arXiv subjects

Botond Tyukodi

Publications and source records attributed to Botond Tyukodi.

14 recordsLinked to original sources

arXiv2025

From toroids to helical tubules: Kirigami-inspired programmable assembly of two-periodic curved crystals

Biology is full of intricate molecular structures whose geometries are inextricably linked to their function. Many of these structures exhibit varying curvature, such as the helical structure of the bacterial flagellum, which is critical for their motility. Because synthetic analogues of these shapes could be valuable platforms for nanotechnologies, including drug delivery and plasmonics, controllable synthesis of variable-curvature structures of various material systems, from fullerenes to supramolecular assemblies, has been a long-standing goal. Like two-dimensional crystals, these structures have a two-periodic symmetry, but unlike standard two-dimensional crystals, they are embedded in three dimensions with complex, spatially-varying curvatures that cause the structures to close upon themselves in one or more dimensions. Here, we develop and implement a design strategy to program the self-assembly of a complex spectrum of two-periodic curved crystals with variable periodicity, spatial dimension, and topology, spanning from toroids to achiral serpentine tubules to both left- and right-handed helical tubules. Our design strategy uses a kirigami-based mapping of 2D planar tilings to 3D curved crystals that preserves the periodicity, two-fold rotational symmetries, and subunit dimensions via the arrangement of disclination defects. We survey the modular geometry of these curved crystals and infer the addressable subunit interactions required to assemble them from triangular subunits. To demonstrate this design strategy, we program the self-assembly of toroids, helical- and serpentine-tubules from DNA origami subunits. A simulation model of the assembly pathways reveals physical considerations for programming the geometric specificity of angular folds in the curved crystal required to avoid defect-mediated misassembly.

cond-mat.soft↗

arXiv2024

Magic sizes enable minimal-complexity, high-fidelity assembly of programmable shells

Recent advances in synthetic methods enable designing subunits that self-assemble into structures with precise, finite sizes and well-defined architectures, but yields are frequently suppressed by the formation of off-target metastable structures. Increasing the complexity (the number of distinct subunit types) can inhibit off-target structures, but leads to slower kinetics and higher synthesis costs. Here, we study icosahedral shells formed of programmable triangular subunits as a model system, and identify design principles that produce the highest target yield at the lowest complexity. We use a symmetry-based construction to create a range of design complexities, starting from the maximal symmetry Caspar-Klug assembly up to the fully addressable, zero-symmetry assembly. Kinetic Monte Carlo simulations reveal that the most prominent defects leading to off-target assemblies are disclinations at sites of rotational symmetry. We derive symmetry-based rules for identifying the optimal (lowest-complexity, highest-symmetry) design that inhibits these disclinations, leading to robust, high-fidelity assembly of targets with arbitrarily large, yet precise, finite sizes. The optimal complexity varies non-monotonically with target size, with `magic' sizes appearing for high-symmetry designs in which symmetry axes do not intersect vertices of the triangular net. The optimal designs at magic sizes require 12 times fewer inequivalent interaction-types than the (minimal symmetry) fully addressable construction, which greatly reduces the timescale and experimental cost required to achieve high fidelity assembly of large targets. This symmetry-based principle for pruning off-target assembly generalizes to diverse architectures with different topologies.

cond-mat.soft↗

arXiv2023

Limits of economy and fidelity for programmable assembly of size-controlled triply-periodic polyhedra

We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply-periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies -- in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g. periodicity) -- is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.

cond-mat.soft↗

arXiv2022

Coarse-graining amorphous plasticity: impact of rejuvenation and disorder

The coarse-graining of amorphous plasticity from the atomistic to the mesoscopic scale is studied in the framework of a simple scalar elasto-plastic model. Building on recent results obtained on the atomistic scale, we discuss the interest in a disordered landscape-informed threshold disorder to reproduce the physics of amorphous plasticity. We show that accounting for a rejuvenation scenario allows us to reproduce quasi-quantitatively the evolution of the mean local yield stress and the localization behavior. We emphasize the crucial role of two dimensionless parameters: the relative strength of the yield stress disorder with respect to the typical stress drops associated with a plastic rearrangement, and the age parameter characterizing the relative stability of the initial glass with respect to the rejuvenated glass that emerges upon shear deformation.

