arXiv subjects

Carl P. Goodrich

Publications and source records attributed to Carl P. Goodrich.

At least 19 recordsLinked to original sources

arXiv2026

Designing bistable nanostructures for target behavior

Many biological machines function through controlled conformational transitions, yet designing synthetic nanostructures with prescribed dynamical behavior remains a major challenge. Here, we develop a modular inverse-design framework for bistable nanostructures whose function is controlled by an energy profile along a geometric reaction coordinate. Inspired by proteins with rigid domains connected by flexible hinges, we introduce a hinge-arm paradigm in which a small bistable hinge controls the energetics of a conformational transition, while rigid arms map this transition onto the separation between external binding sites. Specifically, we ask which features of a target energy profile can be programmed under different design constraints. We find that the energy barriers and the binding-site separations in the two metastable states can be readily designed, while controlling the location of the transition state or the full shape of the energy profile requires additional design freedom. Using a differentiable design framework, we find that some optimized solutions are numerically inexact but still display the functional behavior for which the target profile was selected, emphasizing the importance of function-based evaluation criteria. These results establish a practical hierarchy of designability for bistable nanostructures and provide a route toward synthetic nanomachines that couple conformational transitions to target behavior.

cond-mat.soft↗

arXiv2025

Simultaneous optimization of assembly time and yield in programmable self-assembly

Rational design strategies for self-assembly require a detailed understanding of both the equilibrium state and the assembly kinetics. While the former is starting to be well understood, the latter remains a major theoretical challenge, especially in programmable systems and the so-called semiaddressable regime, where binding is often nondeterministic and the formation of off-target structures negatively influences the assembly. Here, we show that it is possible to simultaneously sculpt the assembly outcome and the assembly kinetics through the underexplored design space of binding energies and particle concentrations. By formulating the assembly process as a complex reaction network, we calculate and optimize the tradeoff between assembly speed and quality, and show that parameter optimization can speed up assembly by many orders of magnitude without lowering the yield of the target structure. Although the exact speedup varies from design to design, we find the largest speedups for nondeterministic systems where unoptimized assembly is the slowest, sometimes even making them assemble faster than optimized fully-addressable designs. Therefore, these results not only solve a key challenge in semiaddressable self-assembly, but further emphasize the utility of semiaddressability, where designs have the potential to be faster as well as cheaper (fewer particle species) and better (higher yield). More broadly, our results highlight the importance of parameter optimization in programmable self-assembly, and provide practical tools for simultaneous optimization of kinetics and yield in a wide range of systems.

cond-mat.soft↗

arXiv2025

Learning by training: emergent return-point memory from cyclically tuning disordered sphere packings

Many living and artificial systems improve their fitness or performance by adapting to changing environments or diverse training data. However, it remains unclear how such environmental variation influences adaptation, what is learned in the process, and whether memory of past conditions is retained. In this work, we investigate these questions using athermal disordered systems that are subject to cyclic inverse design, enabling them to attain target elastic properties spanning a chosen range. We demonstrate that such systems evolve toward a marginally absorbing manifold (MAM), which encodes memory of the training range that closely resembles return-point memory observed in cyclically driven systems. We further propose a general mechanism for the formation of MAMs and the corresponding memory that is based on gradient discontinuities in the trained quantities. Our model provides a simple and broadly applicable physical framework for understanding how adaptive systems learn under environmental change and how they retain memory of past experiences.

physics.comp-ph↗

arXiv2025

Stochastic size control of self-assembled filaments

Controlling the size and shape of assembled structures is a fundamental challenge in self-assembly, and is highly relevant in material design and biology. Here, we show that specific, but promiscuous, short-range binding interactions make it possible to economically assemble linear filaments of user-defined length. Our approach leads to independent control over the mean and width of the filament size distribution and allows us to smoothly explore design trade-offs between assembly quality (spread in size) and cost (number of particle species). We employ a simple hierarchical assembly protocol to minimize assembly times, and show that multiple stages of hierarchy make it possible to extend our approach to the assembly of higher-dimensional structures. Our work provides a simple and experimentally straightforward solution to size control that is immediately applicable to a broad range of systems, from DNA origami assemblies to supramolecular polymers and beyond.

