arXiv subjects

Xiaoming Mao

Publications and source records attributed to Xiaoming Mao.

At least 55 records · Page 3Linked to original sources

arXiv2019

Switchable phonon diodes using nonlinear topological Maxwell lattices

Recent progress in topological mechanics have revealed a family of Maxwell lattices that exhibit topologically protected floppy edge modes. These modes lead to a strongly asymmetric elastic wave response. In this paper, we show how topological Maxwell lattices can be used to realize non-reciprocal transmission of elastic waves. Our design leverages the asymmetry associated with the availability of topological floppy edge modes and the geometric nonlinearity built in the mechanical systems response to achieve the desired non-reciprocal behavior, which can be further turned into strongly one-way phonon transport via the addition of on-site pinning potentials. Moreover, we show that the non-reciprocal wave transmission can be switched on and off via topological phase transitions, paving the way to the design of cellular metamaterials that can serve as tunable topologically protected phonon diodes.

cond-mat.soft↗

arXiv2019

Universal Continuum Theory for Topological Edge Soft Modes

Topological edge zero modes and states of self stress have been intensively studied in discrete lattices at the Maxwell point, offering robust properties concerning surface and interface stiffness and stress focusing. In this paper we present a continuum topological elasticity theory and generalize the Maxwell-Calladine index theorem to continuous elastic media. This theory not only serves as a macroscopic description for topological Maxwell lattices, but also generalizes this physics to continuous media. We define a \emph{gauge-invariant} bulk topological index, independent of microscopic details such as choice of the unit cell and lattice connectivity. This index directly predicts the number of zero modes on edges, and it naturally extends to media that deviate from the Maxwell point, depicting how topological zero modes turn into topological soft modes.

cond-mat.mtrl-sci↗

arXiv2019

Maxwell plates and phonon fractionalization

In the past a few years, topologically protected mechanical phenomena have been extensively studied in discrete lattices and networks, leading to a rich set of discoveries such as topological boundary/interface floppy modes and states of self stress, as well as one-way edge acoustic waves. In contrast, topological states in continuum elasticity without repeating unit cells remain largely unexplored, but offer wonderful opportunities for both new theories and broad applications in technologies, due to their great convenience of fabrication. In this paper we examine continuous elastic media on the verge of mechanical instability, extend Maxwell-Calladine index theorem to continua in the nonlinear regime, classify elastic media based on whether stress can be fully released, and identify two types of elastic media with topological states. The first type, which we name ``Maxwell plates'', are in strong analogy with Maxwell lattices, and exhibit a sub-extensive number of holographic floppy modes. The second type, which arise in thin plates with a small bending stiffness and a negative Gaussian curvature, exhibit fractional excitations and topological degeneracy, in strong analogy to $Z_2$ spin liquids and dimerized spin chains.

cond-mat.soft↗

arXiv2019

Physical limits to sensing material properties

Constitutive relations describe how materials respond to external stimuli such as forces. All materials respond heterogeneously at small scales, which limits what a localized sensor can discern about the global constitution of a material. In this paper, we quantify the limits of such constitutional sensing by determining the optimal measurement protocols for sensors embedded in disordered media. For an elastic medium, we find that the least fractional uncertainty with which a sensor can determine a material constant $λ_0$ is approximately \begin{equation*} \frac{δλ_0}{λ_0 } \sim \left( \frac{Δ_λ }{ λ_0^2} \right)^{1/2} \left( \frac{ d }{ a } \right)^{D/2} \left( \frac{ ξ}{ a } \right)^{D/2} \end{equation*} for $a \gg d \gg ξ$, $λ_0 \gg Δ_λ^{1/2}$, and $D>1$, where $a$ is the size of the sensor, $d$ is its spatial resolution, $ξ$ is the correlation length of fluctuations in the material constant, $Δ_λ$ is the local variability of the material constant, and $D$ is the dimension of the medium. Our results reveal how one can construct microscopic devices capable of sensing near these physical limits, e.g. for medical diagnostics. We show how our theoretical framework can be applied to an experimental system by estimating a bound on the precision of cellular mechanosensing in a biopolymer network.

