Related papers: Hydrodynamical random walker with chemotactic memo…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
We present a principled data-driven strategy for learning deterministic hydrodynamic models directly from stochastic non-equilibrium active particle trajectories. We apply our method to learning a hydrodynamic model for the propagating…
We derive hydrodynamics of a prototypical one dimensional model, having variable-range hopping, which mimics passive diffusion and ballistic motion of active, or self-propelled, particles. The model has two main ingredients - the hardcore…
Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this…
In a recent paper we proposed a non-Markovian random walk model with memory of the maximum distance ever reached from the starting point (home). The behavior of the walker is at variance with respect to the simple symmetric random walk…
We study the scrambling of local quantum information in chaotic many-body systems in the presence of a locally conserved quantity like charge or energy that moves diffusively. The interplay between conservation laws and scrambling sheds…
The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…
Symplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave…
Kinetic-transport equations are, by now, standard models to describe the dynamics of populations of bacteria moving by run-and-tumble. Experimental observations show that bacteria increase their run duration when encountering an increasing…
We study a random walk model in which the jumping probability to a site is dependent on the number of previous visits to the site, as a model of the mobility with memory. To this end we introduce two parameters called the memory parameter…
Starting from the microscopic description of a normal fluid in terms of any kind of local interacting many-particle theory we present a well defined step by step procedure to derive the hydrodynamic equations for the macroscopic phenomena.…
Contrasting the well explored problem on how to steer a macroscopic agent like an airplane or a moon lander to optimally reach a target, "optimal microswimming", i.e. the quest for the optimal navigation strategy for microswimmers, remains…
The motion of microorganisms in their natural habitat is strongly influenced by their propulsion mechanisms, geometrical constraints, and random fluctuations. Here, we study numerically the first-passage-time (FPT) statistics of…
We propose a (time) multiscale method for the coarse-grained analysis of self--propelled particle models of swarms comprising a mixture of `na\"{i}ve' and `informed' individuals, used to address questions related to collective motion and…
The dynamics of a tracer molecule near a fluid membrane is investigated, with particular emphasis given to the interplay between the instantaneous position of the particle and membrane fluctuations. It is found that hydrodynamic…
We investigate the hydrodynamic properties of a fluid simulated with a mesoscopic solvent model. Two distinct regimes are identified, the `particle regime' in which the dynamics is gas-like, and the `collective regime' where the dynamics is…
Consider $N$ points randomly distributed along a line segment of unitary length. A walker explores this disordered medium moving according to a partially self-avoiding deterministic walk. The walker, with memory $\mu$, leaves from the…
Diffusion models power leading generative AI, but when and how they memorize training data, especially on low-dimensional manifolds, remains unclear. We find memorization emerges gradually, not abruptly: as data become scarce, diffusion…
We study different types of microswimmers moving in channels with varying cross section and thereby interacting hydrodynamically with the channel walls. Starting from the Smoluchowski equation for a dilute suspension, for which interactions…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…