arXiv subjects

Chanania Steinbock

Publications and source records attributed to Chanania Steinbock.

9 recordsLinked to original sources

arXiv2025

Dynamics of individual active elastic filaments with chiral self-propulsion

We study the over-damped dynamics of individual one-dimensional elastic filaments subjected to a chiral active force which propels each point of the filament at a fixed angle relative to the tangent vector of the filament at that point. Such a model is a reasonable starting point for describing the behavior of polymers such as microtubules in gliding assay experiments. We derive sixth-order nonlinear coupled partial differential equations for the intrinsic properties of the filament, namely, its curvature and metric, and show that these equations are capable of supporting multiple different stationary solutions in a co-moving frame, i.e.\ that chiral active elastic filaments exhibit dynamic multi-stability in their shapes. A linear stability analysis of these solutions is carried out to determine which solutions are stable and a brief analysis of the time-dependent approach to stationary shape is considered. Finally, simulations are presented which confirm many of our predictions while also revealing additional complexity.

cond-mat.soft↗

arXiv2025

Nonreciprocal random networks and their percolation properties

We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the probability of the reverse link occurring from node j to node i. We analytically determine the degree and percolation properties of such networks with exactly two types of link probability, demonstrating that whether the networks are structured such that the nodes are not statistically indistinguishable has profound effects on these measures, both quantitively and in how such networks need to be approached. In particular, we develop a technique for solving the percolation problem which can be applied to both structured and unstructured networks. The method entails writing self-consistent integral and differential equations for the probability that each node will belong to the network's giant component. Exact solutions to these equations are obtained and simulations which confirm our analytic predictions are presented.

cond-mat.stat-mech↗

arXiv2024

Asymptotic Matching the Self-Consistent Expansion to Approximate the Modified Bessel Functions of the Second Kind

The self-consistent expansion (SCE) is a powerful technique for obtaining perturbative solutions to problems in statistical physics but it suffers from a subtle problem - too much freedom! The SCE can be used to generate an enormous number of approximations but distinguishing the superb approximations from the deficient ones can only be achieved after the fact by comparison to experimental or numerical results. Here, we propose a method of using the SCE to a priori obtain uniform approximations, namely asymptotic matching. If the asymptotic behaviour of a problem can be identified, then the approximations generated by the SCE can be tuned to asymptotically match the desired behaviour and this can be used to obtain uniform approximations over the entire domain of consideration, without needing to resort to empirical comparisons. We demonstrate this method by applying it to the task of obtaining uniform approximations of the modified Bessel functions of the second kind, $K_\alpha(x)$.

cond-mat.stat-mech↗

arXiv2023

Thermally driven elastic membranes are quasi-linear across all scales

We study the static and dynamic structure of thermally fluctuating elastic thin sheets by investigating the overdamped dynamic Föppl-von Kármán equation, in which the Föppl-von Kármán equation from elasticity theory is driven by white noise. This nonlinear equation is governed by a single nondimensional coupling parameter $g$ whose large and small values correspond to weak and strong nonlinear coupling respectively. By analysing the weak coupling case with ordinary perturbation theory and the strong coupling case with a self-consistent methodology known as the self-consistent expansion, precise analytic predictions for the static and dynamic structure factors are obtained. The maximum frequency $n_{\max}$ supported by the system plays a role in determining which of three possible classes such sheets belong to: (1) when $g\gg1$, the system is mostly linear with roughness exponent $ζ=1$ and dynamic exponent $z=4$, (2) when $g\ll2/n_{\max}$, the system is extremely nonlinear with roughness exponent $ζ=1/2$ and dynamic exponent $z=3$, (3) between these regimes, an intermediate behaviour is obtained in which a crossover occurs such that the nonlinear behaviour is observed for small frequencies while the linear behaviour is observed for large frequencies. The large frequency linear tail is found to have a significant impact on the small frequency behaviour of the sheet. Back-of-the-envelope calculations suggest that ultra-thin materials such as graphene lie in this intermediate regime. Despite the existence of these three distinct behaviours, the decay rate of the dynamic structure factor is related to the static structure factor as if the system were completely linear. This quasi-linearity occurs regardless of the size of $g$ and at all length scales. Numerical simulations confirm the existence of the three classes of behaviour and the quasi-linearity of all classes.

cond-mat.soft↗

arXiv2023

Dynamics of Fluctuating Thin Sheets Under Random Forcing

We study the dynamic structure factor of fluctuating elastic thin sheets subject to conservative (athermal) random forcing. In Steinbock, Katzav & Boudaoud, Phys. Rev. Research 4, 033096 (2022), the static structure factor of such a sheet was studied. In this paper, we recap the model developed there and investigate its dynamic properties. Using the self-consistent expansion (SCE), the time dependent two-point function of the height profile is determined and found to decay exponentially in time. Despite strong nonlinear coupling, the decay rate of the dynamic structure factor is found to coincide with the effective coupling constant for the static properties which suggests that the model under investigation exhibits certain quasi-linear behaviour. Confirmation of these results by numerical simulations is also presented.