cond-mat.soft↗

arXiv2022

Polymorphic self-assembly of helical tubules is kinetically controlled

In contrast to most self-assembling synthetic materials, which undergo unbounded growth, many biological self-assembly processes are self-limited. That is, the assembled structures have one or more finite dimensions that are much larger than the size scale of the individual monomers. In many such cases, the finite dimension is selected by a preferred curvature of the monomers, which leads to self-closure of the assembly. In this article, we study an example class of self-closing assemblies: cylindrical tubules that assemble from triangular monomers. By combining kinetic Monte Carlo simulations, free energy calculations, and simple theoretical models, we show that a range of programmable size scales can be targeted by controlling the intricate balance between the preferred curvature of the monomers and their interaction strengths. However, their assembly is kinetically controlled - the tubule morphology is essentially fixed shortly after closure, resulting in a distribution of tubule widths that is significantly broader than the equilibrium distribution. We develop a simple kinetic model based on this observation and the underlying free-energy landscape of assembling tubules that quantitatively describes the distributions. Our results are consistent with recent experimental observations of tubule assembly from triangular DNA origami monomers. The modeling framework elucidates design principles for assembling self-limited structures from synthetic components, such as artificial microtubules that have a desired width and chirality.

cond-mat.soft↗

arXiv2021

Tiling a tubule: How increasing complexity improves the yield of self-limited assembly

The ability to design and synthesize ever more complicated colloidal particles opens the possibility of self-assembling a zoo of complex structures, including those with one or more self-limited length scales. An undesirable feature of systems with self-limited length scales is that thermal fluctuations can lead to the assembly of nearby, off-target states. We investigate strategies for limiting off-target assembly by using multiple types of subunits. Using simulations and energetics calculations, we explore this concept by considering the assembly of tubules built from triangular subunits that bind edge to edge. While in principle, a single type of triangle can assemble into tubules with a monodisperse width distribution, in practice, the finite bending rigidity of the binding sites leads to the formation of off-target structures. To increase the assembly specificity, we introduce tiling rules for assembling tubules from multiple species of triangles. We show that the selectivity of the target structure can be dramatically improved by using multiple species of subunits, and provide a prescription for choosing the minimum number of subunit species required for near-perfect yield. Our approach of increasing the system's complexity to reduce the accessibility of neighboring structures should be generalizable to other systems beyond the self-assembly of tubules.

cond-mat.soft↗

arXiv2021

Thermodynamic size control in curvature-frustrated tubules: Self-limitation with open boundaries

We use computational modeling to investigate the assembly thermodynamics of a particle-based model for geometrically frustrated assembly, in which the local packing geometry of subunits is incompatible with uniform, strain-free large-scale assembly. The model considers discrete triangular subunits that drive assembly towards a closed, hexagonal-ordered tubule, but have geometries that locally favor negative Gaussian curvature. We use dynamical Monte Carlo simulations and enhanced sampling methods to compute the free energy landscape and corresponding self-assembly behavior as a function of experimentally accessible parameters that control assembly driving forces and the magnitude of frustration. The results determine the parameter range where finite-temperature self-limiting assembly occurs, in which the equilibrium assembly size distribution is sharply peaked around a well-defined finite size. The simulations also identify two mechanisms by which the system can escape frustration and assemble to unlimited size, and determine the particle-scale properties of subunits that suppress unbounded growth.

cond-mat.soft↗

arXiv2019

Avalanches, thresholds, and diffusion in meso-scale amorphous plasticity

We present results on a meso-scale model for amorphous matter in athermal, quasi-static (a-AQS), steady state shear flow. In particular, we perform a careful analysis of the scaling with the lateral system size, $L$, of: i) statistics of individual relaxation events in terms of stress relaxation, $S$, and individual event mean-squared displacement, $M$, and the subsequent load increments, $\Delta \gamma$, required to initiate the next event; ii) static properties of the system encoded by $x=\sigma_y-\sigma$, the distance of local stress values from threshold; and iii) long-time correlations and the emergence of diffusive behavior. For the event statistics, we find that the distribution of $S$ is similar to, but distinct from, the distribution of $M$. We find a strong correlation between $S$ and $M$ for any particular event, with $S\sim M^{q}$ with $q\approx 0.65$. $q$ completely determines the scaling exponents for $P(M)$ given those for $P(S)$. For the distribution of local thresholds, we find $P(x)$ is analytic at $x=0$, and has a value $\left. P(x)\right|_{x=0}=p_0$ which scales with lateral system length as $p_0\sim L^{-0.6}$. Extreme value statistics arguments lead to a scaling relation between the exponents governing $P(x)$ and those governing $P(S)$. Finally, we study the long-time correlations via single-particle tracer statistics. The value of the diffusion coefficient is completely determined by $\langle \Delta \gamma \rangle$ and the scaling properties of $P(M)$ (in particular from $\langle M \rangle$) rather than directly from $P(S)$ as one might have naively guessed. Our results: i) further define the a-AQS universality class, ii) clarify the relation between avalanches of stress relaxation and diffusive behavior, iii) clarify the relation between local threshold distributions and event statistics.

