arXiv subjects

Behrooz Yousefzadeh

Publications and source records attributed to Behrooz Yousefzadeh.

16 recordsLinked to original sources

arXiv2026

Waves 2026 Book of Abstracts

WAVES 2026, 17th International Conference on Mathematical and Numerical Aspects of Wave Propagation Concordia University (John Molson Building), Montreal, Canada, June 22-26, 2026 WAVES 2026 is the seventeenth meeting in a long-running biennial series that has, throughout its history, alternated between Europe and North America to advance the mathematical and numerical study of wave propagation. Hosted at the John Molson Building of Concordia University in Montreal from June 22 to 26, 2026, the conference continues this tradition as a leading international forum where theory, computation, and application meet. The scientific program spans the full breadth of mathematical and numerical techniques for wave phenomena, from the modeling and analysis of the governing partial differential equations to the design, analysis, and implementation of efficient computational methods. Representative themes include acoustic, electromagnetic, elastic, and seismic wave propagation; scattering and inverse problems; high-frequency and asymptotic methods; finite element, boundary integral, and time-domain discretizations; and absorbing boundary conditions and domain truncation, with applications reaching across the physical sciences and engineering.

math.NA↗

arXiv2026

Periodic and quasiperiodic traveling waves in nonlinear lattices with odd elasticity

Discrete nonlinear systems support a rich variety of localized and extended wave phenomena, with their dynamics sensitively dependent on the symmetries of the underlying interaction forces within the lattice. Odd elasticity, emerging in effective models of active materials, breaks the action-reaction symmetry of the local interactions and gives rise to new wave behavior. We investigate the existence and stability of traveling waves in a nonlinear lattice with odd elasticity, where the coupling force between adjacent units depends asymmetrically on the deformations of the coupled units (nonreciprocal elastic coupling). We demonstrate the existence of periodic and quasiperiodic traveling waves and analyze their spectral stability using the master stability framework. In particular, we identify the onset of Eckhaus instability based on the curvature of the associated master stability curve. This approach enables a quantitative analysis of size effects, specifically the bounds on lattice sizes for which a given traveling wave is stable. The stability analysis for quasiperiodic waves is based on an effective description of the envelope of the response through a rotating wave approximation, which agrees well with direct numerical simulations. Our findings establish a unified framework for understanding wave propagation characteristics in nonlinear lattices, for both periodic and quasiperiodic wave profiles. We highlight, qualitatively and quantitatively, the role of nonreciprocal stiffness on the existence and stability of nonlinear traveling waves in dissipative systems, and discuss how localization and stability depend on the interplay between nonlinearity, dissipation and odd elasticity.

nlin.PS↗

arXiv2025

Parametric Instability in Discrete Models of Spatiotemporally Modulated Materials

We investigate the phenomenon of parametric instability in discrete models of spatiotemporally modulated materials. These materials are celebrated in part because they exhibit nonreciprocal transmission characteristics. However, parametric instability may occur for strong modulations, or occasionally even at very small modulation amplitudes, and prevent the safe operation of spatiotemporally modulated devices due to an exponential growth in the response amplitude. We use Floquet theory to conduct a detailed computational investigation of parametric instability. We explore the roles of modulation parameters (frequency, amplitude, wavenumber), the number of modulated units, and damping on the stability of the system. We highlight the pivotal role of spatial modulation in parametric instability, a feature that is predominantly overlooked in this context. We use the perturbation method to obtain analytical expressions for modulation frequencies at which the response becomes unstable. We hope that our findings enable and inspire new applications of spatiotemporally modulated materials that operate at higher amplitudes.

cond-mat.mtrl-sci↗

arXiv2025

Phase-preserving nonreciprocal dynamics in coupled nonlinear oscillators

Nonreciprocity is most commonly associated with a large difference in the transmitted energy when the locations of the source and receiver are interchanged. This energy bias is accompanied by a difference in the transmitted phase. We highlight the role of this phase bias in breaking reciprocity in the steady-state vibration transmission characteristics of coupled nonlinear systems to external harmonic excitation. We show that breaking of reciprocity is most commonly accompanied by a simultaneous bias in the transmitted energy and phase. Energy bias alone, without any contribution from phase, can still lead to nonreciprocity, but only at very finely tuned system parameters. We provide a methodology for realizing response regimes of phase-preserving nonreciprocity using two independent symmetry-breaking parameters in the system. Our findings highlight the key contribution of phase in nonlinear nonreciprocity.

