arXiv subjects

Ludvig Lizana

Publications and source records attributed to Ludvig Lizana.

33 records · Page 2Linked to original sources

arXiv2014

First-passage dynamics of obstructed tracer particle diffusion in one-dimensional systems

The standard setup for single-file diffusion is diffusing particles in one dimension which cannot overtake each other, where the dynamics of a tracer (tagged) particle is of main interest. In this article we generalise this system and investigate first-passage properties of a tracer particle when flanked by crowder particles which may, besides diffuse, unbind (rebind) from (to) the one-dimensional lattice with rates $k_{\rm off}$ ($k_{\rm on}$). The tracer particle is restricted to diffuse with rate $k_D$ on the lattice. Such a model is relevant for the understanding of gene regulation where regulatory proteins are searching for specific binding sites ona crowded DNA. We quantify the first-passage time distribution, $f(t)$ ($t$ is time), numerically using the Gillespie algorithm, and estimate it analytically. In terms of our key parameter, the unbinding rate $k_{\rm off}$, we study the bridging of two known regimes: (i) when unbinding is frequent the particles may effectively pass each other and we recover the standard single particle result $f(t)\sim t^{-3/2}$ with a renormalized diffusion constant, (ii) when unbinding is rare we recover well-known single-file diffusion result $f(t)\sim t^{-7/4}$. The intermediate cases display rich dynamics, with the characteristic $f(t)$-peak and the long-time power-law slope both being sensitive to $k_{\rm off}$.

cond-mat.stat-mech↗

arXiv2014

Exact expressions for the mobility and electrophoretic mobility of a weakly charged sphere in a simple electrolyte

We present (asymptotically) exact expressions for the mobility and electrophoretic mobility of a weakly charged spherical particle in an $1:1$ electrolyte solution. This is done by analytically solving the electro and hydrodynamic equations governing the electric potential and fluid flow with respect to an electric field and a nonelectric force. The resulting formulae are cumbersome, but fully explicit and trivial for computation. In the case of a very small particle compared to the Debye screening length ($R \ll r_D$) our results reproduce proper limits of the classical Debye and Onsager theories, while in the case of a very large particle ($R \gg r_D$) we recover, both, the non-monotonous charge dependence discovered by Levich (1958) as well as the scaling estimate given by Long, Viovy, and Ajdari (1996), while adding the previously unknown coefficients and corrections. The main applicability condition of our solution is charge smallness in the sense that screening remains linear.

cond-mat.soft↗

arXiv2013

Aging dynamics in interacting many-body systems

Low-dimensional, complex systems are often characterized by logarithmically slow dynamics. We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly disordered, one-dimensional environment. Each particle in this single file is trapped for a random waiting time $τ$ with power law distribution $ψ(τ)\simeqτ^{-1- α}$, such that the $τ$ values are independent, local quantities for all particles. From scaling arguments and simulations, we find that for the scale-free waiting time case $0<α<1$, the tracer particle dynamics is ultra-slow with a logarithmic mean square displacement (MSD) $\langle x^2(t)\rangle\simeq(\log t)^{1/2}$. This extreme slowing down compared to regular single file motion $\langle x^2(t)\rangle\simeq t^{1/2}$ is due to the high likelihood that the labeled particle keeps encountering strongly immobilized neighbors. For the case $1<α<2$ we observe the MSD scaling $\langle x^2(t)\rangle\simeq t^γ$, where $γ<1/2$, while for $α>2$ we recover Harris law $\simeq t^{1/2}$.

physics.chem-ph↗

arXiv2013

Dynamics of interacting information waves in networks

To better understand the inner workings of information spreading, network researchers often use simple models to capture the spreading dynamics. But most models only highlight the effect of local interactions on the global spreading of a single information wave, and ignore the effects of interactions between multiple waves. Here we take into account the effect of multiple interacting waves by using an agent-based model in which the interaction between information waves is based on their novelty. We analyzed the global effects of such interactions and found that information that actually reaches nodes reaches them faster. This effect is caused by selection between information waves: slow waves die out and only fast waves survive. As a result, and in contrast to models with non-interacting information dynamics, the access to information decays with the distance from the source. Moreover, when we analyzed the model on various synthetic and real spatial road networks, we found that the decay rate also depends on the path redundancy and the effective dimension of the system. In general, the decay of the information wave frequency as a function of distance from the source follows a power law distribution with an exponent between -0.2 for a two-dimensional system with high path redundancy and -0.5 for a tree-like system with no path redundancy. We found that the real spatial networks provide an infrastructure for information spreading that lies in between these two extremes. Finally, to better understand the mechanics behind the scaling results, we provide analytic calculations of the scaling for a one-dimensional system.

