29,035 research outputs found
The XDEM Multi-physics and Multi-scale Simulation Technology: Review on DEM-CFD Coupling, Methodology and Engineering Applications
The XDEM multi-physics and multi-scale simulation platform roots in the Ex-
tended Discrete Element Method (XDEM) and is being developed at the In- stitute
of Computational Engineering at the University of Luxembourg. The platform is
an advanced multi- physics simulation technology that combines flexibility and
versatility to establish the next generation of multi-physics and multi-scale
simulation tools. For this purpose the simulation framework relies on coupling
various predictive tools based on both an Eulerian and Lagrangian approach.
Eulerian approaches represent the wide field of continuum models while the
Lagrange approach is perfectly suited to characterise discrete phases. Thus,
continuum models include classical simulation tools such as Computa- tional
Fluid Dynamics (CFD) or Finite Element Analysis (FEA) while an ex- tended
configuration of the classical Discrete Element Method (DEM) addresses the
discrete e.g. particulate phase. Apart from predicting the trajectories of
individual particles, XDEM extends the application to estimating the thermo-
dynamic state of each particle by advanced and optimised algorithms. The
thermodynamic state may include temperature and species distributions due to
chemical reaction and external heat sources. Hence, coupling these extended
features with either CFD or FEA opens up a wide range of applications as
diverse as pharmaceutical industry e.g. drug production, agriculture food and
processing industry, mining, construction and agricultural machinery, metals
manufacturing, energy production and systems biology
Mean-field theory of collective motion due to velocity alignment
We introduce a system of self-propelled agents (active Brownian particles)
with velocity alignment in two spatial dimensions and derive a mean-field
theory from the microscopic dynamics via a nonlinear Fokker-Planck equation and
a moment expansion of the probability distribution function. We analyze the
stationary solutions corresponding to macroscopic collective motion with finite
center of mass velocity (ordered state) and the disordered solution with no
collective motion in the spatially homogeneous system. In particular, we
discuss the impact of two different propulsion functions governing the
individual dynamics. Our results predict a strong impact of the individual
dynamics on the mean field onset of collective motion (continuous vs
discontinuous). In addition to the macroscopic density and velocity field we
consider explicitly the dynamics of an effective temperature of the agent
system, representing a measure of velocity fluctuations around the mean
velocity. We show that the temperature decreases strongly with increasing level
of collective motion despite constant fluctuations on individual level, which
suggests that extreme caution should be taken in deducing individual behavior,
such as, state-dependent individual fluctuations from mean-field measurements
[Yates {\em et al.}, PNAS, 106 (14), 2009].Comment: corrected version, Ecological Complexity (2011) in pres
On the foundations of cancer modelling: selected topics, speculations, & perspectives
This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution
Active Brownian Particles. From Individual to Collective Stochastic Dynamics
We review theoretical models of individual motility as well as collective
dynamics and pattern formation of active particles. We focus on simple models
of active dynamics with a particular emphasis on nonlinear and stochastic
dynamics of such self-propelled entities in the framework of statistical
mechanics. Examples of such active units in complex physico-chemical and
biological systems are chemically powered nano-rods, localized patterns in
reaction-diffusion system, motile cells or macroscopic animals. Based on the
description of individual motion of point-like active particles by stochastic
differential equations, we discuss different velocity-dependent friction
functions, the impact of various types of fluctuations and calculate
characteristic observables such as stationary velocity distributions or
diffusion coefficients. Finally, we consider not only the free and confined
individual active dynamics but also different types of interaction between
active particles. The resulting collective dynamical behavior of large
assemblies and aggregates of active units is discussed and an overview over
some recent results on spatiotemporal pattern formation in such systems is
given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte
Electrokinetic Lattice Boltzmann solver coupled to Molecular Dynamics: application to polymer translocation
We develop a theoretical and computational approach to deal with systems that
involve a disparate range of spatio-temporal scales, such as those comprised of
colloidal particles or polymers moving in a fluidic molecular environment. Our
approach is based on a multiscale modeling that combines the slow dynamics of
the large particles with the fast dynamics of the solvent into a unique
framework. The former is numerically solved via Molecular Dynamics and the
latter via a multi-component Lattice Boltzmann. The two techniques are coupled
together to allow for a seamless exchange of information between the
descriptions. Being based on a kinetic multi-component description of the fluid
species, the scheme is flexible in modeling charge flow within complex
geometries and ranging from large to vanishing salt concentration. The details
of the scheme are presented and the method is applied to the problem of
translocation of a charged polymer through a nanopores. In the end, we discuss
the advantages and complexities of the approach
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