cond-mat.soft↗

arXiv2022

The Structure of Fluctuating Thin Sheets Under Random Forcing

We propose a mathematical model to describe the athermal fluctuations of thin sheets driven by the type of random driving that might be experienced prior to weak crumpling. The model is obtained by merging the Föppl-von Kármán equations from elasticity theory with techniques from out-of-equilibrium statistical physics to obtain a nonlinear strongly coupled $ϕ^{4}$-Langevin field equation with spatially varying kernel. With the aid of the self-consistent expansion (SCE), this equation is analytically solved for the structure factor of a fluctuating sheet. In contrast to previous research which has suggested that the structure factor follows an anomalous power-law, we find that the structure factor in fact obeys a logarithmically corrected rational function. Numerical simulations of our model confirm the accuracy of our analytical solution.

cond-mat.soft↗

arXiv2019

Analytical results for the in-degree and out-degree distributions of directed random networks that grow by node duplication

We present exact results for the degree distribution in a directed network model that grows by node duplication (ND). Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific citation networks. Starting from an initial seed network, at each time step a random node, a mother node, is selected for duplication. Its daughter node is added to the network and duplicates each outgoing link of the mother node with probability p. In addition, the daughter node forms a directed link to the mother node itself. We obtain analytical results for the in-degree distribution $P_t(K_{in}=k)$, and for the out-degree distribution $P_t(K_{out}=k)$ at time t. The in-degrees follow a shifted power-law, so the network is asymptotically scale free. In contrast, the out-degree distribution is narrow, and converges to a Poisson distribution in the sparse network limit and to a Gaussian distribution in the dense network limit. Such distinction between a broad in-degree distribution and a narrow out-degree distribution is common in empirical networks such as scientific citation networks. Using this we calculate the mean degree $\langle K_{in}\rangle_t=\langle K_{out}\rangle_t$, which converges to $1/(1-p)$ in the large network limit, for the whole range of $0 1/2$ the mean degree diverges in the large network limit. We also present analytical results for the distribution of the number of upstream and downstream nodes from a random node. The mean values $\langle N_{up}\rangle_t=\langle N_{down}\rangle_t$ scale logarithmically with the network size, implying that only a small fraction of pairs of nodes are connected by directed paths, unlike the undirected ND case that consists of a single component, hence not a small-world network.

physics.soc-ph↗

arXiv2019

Analytical results for the distribution of shortest path lengths in directed random networks that grow by node duplication

We present exact analytical results for the distribution of shortest path lengths (DSPL) in a directed network model that grows by node duplication. Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific citation networks. Starting from an initial seed network, at each time step a random node, referred to as a mother node, is selected for duplication. Its daughter node is added to the network and duplicates each outgoing link of the mother node with probability $p$. In addition, the daughter node forms a directed link to the mother node itself. Thus, the model is referred to as the corded directed-node-duplication (DND) model. In this network not all pairs of nodes are connected by directed paths, in spite of the fact that the corresponding undirected network consists of a single connected component. More specifically, in the large network limit only a diminishing fraction of pairs of nodes are connected by directed paths. To calculate the DSPL between those pairs of nodes that are connected by directed paths we derive a master equation for the time evolution of the probability $P_t(L=\ell)$, $\ell=1,2,\dots$, where $\ell$ is the length of the shortest directed path. Solving the master equation, we obtain a closed form expression for $P_t(L=\ell)$. It is found that the DSPL at time $t$ consists of a convolution of the initial DSPL $P_0(L=\ell)$, with a Poisson distribution and a sum of Poisson distributions. The mean distance ${\mathbb E}_t[L|L<\infty]$ between pairs of nodes which are connected by directed paths is found to depend logarithmically on the network size $N_t$. However, since in the large network limit the fraction of pairs of nodes that are connected by directed paths is diminishingly small, the corded DND network is not a small-world network, unlike the corresponding undirected network.

physics.soc-ph↗

arXiv2017

The distribution of shortest path lengths in a class of node duplication network models

We present analytical results for the distribution of shortest path lengths (DSPL) in a network growth model which evolves by node duplication (ND). The model captures essential properties of the structure and growth dynamics of social networks, acquaintance networks and scientific citation networks, where duplication mechanisms play a major role. Starting from an initial seed network, at each time step a random node, referred to as a mother node, is selected for duplication. Its daughter node is added to the network, forming a link to the mother node, and with probability $p$ to each one of its neighbors. The degree distribution of the resulting network turns out to follow a power-law distribution, thus the ND network is a scale-free network. To calculate the DSPL we derive a master equation for the time evolution of the probability $P_t(L=\ell)$, $\ell=1,2,\dots$, where $L$ is the distance between a pair of nodes and $t$ is the time. Finding an exact analytical solution of the master equation, we obtain a closed form expression for $P_t(L=\ell)$. The mean distance, $\langle L \rangle_t$, and the diameter, $Δ_t$, are found to scale like $\ln t$, namely the ND network is a small world network. The variance of the DSPL is also found to scale like $\ln t$. Interestingly, the mean distance and the diameter exhibit properties of a small world network, rather than the ultrasmall world network behavior observed in other scale-free networks, in which $\langle L \rangle_t \sim \ln \ln t$.

physics.soc-ph↗