arXiv subjects

Sidney R. Nagel

Publications and source records attributed to Sidney R. Nagel.

At least 19 recordsLinked to original sources

arXiv2026

The landscape of instabilities versus shear angle in simulations

We argue that, in order to appreciate fully how disordered solids fail under sufficiently large strains or thermal noise, a material should be regarded as a network of potentially interacting instabilities occurring along different directions of forcing. We develop a tool for simulations with periodic boundary conditions that allows strains to be applied at a continuously variable angle, $θ$. This reveals an underlying landscape which consists of lines of instabilities in two dimensions. A modified polar plot provides a visualization of this strain landscape while also allowing a graphic measure of an instability's quadrupolar structure. Many lines persist over a broad angular range of applied strain; some pass through one another; others change continuously with angle or end by smoothly decreasing their magnitudes to zero. Appropriate paths through phase space allow instabilities to be circumvented and hence avoided entirely. We explain this by examining hysterons, i.e., instabilities that undo themselves upon reversing shear direction, and show that as the end of an instability line is approached, the separation between the forward and backward instabilities vanishes.

cond-mat.soft↗

arXiv2026

Basin-volume distributions in monodisperse particle packings -- the soul of memory

Mechanically stable packings of $N$ particles in $d$ dimensions lie at the minima of an $Nd$-dimensional potential energy landscape. Starting from random initial particle positions, the system can relax using gradient-based optimization until it arrives at one of the equilibrium states; all initial conditions that end at the same minimum belong to the same catchment basin. We measure the distribution of the catchment basin volumes for indistinguishable monodisperse soft spheres in both $d=2$ and $d=3$. Ordering the basins at each system size, $N$, according to their volume, $P_N(n)$, from the largest at $n=1$ to smaller at larger $n$, we find a very wide distribution of volumes which is similar in both dimensions: $P_N(n) \approx A_Nn^{-α}$ with $α\approx 1$ which, in our most favorable cases, extends over $7$ decades. We explore aspects of the connectivity of the basins, show that their structure is highly contorted, and demonstrate how these results may be used to understand the imprinting of memories in cyclic strain studies of solids.

cond-mat.soft↗

arXiv2026

Thermally Robust Cooperative Function in Mechanical Networks

Elastic networks can be tuned to exhibit complex mechanical responses and have been extensively used to study protein allostery, where a localized strain regulates the conformation at a distant site. We show that cooperative binding, where one site enhances the other's ability to function, can be improved by tuning for \textit{bidirectional} allostery: a symmetric coupling where the strain propagated between the two sites is independent of which site is perturbed. We identify a crossover temperature above which functionality breaks down due to thermal fluctuations. We introduce a modified tuning process to increase this crossover temperature, showing that function can be robust at biologically relevant temperatures if thermal stability is important.

cond-mat.soft↗

arXiv2025

Effect of translational shear on interfacial structure in the viscous fingering instability

We introduce applied shear as a method to control viscous fingering by smoothing the interface between miscible fluids. In the viscous fingering instability, a less viscous fluid displaces a more viscous one through the formation of fingers. The instability, which requires a confined geometry, is often studied in the thin gap of a quasi-two-dimensional Hele-Shaw cell. When the two fluids are miscible, the structures that form in the dimension traversing the gap are important for determining the instability onset. We demonstrate with experiments and simulations that oscillatory translational shear of the confining plates changes the gap-averaged viscosity profile so that it becomes less abrupt at the finger tips. Increasing the amplitude or velocity of the shear delays the instability onset and decreases the finger growth rate. Shear can thus be used to stabilize a pair of miscible fluids against fingering. The results show a direct correlation between a smoother viscosity profile and delayed instability. TEASER: Oscillatory shear smooths fluid interfaces, stabilizing viscous fingering in miscible fluids.

physics.flu-dyn↗

arXiv2025

Minimal cyclic behavior in sheared amorphous solids

Although jammed packings of soft spheres exist in potential energy landscapes with a vast number of minima, when subjected to cyclic shear they may revisit the same configurations repeatedly. Simple hysteretic spin models, in which particle rearrangements are represented by interacting spin flips called hysterons, capture many features of this periodic behavior. Yet it has been unclear to what extent individual rearrangements can be described by such binary objects and how such objects interact with one another. Using a particularly sensitive algorithm, we identify rearrangements in simulated jammed packings and select pairs of rearrangements that undo one another to create periodic cyclic behavior. We find that the rearrangement pairs surprisingly persist down to the smallest increments in strain, even in the smallest systems we can study. We explore the statistics of these rearrangement pairs and find that there is a relation between the amount of hysteresis and the energy drop and mean-square displacement of the particles; these results are inconsistent with the scaling found in models that treat rearrangements as localized buckling events. Finally, our analysis shows that there is no clean distinction between the "core" of an individual rearrangement and the interactions between rearrangements. These results offer insight into how complex systems such as amorphous solids can reach a limit cycle.

