Mathematical Modelling with Multidisciplinary Applications (M3A)
http://hdl.handle.net/20.500.11824/13
Mon, 29 Jun 2020 03:36:22 GMT2020-06-29T03:36:22ZNeuron-glial Interactions
http://hdl.handle.net/20.500.11824/1111
Neuron-glial Interactions
De Pitta M.
Although lagging behind classical computational neuroscience, theoretical and computational approaches are beginning to emerge to characterize different aspects of neuron-glial interactions. This chapter aims to provide essential knowledge on neuron-glial interactions in the mammalian brain, leveraging on computational studies that focus on structure (anatomy) and function (physiology) of such interactions in the healthy brain. Although our understanding of the need of neuron-glial interactions in the brain is still at its infancy, being mostly based on predictions that await for experimental validation, simple general modeling arguments borrowed from control theory are introduced to support the importance of including such interactions in traditional neuron-based modeling paradigms.
Sun, 07 Jun 2020 00:00:00 GMThttp://hdl.handle.net/20.500.11824/11112020-06-07T00:00:00ZGrigorchuk-Gupta-Sidki groups as a source for Beauvile surfaces
http://hdl.handle.net/20.500.11824/1110
Grigorchuk-Gupta-Sidki groups as a source for Beauvile surfaces
Sükran G.; Uria-Albizuri J.
If $G$ is a Grigorchuk-Gupta-Sidki group defined over a $p$-adic tree, where p is an odd prime, we study the existence of Beauville surfaces associated to the quotients of $G$ by its level stabilizers $st_G(n)$. We prove that if $G$ is periodic then the quotients $G/st_G(n)$ are Beauville groups for every $n\geq 2$ if $p\geq 5$ and $n\geq 3$ if $p=3$. On the other hand, if $G$ is non-periodic, then none of the quotients $G/st_G(n)$ are Beauville groups.
Tue, 14 Apr 2020 00:00:00 GMThttp://hdl.handle.net/20.500.11824/11102020-04-14T00:00:00ZOptimization of an Externally Mixed Biogas Plant Using a Robust CFD Method
http://hdl.handle.net/20.500.11824/1098
Optimization of an Externally Mixed Biogas Plant Using a Robust CFD Method
Müller J.; Schenk C.; Keicher R.; Schmidt D.; Schulz V.; Velten K.
Biogas plants have to be continuously or periodically mixed to ensure the homogenization of fermenting and fresh
substrate. Externally installed mixers provide easier access than submerged mixers but concerns of insufficient
mixing deter many operators from using this technology. In this paper, a new approach to improve homogenization
of the substrate mixture is proposed by optimizing external mixer configurations across a wide range of rheological
properties. Robust optimization of a biogas reactor is coupled with CFD simulations to improve parameters for the
angles of inflow and the position of the substrate outlet in a large-scale fermenter. The optimization objective is to
minimize the area in the tank which is poorly mixed. We propose to define this “dead volume zone” as the region
in which the velocity magnitude during mixing falls below a certain threshold. Different dry substance contents are
being investigated to account for the varying rheological properties of different substrate compositions. The velocity
thresholds are calculated for each dry substance content from the mixer-tank configuration of a real biogas reactor
in Brandenburg, Germany (BGA Warsow GmbH & Co.KG). The robust optimization results comprising the whole
range of rheological properties are compared to simulations of the original configuration and to optimization results
for each individual dry substance content. The robust CFD-based optimized configurations reduce the dead volume
zones significantly across all dry substance contents compared to the original configuration. The outcomes of this
paper can be particularly useful for plant manufacturers and operators for optimal mixer placement in industrial
size biogas fermenters.
Wed, 01 Apr 2020 00:00:00 GMThttp://hdl.handle.net/20.500.11824/10982020-04-01T00:00:00ZNumerical approximations for fractional elliptic equations via the method of semigroups
http://hdl.handle.net/20.500.11824/1076
Numerical approximations for fractional elliptic equations via the method of semigroups
Cusimano N.; Del Teso F.; Gerardo-Giorda L.
We provide a novel approach to the numerical solution of the family of nonlocal elliptic equations $(-\Delta)^su=f$ in $\Omega$, subject to some homogeneous boundary conditions $\mathcal{B}(u)=0$ on $\partial \Omega$, where $s\in(0,1)$, $\Omega\subset \mathbb{R}^n$ is a bounded domain, and $(-\Delta)^s$ is the spectral fractional Laplacian associated to $\mathcal{B}$ on $\partial \Omega$. We use the solution representation $(-\Delta)^{-s}f$ together with its singular integral expression given by the method of semigroups. By combining finite element discretizations for the heat semigroup with monotone quadratures for the singular integral we obtain accurate numerical solutions. Roughly speaking, given a datum $f$ in a suitable fractional Sobolev space of order $r\geq 0$ and the discretization parameter $h>0$, our numerical scheme converges as $O(h^{r+2s})$, providing super quadratic convergence rates up to $O(h^4)$ for sufficiently regular data, or simply $O(h^{2s})$ for merely $f\in L^2(\Omega)$. We also extend the proposed framework to the case of nonhomogeneous boundary conditions and support our results with some illustrative numerical tests.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/20.500.11824/10762020-01-01T00:00:00Z