arXiv subjects

Jürgen Horbach

Publications and source records attributed to Jürgen Horbach.

At least 19 recordsLinked to original sources

arXiv2026

Active Brownian Dynamics from a Hamiltonian Model: Transitioning from Equilibrium to Activity

We introduce a Hamiltonian Active Brownian Particle (HABP) model that connects equilibrium dynamics with the non-equilibrium, two-dimensional overdamped behavior of standard Active Brownian Particles (ABPs). In equilibrium, the system follows overdamped Langevin equations that strictly satisfy the fluctuation-dissipation theorem. Coupling translational and rotational degrees of freedom to separate heat baths ($T_θ > T_{\textrm{tr}}$), drives the system out of equilibrium. In free space, matching the diffusion coefficients yields quantitative agreement with the ABP model in the limit $T_θ/T_{\textrm{tr}}\to \infty$, whereas in a harmonic potential, this matching is recovered even at finite temperature ratios. Entropy production analysis demonstrates that in the ABP limit, all energy injected by the swim force dissipates into the translational bath, leaving the rotational bath as a zero-cost entropy source. These insights provide the first steps toward equilibrium-inspired descriptions of active matter, facilitating the development of new theoretical frameworks to study activity-induced fluctuations, transport, and phase behavior in living and non-living soft matter systems far from equilibrium.

cond-mat.soft↗

arXiv2026

Perspective: The Physics of Active Solids -- From Hamiltonians to Active Matter Models

The physics of active matter, wherein constituent particles consume energy to generate autonomous motion, has revolutionized non-equilibrium statistical mechanics. While a large body of work has successfully elucidated the behavior of dilute active systems, the dense regime -- characterized by ``active glasses and active solids'' -- presents profound challenges that defy conventional theoretical frameworks. Recent observations reveal two striking features in these dense systems: an apparent enhancement of Mermin-Wagner-Hohenberg (MWH) fluctuations leading to anomalous long-wavelength density fluctuations, and a remarkable correspondence between activity-induced annealing and annealing via oscillatory shear. In this perspective article, we propose a novel approach toward a deeper understanding of dense active matter: by developing active Hamiltonian models as equilibrium reference frameworks, we map out pathways toward non-equilibrium active systems. This strategy allows us to elucidate both the correspondence between driven and active systems and the enhanced MWH fluctuations, which likely arise from a strong coupling between spatially random active forces and long-wavelength density (phonon) modes. We outline a comprehensive roadmap employing complementary approaches, including the active Hamiltonian formalism, comparative studies of oscillatory shear in active and passive solids, and investigations of chiral active matter. Establishing this activity-oscillatory shear correspondence across diverse systems is essential to demonstrate its universality, reveal the underlying large-scale emergent physics, and place our hypothesis on a firmer theoretical ground.

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arXiv2025

Entropic alignment of topologically modified ring polymers in cylindrical confinement

Under high cylindrical confinement, segments of ring polymers can be localized along the long axis of the cylinder by introducing internal loops within the ring polymer. The emergent organization of the polymer segments occurs because of the entropic repulsion between internal loops. These principles were used to identify the underlying mechanism of bacterial chromosome organization. Here, we outline functional principles associated with entropic interactions, leading to specific orientations of the ring polymers relative to their neighbors in the cylindrical confinement. We achieve this by modifying the ring polymer topology by creating internal loops of two different sizes within the polymer, and thus create an asymmetry. This allows us to strategically manipulate polymer topology such that segments of a polymer face certain other segments of a neighboring polymer. The polymers therefore behave as if they are subjected to an `effective' entropic interaction reminiscent of interactions between Ising spins. But this emergent spatial and orientational organization is not enthalpy-driven. We consider a bead spring model of flexible polymers with only repulsive excluded volume interactions between the monomers. The polymers entropically repel each other and occupy different halves of the cylinder, and moreover, the adjacent polymers preferentially re-orient themselves along the axis of the cylinder. We further substantiate our observations by free energy calculations. To the best of our knowledge, this is the first study of the emergence of effective orientational interactions by harnessing entropic interactions in flexible polymers. The principles elucidated here could be relevant to understand the interactions between different sized loops within a large chromosome.

