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Nonlinear Sciences

New submissions

[ total of 11 entries: 1-11 ]
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New submissions for Fri, 23 Aug 19

[1]  arXiv:1908.08274 [pdf, other]
Title: Invasion Fronts Outside the Homoclinic Snaking Region in the Planar Swift-Hohenberg Equation
Authors: David J.B. Lloyd
Comments: 42 pages, 22 figures
Subjects: Pattern Formation and Solitons (nlin.PS); Dynamical Systems (math.DS)

In this paper, we carry out numerical bifurcation analysis of depinning of fronts near the homoclinic snaking region, involving a spatial stripe cellular pattern embedded in a quiescent state, in the two-dimensional Swift-Hohenberg equation with either a quadratic-cubic or cubic-quintic nonlinearity. We focus on depinning fronts involving stripes that are orientated either parallel, oblique and perpendicular to the front interface, and almost planar depinning fronts. We show that invading parallel depinning fronts select both a far-field wavenumber and a propagation wavespeed whereas retreating parallel depinning fronts come in families where the wavespeed is a function of the far-field wavenumber. Employing a far-field core decomposition, we propose a boundary value problem for the invading depinning fronts which we numerically solve and use path-following routines to trace out bifurcation diagrams. We then carry out a thorough numerical investigation of the parallel, oblique, perpendicular stripe, and almost planar invasion fronts. We find that almost planar invasion fronts in the cubic-quintic Swift-Hohenberg equation bifurcate off parallel invasion fronts and co-exist close to the homoclinic snaking region. Sufficiently far from the 1D homoclinic snaking region, no almost planar invasion fronts exist and we find that parallel invasion stripe fronts may regain transverse stability if they propagate above a critical speed. Finally, we show that depinning fronts shed light on the time simulations of fully localised patches of stripes on the plane. The numerical algorithms detailed have wider application to general modulated fronts and reaction-diffusion systems.

[2]  arXiv:1908.08470 [pdf, other]
Title: Nests and Chains of Hofstadter Butterflies
Subjects: Chaotic Dynamics (nlin.CD); Quantum Gases (cond-mat.quant-gas)

The \lq Hofstadter butterfly', a plot of the spectrum of an electron in a two-dimensional periodic potential with a uniform magnetic field, contains subsets which resemble small, distorted images of the entire plot. We show how the sizes of these sub-images are determined, and calculate scaling factors describing their self-similar nesting, revealing an un-expected simplicity in the fractal structure of the spectrum. We also characterise semi-infinite chains of sub-images, showing one end of the chain is a result of gap closure, and the other end is at an accumulation point.

Cross-lists for Fri, 23 Aug 19

[3]  arXiv:1908.08105 (cross-list from cond-mat.dis-nn) [pdf, other]
Title: Memristive Networks: from Graph Theory to Statistical Physics
Comments: 7 pages double columns; invited EPL Perspectives paper
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Statistical Mechanics (cond-mat.stat-mech); Adaptation and Self-Organizing Systems (nlin.AO)

We provide an introduction to a very specific toy model of memristive networks, for which an exact differential equation for the internal memory which contains the Kirchhoff laws is known. In particular, we highlight how the circuit topology enters the dynamics via an analysis of directed graph. We try to highlight in particular the connection between the asymptotic states of memristors and the Ising model, and the relation to the dynamics and statics of disordered systems.

[4]  arXiv:1908.08134 (cross-list from quant-ph) [pdf, other]
Title: Quantum Neimark-Sacker bifurcation
Comments: 7 pages, 6 figures
Subjects: Quantum Physics (quant-ph); Chaotic Dynamics (nlin.CD)

Recently, it has been demonstrated that asymptotic states of open quantum system can undergo qualitative changes resembling pitchfork, saddle-node, and period doubling classical bifurcations. Here, making use of the periodically modulated open quantum dimer model, we report and investigate a quantum Neimark-Sacker bifurcation. Its classical counterpart is the birth of a torus (an invariant curve in the Poincar\'{e} section) due to instability of a limit cycle (fixed point of the Poincar\'{e} map). The quantum system exhibits a transition from unimodal to bagel shaped stroboscopic distributions, as for Husimi representation, as for observables. The spectral properties of Floquet map experience changes reminiscent of the classical case, a pair of complex conjugated eigenvalues approaching a unit circle. Quantum Monte-Carlo wave function unraveling of the Lindblad master equation yields dynamics of single trajectories on "quantum torus" and allows for quantifying it by rotation number. The bifurcation is sensitive to the number of quantum particles that can also be regarded as a control parameter.

