Alexander K. Hartmann
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View article: Numerical aspects of large deviations
Numerical aspects of large deviations Open
An introduction to numerical large-deviation sampling is provided. First, direct biasing with a known distribution is explained. As simple example, the Bernoulli process is used throughout the text. Next, Markov chain Monte Carlo (MCMC) si…
View article: Distribution of the Number of Paths in Two-Dimensional Directed Percolation
Distribution of the Number of Paths in Two-Dimensional Directed Percolation Open
In a percolating system, there are typically exponentially many spanning paths. Here, we study numerically, for a two-dimensional L×L diluted system, restricted to percolating realizations, the number N of directed percolating paths. First…
View article: Diffusion with stochastic resetting on a lattice
Diffusion with stochastic resetting on a lattice Open
We provide an exact formula for the mean first-passage time (MFPT) to a target at the origin for a single particle diffusing on a d-dimensional hypercubic starting from a fixed initial position R⃗0 and resetting to R⃗0 with a rate r. Previou…
View article: Exact joint distributions of three global characteristic times for Brownian motion
Exact joint distributions of three global characteristic times for Brownian motion Open
We consider three global chracteristic times for a one-dimensional Brownian motion x(τ) in the interval τ∈[0,t]: the occupation time to denoting the cumulative time where x(τ)>0, the time tm at which the process achieves its global maximum…
View article: Numerical Estimation of Limiting Large-Deviation Rate Functions
Numerical Estimation of Limiting Large-Deviation Rate Functions Open
For statistics of rare events in systems obeying a large-deviation principle, the rate function is a key quantity. When numerically estimating the rate function one is always restricted to finite system sizes. Thus, if the interest is in t…
View article: Non-universality for Crossword Puzzle Percolation
Non-universality for Crossword Puzzle Percolation Open
A percolation model inspired by crossword puzzle games is introduced. A game proceeds by solving words, which are segments of sites in a two-dimensional lattice. As test case, the \emph{iid} variant allows for independently occupying sites…
View article: Resetting by rescaling: exact results for a diffusing particle in one-dimension
Resetting by rescaling: exact results for a diffusing particle in one-dimension Open
In this paper, we study a simple model of a diffusive particle on a line, undergoing a stochastic resetting with rate $r$, via rescaling its current position by a factor $a$, which can be either positive or negative. For $|a|<1$, the posit…
View article: Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks
Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks Open
A regime of coexistence of asynchronous and clustered dynamics is analysed for globally coupled homogeneous and heterogeneous inhibitory networks of quadratic integrate-and-fire (QIF) neurons subject to Gaussian noise. The analysis is base…
View article: The Griffiths phase and beyond: A large deviations study of the magnetic susceptibility of the two-dimensional bond-diluted Ising model
The Griffiths phase and beyond: A large deviations study of the magnetic susceptibility of the two-dimensional bond-diluted Ising model Open
The Griffiths phase in systems with quenched disorder occurs below the ordering transition of the pure system down to the ordering transition of the actual disordered system. While it does not exhibit long-range order, large fluctuations i…
View article: Statistical methods for linking material composition to recombination losses in optoelectronic devices
Statistical methods for linking material composition to recombination losses in optoelectronic devices Open
In light of the accumulation of characterization measurement data in the industrial production of solar cell devices, the investigation of a large amount of samples by statistical means lends itself to be a useful tool to gain further insi…
View article: Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks
Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks Open
A regime of coexistence of asynchronous and clustered dynamics is analyzed for globally coupled homogeneous and heterogeneous inhibitory networks of quadratic integrate-and-fire (QIF) neurons subject to Gaussian noise. The analysis is base…
View article: Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks
Coexistence of asynchronous and clustered dynamics in noisy inhibitory neural networks Open
A regime of coexistence of asynchronous and clustered dynamics is analyzed for globally coupled homogeneous and heterogeneous inhibitory networks of quadratic integrate-and-fire (QIF) neurons subject to Gaussian noise. The analysis is base…
View article: Work Distribution for Unzipping Processes
Work Distribution for Unzipping Processes Open
A simple zipper model is introduced, representing in a simplified way, e.g., the folded DNA double helix or hairpin structures in RNA. The double stranded hairpin is connected to a heat bath at temperature $T$ and subject to an external fo…
View article: Large-deviation analysis of rare resonances for the Many-Body localization transition
Large-deviation analysis of rare resonances for the Many-Body localization transition Open
A central theoretical issue at the core of the current research on many-body localization (MBL) consists in characterizing the statistics of rare long-range resonances in many-body eigenstates. This is of paramount importance to understand…
View article: Energy landscapes of some matching-problem ensembles
Energy landscapes of some matching-problem ensembles Open
The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This method provides insight into the complexity of the ene…
View article: Non-analytic behaviour in large-deviations of the susceptible-infected-recovered model under the influence of lockdowns