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arXiv2025

Active Particle Doping Suppresses Brittle Failure in Ultrastable Glasses

Ultrastable glasses are known for their exceptional mechanical stability but often fail in a brittle manner, typically marked by the formation of shear bands when subjected to shear deformation. An open question is how shear banding is affected by active particles. Here, we address this issue by investigating ultrastable glasses that are doped with self-propelled particles (SPPs) that perform run-and-tumble motions. In the presence of active particles we find a crossover from heterogeneous to homogeneous yielding. Through extensive computer simulations of a polydisperse model, which is capable of producing ultrastable glasses using swap Monte Carlo Methods, we demonstrate the progressive emergence of multiple shear bands under activity, leading to continuous and delayed yielding. Interestingly, we uncover a compensatory relationship between active forces and global shear rates: a rise in one can offset a decline in the other, arising from the isomorphic-like behavior exhibited by different combinations of active forces and strain rates. We also identify a non-monotonic relationship between yielding and persistence time: while the yield stress increases at shorter persistence times with increasing active forces, it tends to decrease with longer persistence times. This observation highlights a tunable range of activity that can modify the yielding mode. Lastly, we show that the spacing between shear bands diminishes in a power law manner as the magnitude of the active force increases.

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arXiv2024

Thermostatting of Active Hamiltonian Systems via Symplectic Algorithms

We consider a class of non-standard, two-dimensional (2D) Hamiltonian models that may show features of active particle dynamics, and therefore, we refer to these models as active Hamiltonian (AH) systems. The idea is to consider a spin fluid where -- on top of spin-spin and particle-particle interactions -- spins are coupled to the particle's velocities via a vector potential. Continuous spin variables interact with each other as in a standard $XY$ model. Typically, the AH models exhibit non-standard thermodynamic properties (e.g., for temperature and pressure) and equations of motion with non-standard forces. This implies that the derivation of symplectic algorithms to solve Hamilton's equations of motion numerically, as well as the thermostatting for these systems, is not straightforward. Here, we derive a symplectic integration scheme and propose a Nosé-Poincaré thermostat, providing a correct sampling in the canonical ensemble. The expressions for AH systems that we find for temperature and pressure might have parallels with the ongoing debate about the definition of pressure and the equation of state in active matter systems. For a specific AH model, recently proposed by Casiulis et al. [Phys. Rev. Lett. {\bf 124}, 198001 (2020)], we rationalize the symplectic algorithm and the proposed thermostatting, and investigate the transition from a fluid at high temperature to a cluster phase at low temperature where, due to the coupling of velocities and spins, the cluster phase shows a collective motion that is reminiscent to that observed in a variety of active systems.

cond-mat.stat-mech↗

arXiv2024

On the growing length scale in a replica-coupled glassforming liquid

Computer simulations are used to study a three-dimensional polydisperse model glassformer in a replica-coupling setup where an attractive field $\propto - \varepsilon Q$ of strength $\varepsilon$ can adjust the similarity of the system to a fixed reference configuration with the overlap parameter $Q$. The polydispersity in the model enables the efficient use of swap Monte Carlo in combination with molecular-dynamics simulation from which we obtain fully equilibrated liquid configurations at very low temperature, i.e., far below the critical temperature of mode-coupling theory, $T_{\rm MCT}$. When the $\varepsilon$-field is switched on, the fast dynamics with swaps allow relaxation to the stationary state at temperatures below $T_{\rm MCT}$. In the stationary state, the overlap $Q$ has a finite value that increases with increasing $\varepsilon$. For a given temperature $T$, fluctuations of the overlap around the average value become maximal at a critical field strength $\varepsilon^\star(T)$. With decreasing $T$ along this $\varepsilon^\star(T)$-line, overlap fluctuations increase and a transition from a unimodal overlap distribution to a bimodal shape occurs. We give evidence that these bimodal distributions are not due to first-order phase transitions. However, they reflect finite-size effects due to a rapidly growing length scale with decreasing temperature. We discuss the significance of this length scale for the understanding of the glass transition.