cond-mat.dis-nn↗

arXiv2019

Jamming as a Multicritical Point

The discontinuous jump in the bulk modulus $B$ at the jamming transition is a consequence of the formation of a critical contact network of spheres that resists compression. We introduce lattice models with underlying under-coordinated compression resistant spring lattices to which next-nearest-neighbor springs can be added. In these models, the jamming transition emerges as a kind of multicritical point terminating a line of rigidity-percolation transitions. Replacing the under-coordinated lattices with the critical network at jamming yields a faithful description of jamming and its relation to rigidity percolation.

cond-mat.soft↗

arXiv2018

Topological mechanics in quasicrystals

We study topological mechanics in two-dimensional quasicrystalline parallelogram tilings. Topological mechanics has been studied intensively in periodic lattices in the past a few years, leading to the discovery of topologically protected boundary floppy modes in Maxwell lattices. In this paper we extend this concept to quasicrystalline parallelogram tillings and we use the Penrose tiling as our example to demonstrate how these topological boundary floppy modes arise with a small geometric perturbation to the tiling. The same construction can also be applied to disordered parallelogram tilings to generate topological boundary floppy modes. We prove the existence of these topological boundary floppy modes using a duality theorem which relates floppy modes and states of self stress in parallelogram tilings and fiber networks, which are Maxwell reciprocal diagrams to one another. We find that, due to the unusual rotational symmetry of quasicrystals, the resulting topological polarization can exhibit orientations not allowed in periodic lattices. Our result reveals new physics about the interplay between topological states and quasicrystalline order, and leads to novel designs of quasicrystalline topological mechanical metamaterials.

cond-mat.soft↗

arXiv2018

Elasticity of colloidal gels: structural heterogeneity, foppy modes, and rigidity

Rheological measurements of model colloidal gels reveal that large variations in the shear moduli as colloidal volume-fraction changes are not reflected by simple structural parameters such as the coordination number, which remains almost a constant. We resolve this apparent contradiction by conducting a normal mode analysis of experimentally measured bond networks of the gels. We find that structural heterogeneity of the gels, which leads to floppy modes and a nonaffine-affine crossover as frequency increases, evolves as a function of the volume fraction and is key to understand the frequency dependent elasticity. Without any free parameters, we achieve good qualitative agreement with the measured mechanical response. Furthermore, we achieve universal collapse of the shear moduli through a phenomenological spring-dashpot model that accounts for the interplay between fluid viscosity, particle dissipation, and contributions from the affine and non-affine network deformation.

cond-mat.soft↗

arXiv2018

Correlated rigidity percolation and colloidal gels

Rigidity percolation (RP) occurs when mechanical stability emerges in disordered networks as constraints or components are added. Here we discuss RP with structural correlations, an effect ignored in classical theories albeit relevant to many liquid-to-amorphous-solid transitions, such as colloidal gelation, which are due to attractive interactions and aggregation. Using a lattice model, we show that structural correlations shift RP to lower volume fractions. Through molecular dynamics simulations, we show that increasing attraction in colloidal gelation increases structural correlation and thus lowers the RP transition, agreeing with experiments. Hence colloidal gelation can be understood as a RP transition, but occurs at volume fractions far below values predicted by the classical RP, due to attractive interactions which induce structural correlation.

cond-mat.soft↗

arXiv2018

Random Walker Models for Durotaxis

Motile biological cells in tissue often display the phenomenon of durotaxis, i.e. they tend to move towards stiffer parts of substrate tissue. The mechanism for this behavior is not completely understood. We consider simplified models for durotaxis based on the classic persistent random walker scheme. We show that even a one-dimensional model of this type sheds interesting light on the classes of behavior cells might exhibit. Our results strongly indicate that cells must be able to sense the gradient of stiffness in order to show the effects observed in experiment. This is in contrast to the claims in recent publications that it is sufficient for cells to be more persistent in their motion on stiff substrates to show durotaxis: i.e., if would be enough to sense the value of the stiffness. We show that these cases give rise to extremely inefficient transport towards stiff regions. Gradient sensing is almost certainly the selected behavior.

