arXiv subjects

Alexei V. Tkachenko

Publications and source records attributed to Alexei V. Tkachenko.

At least 19 recordsLinked to original sources

arXiv2026

Kinetic Criticality in Linker-Mediated Colloidal Aggregation

Linker-mediated aggregation plays an important role in modern nanoscience. We demonstrate that it departs sharply from classical Smoluchowski kinetics because cluster reactivity evolves during growth. Combining theory with DNA-linked gold-nanoparticle experiments, we establish kinetic critical point controlled by linker abundance. Below threshold, active linkers are depleted and growth arrests; above threshold, clusters accumulate reactive sites, self-accelerate, and cross over to diffusion-limited coarsening. Experiments verify the predicted arrest, accelerated growth, and scaling collapse.

cond-mat.soft↗

arXiv2026

Substrate-Mediated Evaporation and Stochastic Evolution of Supported Au Nanoparticles

We use in situ transmission electron microscopy with automated tracking to study supported gold nanoparticles (NPs) during high-temperature vacuum annealing. \rev{The average mass loss per NP is governed by a flat, nearly size-independent substrate-mediated evaporation profile.} On top of \rev{this mean shrinkage}, individual NPs show significant fluctuations in apparent growth or shrinkage, and NP volume follows a \rev{random-walk-like trajectory. To rationalize both the ensemble-mean behavior and the particle-resolved variability, we develop a self-consistent theory that couples substrate-mediated evaporation to collective 2D Ostwald-type mass exchange through a shared adatom field, described in terms of a renormalized screening length and background concentration. In the experimentally relevant regime, the theory predicts an approximately size-independent mean shrinkage rate and clarifies how net mass loss suppresses classical coarsening.} \rev{Superimposed on this deterministic drift, we quantify stochastic volume trajectories and capture their fluctuation spectrum with a minimal Langevin description consistent with intermittent adatom attachment and detachment events.} In addition, we characterize the lateral diffusive motion of NPs, which is responsible for their coalescence. Altogether, our results highlight that stochasticity is intrinsic at the nanoscale \rev{and that predicting the evolution of supported NPs at early and intermediate times requires a unified framework combining substrate-mediated evaporation, collective mass exchange, and stochastic fluctuations.

cond-mat.mtrl-sci↗

arXiv2025

Dehydration-Driven Ion Aggregation and the Onset of Gelation in ZnCl$_2$ Solution

A minimal model of ionic aggregation in concentrated ZnCl$_2$ is developed, guided by molecular dynamics simulations with a machine-learned potential. It explicitly incorporates solvent-site depletion, correlated chloride binding, and allows for loops within Zn-Cl clusters. Dehydration is shown to drive ion binding through two sharp transitions set by the Zn coordination number $Z$: a crossover at $Z=2$ from isolated ions to Cl-bridged clusters, and gelation near $Z\approx 3$. The model agrees quantitatively with MD results, and the critical exponent of the cluster-size distribution matches percolation theory.

cond-mat.soft↗

arXiv2025

Structural and Compositional Complexities of Hierarchical Self-Assembly: a Hypergraph Approach

Programmable self-assembly enables the construction of complex molecular, supramolecular, and crystalline architectures from well-designed building blocks. We introduce a hypergraph-based formalism, Blocks & Bonds (B&B), that generalizes classical chemical graph theory by incorporating directed and multicolored interactions, internal symmetries, and hierarchical organization. Within this framework, we develop the Structure Code (SC), a compact and versatile language for describing self-assembled architectures. We define a Kolmogorov-style Structural Complexity as the total information content of SC, obtained through its tokenization and Shannon information assignment. Complementing this encoding-based measure, we introduce a much simpler quantity, the Compositional Complexity, which depends only on the number and cumulative usage of block and bond types in the construction set. A central result of this work is a strong empirical correlation between the token-based Structural Complexity and the Compositional Complexity across all examined systems. Owing to this agreement, the Compositional Complexity emerges as the most practical and broadly applicable measure: it is easy to compute, requires no explicit encoding, and yet closely tracks the actual information content of structurally diverse architectures. Applications to molecular systems (ethylene glycol, glucose), DNA-origami lattices, and crystalline assemblies show that B\&B hypergraphs provide a unified, scalable, and information-efficient representation of structural organization, naturally capturing symmetry, modularity, and stereochemistry. This framework establishes a quantitative foundation for complexity-aware classification and inverse design of programmable matter.

