arXiv subjects

Uwe C. Täuber

Publications and source records attributed to Uwe C. Täuber.

At least 19 recordsLinked to original sources

arXiv2025

Slow spatial migration can help eradicate cooperative antimicrobial resistance in time-varying environments

Antimicrobial resistance (AMR) is a global threat and combating its spread is of paramount importance. AMR often results from a cooperative behaviour with shared drug protection. Microbial communities generally evolve in volatile, spatially structured settings. Migration, space, fluctuations, and environmental variability all have a significant impact on the development and proliferation of AMR. While drug resistance is enhanced by migration in static conditions, this changes in time-fluctuating spatially structured environments. Here, we consider a two-dimensional metapopulation consisting of demes in which drug-resistant and sensitive cells evolve in a time-changing environment. This contains a toxin against which protection can be shared (cooperative AMR). Cells migrate between demes and connect them. When the environment and the deme composition vary on the same timescale, strong population bottlenecks cause fluctuation-driven extinction events, countered by migration. We investigate the influence of migration and environmental variability on the AMR eco-evolutionary dynamics by asking at what migration rate fluctuations can help clear resistance and what are the near-optimal environmental conditions ensuring the quasi-certain eradication of resistance in the shortest possible time. By combining analytical and computational tools, we answer these questions by determining when the resistant strain goes extinct across the entire metapopulation. While dispersal generally promotes strain coexistence, here we show that slow-but-nonzero migration can speed up and enhance resistance clearance, and determine the near-optimal conditions for this phenomenon. We discuss the impact of our findings on laboratory-controlled experiments and outline their generalisation to lattices of any spatial dimension.

q-bio.PE↗

arXiv2025

Invading activity fronts stabilize excitable systems against stochastic extinction

Stochastic chemical reaction or population dynamics in finite systems often terminates in an absorbing state. Yet in large spatially extended systems, the time to reach species extinction (or fixation) becomes exceedingly long. Tuning control parameters may diminish the survival probability, rendering species coexistence susceptible to stochastic extinction events. In inhomogeneous settings, where a vulnerable subsystem is diffusively coupled to an adjacent stable patch, the former is reanimated through continuous influx from the interfaces, provided the absorbing region sustains spreading activity fronts. We demonstrate this generic elimination of finite-size extinction instabilities via immigration flux in predator-prey, epidemic spreading, and cyclic competition models.

q-bio.PE↗

arXiv2025

Fixation and extinction in time-fluctuating spatially structured metapopulations

Bacteria evolve in volatile environments and complex spatial structures. Migration, fluctuations and environmental variability therefore have a significant impact on the evolution of microbial populations. Here, we consider a class of spatially explicit metapopulation models arranged as regular (circulation) graphs where wild-type and mutant cells compete in a time-fluctuating environment in which demes (subpopulations) are connected by slow cell migration. The carrying capacity is the same at each deme and endlessly switches between two values associated to harsh and mild environmental conditions. Environmental variability can lead to population bottlenecks, following which the population is prone to fluctuation-induced extinction. Here, we analyse how slow migration, spatial structure, and fluctuations affect the phenomena of fixation and extinction on clique, cycle, and square lattice metapopulations. When the carrying capacity remains large, bottlenecks are weak and deme extinction can be ignored. The dynamics is thus captured by a coarse-grained description within which the probability and mean time of fixation are obtained analytically. This allows us to show that, in contrast to static environments, the mutant fixation probability depends on the rate of migration. We also show that the fixation probability and mean fixation time can exhibit a non-monotonic dependence on the switching rate. When the carrying capacity is small under harsh conditions, bottlenecks are strong, and the metapopulation evolution is shaped by the coupling of deme extinction and strain competition. This yields rich dynamical scenarios, among which we identify the best conditions to eradicate mutants without dooming the metapopulation to extinction. We offer an interpretation of these findings in the context of an idealised treatment strategy and discuss possible generalisations of our models.

q-bio.PE↗

arXiv2025

Agent-based Monte Carlo simulations for reaction-diffusion models, population dynamics, and epidemic spreading

