9,633 research outputs found
Onset of synchronization in networks of second-order Kuramoto oscillators with delayed coupling: Exact results and application to phase-locked loops
We consider the inertial Kuramoto model of globally coupled oscillators
characterized by both their phase and angular velocity, in which there is a
time delay in the interaction between the oscillators. Besides the academic
interest, we show that the model can be related to a network of phase-locked
loops widely used in electronic circuits for generating a stable frequency at
multiples of an input frequency. We study the model for a generic choice of the
natural frequency distribution of the oscillators, to elucidate how a
synchronized phase bifurcates from an incoherent phase as the coupling constant
between the oscillators is tuned. We show that in contrast to the case with no
delay, here the system in the stationary state may exhibit either a subcritical
or a supercritical bifurcation between a synchronized and an incoherent phase,
which is dictated by the value of the delay present in the interaction and the
precise value of inertia of the oscillators. Our theoretical analysis,
performed in the limit , is based on an unstable manifold
expansion in the vicinity of the bifurcation, which we apply to the kinetic
equation satisfied by the single-oscillator distribution function. We check our
results by performing direct numerical integration of the dynamics for large
, and highlight the subtleties arising from having a finite number of
oscillators.Comment: 15 pages, 4 figures; v2: 16 pages, 5 figures, published versio
A Review of Some Subtleties of Practical Relevance
This paper reviews some subtleties in time-delay systems of neutral type that are believed to be of particular relevance in practice. Both traditional formulation and the coupled differential-difference equation formulation are used. The discontinuity of the spectrum as a function of delays is discussed. Conditions to guarantee stability under small parameter variations are given. A number of subjects that have been discussed in the literature, often using different methods, are reviewed to illustrate some fundamental concepts. These include systems with small delays, the sensitivity of Smith predictor to small delay mismatch, and the discrete implementation of distributed-delay feedback control. The framework prsented in this paper makes it possible to provide simpler formulation and strengthen, generalize, or provide alternative interpretation of the existing results
Continuous feedback fluid queues
We investigate a fluid buffer which is modulated by a stochastic background process, while the momentary behavior of the background process depends on the current buffer level in a continuous way. Loosely speaking the feedback is such that the background process behaves `as a Markov process' with generator at times when the buffer level is , where the entries of are continuous functions of . Moreover, the flow rates for the buffer may also depend continuously on the current buffer level. Such models are interesting in the context of closed-loop telecommunication networks, in which sources interact with network buffers, but may also be deployed in the study of certain production systems. \u
Influence of pH and sequence in peptide aggregation via molecular simulation
We employ a recently developed coarse-grained model for peptides and proteins
where the effect of pH is automatically included. We explore the effect of pH
in the aggregation process of the amyloidogenic peptide KTVIIE and two related
sequences, using three different pH environments. Simulations using large
systems (24 peptides chains per box) allow us to correctly account for the
formation of realistic peptide aggregates. We evaluate the thermodynamic and
kinetic implications of changes in sequence and pH upon peptide aggregation,
and we discuss how a minimalistic coarse-grained model can account for these
details.Comment: 21 pages, 4 figure
Geometric stabilization of extended S=2 vortices in two-dimensional photonic lattices: theoretical analysis, numerical computation and experimental results
In this work, we focus our studies on the subject of nonlinear discrete
self-trapping of S=2 (doubly-charged) vortices in two-dimensional photonic
lattices, including theoretical analysis, numerical computation and
experimental demonstration. We revisit earlier findings about S=2 vortices with
a discrete model, and find that S=2 vortices extended over eight lattice sites
can indeed be stable (or only weakly unstable) under certain conditions, not
only for the cubic nonlinearity previously used, but also for a saturable
nonlinearity more relevant to our experiment with a biased photorefractive
nonlinear crystal. We then use the discrete analysis as a guide towards
numerically identifying stable (and unstable) vortex solutions in a more
realistic continuum model with a periodic potential. Finally, we present our
experimental observation of such geometrically extended S=2 vortex solitons in
optically induced lattices under both self-focusing and self-defocusing
nonlinearities, and show clearly that the S=2 vortex singularities are
preserved during nonlinear propagation
- …