Related papers: Preface: Characterisation of Physical Processes fr…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
We expose some selected topics concerning the instability of the action variables in a priori unstable Hamiltonian systems, and outline a new strategy that may allow to apply these methods to a priori stable systems.
Anomalous diffusion is discussed in the context of quantum Brownian motion with colored noise. It is shown that earlier results follow simply and directly from the fluctuation-dissipation theorem. The limits on the long-time dependence of…
Sub-diffusion in biological systems is conventionally treated as anomalous, requiring fractional derivatives, heavy-tailed waiting times, or fitted memory kernels. We argue that this anomaly is an artifact of an incomplete phase space.…
In this paper we present in one-dimensional space a numerical solution of a partial differential equation of fractional order. This equation describes a process of anomalous diffusion. The process arises from the interactions within the…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
Understanding processes in porous media is fundamental to a broad spectrum of environmental, energy, and geoscience applications. These processes include multiphase fluid transport, interfacial dynamics, reactive transformations, and…
The paper shows how the diffusive movement of ions through a channel protein can be described as a chemical reaction over an arbitrary shaped potential barrier. The result is simple and intuitive but without approximation beyond the…
A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…
Energy transport in one-dimensional chains of particles with three conservation laws is generically anomalous and belongs to the Kardar-Parisi-Zhang dynamical universality class. Surprisingly, some examples where an apparent normal heat…
This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of…
Anomalous diffusion often arises in complex environments where viscoelastic or crowded conditions influence particle motion. In many biological and soft-matter systems, distinct components of the medium exhibit unique viscoelastic…
Anomalous diffusion is present at all scales, from atomic to large scales. Some exemplary systems are; ultra-cold atoms, telomeres in the nucleus of cells, moisture transport in cement-based materials, the free movement of arthropods, and…
We study the diffusion equation with an appropriate change of variables. This equation is in general a partial differential equation (PDE). With the self-similar and related Ansat\"atze we transform the PDE of diffusion to an ordinary…
We identify the ballistically and diffusively rescaled limit distribution of the second class particle position in a wide range of asymmetric and symmetric interacting particle systems with established hydrodynamic behavior, respectively…
Nonequilibrium thermodynamics has shown its applicability in a wide variety of different situations pertaining to fields such as physics, chemistry, biology, and engineering. As successful as it is, however, its current formulation…
A number of results for reactions involving subdiffusive species all with the same anomalous exponent gamma have recently appeared in the literature and can often be understood in terms of a subordination principle whereby time t in…
Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…
Using the methods of computer modeling this scientific paper studies the special features of diffusion of the particles subjected to the external periodic force in the crystal lattice. The particle motion is described by a Langevin…
In this letter, a theoretical method for the analysis of diffusive flux/current to limited scale self-affine random fractals is presented and compared with experimentally measured electrochemical current for such roughness. The theory…