We provide an overview of Monte Carlo algorithms based on Markovian stochastic dynamics of interacting and reacting many-particle systems not in thermal equilibrium. These agent-based simulations are an effective way of introducing students to current research without requiring much prior knowledge or experience. By starting from the direct visualization of the data, students can gain immediate insight into emerging macroscopic features of a complex system and subsequently apply more sophisticated data analysis to quantitatively characterize its rich dynamical properties, both in the stationary and transient regimes. We utilize simulations of reaction-diffusion systems, stochastic models for population dynamics and epidemic spreading, to exemplify how interdisciplinary computational research can be effectively utilized in bottom-up undergraduate and graduate education through learning by doing. We also give helpful hints for the practical implementation of Monte Carlo algorithms, provide sample codes, explain some typical data analysis tools, and describe various potential error sources and pitfalls and tips for avoiding them.

cond-mat.stat-mech↗

arXiv2024

Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations

Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale kinetics in such systems are effective, scale-dependent parameters that need to be either measured experimentally or computed using a microscopic model. In a Monte Carlo simulation of stochastic reaction-diffusion systems, microscopic probabilities for specific events to happen serve as the input control parameters. Finding the functional dependence of emergent macroscopic rates on the microscopic probabilities is a difficult problem, and there is no systematic analytical way to achieve this goal. Therefore, we introduce a straightforward numerical method of using Monte Carlo simulations to evaluate the macroscopic reaction rates by directly obtaining the count statistics of how many events occur per simulation time step. Our technique is first tested on well-understood fundamental examples, namely restricted birth processes, diffusion-limited two-particle coagulation, and two-species pair annihilation kinetics. Next we utilize the thus gained experience to investigate how the microscopic algorithmic probabilities become coarse-grained into effective macroscopic rates in more complex model systems such as the Lotka--Volterra model for predator-prey competition and coexistence, as well as the rock-paper-scissors or cyclic Lotka--Volterra model as well as its May--Leonard variant that capture population dynamics with cyclic dominance motifs. Thereby we achieve a deeper understanding of coarse-graining in spatially extended stochastic reaction systems and the nontrivial relationships between the associated microscopic and macroscopic model parameters. The proposed technique should generally provide a useful means to better fit Monte Carlo simulation results to experimental or observational data.

physics.bio-ph↗

arXiv2024

Stochastic spatial Lotka-Volterra predator-prey models

Stochastic, spatially extended models for predator-prey interaction display spatio-temporal structures that are not captured by the Lotka-Volterra mean-field rate equations. These spreading activity fronts reflect persistent correlations between predators and prey that can be analyzed through field-theoretic methods. Introducing local restrictions on the prey population induces a predator extinction threshold, with the critical dynamics at this continuous active-to-absorbing state transition governed by the scaling exponents of directed percolation. Novel features in biologically motivated model variants include the stabilizing effect of a periodically varying carrying capacity that describes seasonally oscillating resource availability; enhanced mean species densities and local fluctuations caused by spatially varying reaction rates; and intriguing evolutionary dynamics emerging when variable interaction rates are affixed to individuals combined with trait inheritance to their offspring. The basic susceptible-infected-susceptible and susceptible-infected-recovered models for infectious disease spreading near their epidemic thresholds are respectively captured by the directed and dynamic isotropic percolation universality classes. Systems with three cyclically competing species akin to spatial rock-paper-scissors games may display striking spiral patterns, yet conservation laws can prevent such noise-induced structure formation. In diffusively coupled inhomogeneous settings, one may observe the stabilization of vulnerable ecologies prone to finite-size extinction or fixation due to immigration waves emanating from the interfaces.

cond-mat.stat-mech↗

arXiv2023

Lotka-Volterra predator-prey model with periodically varying carrying capacity

We study the stochastic spatial Lotka-Volterra (LV) model for predator-prey interaction subject to a periodically varying carrying capacity. The LV model with on-site lattice occupation restrictions that represent finite food resources for the prey exhibits a continuous active-to-absorbing phase transition. The active phase is sustained by spatio-temporal patterns in the form of pursuit and evasion waves. Monte Carlo simulations on a two-dimensional lattice are utilized to investigate the effect of seasonal variations of the environment on species coexistence. The results of our simulations are also compared to a mean-field analysis. We find that the parameter region of predator and prey coexistence is enlarged relative to the stationary situation when the carrying capacity varies periodically. The stationary regime of our periodically varying LV system shows qualitative agreement between the stochastic model and the mean-field approximation. However, under periodic carrying capacity switching environments, the mean-field rate equations predict period-doubling scenarios that are washed out by internal reaction noise in the stochastic lattice model. Utilizing visual representations of the lattice simulations and dynamical correlation functions, we study how the pursuit and evasion waves are affected by ensuing resonance effects. Correlation function measurements indicate a time delay in the response of the system to sudden changes in the environment. Resonance features are observed in our simulations that cause prolonged persistent spatial correlations. Different effective static environments are explored in the extreme limits of fast- and slow periodic switching. The analysis of the mean-field equations in the fast-switching regime enables a semi-quantitative description of the stationary state.

