9,344 research outputs found
Breathers in the weakly coupled topological discrete sine-Gordon system
Existence of breather (spatially localized, time periodic, oscillatory)
solutions of the topological discrete sine-Gordon (TDSG) system, in the regime
of weak coupling, is proved. The novelty of this result is that, unlike the
systems previously considered in studies of discrete breathers, the TDSG system
does not decouple into independent oscillator units in the weak coupling limit.
The results of a systematic numerical study of these breathers are presented,
including breather initial profiles and a portrait of their domain of existence
in the frequency-coupling parameter space. It is found that the breathers are
uniformly qualitatively different from those found in conventional spatially
discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely
rewritte
Community Detection as an Inference Problem
We express community detection as an inference problem of determining the
most likely arrangement of communities. We then apply belief propagation and
mean-field theory to this problem, and show that this leads to fast, accurate
algorithms for community detection.Comment: 4 pages, 2 figure
A Renormalization Group for Hamiltonians: Numerical Results
We describe a renormalization group transformation that is related to the
breakup of golden invariant tori in Hamiltonian systems with two degrees of
freedom. This transformation applies to a large class of Hamiltonians, is
conceptually simple, and allows for accurate numerical computations. In a
numerical implementation, we find a nontrivial fixed point and determine the
corresponding critical index and scaling. Our computed values for various
universal constants are in good agreement with existing data for
area-preserving maps. We also discuss the flow associated with the nontrivial
fixed point.Comment: 11 Pages, 2 Figures. For future updates, check
ftp://ftp.ma.utexas.edu/pub/papers/koch
Warren McCulloch and the British cyberneticians
Warren McCulloch was a significant influence on a number of British cyberneticians, as some British pioneers in this area were on him. He interacted regularly with most of the main figures on the British cybernetics scene, forming close friendships and collaborations with several, as well as mentoring others. Many of these interactions stemmed from a 1949 visit to London during which he gave the opening talk at the inaugural meeting of the Ratio Club, a gathering of brilliant, mainly young, British scientists working in areas related to cybernetics. This paper traces some of these relationships and interaction
Out in the field
This commentary expands upon Bracken & Mawdsley's (2004) paper, âMuddy glee: rounding out the picture of women and physical geography fieldworkâ to consider the experiences of LGBTQI+ people. Reflecting on our own fieldwork experiences between the early 1990s and today, we provide personal insight into some of the challenges faced by LGBTQI+ field scientists. Although the nature of our personal challenges differs through time, space and our own specific identities and intersectionalities, we concur that exclusion of LGBTQI+ people is a widespread problem in fieldwork. This is true of many different modes of physical fieldwork, suggesting that redefining what fieldwork looks like does not automatically remove barriers to entry for marginalised groups. Instead, we argue that inclusivity should be championed across all types of field activities, and that discipline-wide effort is required to ensure safe strategies are developed for all at-risk individuals
Quantum affine Toda solitons
We review some of the progress in affine Toda field theories in recent years,
explain why known dualities cannot easily be extended, and make some
suggestions for what should be sought instead.Comment: 16pp, LaTeX. Minor revision
Kramers-Kronig, Bode, and the meaning of zero
The implications of causality, as captured by the Kramers-Kronig relations
between the real and imaginary parts of a linear response function, are
familiar parts of the physics curriculum. In 1937, Bode derived a similar
relation between the magnitude (response gain) and phase. Although the
Kramers-Kronig relations are an equality, Bode's relation is effectively an
inequality. This perhaps-surprising difference is explained using elementary
examples and ultimately traces back to delays in the flow of information within
the system formed by the physical object and measurement apparatus.Comment: 8 pages; American Journal of Physics, to appea
Generalized Grad-Shafranov equation for non-axisymmetric MHD equilibria
The structure of static MHD equilibria that admit continuous families of Euclidean symmetries is well understood. Such field configurations are governed by the classical Grad-Shafranov equation, which is a single elliptic PDE in two space dimensions. By revealing a hidden symmetry, we show that in fact all smooth solutions of the equilibrium equations with non-vanishing pressure gradients away from the magnetic axis satisfy a generalization of the Grad-Shafranov equation. In contrast to solutions of the classical Grad-Shafranov equation, solutions of the generalized equation are not automatically equilibria, but instead only satisfy force balance averaged over the one-parameter hidden symmetry. We then explain how the generalized Grad-Shafranov equation can be used to reformulate the problem of finding exact three-dimensional smooth solutions of the equilibrium equations as finding an optimal volume-preserving symmetry
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