cond-mat.soft↗

arXiv2025

Training and re-training liquid crystal elastomer metamaterials for pluripotent functionality

Training has emerged as a promising materials design technique in which function can be acheived through repeated physical modification of an existing material rather than by direct chemical functionalization, cutting or reprocessing. This work investigates both the ability to train for function and then to erase that function on-demand in macroscopic metamaterials made from liquid crystal elastomers (LCEs). We first show that the Poisson's ratio of these disordered arrays can be tuned via directed aging to induce an auxetic response. We then show that the arrays can be reset and re-trained for another local mechanical function, allostery, thus demonstrating pluripotent functionality.

cond-mat.mtrl-sci↗

arXiv2024

Measurement of Pressure Gradients near the Interface in the Viscous Fingering Instability

The viscous fingering instability, which forms when a less-viscous fluid invades a more-viscous one within a confined geometry, is an iconic system for studying pattern formation. For both miscible and immiscible fluid pairs the growth dynamics change after the initial instability onset and the global structures, typical of late-time growth, are governed by the viscosity ratio. Here we introduce an experimental technique to measure flow throughout the inner and outer fluids. This probes the existence of a new length scale associated with the local pressure gradients around the interface and allows us to compare our results to the predictions of a previously proposed model for late-time finger growth.

physics.flu-dyn↗

arXiv2024

Order in disordered packings with and without permutation symmetry

A disordered solid, such as an athermal jammed packing of soft spheres, exists in a rugged potential-energy landscape in which there are a myriad of stable configurations that defy easy enumeration and characterization. Nevertheless, in three-dimensional monodisperse particle packings, we demonstrate an astonishing regularity in the distribution of basin volumes. The probability of landing randomly in a basin is proportional to its volume. Ordering the basins according to their probability, $P(n)$, from the largest at $n=1$ to smaller at larger $n$, we find approximately: $P(n) \propto n^{-1}$. This order, persisting up to the largest systems for which we can collect sufficient data, has implications for the dynamics of a system as it evolves under perturbations. In monodisperse packings there is ``permutation symmetry'' since identical particles can always be interchanged without affecting the system or its properties. Introducing any distribution of radii breaks this symmetry and leads to a proliferation of distinct configurations. We present an algorithm that partially restores permutation symmetry to such polydisperse packings.

cond-mat.soft↗

arXiv2024

Training physical matter to matter

Biological systems offer a great many examples of how sophisticated, highly adapted behavior can emerge from training. Here we discuss how training might be used to impart similarly adaptive properties in physical matter. As a special form of materials processing, training differs in important ways from standard approaches of obtaining sought after material properties. In particular, rather than designing or programming the local configurations and interactions of constituents, training uses externally applied stimuli to evolve material properties. This makes it possible to obtain different functionalities from the same starting material (pluripotency). Furthermore, training evolves a material in-situ or under conditions similar to those during the intended use; thus, material performance can improve rather than degrade over time. We discuss requirements for trainability, outline recently developed training strategies for creating soft materials with multiple, targeted and adaptable functionalities, and provide examples where the concept of training has been applied to materials on length scales from the molecular to the macroscopic.

cond-mat.soft↗

arXiv2022

State-and-rate friction in contact-line dynamics

In order to probe the dynamics of contact-line motion, we study the macroscopic properties of sessile drops deposited on and then aspirated from carefully prepared horizontal surfaces. By measuring the contact angle and drop width simultaneously during droplet removal, we determine the changes in the shape of the drop as it depins and recedes. Our data indicate that there is a force which opposes the motion of the contact line that depends both on the amount of time that the drop has been in contact with the surface and on the withdrawal rate. For water on silanized glass, we capture the experimentally observed behavior with an overdamped dynamical model of contact-line motion in which the phenomenological drag coefficient and the assumed equilibrium contact angle are the only inputs. For other liquid/substrate pairs, the observed contact-line motion suggests that a maximum static friction force is important in addition to damping. The dependence on time of contact and withdrawal rate, reminiscent of rate-and-state friction between solid surfaces, is qualitatively consistent across three substrate-liquid pairs.

cond-mat.soft↗

arXiv2022

Rifts in Rafts

A particle raft floating on an expanding liquid substrate provides a macroscopic analog for studying material failure. The time scales in this system allow both particle-relaxation dynamics and rift formation to be resolved. In our experiments, a raft, an aggregate of particles, is stretched uniaxially by the expansion of the air-liquid interface on which it floats. Its failure morphology changes continuously with pulling velocity. This can be understood as a competition between two velocity scales: the speed of re-aggregation, in which particles relax towards a low-energy configuration determined by viscous and capillary forces, and the difference of velocity between neighboring particles caused by the expanding fluid. This competition selects the cluster length, i.e., the distance between adjacent rifts. A model based on this competition is consistent with the experimental failure patterns.

