arXiv subjects

Jayson Paulose

Publications and source records attributed to Jayson Paulose.

At least 19 recordsLinked to original sources

arXiv2026

Full-band reciprocal parametric amplification in coupled oscillator arrays

Parametric resonance provides a versatile mechanism to manipulate wave signals in time-modulated metamaterials, but typically operates within narrow wavelength or frequency ranges. Here, we show that one-dimensional arrays of coupled resonators can generically exhibit parametric amplification across an entire band under standing-wave parametric modulation. We develop a general physical framework to describe the parametric resonance of isolated bands, derive modulation conditions needed to achieve band-wide amplification for a given band, and demonstrate their validity in a model of active mechanical metamaterials based on tunable membrane resonator arrays. We numerically demonstrate applications of the proposed strategy in distortion-free amplification and temporal splitting of wave packets, with results in quantitative agreement with our theoretical calculations. Our strategies for broadband amplification can be generalized to other active wave media with nearly flat or cosine-like dispersion relations, with potential applications in loss-mitigation, noise squeezing, and programmable wave manipulation.

physics.app-ph↗

arXiv2026

Nonlinear stabilization of chiral modes in space-time modulated parametric oscillators

Phase control of parametric modulation in coupled oscillator networks enables sculpting of dynamical states with desired spatiotemporal symmetries. Symmetry-aware Floquet analysis successfully predicts such states in linear systems, but whether their symmetry properties persist under nonlinearity remains largely unexplored. Here, we establish the existence of nonlinear chiral steady states in a trio of coupled parametric oscillators with modulation phases chosen to selectively amplify a circulating mode in the linearized system. We find that a cubic nonlinearity arrests exponential growth of the amplified mode, producing a steady finite-amplitude motion that retains the expected chirality. By exploiting space-time symmetry, we reduce the dynamics to a single averaged equation that quantitatively predicts nonlinear trajectories, steady-state amplitudes, and characteristic time scales. The chiral steady states possess finite basins of attraction and are accessible from wide ranges of initial conditions and system parameters. Finite-element simulations of elastic plate resonators quantitatively reproduce these features, establishing the relevance of the reduced model to realistic continuum systems. Our results demonstrate that desirable properties of linear time-modulated systems, such as chirality and directional amplification, persist into strongly nonlinear regimes, opening pathways to robust nonreciprocal signal routing and amplification in parametrically driven platforms.

physics.class-ph↗

arXiv2025

Space-time Floquet operator: Non-reciprocity and fractional topology of space-time crystals

We introduce a space-time Floquet operator, a generalization of the conventional Floquet operator, that captures the long-time behavior of space-time crystals - systems where spatial and temporal periodicities are intrinsically intertwined. Unlike the standard Floquet operator, which describes evolution over a full time period, the space-time Floquet operator evolves the system over a fraction of the period, thereby resolving finer details of its dynamics. Its eigenmode spectrum defines a space-time band structure that unfolds conventional Floquet bands to respect the intertwined crystal symmetry in reciprocal wavevector-frequency space. We relate the topology of these space-time bands to quantized transport phenomena, such as Bloch oscillations and adiabatic charge transport, and uncover a fractional version of the latter. We also demonstrate how nonreciprocal parametric resonances are naturally anticipated by our framework. The approach applies broadly to both classical and quantum systems with space-time symmetry, including non-Hermitian crystals.

cond-mat.other↗

arXiv2023

Connecting the Dots: Range Expansions across Landscapes with Quenched Noise

When biological populations expand into new territory, the evolutionary outcomes can be strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile, spatial variability in the environment can also significantly influence the competition between sub-populations vying for space. Little is known about the interplay of these intrinsic and extrinsic sources of noise in population dynamics: When does environmental heterogeneity dominate over genetic drift or vice versa, and what distinguishes their population genetics signatures? Here, in the context of neutral evolution, we examine the interplay between a population's intrinsic, demographic noise and an extrinsic, quenched random noise provided by a heterogeneous environment. Using a multi-species Eden model, we simulate a population expanding over a landscape with random variations in local growth rates and measure how this variability affects genealogical tree structure, and thus genetic diversity. We find that, for strong heterogeneity, the genetic makeup of the expansion front is to a great extent predetermined by the set of fastest paths through the environment. The landscape-dependent statistics of these optimal paths then supersede those of the population's intrinsic noise as the main determinant of evolutionary dynamics. Remarkably, the statistics for coalescence of genealogical lineages, derived from those deterministic paths, strongly resemble the statistics emerging from demographic noise alone in uniform landscapes. This cautions interpretations of coalescence statistics and raises new challenges for inferring past population dynamics.