q-bio.PE↗

arXiv2023

Stochastic analysis of chemical reactions in multi-component interacting systems at criticality

We numerically and analytically investigate the behavior of a non-equilibrium phase transition in the second Schlögl autocatalytic reaction scheme. Our model incorporates both an interaction-induced phase separation and a bifurcation in the reaction kinetics, with these critical lines coalescing at a bicritical point in the macroscopic limit. We construct a stochastic master equation for the reaction processes to account for the presence of mutual particle interactions in a thermodynamically consistent manner by imposing a generalized detailed balance condition, which leads to exponential corrections for the transition rates. In a non-spatially extended (zero-dimensional) setting, we treat the interactions in a mean-field approximation, and introduce a minimal model that encodes the physical behavior of the bicritical point and permits the exact evaluation of the anomalous scaling for the particle number fluctuations in the thermodynamic limit. We obtain that the system size scaling exponent for the particle number variance changes from $β_0 = 3/2$ at the standard non-interacting bifurcation to $β= 12/7$ at the interacting bicritical point. The methodology developed here provides a generic route for the quantitative analysis of fluctuation effects in chemical reactions occurring in multi-component interacting systems.

cond-mat.stat-mech↗

arXiv2023

Perturbative Field-Theoretical Analysis of Three-Species Cyclic Predator-Prey Models

We apply a perturbative Doi--Peliti field-theoretical analysis to the stochastic spatially extended symmetric Rock-Paper-Scissors (RPS) and May--Leonard (ML) models, in which three species compete cyclically. Compared to the two-species Lotka--Volterra predator-prey (LV) model, according to numerical simulations, these cyclical models appear to be less affected by intrinsic stochastic fluctuations. Indeed, we demonstrate that the qualitative features of the ML model are insensitive to intrinsic reaction noise. In contrast, and although not yet observed in numerical simulations, we find that the RPS model acquires significant fluctuation-induced renormalizations in the perturbative regime, similar to the LV model. We also study the formation of spatio-temporal structures in the framework of stability analysis and provide a clearcut explanation for the absence of spatial patterns in the RPS system, whereas the spontaneous emergence of spatio-temporal structures features prominently in the LV and the ML models.

cond-mat.stat-mech↗

arXiv2022

Effects of lattice dilution on the non-equilibrium phase transition in the stochastic Susceptible-Infectious-Recovered model

We investigate how site dilution, as would be introduced by immunization, affects the properties of the active-to-absorbing non-equilibrium phase transition in the paradigmatic Susceptible-Infectious-Recovered (SIR) model on regular cubic lattices. According to the Harris criterion, the critical behavior of the SIR model, which is governed by the universal scaling exponents of the dynamic isotropic percolation (DyIP) universality class, should remain unaltered after introducing impurities. However, when the SIR reactions are simulated for immobile agents on two- and three-dimensional lattices subject to quenched disorder, we observe a wide crossover region characterized by varying effective exponents. Only after a sufficient increase of the lattice sizes does it becomes clear that the SIR system must transition from that crossover regime before the effective critical exponents asymptotically assume the expected DyIP values. We attribute the appearance of this exceedingly long crossover to a time lag in a complete recovery of small disconnected clusters of susceptible sites which are apt to be generated when the system is prepared with Poisson-distributed quenched disorder. Finally, we demonstrate that this transient region becomes drastically diminished when we significantly increase the value of the recovery rate or enable diffusive agent mobility through short-range hopping.

cond-mat.stat-mech↗

arXiv2022

Critical Dynamics of the Antiferromagnetic $O(3)$ Nonlinear Sigma Model with Conserved Magnetization