cond-mat.soft↗

arXiv2025

Evolutionary chemical learning in dimerization networks

We present a framework for chemical learning based on Competitive Dimerization Networks (CDNs) - systems in which multiple molecular species, e.g., proteins, DNA oligomers, or RNA oligomers, reversibly bind to form dimers. We show numerically that these networks can, in principle, be trained in vitro through directed evolution, enabling the implementation of complex learning tasks such as multiclass classification without digital hardware or prior knowledge of all microscopic association constants. Each molecular species functions analogously to a neuron, with binding affinities acting as tunable synaptic weights. A training protocol involving mutation, selection, and amplification of DNA-based components allows CDNs to robustly discriminate among noisy input patterns. The resulting classifiers exhibit strong output contrast and high mutual information between input and output, especially when guided by a contrast-enhancing loss function. Comparative analysis with in silico gradient descent training reveals closely correlated performance. These results establish CDNs as a promising platform for analog physical computation, bridging synthetic biology and machine learning, and advancing the development of adaptive, energy-efficient molecular computing systems.

cond-mat.stat-mech↗

arXiv2025

Thermodynamic cost of inference and learning in physical neural networks

How much of the energy consumed by artificial neural networks is set by physics rather than by implementation? For irreversible digital hardware the reference is Landauer's principle, which charges $k_B T\ln 2$ per erased bit. We map a generic feedforward network onto a physical Hamiltonian in which each layer relation is an elastic compatibility constraint, and obtain two exact bounds. First, its equilibrium free energy is independent of the input and of every weight and bias, at all temperatures, so quasi-static inference requires no work whatsoever: no thermodynamic cost attaches to computation itself. Second, at finite speed the work exceeds the squared Wasserstein-2 distance between the initial and final thermal states, divided by the protocol duration. Relaxed to an entropic measure of distinguishability, this identifies the cost with the information separating successive inputs, about $k_B T$ per dimension of the widest layer at the fastest usable speed. Learning is fundamentally different: writing the parameters carries an irreducible cost of a few $k_B T$ each that survives the quasi-static limit. The thermodynamic price of a neural network is therefore set by its memory rather than its arithmetic. Simulations confirm both bounds: the inference work saturates the transport bound to within four percent, and accuracy collapses once the dissipated work falls below the thermal scale.

cond-mat.stat-mech↗

arXiv2024

Universality in diffusion-controlled nucleation and growth

Nucleation and growth is studied in a system undergoing diffusion-controlled condensation under gradual changes in parameters, such as cooling. It is demonstrated that when Gibbs-Thompson effect becomes negligible, the system falls into a universal regime. i.e. the final droplet size distribution remains invariant under certain rescaling of system parameters. An approximate yet very accurate analytic form is obtained for the size distribution function in this regime.