q-bio.PE↗

arXiv2023

Space-time symmetry and nonreciprocal parametric resonance in mechanical systems

Linear mechanical systems with time-modulated parameters can harbor oscillations with amplitudes that grow or decay exponentially with time due to the phenomenon of parametric resonance. While the resonance properties of individual oscillators are well understood, those of systems of coupled oscillators remain challenging to characterize. Here, we determine the parametric resonance conditions for time-modulated mechanical systems by exploiting the internal symmetries arising from the real-valued and symplectic nature of classical mechanics. We also determine how these conditions are further constrained when the system exhibits external symmetries. In particular, we analyze systems with space-time symmetry where the system remains invariant after a combination of discrete translation in both space and time. For such systems, we identify a combined space-time translation operator that provides more information about the dynamics of the system than the Floquet operator does, and use it to derive conditions for one-way amplification of traveling waves. Our exact theoretical framework based on symmetries enables the design of exotic responses such as nonreciprocal transport and one-way amplification in dynamic mechanical metamaterials, and is generalizable to all physical systems that obey space-time symmetry.

physics.class-ph↗

arXiv2023

A Geometric Mapping from Rectilinear Material Orthotropy to Isotropy: Insights to Plates and Shells

Orthotropic shell structures are ubiquitous in biology and engineering, from bacterial cell walls to reinforced domes. We present a rescaling transformation that maps an orthotropic shallow shell to an isotropic one with a different local geometry. The mapping is applicable to any shell section for which the material orthotropy directions match the principal curvature directions, assuming a commonly used form for the orthotropic shear modulus. Using the rescaling transformation, we derive exact expressions for the buckling pressure as well as the linear indentation response of orthotropic cylinders and general ellipsoids of revolution, which we verify against numerical simulations. Our analysis disentangles the separate contributions of geometric and material anisotropy to shell rigidity. In particular, we identify the geometric mean of orthotropic elastic constants as the key quantifier of material stiffness, playing a role akin to the Gaussian curvature which captures the geometric stiffness contribution. Besides providing insights into the mechanical response of orthotropic shells, our work rigorously establishes the validity of isotropic approximations to orthotropic shells and also identifies situations in which these approximations might fail.

cond-mat.soft↗

arXiv2023

Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra

We study a classical model of thermally fluctuating polymers confined to two dimensions, experiencing a grooved periodic potential, and subject to pulling forces both along and transverse to the grooves. The equilibrium polymer conformations are described by a mapping to a quantum system with a non-Hermitian Hamiltonian and with fermionic statistics generated by noncrossing interactions among polymers. Using molecular dynamics simulations and analytical calculations, we identify a localized and a delocalized phase of the polymer conformations, separated by a delocalization transition which corresponds (in the quantum description) to the breakdown of a band insulator when driven by an imaginary vector potential. We calculate the average tilt of the many-body system, at arbitrary shear values and filling density of polymer chains, in terms of the complex-valued non-Hermitian band structure. We find the critical shear value, the localization length, and the critical exponent by which the shear modulus diverges in terms of the branch points (exceptional points) in the band structure at which the bandgap closes. We also investigate the combined effects of non-Hermitian delocalization and localization due to both periodicity and disorder, uncovering preliminary evidence that while disorder favours localization at high values, it encourages delocalization at lower values.

cond-mat.soft↗

arXiv2022

Non-singular and singular flat bands in tunable acoustic metamaterials

Dispersionless flat bands can be classified into two types: (1) non-singular flat bands whose eigenmodes are completely characterized by compact localized states; and (2) singular flat bands that have a discontinuity in their Bloch eigenfunctions at a band touching point with an adjacent dispersive band, thereby requiring additional extended states to span their eigenmode space. In this study, we design and numerically demonstrate two-dimensional thin-plate acoustic metamaterials in which tunable flat bands of both kinds can be achieved. Non-singular flat bands are achieved by fine-tuning the ratio of the global tension and the bending stiffness in triangular and honeycomb lattices of plate resonators. A singular flat band arises in a kagome lattice due to the underlying lattice geometry, which can be made degenerate with two additional flat bands by tuning the plate tension. A discrete model of the continuum thin-plate system reveals the interplay of geometric and mechanical factors in determining the existence of flat bands of both types. The singular nature of the kagome lattice flat band is established via a metric called the Hilbert-Schmidt distance calculated between a pair of eigenstates infinitesimally close to the quadratic band touching point. We also simulate an acoustic manifestation of a robust boundary mode arising from the singular flat band and protected by real-space topology in a finite system. Our theoretical and computational study establishes a framework for exploring flat-band physics in a tunable classical system, and for designing acoustic metamaterials with potentially useful sound manipulation capabilities.

physics.app-ph↗

arXiv2022

Branching structure of genealogies in spatially growing populations and its implications for population genetics inference

