arXiv subjects

Sidney R. Nagel

Publications and source records attributed to Sidney R. Nagel.

At least 37 records · Page 2Linked to original sources

arXiv2019

Periodic training of creeping solids

We consider disordered solids in which the microscopic elements can deform plastically in response to stresses on them. We show that by driving the system periodically, this plasticity can be exploited to train in desired elastic properties, both in the global moduli and in local "allosteric" interactions. Periodic driving can couple an applied "source" strain to a target strain over a path in the energy landscape. This coupling allows control of the system's response even at large strains well into the nonlinear regime, where it can be difficult to achieve control simply by design.

cond-mat.soft↗

arXiv2019

Memory formation in matter

Memory formation in matter is a theme of broad intellectual relevance; it sits at the interdisciplinary crossroads of physics, biology, chemistry, and computer science. Memory connotes the ability to encode, access, and erase signatures of past history in the state of a system. Once the system has completely relaxed to thermal equilibrium, it is no longer able to recall aspects of its evolution. Memory of initial conditions or previous training protocols will be lost. Thus many forms of memory are intrinsically tied to far-from-equilibrium behavior and to transient response to a perturbation. This general behavior arises in diverse contexts in condensed matter physics and materials: phase change memory, shape memory, echoes, memory effects in glasses, return-point memory in disordered magnets, as well as related contexts in computer science. Yet, as opposed to the situation in biology, there is currently no common categorization and description of the memory behavior that appears to be prevalent throughout condensed-matter systems. Here we focus on material memories. We will describe the basic phenomenology of a few of the known behaviors that can be understood as constituting a memory. We hope that this will be a guide towards developing the unifying conceptual underpinnings for a broad understanding of memory effects that appear in materials.

cond-mat.soft↗

arXiv2019

Ideal isotropic auxetic networks from random networks

Auxetic materials are characterized by a negative Poisson's ratio, $\mathrmν$. As the Poisson's ratio becomes negative and approaches the lower isotropic mechanical limit of $\mathrm{ν= -1}$, materials show enhanced resistance to impact and shear, making them suitable for applications ranging from robotics to impact mitigation. Past experimental efforts aimed at reaching the $\mathrm{ν= -1}$ limit have resulted in highly anisotropic materials, which show a negative Poisson's ratio only when subjected to deformations along specific directions. Isotropic designs have only attained moderately auxetic behavior, or have led to structures that cannot be manufactured in 3D. Here, we present a design strategy to create isotropic structures from disordered networks that leads to Poisson's ratios as low as $\mathrm{ν= -0.98}$. The materials conceived through this approach are successfully fabricated in the laboratory and behave as predicted. The Poisson's ratio $\mathrmν$ is found to depend on network structure and bond strengths; this sheds light on the structural motifs that lead to auxetic behavior. The ideas introduced here can be generalized to 3D, a wide range of materials, and a spectrum of length scales, thereby providing a general platform that could impact technology.

cond-mat.soft↗

arXiv2019

Directed aging, memory and Nature's greed

Disordered materials are often out of equilibrium and evolve very slowly. This allows a memory of the imposed strains or preparation conditions to be encoded in the material. Here we consider "directed aging", where the elastic properties of a material evolve in the direction defined by its aging history. The evolution to a lower-energy configuration is controlled by steepest decent and affects stressed regions differently from unstressed ones. This process can be considered to be a "greedy algorithm" of Nature. Our experiments and simulations illustrate directed aging in examples in which the material's elasticity evolves as a direct consequence of the imposed deformation; the material itself decides how to evolve in order to produce responses that were not present inherently in the material.

cond-mat.soft↗

arXiv2019

A nonlinear, geometric Hall effect without magnetic field

The classical Hall effect, the traditional means of determining charge-carrier sign and density in a conductor, requires a magnetic field to produce transverse voltages across a current-carrying wire. We show that along curved paths -- $\mathrm{\textit{without}}$ any magnetic field -- geometry alone can produce nonlinear transverse potentials that reflect the charge-carrier sign and density. We demonstrate this effect in curved graphene wires where the transverse potentials are consistent with the doping and change polarity as we switch the carrier sign. In straight wires, we measure transverse potential fluctuations with random polarity demonstrating that the current follows a complex, tortuous path. This geometrically-induced potential offers a sensitive characterization of inhomogeneous current flow in thin films.

