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This thesis focuses on the mechanisms of energy transport in multidimensional heterogeneous lattice models, studying in particular the case of the Klein-Gordon model of coupled anharmonic oscillators in one and two spatial dimensions. We…
We introduce a novel linear transport equation that models the evolution of a one-particle distribution subject to free transport and two distinct scattering mechanisms: one affecting the particle's speed and the other its direction. These…
We develop statistical models for samples of distribution-valued stochastic processes featuring time-indexed univariate distributions, with emphasis on functional principal component analysis. The proposed model presents an intrinsic rather…
Complex fluids in shear flow and biased dynamics in crowded environments exhibit counterintuitive features which are difficult to address both at theoretical level and by molecular dynamic simulations. To understand some of these features…
Inside cells, cargos such as vesicles and organelles are transported by molecular motors to their correct locations via active motion on cytoskeletal tracks and passive, Brownian diffusion. During the transportation of cargos, motor-cargo…
Despite several different measures of efficiency that are applicable to the photosynthetic systems, a precise degree of efficiency of these systems is not completely determined. Introducing an efficient model for the dynamics of…
A kinetic model for granular mixtures is considered to study three different non-equilibrium situations. The model is based on the equivalence between a gas of elastic hard spheres subjected to a drag force proportional to the particle…
Despite the widespread adoption of Virtual Reality (VR) technology, cybersickness remains a barrier for some users. This research investigates head movement patterns as a novel physiological marker for cybersickness detection. Unlike…
This paper deals with simulation of flow and transport in porous media such as transport of groundwater contaminants. We first discuss how macro scale equations are derived and which terms have to be closed by models. The transport of…
We study the transport properties of dilute electrolyte solutions on the basis of the fluctuating hydrodynamic equation, which is a set of nonlinear Langevin equations for the ion densities and flow velocity. The nonlinearity of the…
Transport of spherical Brownian particles of finite size possessing radii through narrow channels with varying cross-section area is considered. Applying the so-called Fick-Jacobs approximation, i.e. assuming fast equilibration in…
The filtration membranes are often elaborated through a phase separation process where a polymer rich phase and a polymer poor phase spontaneously form through spinodal decomposition. One process that is still not well understood from a…
Cerebral aneurysms are pathological dilations of intracranial arteries that can rupture with devastating consequences, including subarachnoid hemorrhage, stroke, and death. Accumulating evidence indicates that local hemodynamic forces play…
The standard model of enhanced ionic conductivities in solid electrolyte heterostructures follows from a continuum mean-field description of defect distributions that makes no reference to crystalline structure. To examine ionic transport…
Within cells, vesicles and proteins are actively transported several micrometers along the cytoskeletal filaments. The transport along microtubules is propelled by dynein and kinesin motors, which carry the cargo in opposite directions.…
Intermediate filaments form an essential structural network, spread throughout the cytoplasm and play a key role in cell mechanics, intracellular organization and molecular signaling. The maintenance of the network and its adaptation to the…
In the recent years, MRI-driven turbulent transport has been found to depend in a significant way on fluid viscosity $\nu$ and resistivity $\eta$ through the magnetic Prandtl number $Pm=\nu/\eta$. In particular, the transport decreases with…
Convolution and deconvolution are essential techniques in various fields, notably in medical imaging, where they play a crucial role in analyzing dynamic processes such as blood flow. This paper explores the convolution and deconvolution of…
Mathematical models are widely recognized as a valuable tool for cardiovascular diagnosis and the study of circulatory diseases, especially to obtain data that require otherwise invasive measurements. To correctly simulate body…
In this article, we demonstrate that in a transport model of particles with kinetic constraints, long-lived spatial structures are responsible for the blocking dynamics and the decrease of the current at strong driving field. Coexistence…