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arXiv2023

The Origin of Deformation Induced Topological Anisotropy in Silica Glass

Oxide glasses with a network structure are omnipresent in daily life. Often, they are regarded as isotropic materials; however, structural anisotropy can be induced through processing in mechanical fields and leads to unique materials properties. Unfortunately, due to the lack of local, atomic-scale analysis methods, the microscopic mechanisms leading to anisotropy remained elusive. Using novel analysis methods on glasses generated by molecular dynamics simulations, this paper provides a microscopic understanding of topological anisotropy in silica (SiO$_2$) glass under mechanical loads. The anisotropy observed in silica glass originates from a preferred orientation of SiO$_4$ tetrahedra at both short- and medium-range levels that can be controlled via the mode of mechanical loading. The findings elucidate the relation between the deformation protocol and the resulting anisotropic structure of the silica network (involving both persistent and transient effects), and thus provide important insight for the design of oxide glasses with tailored materials properties.

cond-mat.mtrl-sci↗

arXiv2023

Understanding the swap Monte Carlo algorithm in a size-polydisperse model glassformer

The dynamics of a polydisperse model glassformer are investigated by augmenting molecular dynamics (MD) simulation with swap Monte Carlo (SMC). Three variants of the SMC algorithm are analyzed with regard to convergence and performance. We elucidate the microscopic mechanism responsible for the drastic speed-up of structural relaxation at low temperature. It manifests in a stepwise increase of the mean squared displacement when the time scale between the application of swap sweeps is significantly larger than a characteristic microscopic time scale. Compared to Newtonian dynamics, with the hybrid MD-SMC dynamics the glass transition shifts to a lower temperature and a different temperature dependence of the localization length is found.

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arXiv2022

On the choice of diameters in a polydisperse model glassformer: deterministic or stochastic?

In particle-based computer simulations of polydisperse glassforming systems, the particle diameters $σ= σ_1, \dots, σ_N$ of a system with $N$ particles are chosen with the intention to approximate a desired distribution density $f$ with the corresponding histogram. One method to accomplish this is to draw each diameter randomly from the density $f$. We refer to this stochastic scheme as model $\mathcal{S}$. Alternatively, one can apply a deterministic method, assigning an appropriate set of $N$ values to the diameters. We refer to this method as model $\mathcal{D}$. We show that especially for the glassy dynamics at low temperatures it matters whether one chooses model $\mathcal{S}$ or model $\mathcal{D}$. Using molecular dynamics computer simulation, we investigate a three-dimensional polydisperse non-additive soft-sphere system with $f(s) \sim s^{-3}$. The Swap Monte Carlo method is employed to obtain equilibrated samples at very low temperatures. We show that for model $\mathcal{S}$ the sample-to-sample fluctuations due to the quenched disorder imposed by the diameters $σ$ can be explained by an effective packing fraction. Dynamic susceptibilities in model $\mathcal{S}$ can be split into two terms: One that is of thermal nature and can be identified with the susceptibility of model $\mathcal{D}$, and another one originating from the disorder in $σ$. At low temperatures the latter contribution is the dominating term in the dynamic susceptibility.

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arXiv2022

Interatomic machine learning potentials for aluminium: application to solidification phenomena

In studying solidification process by simulations on the atomic scale, the modeling of crystal nucleation or amorphisation requires the construction of interatomic interactions that are able to reproduce the properties of both the solid and the liquid states. Taking into account rare nucleation events or structural relaxation under deep undercooling conditions requires much larger length scales and longer time scales than those achievable by \textit{ab initio} molecular dynamics (AIMD). This problem is addressed by means of classical MD simulations using a well established high dimensional neural network potential trained on a relevant set of configurations generated by AIMD. Our dataset contains various crystalline structures and liquid states at different pressures, including their time fluctuations in a wide range of temperatures considering only their energy labels. Applied to elemental aluminium, the resulting potential is shown to be efficient to reproduce the basic structural, dynamics and thermodynamic quantities in the liquid and undercooled states without the need to include neither explicitly the forces nor all kind of configurations in the training procedure. The early stage of crystallization is further investigated on a much larger scale with one million atoms, allowing us to unravel features of the homogeneous nucleation mechanisms in the fcc phase at ambient pressure as well as in the bcc phase at high pressure with unprecedented accuracy close to the \textit{ab initio} one. In both case, a single step nucleation process is observed.

