arXiv subjects

L. Q. English

Publications and source records attributed to L. Q. English.

At least 19 recordsLinked to original sources

arXiv2026

Topologically Protected Spatially Localized Modes: An Easy Experimental Realization of the Su--Schrieffer--Heeger Model

In this paper, we review the basic concepts of topologically protected edge modes using the Su Schrieffer Heeger (SSH) model, originally introduced to describe electrical conductivity in doped polyacetylene polymer chains. We then propose an electrical circuit that emulates this model, provide its mathematical description, and present its experimental realization. The experimental setup is described in detail, with explanations designed to be broadly accessible without much prior familiarity with lattice theory, thus offering an introduction to this active area of research. Both theoretical predictions and experimental results confirm the presence of these modes, showing very good overall agreement. Using this concrete experimental system as a motivating example, we highlight the key aspects of topological protection.

cond-mat.mes-hall↗

arXiv2025

Realization and characterization of an all-bands-flat electrical lattice

We construct an electrical all-bands-flat (ABF) lattice and experimentally generate compact localized states (CLSs) therein. The lattice is a diamond (rhombic) chain and implemented as a network of capacitors and inductors, as well as voltage inverters (using operational amplifiers) in order to introduce a $π$-phase flux within each diamond. The network's normal modes split into three flat bands, and the corresponding CLSs can be excited in isolation via a two-node driving at the flat band frequencies. We also examine the role of the lattice edges and their interaction with the CLSs. Finally, we compare the experimental results to tight-binding predictions and obtain very good agreement. This analysis paves the way for further experimental implementations of ABF systems in electric networks, especially with an eye towards exploring their interplay with nonlinearity.

cond-mat.mes-hall↗

arXiv2024

Compact Localized States in Electric Circuit Flatband Lattices

We generate compact localized states in an electrical diamond lattice, comprised of only capacitors and inductors, via local driving near its flatband frequency. We compare experimental results to numerical simulations and find very good agreement. We also examine the stub lattice, which features a flatband of a different class where neighboring compact localized states share lattice sites. We find that local driving, while exciting the lattice at that flatband frequency, is unable to isolate a single compact localized state due to their non-orthogonality. Finally, we introduce lattice nonlinearity and showcase the realization of nonlinear compact localized states in the diamond lattice. Our findings pave the way of applying flatband physics to complex electric circuit dynamics.

cond-mat.mes-hall↗

arXiv2022

An Ising machine based on networks of subharmonic electrical resonators

We explore a case example of networks of classical electronic oscillators evolving towards the solution of complex optimization problems. We show that when driven into subharmonic response, a network of such nonlinear electrical resonators can minimize the Ising Hamiltonian on non-trivial graphs such as antiferromagnetically coupled rewired-M{ö}bius ladders. In this context, the spin-up and spin-down states of the Ising machine are represented by the oscillators' response at the even or odd driving cycles. Our experimental setting of driven nonlinear oscillators coupled via a programmable switch matrix leads to a unique energy minimizer when one such exists, and probes frustration where appropriate. Theoretical modeling of the electronic oscillators and their couplings allows us to accurately reproduce the qualitative features of the experimental results. This suggests the promise of this setup as a prototypical one for exploring the capabilities and limitations of such an unconventional computing platform.

nlin.PS↗

arXiv2021

Optimizing regenerative braking -- a variational calculus approach

We examine some basic physics surrounding regenerative braking and air drag. First, we analyze under what conditions it becomes energetically favorable to use aggressive regenerative braking to reach a lower speed over ``coasting'' where one relies solely on air drag to slow down. We then proceed to reformulate the question as an optimization problem to find the velocity-profile that maximizes battery charge. Making a simplifying assumption on battery-charging efficiency, we formulate the recovered energy as an integral quantity and solve the associated Euler-Lagrange equation to find the optimal braking curve. Using Lagrange-multipliers, we also explore the effect of adding a fixed-displacement constraint.

physics.class-ph↗

arXiv2020

Flip and Neimark-Sacker Bifurcations in a Coupled Logistic Map System

In this paper we consider a system of strongly coupled logistic maps involving two parameters. We classify and investigate the stability of its fixed points. A local bifurcation analysis of the system using Center Manifold is undertaken and then supported by numerical computations.This reveals the existence of reverse flip and Neimark-Sacker bifurcations.

nlin.CD↗

arXiv2020

Nonlinear edge modes in a honeycomb electrical lattice near the Dirac points

We examine - both experimentally and numerically - a two-dimensional nonlinear driven electrical lattice with honeycomb structure. Drives are considered over a range of frequencies both outside (below and above) and inside the band of linear modes. We identify a number of discrete breathers both existing in the bulk and also (predominantly) ones arising at the domain boundaries, localized either along the arm-chair or along the zig-zag edges. The types of edge-localized breathers observed and computed emerge in distinct frequency bands near the Dirac-point frequency of the dispersion surface while driving the lattice subharmonically (in a spatially homogeneous manner). These observations/computations can represent a starting point towards the exploration of the interplay of nonlinearity and topology in an experimentally tractable system such as the honeycomb electrical lattice.

