Session C57: GSNP Student and Postdoctoral Speaker Award Session

Characterization of fracture in topology-optimized bio-inspired networks

Trabecular bone is a flexible, lightweight bone tissue that exhibits an anisotropic microarchitecture resembling a web of interconnected struts (trabeculae). We simulate trabecular bone architectures with multi-objective topology optimization, effectively reverse-engineering trabecular structure by optimizing biologically-motivated objectives. Starting from an identical volume, we generate different topologies by varying the objective weights for compliance, surface area, and stability. We model these topologies as disordered, spatially-embedded networks where edges represent trabeculae and nodes represent branch points where trabeculae meet. We simulate mechanical loading on finite-element models where each edge is replaced by a beam, enabling direct comparison of mechanics and topology at multiple scales ranging from that of individual edges/beams to the network at large. We compare the mechanical response of the various topology-optimized networks and identify mechanisms of crack propagation. We characterize and predict crack pathways with community detection methods inspired by similar applications in the study of granular materials.   

Directed aging and memory: Teaching an old foam new tricks

As a material ages, its physical properties change. Under an applied stress, it plastically deforms in order to relieve the internal stress in incremental steps. At each instant, it lowers the stress in the most effective way. Thus, over long times, the final state of the material depends on the external stresses it was exposed to during the aging process. A material thus has a memory of the stresses to which it was exposed during the aging process. We exploit this property and direct the aging process with specific protocols in such a way that our material reaches a distinct, final state with a prescribed and desired functionality. In order to demonstrate this behavior, we use sheets of foam that we cut with a laser cutter and place under stress in such a way that the material develops unusual elastic properties. To accelerate the aging process, we apply heat to the sample. We have been able to modify the Poisson’s ratio of our system considerably; we can make a sample that was initially nearly incompressible and make it auxetic (negative Poisson’s ratio). We can likewise take an auxetic sample and make it incompressible. We have also been able to train local behavior so that a sample responds with a prescribed local deformation in response to a global perturbation.   

Design and Control of Finite Conformational Changes in Mechanical Networks

Conformational changes in physical networks play a crucial role in many systems, enabling error correction in DNA replication, cooperativity in hemoglobin, and mechanical capacities in metamaterials. Important work has begun to delineate the relationship between network structure and instantaneous conformational change. However, these efforts have failed to address finite conformations, which are critical for the successful function of most physical networks. Here we establish a simple framework for the design and control of mechanical spring networks in 2 and 3 dimensions. Specifically, for a set of nodes with arbitrarily specified initial and final positions, we characterize all bipartite networks with zero energy at these positions, demonstrate transitions between these positions, and design multi-stable networks for information storage. Finally, we use hysteresis and bi-stability to design networks demonstrating cooperativity.   

Pattern Selection in Brine Shrimp Swarms

Swarming is a ubiquitous self-organization phenomenon which occurs in many biological systems such as flocks of bird and insect, schools of fish, and collections of bacteria. This sort of behavior emerges spontaneously, arising without any sort of centralized control or leadership. Many crustaceans such as brine shrimp produce swarms, in which individuals cluster together rather than spreading out uniformly in their environment. The size and distribution of these swarms are governed by local interactions between individuals. We will discuss the three-dimensional patterns that can be observed in brine shrimp swarms, specifically of the Great Salt Lake strain of Artemia franciscana, at high concentration. These patterns can be easily observed with simple tabletop experiments; however, the causes of these patterns are unknown. We experimentally test the effects of certain environmental conditions on the development of these swarms. We then develop a model an agent based model of shrimp which yields the same sort of spatial patterns as those that are observed. The model reproduces the basic length and times scales of the patterns, the type patterns selected, and the stability of those patterns.   

The effects of inhibitory neuron fraction on the dynamics of an avalanching neural network

The statistical analysis of the collective neural activity known as avalanches provides insight into the proper behavior of brains across many species. In this talk we present a neural network model based on the work of Lombardi, Herrmann, de Arcangelis et al. that captures the relevant dynamics of neural avalanches, and we show how the active neuron fraction can be used as a control mechanism to introduce exponential cut-offs in the distributions of avalanche strength and duration, transition the power spectral density of the network out of an epileptic regime, and drive the evolution of the network structure over time.   