cond-mat.mes-hall↗

arXiv2018

Topology and ground state degeneracy of tetrahedral smectic vesicles

Chemical design of block copolymers makes it possible to create polymer vesicles with tunable microscopic structure. Here we focus on a model of a vesicle made of smectic liquid-crystalline block copolymers at zero temperature. The vesicle assumes a faceted tetrahedral shape and the smectic layers arrange in a stack of parallel straight lines with topological defects localized at the vertices. We counted the number of allowed states at $T=0$. For any fixed shape, we found a two-dimensional countable degeneracy in the smectic pattern depending on the tilt angle between the smectic layers and the edge of the tetrahedral shell. For most values of the tilt angle, the smectic layers contain spiral topological defects. The system can spontaneously break chiral symmetry when the layers organize into spiral patterns, composed of a bound pair of $+1/2$ disclinations. Finally, we suggest possible applications of tetrahedral smectic vesicles in the context of functionalizing defects and the possible consequences of the spiral structures for the rigidity of the vesicle.

cond-mat.soft↗

arXiv2018

Diffusion-driven transition between two regimes of viscous fingering

Viscous fingering patterns can form at the interface between two immiscible fluids confined in the gap between a pair of flat plates; whenever the fluid with lower viscosity displaces the one of higher viscosity the interface is unstable. For miscible fluids the situation is more complicated due to the formation of interfacial structure in the thin dimension spanning the gap. Here we study the effect of the inherent diffusion between the two miscible fluids on this structure and on the viscous fingering patterns that emerge. We discover an unexpected transition separating two distinct regimes where the pattern morphologies and mode of onset are different. This transition is marked by a regime of transient stability as the structure of the fingers evolves from having three-dimensional structure to being quasi-two dimensional. The presence of diffusion allows an instability to form where it was otherwise forbidden.

physics.flu-dyn↗

arXiv2018

The limits of multifunctionality in tunable networks

Nature is rife with networks that are functionally optimized to propagate inputs in order to perform specific tasks. Whether via genetic evolution or dynamic adaptation, many networks create functionality by locally tuning interactions between nodes. Here we explore this behavior in two contexts: strain propagation in mechanical networks and pressure redistribution in flow networks. By adding and removing links, we are able to optimize both types of networks to perform specific functions. We define a single function as a tuned response of a single "target" link when another, predetermined part of the network is activated. Using network structures generated via such optimization, we investigate how many simultaneous functions such networks can be programmed to fulfill. We find that both flow and mechanical networks display qualitatively similar phase transitions in the number of targets that can be tuned, along with the same robust finite-size scaling behavior. We discuss how these properties can be understood in the context of a new class of constraint-satisfaction problems.

cond-mat.soft↗

arXiv2018

Characteristic interfacial structure behind a rapidly moving contact line

In forced wetting, a rapidly moving surface drags with it a thin layer of trailing fluid as it is plunged into a second fluid bath. Using high-speed interferometry, we find characteristic structure in the thickness of this layer with multiple thin flat triangular structures separated by much thicker regions. These features, depending on liquid viscosity and penetration velocity, are robust and occur in both wetting and de-wetting geometries. Their presence clearly shows the inadequacy of theoretical analysis that ignores the instability in the transverse direction.

cond-mat.soft↗

arXiv2018

Two diverging length scales in the structure of jammed packings

At densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first, $ξ_{Z}$, is associated with the two-point correlation function for the number of contacts on two particles as a function of the particle separation. The second, $ξ_{f}$, is associated with contact-number fluctuations in subsystems of different sizes. On scales below $ξ_{f}$ the fluctuations are highly suppressed, similar to the phenomenon of hyperuniformity usually associated with density fluctuations. The exponents for the divergence of $ξ_{Z}$ and $ξ_{f}$ are different and appear to be different in two and three dimensions.

cond-mat.soft↗

arXiv2018

Drop splashing is independent of substrate wetting

A liquid drop impacting a dry solid surface with sufficient kinetic energy will splash, breaking apart into numerous secondary droplets. This phenomenon shows many similarities to forced wetting, including the entrainment of air at the contact line. Because of these similarities and the fact that forced wetting has been shown to depend on the wetting properties of the surface, existing theories predict splashing to depend on wetting properties as well. However, using high-speed interference imaging we observe that at high capillary numbers wetting properties have no effect on splashing for various liquid-surface combinations. Additionally, by fully resolving the Navier-Stokes equations at length and time scales inaccessible to experiments, we find that the shape and motion of the air-liquid interface at the contact line at the edge of the droplet are independent of wettability. We use these findings to evaluate existing theories and to compare splashing with forced wetting.

physics.flu-dyn↗

arXiv2017

Role of local response in manipulating the elastic properties of disordered solids by bond removal