cond-mat.soft↗

arXiv2023

Timeless Histories: Quantum Measurement and the Maximum Entropy Principle

The quantum measurement problem, i.e. the apparent conflict between unitary quantum evolution and non-unitary, stochastic wave-function collapse, remains unresolved a century after the formulation of quantum mechanics. We first review the standard picture, from the Copenhagen prescription with its Heisenberg cut, through von Neumann's movable cut, to environment-induced decoherence, which explains the emergence of stable classical records but still presupposes the Born rule and therefore cannot by itself replace the measurement postulates. We then connect this problem to the Maximum Entropy Principle in two complementary ways. First, decoherence drives the measurement apparatus toward the least biased state compatible with the dynamically protected pointer distribution, so that the emergent collapse may be viewed as a thermodynamic relaxation toward constrained maximum entropy. Second, we propose a Timeless Histories formulation of quantum mechanics in which the primitive objects are ordered sequences of events rather than evolving wave functions. Their conditional probabilities are assigned, relative to specified refinements, by a single Born-Boltzmann rule that combines the quadratic structure of Born's rule with Boltzmann's counting of equally probable microstates. The textbook form of Born's rule, the projection postulate, density operators, and wave functions are then recovered as derived informational constructs, while collapse becomes Bayesian conditioning on recorded events. Time and space enter only subsequently through unitary translation symmetry. Because the probability rule is postulated independently of any physical collapse or classical observer, decoherence is no longer asked to justify the rule used to interpret its own reduced states, and can be invoked to explain the approximate additivity and stability of macroscopic records, i.e. the emergence of classicality.

quant-ph↗

arXiv2023

Symmetry-specific characterization of bond orientation order in DNA-assembled nanoparticle lattices

Bond-orientational order in DNA-assembled nanoparticle lattices is explored with the help of recently introduced Symmetry-specific Bond Order Parameters (SymBOPs). This approach provides a more sensitive analysis of local order than traditional scalar Bond Order Parameters, facilitating the identification of coherent domains at the single bond level. The present study expands the method initially developed for assemblies of anisotropic particles to the isotropic ones or cases where particle orientation information is unavailable. The SymBOP analysis was applied to experiments on DNA-frame-based assembly of nanoparticle lattices. It proved highly sensitive in identifying coherent crystalline domains with different orientations, as well as detecting topological defects, such as dislocations. Furthermore, the analysis distinguishes individual sublattices within a single crystalline domain, such as pair of interpenetrating FCC lattices within a cubic diamond. The results underscore the versatility and robustness of SymBOPs in characterizing ordering phenomena, making them valuable tools for investigating structural properties in various systems.

cond-mat.soft↗

arXiv2022

Chaos over Order: Mapping 3D Rotation of Triaxial Asteroids and Minor Planets

Celestial bodies approximated with rigid triaxial ellipsoids in a two-body system can rotate chaotically due to the time-varying gravitational torque from the central mass. At small orbital eccentricity values, rotation is short-term orderly and predictable within the commensurate spin-orbit resonances, while at eccentricity approaching unity, chaos completely takes over. Here, we present the full 3D rotational equations of motion around all three principle axes for triaxial minor planets and two independent methods of numerical solution based on Euler rotations and quaternion algebra. The domains of chaotic rotation are numerically investigated over the entire range of eccentricity with a combination of trial integrations of Euler's equations of motion and the GALI($k$) method. We quantify the dependence of the order--chaos boundaries on shape by changing a prolateness parameter, and find that the main 1:1 spin-orbit resonance disappears for specific moderately prolate shapes already at eccentricities as low as 0.3. The island of short-term stability around the main 1:1 resonance shrinks with increasing eccentricity at a fixed low degree of prolateness and completely vanishes at approximately 0.8. This island is also encroached by chaos on longer time scales indicating longer Lyapunov exponents. Trajectories in the close vicinity of the 3:2 spin-orbit resonance become chaotic at smaller eccentricities, but separated enclaves of orderly rotation emerge at eccentricities as high as 0.8. Initial perturbations of rotational velocity in latitude away from the exact equilibrium result in a spectrum of free libration, nutation, and polar wander, which is not well matched by the linearized analysis omitting the inertial terms.