physics.app-ph↗

arXiv2025

Unilateral vibration transmission in mechanical systems with bilinear coupling

Unilateral transmission refers to the scenario in which the waves transmitted through a system remain in pure tension or pure compression. This transmission phenomenon may occur in systems that exhibit different effective elasticity in compression and tension; i.e. bilinear elasticity. We present a computational investigation of unilateral transmission in the steady-state response of harmonically driven mechanical systems with bilinear coupling. Starting with two bilinearly coupled oscillators, we find that breaking the mirror symmetry of the system, in either elastic or inertial properties, facilitates unilateral transmission by allowing it to occur near a primary resonance. This asymmetry also enables nonreciprocal transmission to occur. We then investigate the nonreciprocal dynamics of the system, including linear stability analysis, with a focus on unilateral transmission. We also extend our discussion to a bilinear periodic structure, for which we investigate the influence of the number of units and energy dissipation on unilateral transmission. We report on the existence of stable nonreciprocal unilateral transmission near primary and internal resonances of the system, as well as other nonreciprocal features such as period-doubled and quasiperiodic response characteristics.

nlin.PS↗

arXiv2024

Nonreciprocal Phase Shifts in Spatiotemporally Modulated Systems

Materials and devices subject to spatiotemporal modulation of their effective properties have a demonstrated ability to support nonreciprocal transmission of waves. Most notably, spatiotemporally modulated systems can restrict wave transmission to only one direction; i.e. a very large difference in the energy transmitted between two points in opposite directions. Taking on a different perspective on nonreciprocity, we here present a response regime in spatiotemporally modulated systems that is characterized by equal transmitted amplitudes (energies) but different phases. The only contributor to nonreciprocity is therefore the nonreciprocal phase shift, the difference between the transmitted phases in the opposite directions. We develop a methodology for realization of nonreciprocal phase shifts based on the response envelopes. This includes a formulation that ensures the same transmitted waveform, along with a special case of near-reciprocal transmission. We focus primarily on steady-state vibration transmission in short, weakly modulated systems, but include a special case of nonreciprocal phase shifts for systems with arbitrary length and strength of modulation. We discuss the main limitations of our methodology, as well as a pathway to overcome it, to motivate further developments on strongly modulated systems. While showcasing a new way for controlling vibration information transmission, our findings highlight the potential role of phase as an additional parameter in nonreciprocal transmission in spatiotemporally modulated systems.

physics.app-ph↗

arXiv2024

Pattern formation in coiling of falling viscous threads: Revisiting the geometric model

The "Fluid Mechanic Sewing Machine" creates periodic patterns through the coiling nature of a viscous fluid falling onto a moving surface. At relatively moderate heights, the reported patterns are translating coiling, alternating loops, W pattern, and meander. A simplified theoretical model based on the geometry and local bending of the contact point can predict these patterns. We experimentally explore the patterns in this region by collecting new data to compare with the model. Our review of the model's bifurcation diagram reveals additional patterns beyond the ones reported, although current experiments have not shown their existence. The W pattern, previously omitted in a regime diagram because of its small region, is now shown explicitly. We report on the consistent appearance of a period-doubled version of the W pattern, as well as rare appearances of resonant patterns, both reported for the first time. Comparing the theoretical model to experimental data, we find that the predicted phase diagram and the meander variation deviate from observations. These deviations hint at an unaccounted dynamics that merits further study.

nlin.PS↗

arXiv2024

Linear Nonreciprocal Dynamics of Coupled Modulated Systems

Waveguides subject to spatiotemporal modulations are known to exhibit nonreciprocal vibration transmission, whereby interchanging the locations of the source and receiver change the end-to-end transmission characteristics. The scenario of typical interest is unidirectional transmission in long, weakly modulated systems: when transmission is possible in one direction only. Here, with a view toward expanding their potential application as devices, we explore the vibration characteristics of spatiotemporally modulated systems that are short and strongly modulated. Focusing on two coupled systems, we develop a methodology to investigate the nonreciprocal vibration characteristics of both weakly and strongly modulated systems. In particular, we highlight the contribution of phase to nonreciprocity, a feature that is often overlooked. We show that the difference between the transmitted phases is the main contributor to breaking reciprocity in short systems. We clarify the roles of primary and side-band resonances, and their overlaps, in breaking reciprocity. We discuss the influence of modulation amplitude and wavenumber on the resonances of the modulated system.