cond-mat.soft↗

arXiv2025

Electrostatics overcome acoustic collapse to assemble, adapt, and activate levitated matter

Acoustic levitation provides a unique method for manipulating small particles as it completely evades effects from gravity, container walls, or physical handling. These advantages make it a tantalizing platform for studying complex phenomena in many-particle systems, save for one severe limitation -- particles suspended by sound interact via acoustic scattering forces, which cause them to merge into a single dense object. To overcome this "acoustic collapse", we have developed a strategy that combines acoustic levitation with controlled electrostatic charging to assemble, adapt, and activate complex, many-particle systems. The key idea is to introduce electrostatic repulsion, which renders a so-called "mermaid" potential where interactions are attractive at short range and repulsive at long range. By controlling the balance between attraction/repulsion, we are able to levitate fully expanded structures where all particles are separated, fully collapsed structures where they are all in contact, and hybrid ones consisting of both expanded and collapsed components. We find that fully collapsed and expanded structures are inherently stable, whereas hybrid ones exhibit transient stability governed by acoustically unstable dimers. Furthermore, we show how electrostatics allow us to adapt between configurations on the fly, either by quasistatic discharge or discrete up/down charge steps. Finally, we demonstrate how large structures experience selective energy pumping from the acoustic field -- thrusting some particles into motion while others remain stationary -- leading to complex dynamics including coupled rotations and oscillations. Our approach provides an easy-to-implement and easy-to-understand solution to the pervasive problem of acoustic collapse, while simultaneously providing new insights into the assembly and activation of many-particle systems with complex interactions.

cond-mat.soft↗

arXiv2025

Controlling energy delivery with bistable nanostructures

Countless biological processes are fueled by energy-rich molecules like ATP and GTP that supply energy with extreme efficiency. However, designing similar energy-delivery schemes from the bottom up, essential for the development of powered nanostructures and other \emph{de novo} machinery, presents a significant challenge: how can an energy-rich structure be stable in solution yet still deliver this energy at precisely the right time? In this paper, we present a purely physical mechanism that solves this challenge, facilitating energy transfer akin to ATP hydrolysis, yet occurring between synthetic nanostructures without any biochemical interactions. This targeted energy delivery is achieved by exploiting a differentiable state-based model to balance the energy profiles that govern the structural transitions in the two nanostructures, creating a coupled relaxation pathway with minimal barriers that facilitates energy delivery. We verify the effectiveness and robustness of this mechanism through Langevin Dynamics simulations, demonstrating that a bath of the high-energy structures can systematically and repeatedly drive the target structure out of equilibrium, enabling it to perform tasks. As the mechanism operates only through explicit physical forces without any biochemistry or internal state variables, our results present generic and far-reaching design principles, setting the stage for the next generation of synthetic nanomachines.

cond-mat.soft↗

arXiv2025

Fully independent response in disordered solids

Unlike in crystals, it is difficult to trace emergent material properties of amorphous solids to their underlying structure. Nevertheless, one can tune features of a disordered spring network, ranging from bulk elastic constants to specific allosteric responses, through highly precise alterations of the structure. This has been understood through the notion of independent bond-level response -- the observation that in many cases, different springs have different effects on different properties. While this idea has motivated inverse design in numerous contexts, it has not been formalized and quantified in a general context that not just informs but enables and predicts inverse design. Here, we show how to quantify independent response by linearizing the simultaneous change in multiple emergent features, and introduce the much stronger notion of fully independent response. Remarkably, we find that the mechanical properties of disordered solids are always fully independent across a wide array of scenarios, regardless of the target features, tunable parameters, and details of particle-particle interactions. Furthermore, our formulation quantifies the susceptibility of feature changes to parameter changes, which we find to be correlated with the maximum linear tunability. These results formalize our understanding of a key fundamental difference between ordered and disordered solids while also creating a practical tool to both understand and perform inverse design.