cond-mat.soft↗

arXiv2018

Diffusion in mesoscopic lattice models of amorphous plasticity

We present results on tagged particle diffusion in a meso-scale lattice model for sheared amorphous material in athermal quasi-static conditions. We find a short time diffusive regime and a long time diffusive regime whose diffusion coefficients depend on system size in dramatically different ways. At short time, we find that the diffusion coefficient, $D$, scales roughly linearly with system length, $D\sim L^{1.05}$. This short time behavior is consistent with particle-based simulations. The long-time diffusion coefficient scales like $D\sim L^{1.6}$, close to previous studies which found $D\sim L^{1.5}$. Furthermore, we show that the near-field details of the interaction kernel do not affect the short time behavior, but qualitatively and dramatically affect the long time behavior, potentially causing a saturation of the mean-squared displacement at long times. Our finding of a $D\sim L^{1.05}$ short time scaling resolves a long standing puzzle about the disagreement between the diffusion coefficient measured in particle-based models and meso-scale lattice models of amorphous plasticity.

cond-mat.soft↗

arXiv2017

Anisotropic super-attenuation of capillary waves on driven glass interfaces

Metrological AFM measurements are performed on the silica glass interfaces of photonic band-gap fibres and hollow capillaries. The freezing of attenuated out-of-equilibrium capillary waves during the drawing process is shown to result in a reduced surface roughness. The roughness attenuation with respect to the expected thermodynamical limit is determined to vary with the drawing stress following a power law. A striking anisotropic character of the height correlation is observed: glass surfaces thus retain a structural record of the direction of the flow to which the liquid was submitted.

cond-mat.soft↗

arXiv2016

From depinning transition to plastic yielding of amorphous media: A soft modes perspective

A mesoscopic model of amorphous plasticity is discussed in the context of depinning models. After embedding in a d + 1 dimensional space, where the accumulated plastic strain lives along the additional dimension, the gradual plastic deformation of amorphous media can be regarded as the motion of an elastic manifold in a disordered landscape. While the associated depinning transition leads to scaling properties, the quadrupolar Eshelby interactions at play in amorphous plasticity induce specific additional features like shear-banding and weak ergodicity breakdown. The latters are shown to be controlled by the existence of soft modes of the elastic interaction, the consequence of which is discussed in the context of depinning.

cond-mat.soft↗

arXiv2015

Finite size effects in a model for plasticity of amorphous composites

We discuss the plastic behavior of an amorphous matrix reinforced by hard particles. A mesoscopic depinning-like model accounting for Eshelby elastic interactions is implemented. Only the effect of a plastic disorder is considered. Numerical results show a complex size-dependence of the effective flow stress of the amorphous composite. In particular the departure from the mixing law shows opposite trends associated to the competing effects of the matrix and the reinforcing particles respectively. The reinforcing mechanisms and their effects on localization are discussed. Plastic strain is shown to gradually concentrate on the weakest band of the system. This correlation of the plastic behavior with the material structure is used to design a simple analytical model. The latter nicely captures reinforcement size effects in $-(\log N/N)^{1/2}$ observed numerically. Predictions of the effective flow stress accounting for further logarithmic corrections show a very good agreement with numerical results.

cond-mat.mtrl-sci↗

arXiv2014

Kinetic roughening of a soft dewetting line under quenched disorder - a numerical study

A molecular-dynamics type simulation method, which is suitable for investigating the dewetting dynamics of thin and viscous liquid layers, is discussed. The efficiency of the method is exemplified by studying a two-parameter depinning-like model defined on inhomogeneous solid surfaces. The morphology and the statistical properties of the contact line is mapped in the relevant parameter space, and as a result critical behavior in the vicinity of the depinning transition is revealed. The model allows for the tearing of the layer, which leads to a new propagation regime resulting in non-trivial collective behavior. The large deformations observed for the interface is a result of the interplay between the substrate inhomogeneities and the capillary forces.

cond-mat.soft↗

arXiv2013

The rhythm of coupled metronomes

Spontaneous synchronization of an ensemble of metronomes placed on a freely rotating platform is studied experimentally and by computer simulations. A striking in-phase synchronization is observed when the metronomes' beat frequencies are fixed above a critical limit. Increasing the number of metronomes placed on the disk leads to an observable decrease in the level of the emerging synchronization. A realistic model with experimentally determined parameters is considered in order to understand the observed results. The conditions favoring the emergence of synchronization are investigated. It is shown that the experimentally observed trends can be reproduced by assuming a finite spread in the metronomes' natural frequencies. In the limit of large numbers of metronomes, we show that synchronization emerges only above a critical beat frequency value.

nlin.CD↗