Non-analytic behaviour in large-deviations of the susceptible-infected-recovered model under the influence of lockdowns Open
We numerically investigate the dynamics of an SIR model with infection level-based lockdowns on Small-World networks. Using a large-deviation approach, namely the Wang–Landau algorithm, we study the distribution of the cumulative fraction …
View article: First-passage area distribution and optimal fluctuations of fractional Brownian motion
First-passage area distribution and optimal fluctuations of fractional Brownian motion Open
We study the probability distribution $P(A)$ of the area $A=\int_0^T x(t) dt$ swept under fractional Brownian motion (fB\ m) $x(t)$ until its first passage time $T$ to the origin. The process starts at $t=0$ from a specified point $x=L$. W…
View article: Optimized Finite-Time Work Protocols for the Higgs RNA-Model
Optimized Finite-Time Work Protocols for the Higgs RNA-Model Open
The Higgs RNA-Model is studied in regard to finite-time driving protocols with minimal-work requirement. In this paper, RNA sequences which at low temperature exhibits hairpins are considered, which are often cited as typical template syst…
View article: The distribution of the maximum of independent resetting Brownian motions
The distribution of the maximum of independent resetting Brownian motions Open
The probability distribution of the maximum $M_t$ of a single resetting Brownian motion (RBM) of duration $t$ and resetting rate $r$, properly centred and scaled, is known to converge to the standard Gumbel distribution of the classical ex…
View article: Time-dependent probability density function for partial resetting dynamics
Time-dependent probability density function for partial resetting dynamics Open
Stochastic resetting is a rapidly developing topic in the field of stochastic processes and their applications. It denotes the occasional reset of a diffusing particle to its starting point and effects, inter alia, optimal first-passage ti…
View article: Probing the large deviations for the Beta random walk in random medium
Probing the large deviations for the Beta random walk in random medium Open
We consider a discrete-time random walk on a one-dimensional lattice with space and time-dependent random jump probabilities, known as the Beta random walk. We are interested in the probability that, for a given realization of the jump pro…
View article: Rare Events of Host Switching for Diseases using a SIR Model with Mutations
Rare Events of Host Switching for Diseases using a SIR Model with Mutations Open
We numerically study disease dynamics that lead to the disease switching from one host species to another, resulting in diseases gaining the ability to infect, e.g., humans. Unlike previous studies that focused on branching processes start…
View article: Non-Analytic Behaviour in Large-deviations of the SIR model under the influence of Lockdowns
Non-Analytic Behaviour in Large-deviations of the SIR model under the influence of Lockdowns Open
We numerically investigate the dynamics of an SIR model with infection level-based lockdowns on Small-World networks. Using a large-deviation approach, namely the Wang-Landau algorithm, we study the distribution of the cumulative fraction …
View article: Large-deviations of disease spreading dynamics with vaccination
Large-deviations of disease spreading dynamics with vaccination Open
We numerically simulated the spread of disease for a Susceptible-Infected-Recovered (SIR) model on contact networks drawn from a small-world ensemble. We investigated the impact of two types of vaccination strategies, namely random vaccina…
View article: Current fluctuations in stochastically resetting particle systems
Current fluctuations in stochastically resetting particle systems Open
We consider a system of noninteracting particles on a line with initial positions distributed uniformly with density ρ on the negative half-line. We consider two different models: (i) Each particle performs independent Brownian motion with…
View article: Large-deviation properties of SIR model incorporating protective measures
Large-deviation properties of SIR model incorporating protective measures Open
We simulate spreads of diseases for the susceptible–infected–recovered (SIR) model on contact networks with a particular focus on incorporated protective measures such as face masks. We consider the small-world network model. By using a la…
View article: Optimized Power Flow Control to Minimize Congestion in a Modern Power System
Optimized Power Flow Control to Minimize Congestion in a Modern Power System Open
The growing integration of renewable energy sources (RES) into the power system causes congestion to occur more frequently. In order to reduce congestion in the short term and to make the utilization of the power system more efficient in t…
View article: Time-dependent probability density function for partial resetting dynamics
Time-dependent probability density function for partial resetting dynamics Open
Stochastic resetting is a rapidly developing topic in the field of stochastic processes and their applications. It denotes the occasional reset of a diffusing particle to its starting point and effects, inter alia, optimal first-passage ti…
View article: Optimized Power Flow Control to Minimize Congestion in a Modern Power System
Optimized Power Flow Control to Minimize Congestion in a Modern Power System Open
The growing integration of renewable energy sources (RES) into the power system causes congestion to occur more frequently. In order to reduce congestion in the short term and to make the utilization of the power system more efficient in t…
View article: Energy landscapes of some matching-problem ensembles
Energy landscapes of some matching-problem ensembles Open
The maximum-weight matching problem and the behavior of its energy landscape is numerically investigated. We apply a perturbation method adapted from the analysis of spin glasses. This gives inside into the complexity of the energy landsca…