nlin.PS↗

arXiv2019

Linear impurity modes in an electrical lattice: Theory and Experiment

We examine theoretically and experimentally the localized %and extended electrical modes existing in a bi-inductive electrical lattice containing a bulk or a surface capacitive impurity. By means of the formalism of lattice Green's functions, we are able to obtain closed-form expressions for the frequencies of the impurity (bound-state) eigenmodes and for their associated spatial profiles. This affords us a systematic understanding of how these mode properties change as a function of the system parameters. We test these analytical results against experimental measurements, in both the bulk and surface cases, and find very good agreement. Lastly, we turn to a series of quench experiments, where either a parameter of the lattice or the lattice geometry itself is rapidly switched between two values or configurations. In all cases, we are able to naturally explain the results of such quench experiments from the larger analytical picture that emerges as a result of the detailed characterization of the impurity-mode solution branches.

nlin.PS↗

arXiv2018

Experimental and numerical observation of dark and bright discrete solitons in the band-gap of a diatomic-like electrical lattice

We observe dark and bright intrinsic localized modes (ILMs) or discrete breathers (DB) experimentally and numerically in a diatomic-like electrical lattice. The generation of dark ILMs by driving a dissipative lattice with spatially-homogenous amplitude is, to our knowledge, unprecedented. In addition, the experimental manifestation of bright breathers within the bandgap is also novel in this system. In experimental measurements the dark modes appear just below the bottom of the top branch in frequency. As the frequency is then lowered further into the band-gap, the dark DBs persist, until the nonlinear localization pattern reverses and bright DBs appear on top of the finite background. Deep into the bandgap, only a single bright structure survives in a lattice of 32 nodes. The vicinity of the bottom band also features bright and dark self-localized excitations. These results pave the way for a more systematic study of dark breathers and their bifurcations in diatomic-like chains.

nlin.PS↗

arXiv2018

Resonant Localized Modes in Electrical Lattices with Second Neighbor Coupling

We demonstrate experimentally and corroborate numerically that an electrical lattice with nearest-neighbor and second-neighbor coupling can simultaneously support long-lived coherent structures in the form of both standard intrinsic localized modes (ILMs), as well as resonant ILMs. In the latter case, the wings of the ILM exhibit oscillations due to resonance with a degenerate plane-wave mode. This kind of localized mode has also been termed nanopteron. Here we show experimentally and using realistic simulations of the system that the nanopteron can be stabilized via both direct and subharmonic driving. In the case of excitations at the zone center (i.e., at wavenumber $k=0$), we observed stable ILMs, as well as a periodic localization pattern in certain driving regimes. In the zone boundary case (of wavenumber $k=π/a$, where $a$ is the lattice spacing), the ILMs are always resonant with a plane-wave mode, but can nevertheless be stabilized by direct (staggered) and subharmonic driving.

nlin.PS↗

arXiv2018

Impulse-induced localized nonlinear modes in an electrical lattice

Intrinsic localized modes, also called discrete breathers, can exist under certain conditions in one-dimensional nonlinear electrical lattices driven by external harmonic excitations. In this work, we have studied experimentally the efectiveness of generic periodic excitations of variable waveform at generating discrete breathers in such lattices. We have found that this generation phenomenon is optimally controlled by the impulse transmitted by the external excitation (time integral over two consecutive zeros

nlin.PS↗

arXiv2017

Direct observation of chimera-like states in a ring of coupled electronic self-oscillators

Chimera states are characterized by the symmetry-breaking coexistence of synchronized and incoherent groups of oscillators in certain chains of identical oscillators. We report on the direct experimental observation of states reminiscent of such chimeras within a ring of coupled electronic (Wien-bridge) oscillators, and compare these to numerical simulations of a theoretically derived model. Following up on earlier work characterizing the pairwise interaction of Wien-bridge oscillators by Kuramoto-Sakaguchi phase dynamics, we develop a lattice model for a chain thereof, featuring an {\it exponentially decaying} spatial kernel. We find that for certain values of the Sakaguchi parameter $α$, chimera-like states involving the coexistence of two clearly-separated regions of distinct dynamical behavior can establish themselves in the ring lattice, characterized by both traveling and stationary coexistence domains of synchronization.

nlin.PS↗

arXiv2016

The emergence and analysis of Kuramoto-Sakaguchi-like models as an effective description for the dynamics of coupled Wien-bridge oscillators

