the symmetry-protected degenerate
state and the gapped state associated with the dispersive Dirac nodal line at
the Fermi energy. The calculated spin Hall conductivity strongly depends on the
N\'eel vector orientation and can be used to experimentally detect the
predicted effect using a proposed spin-orbit torque device. Our results
indicate that AFM Dirac nodal line metal MnPd represents a promising
material for topological AFM spintronics
Dynamical mechanism of atrial fibrillation: a topological approach
While spiral wave breakup has been implicated in the emergence of atrial
fibrillation, its role in maintaining this complex type of cardiac arrhythmia
is less clear. We used the Karma model of cardiac excitation to investigate the
dynamical mechanisms that sustain atrial fibrillation once it has been
established. The results of our numerical study show that spatiotemporally
chaotic dynamics in this regime can be described as a dynamical equilibrium
between topologically distinct types of transitions that increase or decrease
the number of wavelets, in general agreement with the multiple wavelets
hypothesis. Surprisingly, we found that the process of continuous excitation
waves breaking up into discontinuous pieces plays no role whatsoever in
maintaining spatiotemporal complexity. Instead this complexity is maintained as
a dynamical balance between wave coalescence -- a unique, previously
unidentified, topological process that increases the number of wavelets -- and
wave collapse -- a different topological process that decreases their number.Comment: 15 pages, 14 figure
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