We study the near-equilibrium critical dynamics of the $O(3)$ nonlinear sigma model describing isotropic antiferromagnets with non-conserved order parameter reversibly coupled to the conserved total magnetization. To calculate response and correlation functions, we set up a description in terms of Langevin stochastic equations of motion, and their corresponding Janssen--De~Dominicis response functional. We find that in equilibrium, the dynamics is well-separated from the statics, at least to one-loop order in a perturbative treatment with respect to the static and dynamical nonlinearities. Since the static nonlinear sigma model must be analyzed in a dimensional $d = 2 + \varepsilon$ expansion about its lower critical dimension $d_\textrm{lc} = 2$, whereas the dynamical mode-coupling terms are governed by the upper critical dimension $d_c = 4$, a simultaneous perturbative dimensional expansion is not feasible, and the reversible critical dynamics for this model cannot be accessed at the static critical renormalization group fixed point. However, in the coexistence limit addressing the long-wavelength properties of the low-temperature ordered phase, we can perform an $ε= 4 - d$ expansion near $d_c$. This yields anomalous scaling features induced by the massless Goldstone modes, namely sub-diffusive relaxation for the conserved magnetization density with asymptotic scaling exponent $z_Γ= d - 2$ which may be observable in neutron scattering experiments. Intriguingly, if initialized near the critical point, the renormalization group flow for the effective dynamical exponents recovers their universal critical values $z_c = d / 2$ in an intermediate crossover region.

cond-mat.stat-mech↗

arXiv2021

Stabilizing spiral structures in the asymmetric May-Leonard model

We study the induction and stabilization of spiral structures for the cyclic three-species stochastic May-Leonard model with asymmetric predation rates on a spatially inhomogeneous two-dimensional toroidal lattice using Monte Carlo simulations. In an isolated setting, strongly asymmetric predation rates lead to rapid extinction from coexistence of all three species to a single surviving population. Even for weakly asymmetric predation rates, only a fraction of ecologies in a statistical ensemble manages to maintain full three-species coexistence. However, when the asymmetric competing system is coupled via diffusive proliferation to a fully symmetric May-Leonard patch, the stable spiral patterns from this region induce transient plane-wave fronts and ultimately quasi-stationary spiral patterns in the vulnerable asymmetric region. Thus the endangered ecological subsystem may effectively become stabilized through immigration from even a much smaller stable region. To describe the stabilization of spiral population structures in the asymmetric region, we compare the increase in the robustness of these topological defects at extreme values of the asymmetric predation rates in the spatially coupled system with the corresponding asymmetric May-Leonard model in isolation. We delineate the quasi-stationary nature of coexistence induced in the asymmetric subsystem by its diffusive coupling to a symmetric May-Leonard patch, and propose a (semi-)quantitative criterion for the spiral oscillations to be sustained in the asymmetric region.

q-bio.PE↗

arXiv2020

Social distancing and epidemic resurgence in agent-based Susceptible-Infectious-Recovered models

Once an epidemic outbreak has been effectively contained through non-pharmaceutical interventions, a safe protocol is required for the subsequent release of social distancing restrictions to prevent a disastrous resurgence of the infection. We report individual-based numerical simulations of stochastic susceptible-infectious-recovered model variants on four distinct spatially organized lattice and network architectures wherein contact and mobility constraints are implemented. We robustly find that the intensity and spatial spread of the epidemic recurrence wave can be limited to a manageable extent provided release of these restrictions is delayed sufficiently (for a duration of at least thrice the time until the peak of the unmitigated outbreak) and long-distance connections are maintained on a low level (limited to less than five percent of the overall connectivity).

physics.soc-ph↗

arXiv2020

Critical Dynamics of Anisotropic Antiferromagnets in an External Field

We numerically investigate the non-equilibrium critical dynamics in three-dimensional anisotropic antiferromagnets in the presence of an external magnetic field. The phase diagram of this system exhibits two critical lines that meet at a bicritical point. The non-conserved components of the staggered magnetization order parameter couple dynamically to the conserved component of the magnetization density along the direction of the external field. Employing a hybrid computational algorithm that combines reversible spin precession with relaxational Monte Carlo updates, we study the aging scaling dynamics for the model C critical line, identifying the critical initial slip, autocorrelation, and aging exponents for both the order parameter and conserved field, thus also verifying the dynamic critical exponent. We further probe the model F critical line by investigating the system size dependence of the characteristic spin wave frequencies near criticality, and measure the dynamic critical exponents for the order parameter including its aging scaling at the bicritical point.