[5]  arXiv:1908.08325 (cross-list from q-bio.CB) [pdf, other]
Title: Modelling physical limits of migration by a kinetic model with non-local sensing
Subjects: Cell Behavior (q-bio.CB); Adaptation and Self-Organizing Systems (nlin.AO)

Migrating cells choose their preferential direction of motion in response to different signals and stimuli sensed by spanning their external environment. However, the presence of dense fibrous regions, lack of proper substrate, and cell overcrowding may hamper cells from moving in certain directions or even from sensing beyond regions that practically act like physical barriers. We extend the non-local kinetic model proposed by Loy and Preziosi (2019) to include situations in which the sensing radius is not constant, but depends on position, sensing direction and time as cells' behavior might be determined on the basis of information collected before reaching physically limiting configurations. We analyze how the actual possible sensing of the environment influences the dynamics by recovering the appropriate macroscopic limits and by integrating numerically the kinetic transport equation.

Replacements for Fri, 23 Aug 19

[6]  arXiv:1710.04522 (replaced) [pdf, ps, other]
Title: Haantjes Algebras and Diagonalization
Comments: 27 pages, no figures
Subjects: Mathematical Physics (math-ph); Differential Geometry (math.DG); Operator Algebras (math.OA); Exactly Solvable and Integrable Systems (nlin.SI)
[7]  arXiv:1810.01444 (replaced) [pdf, other]
Title: Regenesis and quantum traversable wormholes
Authors: Ping Gao, Hong Liu
Subjects: High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); General Relativity and Quantum Cosmology (gr-qc); Chaotic Dynamics (nlin.CD); Quantum Physics (quant-ph)
[8]  arXiv:1810.11474 (replaced) [pdf, other]
Title: Generating Multi-Scroll Chua's Attractors via Simplified Piecewise-Linear Chua's Diode
Comments: 14 pages, 15 figures
Journal-ref: IEEE Transactions on Circuits and Systems I: Regular Papers, 2019
Subjects: Chaotic Dynamics (nlin.CD); Signal Processing (eess.SP)
[9]  arXiv:1903.02690 (replaced) [pdf, other]
Title: Energy extraction of a chaotic system in a cyclic process: a Szilárd Engine perspective
Comments: 22 pages, 15 figures
Journal-ref: Soriani, A and Bonan\c{c}a, M V S, Energy extraction of a chaotic system in a cyclic process: a Szil\'ard engine perspective, J. Stat. Mech (2019) 083210
Subjects: Statistical Mechanics (cond-mat.stat-mech); Chaotic Dynamics (nlin.CD)
[10]  arXiv:1903.10030 (replaced) [pdf, ps, other]
Title: On symmetries of generalized Calogero model and Polychronakos-Frahm chain
Authors: Tigran Hakobyan
Comments: 9 pages
Journal-ref: Phys. Rev. D 99, 105011 (2019)
Subjects: High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); Mathematical Physics (math-ph); Exactly Solvable and Integrable Systems (nlin.SI)
[11]  arXiv:1905.04367 (replaced) [pdf, ps, other]
Title: Emergence of Subcritical Bifurcations in a System of Randomly Coupled Supercritical Andronov-Hopf Oscillators: A Potential Mechanism for Neural Network Type Switching
Subjects: Dynamical Systems (math.DS); Adaptation and Self-Organizing Systems (nlin.AO); Biological Physics (physics.bio-ph); Neurons and Cognition (q-bio.NC)
[ total of 11 entries: 1-11 ]
[ showing up to 2000 entries per page: fewer | more ]

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