Spatial models where growth is limited to the edge of the expansions have been instrumental to understand the population dynamics and the clone size distribution in growing cellular populations, such as microbial colonies and avascular tumours. A complete characterization of the coalescence process generated by spatial growth is still lacking, limiting our ability to apply classic population genetics inference to spatially growing populations. Here, we start filling this gap by investigating the statistical properties of the cell lineages generated by the two dimensional Eden model, leveraging their physical analogy with directed polymers. Our analysis provides quantitative estimates for population measurements that can easily be assessed via sequencing, such as the average number of segregating sites and the clone size distribution of a subsample of the population. Our results not only reveal remarkable features of the genealogies generated during growth, but also highlight new properties that can be misinterpreted as signs of selection if non-spatial models are inappropriately applied.

q-bio.PE↗

arXiv2021

Non-dispersive one-way signal amplification in sonic metamaterials

Parametric amplification -- injecting energy into waves via periodic modulation of system parameters -- is typically restricted to specific multiples of the modulation frequency. However, broadband parametric amplification can be achieved in active metamaterials which allow local parameters to be modulated both in space and in time. Inspired by the concept of luminal metamaterials in optics, we describe a mechanism for one-way amplification of sound waves across an entire frequency band using spacetime-periodic modulation of local stiffnesses in the form of a traveling wave. When the speed of the modulation wave approaches that of the speed of sound in the metamaterial -- a regime called the sonic limit -- nearly all modes in the forward-propagating acoustic band are amplified, whereas no amplification occurs in the reverse-propagating band. To eliminate divergences that are inherent to the sonic limit in continuum materials, we use an exact Floquet-Bloch approach to compute the dynamic excitation bands of discrete periodic systems. We find wide ranges of parameters for which the amplification is nearly uniform across the lowest-frequency band, enabling amplification of wavepackets while preserving their speed, shape, and spectral content. Our mechanism provides a route to designing acoustic metamaterials which can propagate wave pulses without losses or distortion across a wide range of frequencies.

cond-mat.soft↗

arXiv2021

Indentation responses of pressurized ellipsoidal and cylindrical elastic shells: Insights from shallow-shell theory

Pressurized elastic shells are ubiquitous in nature and technology, from the outer walls of yeast and bacterial cells to artificial pressure vessels. Indentation measurements simultaneously probe the internal pressure and elastic properties of thin shells, and serve as a useful tool for strength testing and for inferring internal biological functions of living cells. We study the effects of geometry and pressure-induced stress on the indentation stiffness of ellipsoidal and cylindrical elastic shells using shallow-shell theory. We show that the linear indentation response reduces to a single integral with two dimensionless parameters that encode the asphericity and internal pressure. This integral can be numerically evaluated in all regimes and is used to generate compact analytical expressions for the indentation stiffness in various regimes of technological and biological importance. Our results provide theoretical support for previous scaling and numerical results describing the stiffness of ellipsoids, reveal a new pressure scale that dictates the large-pressure response, and give new insights to the linear indentation response of pressurized cylinders.

cond-mat.soft↗

arXiv2021

Stopping and reversing sound via dynamic dispersion tuning in a phononic metamaterial

Slowing down, stopping, and reversing a signal is a core functionality for information processing. Here, we show that this functionality can be realized by tuning the dispersion of a periodic system through a dispersionless, or flat, band. Specifically, we propose a phononic metamaterial based on plate resonators, in which the phonon band dispersion can be modified from an acoustic-like to an optical character by modulating a uniform prestress. The switch is enabled by the change in sign of an effective coupling between fundamental modes, which generically leads to a nearly dispersion-free band at the transition point. We demonstrate how adiabatic tuning of the band dispersion can immobilize and reverse the propagation of a sound pulse in simulations of a one-dimensional resonator chain. Our study relies on the basic principles of thin-plate elasticity independently of any specific material, making our results applicable across varied length scales and experimental platforms. More broadly, our approach could be metamaterials and electronic heterostructures.

cond-mat.soft↗

arXiv2018

Topological protection can arise from thermal fluctuations and interactions

Topological quantum and classical materials can exhibit robust properties that are protected against disorder, for example for noninteracting particles and linear waves. Here, we demonstrate how to construct topologically protected states that arise from the combination of strong interactions and thermal fluctuations inherent to soft materials or miniaturized mechanical structures. Specifically, we consider fluctuating lines under tension (e.g., polymer or vortex lines), subject to a class of spatially modulated substrate potentials. At equilibrium, the lines acquire a collective tilt proportional to an integer topological invariant called the Chern number. This quantized tilt is robust against substrate disorder, as verified by classical Langevin dynamics simulations. This robustness arises because excitations in this system of thermally fluctuating lines are gapped by virtue of inter-line interactions. We establish the topological underpinning of this pattern via a mapping that we develop between the interacting-lines system and a hitherto unexplored generalization of Thouless pumping to imaginary time. Our work points to a new class of classical topological phenomena in which the topological signature manifests itself in a structural property observed at finite temperature rather than a transport measurement.