physics.bio-ph↗

arXiv2018

Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies

Although topological mechanical metamaterials have been extensively studied from a theoretical perspective, their experimental characterization has been lagging. To address this shortcoming, we present a systematic laser-assisted experimental characterization of topological kagome lattices, aimed at elucidating their in-plane phononic and topological characteristics. We specifically explore the continuum elasticity limit, which is established when the ideal hinges that appear in the theoretical models are replaced by ligaments capable of supporting bending deformation, as observed for instance in realistic physical lattices. We reveal how the zero-energy floppy edge modes predicted for ideal configurations morph into finite-frequency phonon modes that localize at the edges. By probing the lattices with carefully designed excitation signals, we are able to extract and characterize all the features of a complex low-frequency acoustic regime in which bulk modes and topological edge modes overlap and entangle in response. The experiments provide unequivocal evidence of the existence of strong asymmetric wave transport regimes at finite frequencies.

cond-mat.mtrl-sci↗

arXiv2018

Folding mechanisms at finite temperature

Folding mechanisms are zero elastic energy motions essential to the deployment of origami, linkages, reconfigurable metamaterials and robotic structures. In this paper, we determine the fate of folding mechanisms when such structures are miniaturized so that thermal fluctuations cannot be neglected. First, we identify geometric and topological design strategies aimed at minimizing undesired thermal energy barriers that generically obstruct kinematic mechanisms at the microscale. Our findings are illustrated in the context of a quasi one-dimensional linkage structure that harbors a topologically protected mechanism. However, thermal fluctuations can also be exploited to deliberately lock a reconfigurable metamaterial into a fully expanded configuration, a process reminiscent of order by disorder transitions in magnetic systems. We demonstrate that this effect leads certain topological mechanical structures to exhibit an abrupt change in the pressure -- a bulk signature of the underlying topological invariant at finite temperature. We conclude with a discussion of anharmonic corrections and potential applications of our work to the the engineering of DNA origami devices and molecular robots.

cond-mat.soft↗

arXiv2018

Capillary-driven binding of thin triangular prisms at fluid interfaces

We observe capillary-driven binding between thin, equilateral triangular prisms at a flat air-water interface. The edge length of the equilateral triangle face is 120 $μm$, and the thickness of the prism is varied between 2 and 20 $μm$. For thickness to length (T/L) ratios of 1/10 or less, pairs of triangles preferentially bind in either a tip-to-tip or tip-to-midpoint edge configurations; for pairs of particles of thickness T/L = 1/5, the tip of one triangle binds to any position along the other triangle's edge. The distinct binding configurations for small T/L ratios result from physical bowing of the prisms, a property that arises during their fabrication. When bowed prisms are placed at the air-water interface, two distinct polarity states arise: prisms either sit with their center of mass above or below the interface. The interface pins to the edge of the prism's concave face, resulting in an interface profile that is similar to that of a capillary hexapole, but with important deviations close to the particle that enable directed binding. We present corresponding theoretical and numerical analysis of the capillary interactions between these prisms and show how particle bowing and contact-line pinning yield a capillary hexapole-like interaction that results in the two sets of distinct, highly-directional binding events. Prisms of all T/L ratios self-assemble into space-spanning open networks; the results suggest design parameters for the fabrication of building blocks of ordered open structures such as the Kagome lattice.

cond-mat.soft↗

arXiv2018

Fracturing of topological Maxwell lattices

We present fracturing analysis of topological Maxwell lattices when they are stretched by applied stress. Maxwell lattices are mechanical structures containing equal numbers of degrees of freedom and constraints in the bulk and are thus on the verge of mechanical instability. Recent progress in topological mechanics led to the discovery of topologically protected floppy modes and states of self stress at edges and domain walls of Maxwell lattices. When normal brittle materials are being stretched, stress focuses on crack tips, leading to catastrophic failure. In contrast, we find that when topological Maxwell lattices are being stretched, stress focuses on states of self stress domain walls instead, and bond-breaking events start at these domain walls, even in presence of cracks. Remarkably, we find that the stress-focusing feature of the self-stress domain walls persists deep into the the failure process, when a lot of damages already occurred at these domain walls. We explain the results using topological mechanics theory and discuss the potential use of these topological Maxwell lattice structures as mechanical metamaterials that exhibit high strength against fracturing and well controlled fracturing process.