We explore the range over which the elasticity of disordered spring networks can be manipulated by the removal of selected bonds. By taking into account the local response of a bond, we demonstrate that the effectiveness of pruning can be improved so that auxetic (i.e., negative Poisson's ratio) materials can be designed without the formation of cracks even while maintaining the global isotropy of the network. The bulk, $B$, and shear, $G$, moduli scale with the number of bonds removed and we estimate the exponents characterizing these power laws. We also find that there are spatial correlation lengths in the change of $B$ and $G$ upon removing different bonds that diverge as the network approaches the isostatic limit where the excess coordination number $ΔZ\rightarrow0$.

cond-mat.soft↗

arXiv2017

Linking microscopic and macroscopic response in disordered solids

The modulus of a rigid network of harmonic springs depends on the sum of the energies in each of the bonds due to the applied distortion: compression in the case of the bulk modulus, $B$, or shear in the case of the shear modulus, $\mathcal{G}$. The distortion need not be global and we introduce a local modulus, $L_{i}$, associated with changing the equilibrium length of a single bond, $i$, in the network. We show that $L_{i}$ is useful for understanding many aspects of the mechanical response of the entire system. For example, it allows an understanding, and efficient computation, of how each bond in a network contributes to global properties such as $B$ and $\mathcal{G}$ and sheds light on how a particular bond's contribution to one modulus is, or is not, correlated with its contribution to another.

cond-mat.soft↗

arXiv2017

Period proliferation in periodic states in cyclically sheared jammed solids

Athermal disordered systems can exhibit a remarkable response to an applied oscillatory shear: after a relatively few shearing cycles, the system falls into a configuration that had already been visited in a previous cycle. After this point the system repeats its dynamics periodically despite undergoing many particle rearrangements during each cycle. We study the behavior of orbits as we approach the jamming point in simulations of jammed particles subject to oscillatory shear at fixed pressure and zero temperature. As the pressure is lowered, we find that it becomes more common for the system to find periodic states where it takes multiple cycles before returning to a previously visited state. Thus, there is a proliferation of longer periods as the jamming point is approached.

cond-mat.soft↗

arXiv2017

Instabilities of jammed packings of frictionless spheres under compression

We consider the contribution to the density of vibrational states and the distribution of energy barrier heights of incipient instabilities in a glass modeled by a jammed packing of spheres. On approaching an instability, the frequency of a normal mode and the height of the energy barrier to cross into a new ground state both vanish. These instabilities produce a contribution to the density of vibrational states that scales as $ω^3$ at low frequencies $ω$, but which vanishes in the thermodynamic limit. In addition, they affect an anharmonic property, the distribution of energy barriers $ΔH$, giving a contribution that scales as $ΔH^{-1/3}$ at low barrier heights, which should be universal for jammed and glassy systems.

cond-mat.soft↗

arXiv2017

Emergent SO(3) Symmetry of the Frictionless Shear Jamming Transition

We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actually have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor.

cond-mat.soft↗

arXiv2017

A model for approximately stretched-exponential relaxation with continuously varying stretching exponents

Relaxation in glasses is often approximated by a stretched-exponential form: $f(t) = A \exp [-(t/τ)^β]$. Here, we show that the relaxation in a model of sheared non-Brownian suspensions developed by Corté et al. [Nature Phys. 4, 420 (2008)] can be well approximated by a stretched exponential with an exponent $β$ that depends on the strain amplitude: $0.25 < β< 1$. In a one-dimensional version of the model, we show how the relaxation originates from density fluctuations in the initial particle configurations. Our analysis is in good agreement with numerical simulations and reveals a functional form for the relaxation that is distinct from, but well approximated by, a stretched-exponential function.

cond-mat.soft↗

arXiv2017

Perspectives on opportunities in experimental soft-matter science

Soft materials consist of basic units that are significantly larger than an atom but much smaller than the overall dimensions of the sample. The label "soft condensed matter" emphasizes that the large basic building blocks of these materials produce low elastic moduli that govern a material's ability to withstand deformations. Aside from softness, there are many other properties that are also caused by the large size of the constituent building blocks. Soft matter is dissipative, disordered, far-from-equilibrium, non-linear, thermal and entropic, slow, observable, gravity-affected, patterned, non-local, interfacially elastic and active. This is only a partial list of how matter created from large component particles is distinct from "hard matter" composed of constituents at an atomic scale. Issues inherent in soft matter raise problems that are broadly important in diverse areas of science and require multiple modes of attack. For example, far-from-equilibrium behavior is confronted in biology, chemistry, geophysics, astrophysics and nuclear physics. Similarly, issues dealing with disorder appear broadly throughout many branches of inquiry wherever rugged landscapes are invoked. This article reviews the discussions that occurred during a workshop held on January 30-31, 2016 in which opportunities in soft-matter experiment were surveyed. Soft matter has had an exciting history of discovery and continues to be a fertile ground for future research.

cond-mat.soft↗