Condensed Matter

Geometric frustration arises whenever the constituents of a physical assembly locally favor an arrangement that cannot be realized globally. Recently, such frustrated assemblies were shown to exhibit filamentation, size limitation, large morphological variations, and exotic response properties. These unique characteristics can be shown to be a direct outcome of geometric frustration. There are, however, geometrically frustrated systems that do not exhibit any of the above characteristics. The epitome of frustration in condensed matter physics, the Ising anti-ferromagnet on a triangular lattice, is one such system. In this work, we provide a framework for directly addressing the frustration in physical assemblies and their expected energy scaling exponents. We also present a new spin model that exhibits cumulative geometric frustration and use the newly devised framework to analyze it.

We study the three-dimensional equilibrium shape of a shell formed by a deployed accordion-like origami, made from an elastic sheet decorated by a series of parallel creases crossed by a central longitudinal crease. Surprisingly, while the imprinted crease network does not exhibit a geodesic curvature, the emergent structure is characterized by an effective curvature produced by the deformed central fold. Moreover, both finite element analysis and manually made mylar origamis show a robust empirical relation between the imprinted crease network's dimensions and the apparent curvature. A detailed examination of this geometrical relation shows the existence of three typical elastic deformations, which in turn induce three distinct types of morphogenesis. We characterize the corresponding kinematics of crease network deformations and determine their phase diagram. Taking advantage of the frustration caused by the competition between crease stiffness and kinematics of crease network deformations, we provide a novel tool for designing curved origami structures constrained by strong geometrical properties.

Driving an inertial many-body system out of equilibrium generates complex dynamics due to memory effects and the intricate relationships between the external driving force, internal forces, and transport effects. Understanding the underlying physics is challenging and often requires carrying out case-by-case analysis. To systematically study the interplay between all types of forces that contribute to the dynamics, a method to generate prescribed flow patterns could be of great help. We develop a custom flow method to numerically construct the external force field required to obtain the desired time evolution of an inertial many-body system, as prescribed by its one-body current and density profiles. We validate the custom flow method in a Newtonian system of purely repulsive particles by creating a slow motion dynamics of an out-of-equilibrium process and by prescribing the full time evolution between two distinct equilibrium states. The method can also be used with thermostat algorithms to control the temperature.

A folded disk is bistable, as it can be popped through to an inverted state with elastic energy localized in a small, highly-deformed region on the fold. Cutting out this singularity relaxes the surrounding material and leads to a loss of bistability when the hole dimensions reach a critical size. These dimensions are strongly anisotropic and feature a surprising re-entrant behavior, such that removal of additional material can re-stabilize the inverted state. A model of the surface as a wide annular developable strip is found to capture the qualitative observations in experiments and simulations. These phenomena are consequential to the mechanics and design of crumpled elastic sheets, developable surfaces, origami and kirigami, and other deployable and compliant structures.

We report an accurate method to determine DNA barcodes from the dwell time measurement of protein tags (barcodes) along the DNA backbone using Brownian dynamics simulation of a model DNA and use a recursive theoretical scheme which improves the measurements to almost 100 % accuracy. The heavier protein tags along the DNA backbone introduce a large speed variation in the chain that can be understood using the idea of non-equilibrium tension propagation theory. However, from an initial rough characterization of velocities into "fast" (nucleotides) and "slow" (protein tags) domains, we introduce a physically motivated interpolation scheme that enables us to determine the barcode velocities rather accurately. Our theoretical analysis of the motion of the DNA through a cylindrical nanopore opens up the possibility of its experimental realization and carries over to multi-nanopore devices used for barcoding.

The potential of a double nanopore system to determine DNA barcodes has been demonstrated experimentally. By carrying out Brownian dynamics simulation on a coarse-grained model DNA with protein tag (barcodes) at known locations along the chain backbone, we demonstrate that due to large variation of velocities of the chain segments between the tags, it is inevitable to under/overestimate the genetic lengths from the experimental current blockade and time of flight data. We demonstrate that it is the tension propagation along the chain's backbone that governs the motion of the entire chain and is the key element to explain the non uniformity and disparate velocities of the tags and DNA monomers under translocation that introduce errors in measurement of the length segments between protein tags. Using simulation data we further demonstrate that it is important to consider the dynamics of the entire chain and suggest methods to accurately decipher barcodes. We introduce and validate an interpolation scheme using simulation data for a broad distribution of tag separations and suggest how to implement the scheme experimentally.

We establish an explicit data-driven criterion for identifying the solid-liquid transition of two-dimensional self-propelled colloidal particles in the far from equilibrium parameter regime, where the transition points predicted by different conventional empirical criteria for melting and freezing diverge. This is achieved by applying a hybrid machine learning approach that combines unsupervised learning with supervised learning to analyze over one million of system's configurations in the nonequilibrium parameter regime. Furthermore, we establish a generic data-driven evaluation function, according to which the performance of different empirical criteria can be systematically evaluated and improved. In particular, by applying this evaluation function, we identify a new nonequilibrium threshold value for the long-time diffusion coefficient, based on which the predictions of the corresponding empirical criterion are greatly improved in the far from equilibrium parameter regime. These data-driven approaches provide a generic tool for investigating phase transitions in complex systems where conventional empirical ones face difficulties.

Cellulose nanocrystals (CNC) can be considered as model colloidal rods and have practical applications in the formation of soft materials with tailored anisotropy. Here, we employ two contrasting microfluidic devices to quantitatively elucidate the role of shearing and extensional flows on the alignment of a dilute CNC dispersion. Characterization of the flow field by micro-particle image velocimetry is coupled to flow-induced birefringence analysis to quantify the deformation rate--alignment relationship. The deformation rate required for CNC alignment is 4 × smaller in extension than in shear. Alignment in extension is independent of the deformation rate magnitude, but is either 0 ∘ or 90 ∘ to the flow, depending on its sign. In shear flow the colloidal rods orientate progressively towards 0 ∘ as the deformation rate magnitude increases. Our results decouple the effects of shearing and extensional kinematics at aligning colloidal rods, establishing coherent guidelines for the manufacture of structured soft materials.

In many mechanistic medical, biological, physical and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs) can make simulations impractically slow. Biological models require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. PDE surrogates enable use of larger models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1e3 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application.

Topological defects play a key role in two-dimensional active nematics, and a transient role in two-dimensional active polar fluids. In this paper, we study both the transient and long-time behavior of defects in two-dimensional active polar fluids in the limit of strong order and overdamped, compressible flow, and compare the defect dynamics with the corresponding active nematics model studied recently. One result is non-central interactions between defect pairs for active polar fluids, and by extending our analysis to allow orientation dynamics of defects, we find that the orientation of +1 defects, unlike that of ±1/2 defects in active nematics, is not locked to defect positions and relaxes to asters. Moreover, using a scaling argument, we explain the transient feature of active polar defects and show that in the steady state, active polar fluids are either devoid of defects or consist of a single aster. We argue that for contractile (extensile) active nematic systems, +1 vortices (asters) should emerge as bound states of a pair of +1/2 defects, which has been recently observed. Moreover, unlike the polar case, we show that for active nematics, a linear chain of equally spaced bound states of pairs of +1/2 defects can screen the activity term. A common feature in both models is the appearance of +1 defects (elementary in polar and composite in nematic) in the steady state.