cond-mat.soft↗

arXiv2017

Topological edge floppy modes in disordered fiber networks

Disordered fiber networks are ubiquitous in a broad range of natural (e.g., cytoskeleton) and manmade (e.g., aerogels) materials. In this paper, we discuss the emergence of topological floppy edge modes in these fiber networks as a result of deformation or active driving. It is known that a network of straight fibers exhibits bulk floppy modes which only bend the fibers without stretching them. We find that, interestingly, with a perturbation in geometry, these bulk modes evolve into edge modes. We introduce a topological index for these edge modes and discuss their implications in biology.

cond-mat.soft↗

arXiv2016

Fiber networks below the isostatic point: fracture without stress concentration

Crack nucleation is a ubiquitous phenomena during materials failure, because stress focuses on crack tips. It is known that exceptions to this general rule arise in the limit of strong disorder or vanishing mechanical stability, where stress distributes over a divergent length scale and the material displays diffusive damage. Here we show, using simulations, that a class of diluted lattices displays a new critical phase when they are below isostaticity, where stress never concentrates, damage always occurs over a divergent length scale, and catastrophic failure is avoided.

cond-mat.soft↗

arXiv2016

Elasticity of randomly diluted honeycomb and diamond lattices with bending forces

We use numerical simulations and an effective-medium theory to study the rigidity percolation transition of the honeycomb and diamond lattices when weak bond-bending forces are included. We use a rotationally invariant bond-bending potential, which, in contrast to the Keating potential, does not involve any stretching. As a result, the bulk modulus does not depend on the bending stiffness $κ$. We obtain scaling functions for the behavior of some elastic moduli in the limits of small $Δ\mathcal{P} = 1 - \mathcal{P}$, and small $δ\mathcal{P} = \mathcal{P} - \mathcal{P}_c$, where $\mathcal{P}$ is an occupation probability of each bond, and $\mathcal{P}_c$ is the critical probability at which rigidity percolation occurs. We find good quantitative agreement between effective-medium theory and simulations for both lattices for $\mathcal{P}$ close to one.

cond-mat.dis-nn↗

arXiv2015

Transformable topological mechanical metamaterials

Mechanical metamaterials are engineered materials that gain their remarkable mechanical properties, such as negative Poisson's ratios, negative compressibility, phononic bandgaps, and topological phonon modes, from their structure rather than composition. Here we propose a new design principle, based on a uniform soft deformation of the whole structure, to allow metamaterials to be immediately and reversibly transformed between states with contrasting mechanical and acoustic properties. These properties are protected by the topological structure of the phonon band of the whole structure and are thus highly robust against disorder and noise. We discuss the general classification of all structures that exhibit such soft deformations, and provide specific examples to demonstrate how to utilize soft deformations to transform a system between different regimes such that remarkable changes in their properties, including edge stiffness and speed of sound, can be achieved.

cond-mat.soft↗

arXiv2015

Nonlinear elasticity of disordered fiber networks

Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a stretching dominated regime of elasticity. The physics of this crossover is related to the existence of a central-force isostatic point and to the fact that for most gels the bending modulus is small. This crossover induces scaling behavior for the elastic moduli. In particular, for linear elasticity such a scaling law has been demonstrated [Broedersz et al. Nature Physics, 2011 7, 983]. In this work we generalize the scaling to the nonlinear regime with a two-parameter scaling law involving three critical exponents. We test the scaling law numerically for two disordered lattice models, and find a good scaling collapse for the shear modulus in both the linear and nonlinear regimes. We compute all the critical exponents for the two lattice models and discuss the applicability of our results to real systems.

cond-mat.soft↗