cond-mat.mtrl-sci↗

arXiv2022

Rheological response of a glass-forming liquid having large bidispersity

Using extensive numerical simulations, we investigate the flow behaviour of a model glass-forming binary mixture whose constituent particles have a large size ratio. The rheological response to applied shear is studied in the regime where the larger species are spatially predominant. We demonstrate that the macroscopic rigidity that emerges with increasing density occurs in the regime where the larger species undergo a glass transition while the smaller species continue to be highly diffusive. We analyse the interplay between the timescale imposed by the shear and the quiescent relaxation dynamics of the two species to provide a microscopic insight into the observed rheological response. Finally, by tuning the composition of the mixture, we illustrate that the systematic insertion of the smaller particles affects the rheology by lowering of viscosity of the system.

cond-mat.soft↗

arXiv2022

Brittle yielding in supercooled liquids below the critical temperature of mode coupling theory

Molecular Dynamics (MD) computer simulations of a polydisperse soft-sphere model under shear are presented. Starting point for these simulations are deeply supercooled samples far below the critical temperature, $T_c$, of mode coupling theory. These samples are fully equilibrated with the aid of the swap Monte Carlo technique. For states below $T_c$, we identify a life time $τ_{\rm lt}$ that measures the time scale on which the system can be considered as an amorphous solid. The temperature dependence of $τ_{\rm lt}$ can be well described by an Arrhenius law. The existence of transient amorphous solid states below $T_c$ is associated with the possibility of brittle yielding, as manifested by a sharp stress drop in the stress-strain relation and shear banding. We show that brittle yielding requires on the one hand low shear rates and on the other hand, the time scale corresponding to the inverse shear rate has to be smaller or of the order of $τ_{\rm lt}$. Both conditions can be only met for large life time $τ_{\rm lt}$, i.e.~for states far below $T_c$.

cond-mat.soft↗

arXiv2022

Finite-size effects in the diffusion dynamics of a glass-forming binary mixture with large size ratio

Extensive molecular dynamics (MD) computer simulations of an equimolar glass-forming AB mixture with large size ratio are presented. While the large A particles show a glass transition around the critical density of mode coupling theory $ρ_c$, the small B particles remain mobile with a relatively weak decrease of their self diffusion coefficient $D_{\rm B}$ with increasing density. Surprisingly, around $ρ_c$, the self-diffusion coefficient of the A particles, $D_{\rm A}$, also starts to follow a rather weak dependence on density. We show that this is due to finite-size effects that can be understood from the analysis of the collective interdiffusion dynamics.

cond-mat.soft↗

arXiv2020

Wrinkles, folds and ripplocations: unusual deformation structures of confined elastic sheets at non-zero temperatures

We study the deformation of a fluctuating crystalline sheet confined between two flat rigid walls as a simple model for layered solids where bonds among atoms {\it within} the same layer are much stronger than those {\it between} layers. When subjected to sufficiently high loads in an appropriate geometry, these solids deform and fail in unconventional ways. Recent experiments suggest that configurations named {\it ripplocations}, where a layer folds backwards over itself, are involved. These structures are distinct and separated by large free energy barriers from smooth {\it ripples} of the atomic layers that are always present at any non-zero temperature. We use Monte Carlo simulation in combination with an umbrella sampling technique to obtain conditions under which such structures form and study their specific experimental signatures.