physics.comp-ph↗

arXiv2025

The polyhedral structure underlying programmable self-assembly

Experiments have reached a monumental capacity for designing and synthesizing microscopic particles for self-assembly, making it possible to precisely control particle concentrations, shapes, and interactions. However, more physical insight is needed before we can take full advantage of this vast design space to assemble nanostructures with complex form and function. Here we show how a significant part of this design space can be quickly and comprehensively understood by identifying a class of thermodynamic constraints that act on it. These thermodynamic constraints form a high-dimensional convex polyhedron that determines which nanostructures can be assembled at high equilibrium yield and reveals limitations that govern the coexistence of structures, which we verify through detailed, quantitative assembly experiments of nanoscale particles synthesized using DNA origami. Strong experimental agreement confirms the importance of the polyhedral structure and motivates its use as a predictive tool for the rational design of self-assembly. These results uncover fundamental physical relationships underpinning many-component programmable self-assembly in equilibrium and form the basis for robust inverse-design, applicable to a wide array of systems from biological protein complexes to synthetic nanomachines.

cond-mat.soft↗

arXiv2024

Accessing Semi-Addressable Self Assembly with Efficient Structure Enumeration

Modern experimental methods enable the creation of self-assembly building blocks with tunable interactions, but optimally exploiting this tunability for the self-assembly of desired structures remains an important challenge. Many studies of this inverse problem start with the so-called fully-addressable limit, where every particle in a target structure is different. This leads to clear design principles that often result in high assembly yield, but it is not a scaleable approach -- at some point, one must grapple with "reusing" building blocks, which lowers the degree of addressability and may cause a multitude of off-target structures to form, complicating the design process. Here, we solve a key obstacle preventing robust inverse design in the "semi-addressable regime" by developing a highly efficient algorithm that enumerates all structures that can be formed from a given set of building blocks. By combining this with established partition-function-based yield calculations, we show that it is almost always possible to find economical semi-addressable designs where the entropic gain from reusing building blocks outweighs the presence of off-target structures and even increases the yield of the target. Thus, not only does our enumeration algorithm enable robust and scalable inverse design in the semi-addressable regime, our results demonstrate that it is possible to operate in this regime while maintaining the level of control often associated with full addressability.

cond-mat.soft↗

arXiv2024

Unravelling the multiscale surface mechanics of soft solids

Soft solids and their surface deformations control the response of many natural and artificial systems. Yet, their underlying properties are vigorously debated, particularly for polymer networks. While molecular-scale theories predict no interfacial changes with macroscopic deformation, multiple experiments suggest otherwise. To settle this issue, we measure displacement fields near the interface of a silicone gel, in the limit of small deformations. We discover an unexpected multiscale response. The shear modulus decreases smoothly by half with 20 microns of the interface. At the same time we observe a surface excess elasticity, that depends on history and outer medium composition. These results reveal the fundamentally multiscale nature of polymeric surfaces, and call for further experimental and theoretical investigations into the basic understanding of soft solid interfaces

cond-mat.soft↗

arXiv2020

Self-assembling kinetics: Accessing a new design space via differentiable statistical-physics models

The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing emergent kinetics, but this has received considerably less attention. Using recent advances in automatic differentiation, we show how kinetic pathways can be precisely designed by directly differentiating through statistical-physics models, namely free energy calculations and molecular dynamics simulations. We consider two systems that are crucial to our understanding of structural self-assembly: bulk crystallization and small nanoclusters. In each case we are able to assemble precise dynamical features. Using gradient information, we manipulate interactions among constituent particles to tune the rate at which these systems yield specific structures of interest. Moreover, we use this approach to learn non-trivial features about the high-dimensional design space, allowing us to accurately predict when multiple kinetic features can be simultaneously and independently controlled. These results provide a concrete and generalizable foundation for studying non-structural self-assembly, including kinetic properties as well as other complex emergent properties, in a vast array of systems.

physics.comp-ph↗

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↗

arXiv2016

Deformation of crystals: Connections with statistical physics

We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, and a broad introduction into the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in magnets, spin glasses, charge density waves, and dilute colloidal suspensions are discussed in relation to the onset of plastic yielding in crystals. Dislocation avalanches and complex dislocation tangles are discussed via a brief introduction to the renormalization group and scaling. Analogies to emergent scale invariance in fracture, jamming, coarsening, and a variety of depinning transitions are explored. Dislocation dynamics in crystals challenges non equilibrium statistical physics. Statistical physics provides both cautionary tales of subtle memory effects in nonequilibrium systems, and systematic tools designed to address complex scale-invariant behavior on multiple length and time scales.