cond-mat.soft↗

arXiv2017

Localizing softness and stress along loops in three-dimensional topological metamaterials

Topological states can be used to control the mechanical properties of a material along an edge or around a localized defect. The surface rigidity of elastic networks is characterized by a bulk topological invariant called the polarization; materials with a well-defined uniform polarization display a dramatic range of edge softnesses depending on the orientation of the polarization relative to the terminating surface. However, in all three-dimensional mechanical metamaterials proposed to date, the topological edge modes are mixed with bulk soft modes and so-called Weyl loops. Here, we report the design of a gapped 3D topological metamaterial with a uniform polarization that displays a corresponding asymmetry between the number of soft modes on opposing surfaces and, in addition, no bulk soft modes. We then use this construction to localize topological soft modes in interior regions of the material by including defect structures---dislocation loops---that are unique to three dimensions. We derive a general formula that relates the difference in the number of soft modes and states of self-stress localized along the dislocation loop to the handedness of the vector triad formed by the lattice polarization, Burgers vector, and dislocation-line direction. Our findings suggest a novel strategy for pre-programming failure and softness localized along lines in 3D, while avoiding extended periodic failure modes associated with Weyl loops.

cond-mat.soft↗

arXiv2016

Spatiotemporal order and emergent edge currents in active spinner materials

Collections of interacting, self-propelled particles have been extensively studied as minimal models of many living and synthetic systems from bird flocks to active colloids. However, the influence of active rotations in the absence of self-propulsion i.e. spinning without walking) remains less explored. Here, we numerically and theoretically investigate the behaviour of ensembles of self-spinning dimers. We find that geometric frustration of dimer rotation by interactions yields spatiotemporal order and active melting with no equilibrium counterparts. At low density, the spinning dimers self-assemble into a triangular lattice with their orientations phase-locked into spatially periodic phases. The phase-locked patterns form dynamical analogues of the ground states of various spin models, transitioning from the 3-state Potts antiferromagnet at low densities to the striped herringbone phase of planar quadrupoles at higher densities. As the density is raised further, the competition between active rotations and interactions leads to melting of the active spinner crystal. Emergent edge currents, whose direction is set by the chirality of the active spinning, arise as a non-equilibrium signature of the transition to the active spinner liquid and vanish when the system eventually undergoes kinetic arrest at very high densities. Our findings may be realized in systems ranging from liquid crystal and colloidal experiments to tabletop realizations using macroscopic chiral grains.

cond-mat.soft↗

arXiv2016

Sonic Landau-level lasing and synthetic gauge fields in mechanical metamaterials

Mechanical strain can lead to a synthetic gauge field that controls the dynamics of electrons in graphene sheets as well as light in photonic crystals. Here, we show how to engineer an analogous synthetic gauge field for lattice vibrations. Our approach relies on one of two strategies: shearing a honeycomb lattice of masses and springs or patterning its local material stiffness. As a result, vibrational spectra with discrete Landau levels are generated. Upon tuning the strength of the gauge field, we can control the density of states and transverse spatial confinement of sound in the metamaterial. We also use the gauge field to design waveguides in which sound propagates robustly, as a consequence of the change in topological polarization that occurs along a domain wall in the bulk of the metamaterial. By introducing dissipation, we can selectively enhance the domain-wall-bound topological sound mode, a feature that may be exploited for the design of sound amplification by stimulated emission of radiation - SASERs, the mechanical analogs of lasers.

cond-mat.mes-hall↗

arXiv2016

Geared topological metamaterials with tunable mechanical stability

The classification of materials into insulators and conductors has been shaken up by the discovery of topological insulators that conduct robustly at the edge but not in the bulk. In mechanics, designating a material as insulating or conducting amounts to asking if it is rigid or floppy. Although mechanical structures that display topological floppy modes have been proposed, they are all vulnerable to global collapse. Here, we design and build mechanical metamaterials that are stable and yet capable of harboring protected edge and bulk modes, analogous to those in electronic topological insulators and Weyl semimetals. To do so, we exploit gear assemblies that, unlike point masses connected by springs, incorporate both translational and rotational degrees of freedom. Global structural stability is achieved by eliminating geometrical frustration of collective gear rotations extending through the assembly. The topological robustness of the mechanical modes makes them appealing across scales from engineered macrostructures to networks of toothed microrotors of potential use in micro-machines.

cond-mat.soft↗

arXiv2016

Topological mechanics of origami and kirigami

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom.

cond-mat.soft↗