We derive the Kuramoto-Sakaguchi model from the basic circuit equations governing two coupled Wien-bridge oscillators. A Wien-bridge oscillator is a particular realization of a tunable autonomous oscillator that makes use of frequency filtering (via a RC band-pass filter) and positive feedback (via an Op-Amp). In the last few years, such oscillators have started to be utilized in synchronization studies. We first show that the Wien-bridge circuit equations can be cast in the form of a coupled pair of Duffing - Van der Pol equations. Subsequently, by applying the method of multiple time scales, we derive the differential equations that govern the slow evolution of the oscillator phases and amplitudes. These equations are directly reminiscent of the Kuramoto-Sakaguchi type models for the study of synchronization. We analyze the resulting system in terms of existence and stability of various coupled oscillator solutions and explain on that basis how their synchronization emerges. The phase-amplitude equations are also compared numerically to the original circuit equations, and good agreement is found. Finally, we report on experimental measurements on two coupled Wien-bridge oscillators and relate the results back to the theoretical predictions.

nlin.PS↗

arXiv2015

Multifrequency and edge breathers in the discrete sine-Gordon system via subharmonic driving: theory, computation and experiment

We consider a chain of torsionally-coupled, planar pendula shaken horizontally by an external sinusoidal driver. It has been known that in such a system, theoretically modeled by the discrete sine-Gordon equation, intrinsic localized modes, also known as discrete breathers, can exist. Recently, the existence of multifrequency breathers via subharmonic driving has been theoretically proposed and numerically illustrated by Xu {\em et al.} in Phys. Rev. E {\bf 90}, 042921 (2014). In this paper, we verify this prediction experimentally. Comparison of the experimental results to numerical simulations with realistic system parameters (including a Floquet stability analysis), and wherever possible to analytical results (e.g. for the subharmonic response of the single driven-damped pendulum), yields good agreement. Finally, we report on period-1 and multifrequency edge breathers which are localized at the open boundaries of the chain, for which we have again found good agreement between experiments and numerical computations

nlin.PS↗

arXiv2013

Nonlinear localized modes in two-dimensional electrical lattices

We report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear electrical lattices. Both stationary and traveling self-localized modes were generated experimentally and theoretically in a family of two-dimensional square, as well as hon- eycomb lattices composed of 6x6 elements. Specifically, we find regions in driver voltage and frequency where stationary discrete breathers, also known as intrinsic localized modes (ILM), exist and are stable due to the interplay of damping and spatially homogeneous driving. By introduc- ing additional capacitors into the unit cell, these lattices can controllably induce traveling discrete breathers. When more than one such ILMs are experimentally generated in the lattice, the interplay of nonlinearity, discreteness and wave interactions generate a complex dynamics wherein the ILMs attempt to maintain a minimum distance between one another. Numerical simulations show good agreement with experimental results, and confirm that these phenomena qualitatively carry over to larger lattice sizes.

nlin.PS↗

arXiv2011

Discrete breathers in a nonlinear electric line: Modeling, Computation and Experiment

We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is proposed by using a nonlinear form for the varactor characteristics through the current and capacitance dependence on the voltage. For an electrical line composed of 32 elements, we find the regions, in driver voltage and frequency, where $n$-peaked breather solutions exist and characterize their stability. The results are compared to experimental measurements with good quantitative agreement. We also examine the spontaneous formation of $n$-peaked breathers through modulational instability of the homogeneous steady state. The competition between different discrete breathers seeded by the modulational instability eventually leads to stationary $n$-peaked solutions whose precise locations is seen to sensitively depend on the initial conditions.

nlin.PS↗

arXiv2009

Learning-rate dependent clustering and self-development in a network of coupled phase oscillators

We investigate the role of the learning rate in a Kuramoto Model of coupled phase oscillators in which the coupling coefficients dynamically vary according to a Hebbian learning rule. According to the Hebbian theory, a synapse between two neurons is strengthened if they are simultaneously co-active. Two stable synchronized clusters in anti-phase emerge when the learning rate is larger than a critical value. In such a fast learning scenario, the network eventually constructs itself into an all-to-all coupled structure, regardless of initial conditions in connectivity. In contrast, when learning is slower than this critical value, only a single synchronized cluster can develop. Extending our analysis, we explore whether self-development of neuronal networks can be achieved through an interaction between spontaneous neural synchronization and Hebbian learning. We find that self-development of such neural systems is impossible if learning is too slow. Finally, we demonstrate that similar to the acquisition and consolidation of long-term memory, this network is capable of generating and remembering stable patterns.

nlin.AO↗

arXiv2007

Driven Intrinsic Localized Modes in a Coupled Pendulum Array

Intrinsic localized modes (ILMs), also called discrete breathers, are directly generated via modulational instability in an array of coupled pendulums. These ILMs can be stabilized over a range of driver frequencies and amplitudes. They are characterized by a pi-phase difference between their center and wings. At higher driver frequencies, these ILMs are observed to disintegrate via a pulsating instability, and the mechanism of this breather instability is investigated.

nlin.PS↗