astro-ph.EP↗

arXiv2021

Controlling morphology in hybrid isotropic/patchy particle assemblies

Brownian Dynamics is used to study self-assembly in a hybrid system of istotropic particles (IPs), combined with anisotropic building blocks that represent special "designer particles". Those are modeled as spherical patchy particles (PPs) with binding only allowed between their patches and IPs. In this study, two types of PPs are considered: Octahedral PPs (Oh-PPs) and Square PPs (Sq-PPs), with octahedral and square arrangements of patches, respectively. The self-assembly is additionally facilitated by the simulated annealing procedure. The resultant structures are characterized by a combination of local correlations in cubatic ordering, and a symmetry-specific variation of bond orientation order parameters (SymBOPs). By varying the PP/IP size ratio, we detected a sharp crossover between two distinct morphologies, in both types of systems. High symmetry phases, NaCl crystal for Oh-PP and square lattice for Sq-PP, are observed for larger size ratios. For smaller ones, the dominant morphologies are significantly different, e.g., Oh-PPs form a compact amorphous structure with predominantly Face-to-Face orientation of neighboring PPs. Unusually for a morphology without a long range order, it is still possible to identify well organized coherent clusters of this structure, thanks to the adoption of our SymBOP-based characterization.

cond-mat.soft↗

arXiv2021

Symmetry-specific orientational order parameters for complex structures

A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries. Two classes of tensor order parameters are associated with polyhedral nematic, and bond orientational order, respectively. For the latter, a variation of classical bond order parameters is introduced that takes advantage of the symmetry of constituent particles, and/or expected crystalline phases. These Symmetrized Bond Order Parameters (SymBOPs) can be averaged over an entire system, or assigned locally to an individual bond. By combining that with bond percolation procedure, one is able to identify coherent domains within a self-assembled structure. As a demonstration of the proposed framework, we apply it to a simulated hybrid system that combines isotropic and patchy particles with octahedral symmetry. Not only does the methodology allow one to identify individual crystalline domains, but it also detects coherent clusters of a peculiar compact amorphous structure that is not space-filling and lacks any long-range order.

cond-mat.soft↗

arXiv2021

Empty perovskites as Coulomb floppy networks: entropic elasticity and negative thermal expansion

Floppy Networks (FNs) provide valuable insight into the origin of anomalous mechanical and thermal properties in soft matter systems, from polymers, rubber, and biomolecules to glasses and granular materials. Here, we use the very same FN concept to construct a quantitative microscopic theory of empty perovskites, a family of crystals with ReO$_3$ structure, which exhibit a number of unusual properties. One remarkable example is ScF$_3$, which shows a near-zero-temperature structural instability and large negative thermal expansion (NTE). We trace these effects to an FN-like crystalline architecture formed by strong nearest-neighbor bonds, which is stabilized by net electrostatic repulsion that plays a role similar to osmotic pressure in polymeric gels. NTE in these crystalline solids, which we conceptualize as Coulomb Floppy Networks, emerges from the tension effect of Coulomb repulsion combined with the FN's entropic elasticity, and has the same physical origin as in gels and rubber. Our theory provides an accurate, quantitative description of phonons, thermal expansion, compressibility, and structural phase diagram, all in excellent agreement with experiments. The entropic stabilization of critical soft modes, which play only a secondary role in NTE, explains the observed phase diagram. Significant entropic elasticity resolves the puzzle of a marked, $\approx$50\% discrepancy between the experimentally observed bulk modulus and ab initio calculations. The Coulomb FN approach is potentially applicable to other important materials with markedly covalent bonds, from perovskite oxides to iron chalcogenides, whose anomalous vibrational and structural properties are still poorly understood.

cond-mat.mtrl-sci↗

arXiv2021

Geometric and Topological Entropies of Sphere Packing

We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two contributions: geometric, reflecting statistical weights of individual configurations, and topological, which corresponds to the number of topologically distinct states. Both of them are computed in the thermodynamic limit for isostatic packings in 2D and 3D, and the result is further expanded to the case of "floppy" particle clusters. The theory is directly applicable to sticky colloids, and in addition, generalizes concepts of granular and glassy configurational entropies for the case of non-jammed systems.

