Related papers: Subdiffusion from competition between multi-expone…
The effects of a "diffusing diffusivity" (DD), a stochastically time-varying diffusion coefficient, are explored within the frameworks of three different forms of fractional Brownian motion (FBM): (i) the Langevin equation driven by…
Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data…
Water molecules play an important role in providing unique environments for biological reactions on cell membranes. It is widely believed that water molecules form bridges that connect lipid molecules and stabilize cell membranes. Using…
Diffusion of colloidal particles in a complex environment such as polymer networks or biological cells is a topic of high complexity with significant biological and medical relevance. In such situations, the interaction between the…
We present a model for diffusion in a molecularly crowded environment. The model consists of random barriers in percolation network. Random walks in the presence of slowly moving barriers show normal diffusion for long times, but anomalous…
The physical approach of a small particle (virus, medical drug) to the cell membrane represents the crucial first step before active internalization and is governed by thermal diffusion. Using a fully analytical theory we show that the…
We study subdiffusive overdamped Brownian ratchets periodically rocked by an external zero-mean force in viscoelastic media within the framework of non-Markovian Generalized Langevin equation (GLE) approach and associated multi-dimensional…
Diffusion models, though originally designed for generative tasks, have demonstrated impressive self-supervised representation learning capabilities. A particularly intriguing phenomenon in these models is the emergence of unimodal…
Intracellular transport of large cargoes, such as organelles, vesicles or large proteins, is a complex dynamical process that involves the interplay of ATP-consuming molecular motors, cytoskeleton filaments and the viscoelastic cytoplasm.…
Diffusion of a tagged particle near a constraining biological surface is examined numerically by modeling the surface-water interaction by an effective potential. The effective potential is assumed to be given by an asymmetric double well…
Diffusion is the macroscopic manifestation of disordered molecular motion. Mathematically, diffusion equations are partial differential equations describing the fluid-like large-scale dynamics of parcels of molecules. Spatially…
This paper shows that generative diffusion processes converge to associative memory systems at vanishing noise levels and characterizes the stability, robustness, memorization, and generation dynamics of both model classes. Morse-Smale…
This work puts forward a generalization of the well-known rocking Markovian Brownian ratchets to the realm of antipersistent non-Markovian subdiffusion in viscoelastic media. A periodically forced subdiffusion in a parity-broken ratchet…
Polydimethylsiloxane (PDMS) is a glassy polymer widely used in biomedical engineering, namely in microfluidics applications. However, PDMS is known to interact with hydrophobic chemicals. This interaction is exacerbated at the scale of…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
Reaction-diffusion equations are one of the most common mathematical models in the natural sciences and are used to model systems that combine reactions with diffusive motion. However, rather than normal diffusion, anomalous subdiffusion is…
Over the years the field of non-Markovian stochastic processes and anomalous diffusion evolved from a specialized topic to mainstream theory, which transgressed the realms of physics to chemistry, biology and ecology. Numerous…
Anomalous diffusion constitutes a relation between tracer flux and tracer density gradient that is inherently nonlocal in space and/or time. Previous studies emphasize the non-Gaussian character of the tracer distribution that arises from…
A generalized Langevin equation with fluctuating diffusivity (GLEFD) is proposed, and it is shown that the GLEFD satisfies a generalized fluctuation-dissipation relation. If the memory kernel is a power law, the GLEFD exhibits anomalous…
We derive a Thermodynamic Uncertainty Relation bounding the mean squared displacement of a Gaussian process with memory, driven out of equilibrium by unbalanced thermal baths and/or by external forces. Our bound is tighter with respect to…