physics.app-ph↗

arXiv2023

Nonreciprocal phase shifts in a nonlinear periodic waveguide

We explore nonreciprocal vibration transmission in a nonlinear periodic waveguide. Nonlinearity and asymmetry, the two necessary requirements for nonreciprocity, are both introduced within the unit cell of the periodic waveguide. We focus primarily on the contribution of phase to the nonreciprocal steady-state response of the system. To highlight the phase effects, which are rarely discussed in the literature, we investigate response regimes in which nonreciprocity is solely due to nonreciprocal phase shifts: when the locations of the source and receiver are interchanged, the amplitude of transmitted vibrations remains unchanged but the transmitted phases are not equal. We present a computational analysis of this state of phase nonreciprocity in the weakly nonlinear frequency-preserving response regime, where we characterize the response using its nonreciprocal phase shift. This allows us to systematically find a set of system parameters (including two symmetry-breaking parameters) that lead to reciprocal nonlinear response in a system with broken mirror symmetry. In other words, we show that breaking the mirror symmetry of a passive nonlinear waveguide is a necessary but insufficient condition for nonreciprocal dynamics to exist. Our findings highlight the important role of phase in nonlinear nonreciprocity and showcase the potential of asymmetry to serve as an additional design parameter.

nlin.PS↗

arXiv2022

Restoring the reciprocity invariance in nonlinear systems with broken mirror symmetry

Circumventing the reciprocity invariance has posed an interesting challenge in the design of modern devices for wave engineering. In passive devices, operating the device in the nonlinear response regime is a common means for realizing nonreciprocity. Because mirror-symmetric systems are trivially reciprocal, breaking the mirror symmetry is a necessary requirement for nonreciprocal dynamics to exist in nonlinear systems. However, the response of an asymmetric nonlinear system is not necessarily nonreciprocal. In this work, we report on the existence of stable, steady-state nonlinear reciprocal dynamics in coupled asymmetric systems subject to external harmonic excitation. We restore reciprocity in the asymmetric system by tuning two symmetry-breaking parameters simultaneously. We identify response regimes in the vicinity of the primary resonances of the system where the steady-state left-to-right transmission characteristics are identical to the right-to-left characteristics in terms of frequency, amplitude and phase. We interpret these regimes of reciprocal dynamics in the context of phase nonreciprocity, wherein incident waves undergo a nonreciprocal phase shift depending on their direction of travel. We hope these findings help design devices with new functionalities for controlling and steering of elastic waves.

physics.app-ph↗

arXiv2021

Rayleigh wave propagation in nonlinear metasurfaces

We investigate the propagation of Rayleigh waves in a half-space coupled to a nonlinear metasurface. The metasurface consists of an array of nonlinear oscillators attached to the free surface of a homogeneous substrate. We describe, analytically and numerically, the effects of nonlinear interaction force and energy loss on the dispersion of Rayleigh waves. We develop closed-form expressions to predict the dispersive characteristics of nonlinear Rayleigh waves by adopting a leading-order effective medium description. In particular, we demonstrate how hardening nonlinearity reduces and eventually eliminates the linear filtering bandwidth of the metasurface. Softening nonlinearity, in contrast, induces lower and broader spectral gaps for weak to moderate strengths of nonlinearity, and narrows and eventually closes the gaps at high strengths of nonlinearity. We also observe the emergence of a spatial gap (in wavenumber) in the in-phase branch of the dispersion curves for softening nonlinearity. Finally, we investigate the interplay between nonlinearity and energy loss and discuss their combined effects on the dispersive properties of the metasurface. Our analytical results, supported by finite element simulations, demonstrate the mechanisms for achieving tunable dispersion characteristics in nonlinear metasurfaces.