cond-mat.soft↗

arXiv2021

Stochastic social behavior coupled to COVID-19 dynamics leads to waves, plateaus and an endemic state

It is well recognized that population heterogeneity plays an important role in the spread of epidemics. While individual variations in social activity are often assumed to be persistent, i.e. constant in time, here we discuss the consequences of dynamic heterogeneity. By integrating the stochastic dynamics of social activity into traditional epidemiological models we demonstrate the emergence of a new long timescale governing the epidemic in broad agreement with empirical data. Our model captures multiple features of real-life epidemics such as COVID-19, including prolonged plateaus and multiple waves, which are transiently suppressed due to the dynamic nature of social activity. The existence of the long timescale due to the interplay between epidemic and social dynamics provides a unifying picture of how a fast-paced epidemic typically will transition to the endemic state.

q-bio.PE↗

arXiv2021

Time-dependent heterogeneity leads to transient suppression of the COVID-19 epidemic, not herd immunity

Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, super-spreading events lead to burstiness and overdispersion, while long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both timescales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through parameterization. We derive a non-linear dependence of the effective reproduction number Re on the susceptible population fraction S. We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is a fragile state that wanes over time due to changing levels of social activity, and so the infection peak is not an indication of herd immunity: subsequent waves can and will emerge due to behavioral changes in the population, driven (e.g.) by seasonal factors. Transient and long-term levels of heterogeneity are estimated by using empirical data from the COVID-19 epidemic as well as from real-life face-to-face contact networks. These results suggest that the hardest-hit areas, such as NYC, have achieved TCI following the first wave of the epidemic, but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these regions can still experience subsequent waves.

q-bio.PE↗

arXiv2020

Ligation of random oligomers leads to emergence of autocatalytic sequence network

The emergence of longer information-carrying and functional nucleotide polymers from random short strands was a major stepping stone at the dawn of life. But the formation of those polymers under temperature oscillation required some form of selection. A plausible mechanism is template-based ligation where theoretical work already suggested a reduction in information entropy. Here, we show how nontrivial sequence patterns emerge in a system of random 12mer DNA sequences subject to enzyme-based templated ligation reaction and temperature cycling. The strands acted both as a template and substrates of the reaction and thereby formed longer oligomers. The selection for templating sequences leads to the development of a multiscale ligation landscape. A position-dependent sequence pattern emerged with a segregation into mutually complementary pools of A-rich and T-rich sequences. Even without selection for function, the base pairing of DNA with ligation showed a dynamics resembling Darwinian evolution.

physics.bio-ph↗

arXiv2020

Modeling COVID-19 dynamics in Illinois under non-pharmaceutical interventions

We present modeling of the COVID-19 epidemic in Illinois, USA, capturing the implementation of a Stay-at-Home order and scenarios for its eventual release. We use a non-Markovian age-of-infection model that is capable of handling long and variable time delays without changing its model topology. Bayesian estimation of model parameters is carried out using Markov Chain Monte Carlo (MCMC) methods. This framework allows us to treat all available input information, including both the previously published parameters of the epidemic and available local data, in a uniform manner. To accurately model deaths as well as demand on the healthcare system, we calibrate our predictions to total and in-hospital deaths as well as hospital and ICU bed occupancy by COVID-19 patients. We apply this model not only to the state as a whole but also its sub-regions in order to account for the wide disparities in population size and density. Without prior information on non-pharmaceutical interventions (NPIs), the model independently reproduces a mitigation trend closely matching mobility data reported by Google and Unacast. Forward predictions of the model provide robust estimates of the peak position and severity and also enable forecasting the regional-dependent results of releasing Stay-at-Home orders. The resulting highly constrained narrative of the epidemic is able to provide estimates of its unseen progression and inform scenarios for sustainable monitoring and control of the epidemic.

q-bio.PE↗