cond-mat.mtrl-sci↗

arXiv2016

Collective dynamics of soft active particles

We present a model of soft active particles that leads to a rich array of collective behavior found also in dense biological swarms of bacteria and other unicellular organisms. Our model uses only local interactions, such as Vicsek-type nearest neighbor alignment, short-range repulsion, and a local boundary term. Changing the relative strength of these interactions leads to migrating swarms, rotating swarms and jammed swarms, as well as swarms that exhibit run-and-tumble motion, alternating between migration and either rotating or jammed states. Interestingly, although a migrating swarm moves slower than an individual particle, the diffusion constant can be up to three orders of magnitude larger, suggesting that collective motion can be highly advantageous, for example, when searching for food.

cond-mat.soft↗

arXiv2016

Designing allostery-inspired response in mechanical networks

Recent advances in designing meta-materials have demonstrated that global mechanical properties of disordered spring networks can be tuned by selectively modifying only a small subset of bonds. Here, using a computationally-efficient approach, we extend this idea in order to tune more general properties of networks. With nearly complete success, we are able to produce a strain between any pair of target nodes in a network in response to an applied source strain on any other pair of nodes by removing only ~1% of the bonds. We are also able to control multiple pairs of target nodes, each with a different individual response, from a single source, and to tune multiple independent source/target responses simultaneously into a network. We have fabricated physical networks in macroscopic two- and three-dimensional systems that exhibit these responses. This targeted behavior is reminiscent of the long-range coupled conformational changes that often occur during allostery in proteins. The ease with which we create these responses may give insight into why allostery is a common means for the regulation of activity in biological molecules.

cond-mat.soft↗

arXiv2016

Pinning Susceptibility: The effect of dilute, quenched disorder on jamming

We study the effect of dilute pinning on the jamming transition. Pinning reduces the average contact number needed to jam unpinned particles and shifts the jamming threshold to lower densities, leading to a pinning susceptibility, $χ_p$. Our main results are that this susceptibility obeys scaling form and diverges in the thermodynamic limit as $χ_p \propto |ϕ- ϕ_c^\infty|^{-γ_p}$ where $ϕ_c^\infty$ is the jamming threshold in the absence of pins. Finite-size scaling arguments yield these values with associated statistical (systematic) errors $γ_p = 1.018 \pm 0.026 (0.291) $ in $d=2$ and $γ_p =1.534 \pm 0.120 (0.822)$ in $d=3$. Logarithmic corrections raise the exponent in $d=2$ to close to the $d=3$ value, although the systematic errors are very large.

cond-mat.soft↗

arXiv2016

Spatial structure of states of self stress in jammed systems

States of self stress, organizations of internal forces in many-body systems that are in equilibrium with an absence of external forces, can be thought of as the constitutive building blocks of the elastic response of a material. In overconstrained disordered packings they have a natural mathematical correspondence with the zero-energy vibrational modes in underconstrained systems. While substantial attention in the literature has been paid to diverging length scales associated with zero- and finite-energy vibrational modes in jammed systems, less is known about the spatial structure of the states of self stress. In this work we define a natural way in which a unique state of self stress can be associated with each bond in a disordered spring network derived from a jammed packing, and then investigate the spatial structure of these bond-localized states of self stress. This allows for an understanding of how the elastic properties of a system would change upon changing the strength or even existence of any bond in the system.

cond-mat.soft↗

arXiv2015

Divergence of Voronoi cell anisotropy vector: A threshold-free characterization of local structure in amorphous materials

Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to the centroid of the Voronoi cell in which the particle resides. These vectors tend to point in toward regions of high free volume and away from regions of low free volume, reminiscent of sinks and sources in a vector field. We compute the local divergence of these vectors, for which positive values correspond to overpacked regions and negative values identify underpacked regions within the material. Distributions of this divergence are nearly Gaussian with zero mean, allowing for structural characterization using only the moments of the distribution. We explore how the standard deviation and skewness vary with packing fraction for simulations of bidisperse systems and find a kink in these moments that coincides with the jamming transition.

cond-mat.soft↗