cond-mat.soft↗

arXiv2022

Competition between energy and dynamics in memory formation

Bi-stable objects that are pushed between states by an external field are often used as a simple model to study memory formation in disordered materials. Such systems, called hysterons, are typically treated quasistatically. Here, we generalize hysterons to explore the effect of dynamics in a simple spring system with tunable bistability and study how the system chooses a minimum. Changing the timescale of the forcing allows the system to transition between a situation where its fate is determined by following the local energy minimum to one where it is trapped in a shallow well determined by the path taken through configuration space. Oscillatory forcing can lead to transients lasting many cycles, a behavior not possible for a single quasistatic hysteron.

cond-mat.soft↗

arXiv2022

Learning to self-fold at a bifurcation

Disordered mechanical systems can deform along a network of pathways that branch and recombine at special configurations called bifurcation points. Multiple pathways are accessible from these bifurcation points; consequently, computer-aided design algorithms have been sought to achieve a specific structure of pathways at bifurcations by rationally designing the geometry and material properties of these systems. Here, we explore an alternative physical training framework in which the topology of folding pathways in a disordered sheet is changed in a desired manner due to changes in crease stiffnesses induced by prior folding. We study the quality and robustness of such training for different `learning rules', that is, different quantitative ways in which local strain changes the local folding stiffness. We experimentally demonstrate these ideas using sheets with epoxy-filled creases whose stiffnesses change due to folding before the epoxy sets. Our work shows how specific forms of plasticity in materials enable them to learn non-linear behaviors through their prior deformation history in a robust manner.

cond-mat.soft↗

arXiv2021

Free-then-freeze: transient learning degrees of freedom for introducing function in materials

The introduction of transient learning degrees of freedom into a system can lead to novel material design and training protocols that guide a system into a desired metastable state. In this approach, some degrees of freedom, which were not initially included in the system dynamics, are first introduced and subsequently removed from the energy minimization process once the desired state is reached. Using this conceptual framework, we create stable jammed packings that exist in exceptionally deep energy minima marked by the absence of low-frequency quasilocalized modes; this added stability persists in the thermodynamic limit. The inclusion of particle radii as transient degrees of freedom leads to deeper and much more stable minima than does the inclusion of particle stiffnesses. This is because particle radii couple to the jamming transition whereas stiffnesses do not. Thus different choices for the added degrees of freedom can lead to very different training outcomes.

cond-mat.soft↗

arXiv2021

Poisson's ratio and angle bending in spring networks

The Poisson's ratio of a spring network system has been shown to depend not only on the geometry but also on the relative strength of angle-bending forces in comparison to the bond-compression forces in the system. Here we derive the very simple analytic result that in systems where the spring interaction strength is equal to the bond-reorientation interaction, the Poisson's ratio identically goes to zero and is independent of the network geometry.

cond-mat.soft↗

arXiv2021

Multiple memory formation in glassy landscapes

Cyclically sheared jammed packings form memories of the shear amplitude at which they were trained by falling into periodic orbits where each particle returns to the identical position in subsequent cycles. While simple models that treat clusters of rearranging particles as isolated two-state systems offer insight into this memory formation, they fail to account for the long training times and multi-period orbits observed in simulated sheared packings. We show that adding interactions between rearranging clusters overcomes these deficiencies. In addition, interactions allow simultaneous encoding of multiple memories which would not have been possible otherwise. These memories are different in an essential way from those found in other systems, such as multiple transient memories observed in sheared suspensions, and contain information about the strength of the interactions.

cond-mat.soft↗

arXiv2020

Effect of aging on the non-linear elasticity and memory formation in materials

Disordered solids often change their elastic response as they slowly age. Using experiments and simulations, we study how aging disordered planar networks under an applied stress affects their nonlinear elastic response. We are able to modify dramatically the elastic properties of our systems in the non-linear regime. Using simulations, we study two models for the microscopic evolution of properties of such a material; the first considers changes in the material strength while the second considers distortions in the microscopic geometry. Both models capture different aspects of the experiments including the encoding of memories of the aging history of the system and the dramatic effects on the material's nonlinear elastic properties. Our results demonstrate how aging can be used to create complex elastic behavior in the nonlinear regime.

cond-mat.soft↗

arXiv2020

Determining the refractive index, absolute thickness and local slope of a thin transparent film using multi-wavelength and multi-incident-angle interference

We describe a high-speed interferometric method, using multiple angles of incidence and multiple wavelengths, to measure the absolute thickness, tilt, the local angle between the surfaces, and the refractive index of a fluctuating transparent wedge. The method is well suited for biological, fluid and industrial applications.

physics.optics↗