cond-mat.soft↗

arXiv2020

Flow heterogeneities in supercooled liquids and glasses under shear

Using extensive non-equilibrium molecular dynamics simulations, we investigate a glassforming binary Lennard-Jones mixture under shear. Both supercooled liquids and glasses are considered. Our focus is on the characterization of inhomogeneous flow patterns such as shear bands that appear as a transient response to the external shear. For the supercooled liquids, we analyze the crossover from Newtonian to non-Newtonian behavior with increasing shear rate $\dotγ$. Above a critical shear rate $\dotγ_c$ where a non-Newtonian response sets in, the transient dynamics are associated with the occurrence of short-lived vertical shear bands, i.e. bands of high mobility that form perpendicular to the flow direction. In the glass states, long-lived horizontal shear bands, i.e. bands of high mobility parallel to the flow direction, are observed in addition to vertical ones. The systems with shear bands are characterized in terms of mobility maps, stress-strain relations, mean-squared displacements, and (local) potential energies. The initial formation of a horizontal shear band provides an efficient stress release, corresponds to a local minimum of the potential energy, and is followed by a slow broadening of the band towards the homogeneously flowing fluid in the steady-state. Whether a horizontal or a vertical shear band forms cannot be predicted from the initial undeformed sample. Furthermore, we show that with increasing system size the probability for the occurrence of horizontal shear bands increases.

cond-mat.soft↗

arXiv2019

A nucleation theory for yielding of nearly defect-free crystals: understanding rate dependent yield points

Experiments and simulations show that when an initially defect free rigid crystal is subjected to deformation at a constant rate, irreversible plastic flow commences at the so-called {\em yield point}. The yield point is a weak function of the deformation rate, which is usually expressed as a power law with an extremely small non-universal exponent. We re-analyze a representative set of published data on nanometer sized, mostly defect free, Cu, Ni and Au crystals in the light of a recently proposed theory of yielding based on nucleation of stable stress-free regions inside the metastable rigid solid. The single relation derived here, which is {\em not} a power law, explains data covering {\em fifteen} orders of magnitude in time scales.

cond-mat.mtrl-sci↗

arXiv2019

Geometry-controlled Failure Mechanisms of Amorphous Solids on the Nanoscale

Amorphous solids, confined on the nano-scale, exhibit a wealth of novel phenomena yet to be explored. In particular, the response of such solids to a mechanical load is not well understood and, as has been demonstrated experimentally, it differs strongly from bulk samples made of the same materials. Failure patterns and mechanisms are strongly affected by the geometry of the confinement and the interplay between interfacial effects in the sample and the time scale, imposed by an external mechanical field. Here, we present the mechanism of cavity formation in a confined model glass, subjected to expansion with a constant strain rate. This system is studied for varying geometric aspect ratio and sample size. Our results show that for a given temperature and straining condition, the sample shows cavitation when the aspect ratio reaches a critical value and below this aspect ratio the sample breaks by forming a neck. The critical aspect ratio is associated with a critical curvature of the neck that depends on strain rate and temperature. If this critical curvature is exceeded, the free energy of the system is minimized by the formation of a cavity. Our study reveals a novel mechanism of cavity formation on the nanoscale. This is probably a generic mechanism for material's failure in small confined systems under mechanical load.

cond-mat.stat-mech↗

arXiv2018

Plastic deformation of a permanently bonded network: stress relaxation by pleats

We show that a flat two dimensional network of connected vertices, when stretched, may deform plastically by producing `pleats'; system spanning linear structures with width comparable to the lattice spacing, where the network overlaps on itself. To understand the pleating process, we introduce an external field that couples to local {\em non-affine} displacements, i.e. those displacements of neighbouring vertices that cannot be represented as a local affine strain. We obtain both zero and finite temperature phase diagrams in the strain -- field plane. Pleats occur here as a result of an equilibrium first-order transition from the homogeneous network to a heterogeneous phase where stress is localised within pleats and eliminated elsewhere. We show that in the thermodynamic limit the un-pleated state is always metastable at vanishing field for infinitesimal strain. Plastic deformation of the initially homogeneous network is akin to the decay of a metastable phase via a dynamical transition. We make predictions concerning local stress distributions and thermal effects associated with pleats which may be observable in suitable experimental systems.

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