physics.app-ph↗

arXiv2020

Surface wave non-reciprocity via time-modulated metamaterials

We investigate how Rayleigh waves interact with modulated resonators located on the free surface of a semi-infinite elastic medium. We begin by studying the dynamics of a single resonator with time-modulated stiffness. In particular, we evaluate the accuracy of an analytical approximation of the resonator response and identify the parameter ranges in which its behavior remains stable. Then, we develop an analytical model to describe the interaction between surface waves and an array of resonators with spatio-temporally modulated stiffness. By combining our analytical models with full-scale numerical simulations, we demonstrate that spatio-temporal stiffness modulation of this elastic metasurface leads to the emergence of non-reciprocal features in the Rayleigh wave spectrum. Specifically, we show how the frequency content of a propagating signal can be filtered and converted when traveling through the modulated medium, and illustrate how surface-to-bulk wave conversion plays a role in these phenomena. Throughout this article, we indicate bounds of modulation parameters for which our theory is reliable, thus providing guidelines for future experimental studies on the topic.

physics.app-ph↗

arXiv2020

Bandgap widening by disorder in rainbow metamaterials

Stubbed plates, i.e., thin elastic sheets endowed with pillar-like resonators, display subwavelength, locally-resonant bandgaps that are primarily controlled by the intrinsic resonance properties of the pillars. In this work, we experimentally study the bandgap response of a tunable heterogeneous plate endowed with reconfigurable families of pillars. We demonstrate that, under certain circumstances, both the spectrum of resonant frequencies of the pillars and their spatial arrangement influence the filtering characteristics of the system. Specifically, both spatially graded and disordered arrangements result in bandgap widening. Moreover, the spectral range over which attenuation is achieved with random arrangements is on average wider than the one observed with graded configurations.

cond-mat.mtrl-sci↗

arXiv2018

Observation of nonreciprocal wave propagation in a dynamic phononic lattice

Acoustic waves in a linear time-invariant medium are generally reciprocal; however, reciprocity can break down in a time-variant system. In this Letter, we report on an experimental demonstration of nonreciprocity in a dynamic one-dimensional phononic crystal, where the local elastic properties are dependent on time. The system consists of an array of repelling magnets, and the on-site elastic potentials of the constitutive elements are modulated by an array of electromagnets. The modulation in time breaks time-reversal symmetry and opens a directional band gap in the dispersion relation. As shown by experimental and numerical results, nonreciprocal mechanical systems like the one presented here offer opportunities to create phononic diodes that can serve for rectification applications.

physics.app-ph↗

arXiv2017

Complete Delocalization in a Defective Periodic Structure

We report on the existence of stable, completely delocalized response regimes in a nonlinear defective periodic structure. In this state of complete delocalization, despite the presence of the defect, the system exhibits in-phase oscillation of all units with the same amplitude. This elimination of defect-borne localization may occur in both the free and forced responses of the system. In the absence of external driving, the localized defect mode becomes completely delocalized at a certain energy level. In the case of a damped-driven system, complete delocalization may be realized if the driving amplitude is beyond a certain threshold. We demonstrate this phenomenon numerically in a linear periodic structure with one and two defective units possessing a nonlinear restoring force. We derive closed-form analytical expressions for the onset of complete delocalization and discuss the necessary conditions for its occurrence.

nlin.PS↗

arXiv2016

Supratransmission in a Disordered Nonlinear Periodic Structure

We study the interaction among dispersion, nonlinearity, and disorder effects in the context of wave transmission through a discrete periodic structure, subjected to continuous harmonic excitation in its stop band. We consider a damped nonlinear periodic structure of finite length with disorder. Disorder is introduced throughout the structure by small changes in the stiffness parameters drawn from a uniform statistical distribution. Dispersion effects forbid wave transmission within the stop band of the linear periodic structure. However, nonlinearity leads to supratransmission phenomenon, by which enhanced wave transmission occurs within the stop band of the periodic structure when forced at an amplitude exceeding a certain threshold. The frequency components of the transmitted waves lie within the pass band of the linear structure, where disorder is known to cause Anderson localization. There is therefore a competition between dispersion, nonlinearity, and disorder in the context of supratransmission. We show that supratransmission persists in the presence of disorder. The influence of disorder decreases in general as the forcing frequency moves away from the pass band edge, reminiscent of dispersion effects subsuming disorder effects in linear periodic structures. We compute the dependence of the supratransmission force threshold on nonlinearity and strength of coupling between units. We observe that nonlinear forces are confined to the driven unit for weakly coupled systems. This observation, together with the truncation of higher-order nonlinear terms, permits us to develop closed-form expressions for the supratransmission force threshold. In sum, in the frequency range studied here, disorder does not influence the supratransmission force threshold in the ensemble-average sense, but it does reduce the average transmitted wave energy.

nlin.PS↗