physics.soc-ph↗

arXiv2013

Single-file diffusion with non-thermal initial conditions

Single-file diffusion is a theoretically challenging many-body problem where the calculation of even the simplest observables, e.g. mean square displacement, for a tracer particle requires a heavy mathematical machinery. There is therefore a need for simple approaches which predict qualitatively correct behaviours. Here we put forward one such method which we use to investigate the influence of non-thermal initial conditions on the dynamics of a tracer particle. With our new approach we reproduce, up to scaling, several known asymptotic results for the tracer particle mean square displacement.

cond-mat.stat-mech↗

arXiv2013

Transition dynamics in aging systems: microscopic origin of logarithmic time evolution

There exists compelling experimental evidence in numerous systems for logarithmically slow time evolution, yet its theoretical understanding remains elusive. We here introduce and study a generic transition process in complex systems, based on non-renewal, aging waiting times. Each state n of the system follows a local clock initiated at t=0. The random time τbetween clock ticks follows the waiting time density ψ(τ). Transitions between states occur only at local clock ticks and are hence triggered by the local forward waiting time, rather than by ψ(τ). For power-law forms ψ(τ) ~ τ^{-1-α} (0<α<1) we obtain a logarithmic time evolution of the state number ~ log(t/t_0), while for α>2 the process becomes normal in the sense that ~ t. In the intermediate range 1<α<2 we find the power-law growth ~ t^{α-1}. Our model provides a universal description for transition dynamics between aging and non-aging states.

cond-mat.stat-mech↗

arXiv2012

Effects of city-size heterogeneity on epidemic spreading in a metapopulation: A reaction-diffusion approach

We review and introduce a generalized reaction-diffusion approach to epidemic spreading in a metapopulation modeled as a complex network. The metapopulation consists of susceptible and infected individuals that are grouped in subpopulations symbolising cities and villages that are coupled by human travel in a transportation network. By analytic methods and numerical simulations we calculate the fraction of infected people in the metaopoluation in the long time limit, as well as the relevant parameters characterising the epidemic threshold that separates an epidemic from a non-epidemic phase. Within this model, we investigate the effect of a heterogeneous network topology and a heterogeneous subpopulation size distribution. Such a system is suited for epidemic modeling where small villages and big cities exist simultaneously in the metapopulation. We find that the heterogeneous conditions cause the epidemic threshold to be a non-trivial function of the reaction rates (local parameters), the network's topology (global parameters) and the cross-over population size that separates "village dynamics" from "city dynamics".

physics.soc-ph↗

arXiv2012

Quality Control System Response to Stochastic Growth of Amyloid Fibrils

We introduce a stochastic model describing aggregation of misfolded proteins and degradation by the protein quality control system in a single cell. In analogy with existing literature, aggregates can grow, nucleate and fragment stochastically. We assume that the quality control system acts as an enzyme that can degrade aggregates at different stages of the growth process, with an efficiency that decreases with the size of the aggregate. We show how this stochastic dynamics, depending on the parameter choice, leads to two qualitatively different behaviors: a homeostatic state, where the quality control system is stable and aggregates of large sizes are not formed, and an oscillatory state, where the quality control system periodically breaks down, allowing for the formation of large aggregates. We discuss how these periodic breakdowns may constitute a mechanism for the sporadic development of neurodegenerative diseases.

q-bio.CB↗

arXiv2011

Modelling the Spatial Dynamics of Culture Spreading in the Presence of Cultural Strongholds

Cultural competition has throughout our history shaped and reshaped the geography of boundaries between humans. Language and culture are intimately connected and linguists often use distinctive keywords to quantify the dynamics of information spreading in societies harbouring strong culture centres. One prominent example, which is addressed here, is Kyoto's historical impact on Japanese culture. We construct a first minimal model, based on shared properties of linguistic maps, to address the interplay between information flow and geography. In particular, we show that spreading of information over Japan in the pre-modern time can be described as a Eden growth process, with noise levels corresponding to coherent spatial patches of sizes given by a single days walk, and with patch-to-patch communication time comparable to the time between human generations.