cond-mat.stat-mech↗

arXiv2020

Parallel Temperature Interfaces in the Katz-Lebowitz-Spohn Driven Lattice Gas

We explore a variant of the Katz-Lebowitz-Spohn (KLS) driven lattice gas in two dimensions, where the lattice is split into two regions that are coupled to heat baths with distinct temperatures. The temperature boundaries are oriented parallel to the external particle drive. If the hopping rates at the interfaces satisfy particle-hole symmetry, the current difference across them generates a vector flow diagram akin to a vortex sheet. We have studied the finite-size scaling of the particle density fluctuations in both temperature regions, and observed that it is controlled by the respective temperature values. If the colder subsystem is maintained at the KLS critical temperature, while the hotter subsystem's temperature is set much higher, the interface current greatly suppresses particle exchange between the two regions. As a result of the ensuing effective subsystem decoupling, strong fluctuations persist in the critical region, whence the particle density fluctuations scale with the KLS critical exponents. However, if both temperatures are set well above the critical temperature, the particle density fluctuations scale according to the totally asymmetric exclusion process (TASEP). We have also measured the entropy production rate in both subsystems; it displays intriguing algebraic decay in the critical region, while it saturates quickly at a small but non-zero level in the hotter region. We have also considered another possible choice of the hopping rates across the temperature interfaces that explicitly breaks particle-hole symmetry. In that case the boundary rates induce a net particle flux across the interfaces that displays power-law behavior, until ultimately the particle exclusion constraints generate a clogging transition to an inert state.

cond-mat.stat-mech↗

arXiv2020

A coupled two-species model for the pair contact process with diffusion

The contact process with diffusion (PCPD) defined by the binary reactions 2 B -> 3 B, 2 B -> 0 and diffusive particle spreading exhibits an unusual active to absorbing phase transition whose universality class has long been disputed. Multiple studies have indicated that an explicit account of particle pair degrees of freedom may be required to properly capture this system's effective long-time, large-scale behavior. We introduce a two-species representation in which single particles B and pairs A are coupled according to the stochastic reactions B + B -> A, A -> A + B, A -> 0, and A -> B + B. Mean-field analysis reveals that the phase transition is driven by competition and balance between both species. We employ Monte Carlo simulations to demonstrate that this model captures the pertinent PCPD features. In the inactive phase, A particles rapidly go extinct, leaving the B species to undergo pure pair annihilation kinetics. At criticality, both A and B densities decay with the same exponents as the PCPD order parameters, and display mean-field scaling above the critical dimension 2. In one dimension, the critical exponents for the B species obtained from seed simulations agree well with previously reported exponent values. We demonstrate that the scaling properties of consecutive particle pairs in the PCPD are identical with that of the A species in the coupled model. This two-species picture resolves the conceptual difficulty for seed simulations in the original PCPD and naturally introduces multiple length and time scales, which cause strong corrections to scaling. The extracted moment ratios from our simulations indicate that our model displays the same temporal crossover behavior as the PCPD, which further corroborates its full dynamical equivalence with our coupled model.

cond-mat.stat-mech↗

arXiv2020

Critical Scaling and Aging near the Flux Line Depinning Transition

We utilize Langevin molecular dynamics simulations to study dynamical critical behavior of magnetic flux lines near the depinning transition in type-II superconductors subject to randomly distributed attractive point defects. We employ a coarse-grained elastic line Hamiltonian for the mutually repulsive vortices and purely relaxational kinetics. In order to infer the stationary-state critical exponents for the continuous non-equilibrium depinning transition at zero temperature T = 0 and at the critical driving current density j_c, we explore two-parameter scaling laws for the flux lines' gyration radius and mean velocity as functions of the two relevant scaling fields T and j - j_c. We also investigate critical aging scaling for the two-time height auto-correlation function in the early-time non-equilibrium relaxation regime to independently measure critical exponents. We provide numerical exponent values for the distinct universality classes of non-interacting and repulsive vortices.

cond-mat.stat-mech↗

arXiv2019

Feedback control of surface roughness in a one-dimensional KPZ growth process

Control of generically scale-invariant systems, i.e., targeting specific cooperative features in non-linear stochastic interacting systems with many degrees of freedom subject to strong fluctuations and correlations that are characterized by power laws, remains an important open problem. We study the control of surface roughness during a growth process described by the Kardar--Parisi--Zhang (KPZ) equation in $(1+1)$ dimensions. We achieve the saturation of the mean surface roughness to a prescribed value using non-linear feedback control. Numerical integration is performed by means of the pseudospectral method, and the results are used to investigate the coupling effects of controlled (linear) and uncontrolled (non-linear) KPZ dynamics during the control process. While the intermediate time kinetics is governed by KPZ scaling, at later times a linear regime prevails, namely the relaxation towards the desired surface roughness. The temporal crossover region between these two distinct regimes displays intriguing scaling behavior that is characterized by non-trivial exponents and involves the number of controlled Fourier modes. Due to the control, the height probability distribution becomes negatively skewed, which affects the value of the saturation width.

cond-mat.stat-mech↗