A general geometric framework for knitted fabric elasticity

Knitting is a process in which yarn, an essentially filament-like material, is shaped in space to form a fabric, an essentially sheet-like material, via stitching together a lattice of slip-knots. Due to fabric-level dependence on the stitch pattern, a single yarn can be used to create a large variety of fabric geometries and material responses. Moreover, the elasticity of knits remains poorly understood, as evidenced by the lackluster performance of spring-lattice models. We seek a continuum elastic model that predicts the three-dimensional shape of knitted fabric. This model should have the flexibility to be adapted to describe a wide range of stitch patterns and elasticity models. To this end, we have developed a geometric framework for relating the yarn path to the emergent surface geometry of the fabric. The generality of our approach allows for a systematic coarse-graining of yarn degrees of freedom, without a priori specification of a model of yarn elasticity. Thus, we are able to arrive at a stitch pattern-dependent, continuum elastic model of knits by assuming a simple phenomenological model of yarn, whilst allowing for the possibility of including more realistic yarn mechanics and experimental comparison.   

Model-dependent and model-independent control of biological network models

Network models of cell signaling and regulation are ubiquitous because of their ability to integrate the current knowledge of a biological process and test new findings and hypotheses. An often asked question is how to control a network model and drive it towards its dynamical attractors (which are often identifiable with phenotypes or stable patterns of activity of the modeled system), and which nodes and interventions are required to do so. In this talk, we introduce two recently developed network control methods - feedback vertex set control and stable motif control - that use the graph structure of a network model to identify nodes that drive the system towards an attractor of interest (i.e., nodes sufficient for attractor control). Feedback vertex set control makes predictions that apply to all network models with a given graph structure and stable motif control makes predictions for a specific model instance, and this allows us to compare the results of model-independent and model-dependent network control. We illustrate these methods with various examples and discuss the aspects of each method that makes its predictions dependent or independent of the model.   

Bulk metallic glass design: What properties determine the glass-forming ability of multi-component alloys?

Bulk metallic glasses (BMGs) possess a number of important properties, such as high strength and thermoplastic formability, which stem from the fact that they are structurally disordered in contrast to crystalline metals. Materials scientists have identified several features that are correlated with the glass-forming ability (GFA) of alloys. For example, good glass-formers are typically multi-component alloys composed of elements with atomic radii that differ by more than 10%. Most BMGs also possess a negative heat of mixing, which disfavors clustering of like atoms and hinders phase separation. However, researchers have not been able to a priori predict a new BMG-forming alloy. In this work, we perform computational studies of binary alloys to understand the relative contributions of geometric frustration and energetic frustration in determining the GFA. From a database of the heats of mixing and cohesive energies of binary atomic systems with atoms A and B, we show that most binary alloys follow a Berthelot combining rule, εAB=(εAAεBB)½ , where εAB, εAA and εBB are the depths of the attractive energy for pair interactions between AB, AA, and BB. We employ this mixing rule in molecular dynamics simulations of binary Lennard-Jones mixtures of atoms with equal sizes, but different cohesive energies. We measure the critical cooling rates of binary systems over the full range of cohesive energies and number fraction fA of A and 1-fA of B atoms. We show that good glass formers satisfy εAA>εAB>εBB when fA<fB. We find that good glass-forming ability is determined by the conditions εBB<<εAA and fA<fB, and not correlated with the magnitude of the heat of mixing. In future studies, we will identify the variables that control the glass-forming ability in ternary alloys with atoms of different sizes and cohesive energies.   

Thouless and Relaxation Time Scales in Many-Body Quantum Systems

We study the time scales involved in the relaxation process of isolated quantum many-body systems. Using experimental observables and a realistic many-body quantum model, we unveil three different time scales: a very short time that characterizes the early fast decay of the initial state, and two much longer times that increase exponentially with system size. These are the Thouless time, t_Th, and the relaxation time, t_R. The Thouless time refers to the point beyond which the dynamics acquire universal features, and relaxation happens when the evolution reaches a stationary state. We show that in chaotic systems, t_Th<<t_R, while for systems approaching a many-body localized phase, t_Th tends to t_R. We also compare these results with those for random matrices, and study how self-averaging properties depend on time scales.   

Cyber-physical risks of hacked Internet-connected vehicles

The interface of Internet-connectivity and automotive technology promises to dramatically improve transportation. However, with these known benefits come unknown risks, especially since Internet-connected vehicles have become targets for computer hacking. Vehicles, unlike sensitive data, can collide or physically interact when their systems become compromised, and there is a broad class of scenarios generically leading to Internet-connected vehicles being suddenly and simultaneously disabled. Here, we investigate how large-scale hacking affects traffic flow using agent-based simulations, and discover the critical relevance of percolation for predicting outcomes on a multi-lane road. Inspired by this discovery, we develop and validate an analytic percolation-based model to rapidly assess the effect of hacking. We then apply our analytic model to investigate the outcomes on the street network of Manhattan (NY, USA), revealing a latent risk. A small number of disabled vehicles can gridlock the city and substantially reduce access to emergency services. By discovering percolation as the phenomenological driver of city-wide disruption, we simultaneously uncover a strategy for risk-mitigation.