physics.soc-ph↗

arXiv2010

Dissimilar bouncy walkers

We consider the dynamics of a one-dimensional system consisting of dissimilar hardcore interacting (bouncy) random walkers. The walkers' (diffusing particles') friction constants xi_n, where n labels different bouncy walkers, are drawn from a distribution rho(xi_n). We provide an approximate analytic solution to this recent single-file problem by combining harmonization and effective medium techniques. Two classes of systems are identified: when rho(xi_n) is heavy-tailed, rho(xi_n)=A xi_n^(-1-α) (0<alpha<1) for large xi_n, we identify a new universality class in which density relaxations, characterized by the dynamic structure factor S(Q,t), follows a Mittag-Leffler relaxation, and the the mean square displacement of a tracer particle (MSD) grows as t^delta with time t, where delta=alpha/(1+α). If instead rho is light-tailedsuch that the mean friction constant exist, S(Q,t) decays exponentially and the MSD scales as t^(1/2). We also derive tracer particle force response relations. All results are corroborated by simulations and explained in a simplified model.

cond-mat.soft↗

arXiv2010

Foundation of Fractional Langevin Equation: Harmonization of a Many Body Problem

In this study we derive a single-particle equation of motion, from first-principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential. Using a new harmonization technique, we show that the resulting dynamical equation belongs to the class of fractional Langevin equations, a stochastic framework which has been proposed in a large body of works as a means of describing anomalous dynamics. Our work sheds light on the fundamental assumptions of these phenomenological models.

cond-mat.stat-mech↗

arXiv2010

Time walkers and spatial dynamics of ageing information

The distribution of information is essential for living system's ability to coordinate and adapt. Random walkers are often used to model this distribution process and, in doing so, one effectively assumes that information maintains its relevance over time. But the value of information in social and biological systems often decay and must continuously be updated. To capture the spatial dynamics of ageing information, we introduce time walkers. A time walker moves like a random walker, but interacts with traces left by other walkers, some representing older information, some newer. The traces forms a navigable information landscape. We quantify the dynamical properties of time walkers moving on a two-dimensional lattice and the quality of the information landscape generated by their movements. We visualise the self-similar landscape as a river network, and show that searching in this landscape is superior to random searching and scales as the length of loop-erased random walks.

cond-mat.stat-mech↗

arXiv2009

Diffusion of Finite-Sized Hard-Core Interacting Particles In a One-Dimensional Box - Tagged Particle Dynamics

We solve a non-equilibrium statistical mechanics problem exactly, namely, the single-file dynamics of N hard-core interacting particles (the particles cannot pass each other) of size Δdiffusing in a one dimensional system of finite length L with reflecting boundaries at the ends. We obtain an exact expression for the conditional probability density function P_T(y_T,t|y_{T,0}) that a tagged particle T (T=1,...,N) is at position y_T at time t given that it at time t=0 was at position y_{T,0}. Going beyond previous studies, we consider the asymptotic limit of large N, maintaining L finite, using a non-standard asymptotic technique. We derive an exact expression for P_T(y_T,t|y_{T,0}) for a a tagged particle located roughly in the middle of the system, from which we find that there are three time regimes of interest for finite-sized systems: (A) For times much smaller than the collision time t<< t_coll=1/(ρ^2D), where ρ=N/L is the particle concentration and D the diffusion constant for each particle, the tagged particle undergoes normal diffusion; (B) for times much larger than the collision time t>> t_coll but times smaller than the equilibrium time t<< t_eq=L^2/D we find a single-file regime where P_T(y_T,t|y_{T,0}) is a Gaussian with a mean square displacement scaling as t^{1/2}; (C) For times longer than the equilibrium time $t>> t_eq, P_T(y_T,t|y_{T,0}) approaches a polynomial-type equilibrium probability density function.

cond-mat.stat-mech↗

arXiv2008

Single-file dynamics with different diffusion constants

We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have different diffusion constants. For the two particle case an exact result for the conditional probability density function (PDF) is obtained for arbitrary initial particle positions and all times. The two-particle PDF is used to obtain the tagged particle PDF. For the general N-particle case (N large) we perform stochastic simulations using our new computationally efficient stochastic simulation technique based on the Gillespie algorithm. We find that the mean square displacement for a tagged particle scales as the square root of time (as for identical particles) for long times, with a prefactor which depends on the diffusion constants for the particles; these results are in excellent agreement with very recent analytic predictions in the mathematics literature.

cond-mat.stat-mech↗

arXiv2008

Single-File diffusion in a Box

We study diffusion of (fluorescently) tagged hard-core interacting particles of finite size in a finite one-dimensional system. We find an exact analytical expression for the tagged particle probability density using a coordinate Bethe-ansatz, from which the mean square displacement is calculated. The analysis show the existence of three regimes of drastically different behavior for short, intermediate and large times. The results show excellent agreement with stochastic simulations (Gillespie algorithm). The findings of the Letter holds promise for the development of novel bio-nano sensors.

cond-mat.soft↗