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Time-adaptive Adomian decomposition-based numerical scheme for Euler equations
No full textTime efficiency is one of the more critical concerns in computational fluid dynamics simulations of industrial applications. Extensive research has been conducted to improve the underlying numerical schemes to achieve time process reduction. Within this context, this paper presents a new time discretization method based on the Adomian decomposition technique for Euler equations. The obtained scheme is time-order adaptive; the order is automatically adjusted at each time step and over the space domain, leading to significant processing time reduction. The scheme is formulated in an appropriate recursive formula, and its efficiency is demonstrated through numerical tests by comparison to exact solutions and the popular Runge–Kutta-discontinuous Galerkin method.Alfaisal University Grant. Grant Number: IRG20411
BFA/DFB-6/12/TK/2012/00020
PRE-2013-1-1216
MTM2013-40824-P, SEV-2013-0323, SEV-2017-0718
BERC 2014-201
Time Dynamics in Quantum Field Theory Systems
Get PDFIn this doctoral thesis, we develop and investigate new mathematical tools that are intended to allow for a rigorous description of non–perturbative quantum field theory (QFT) dynamics. Here, the term QFT is to be understood as describing a quantum system with particle creation and annihilation that can, but does not need to, comply with special relativity. The tools aim at cases where a formal Hamiltonian exists but is ill–defined.Wilhelm Schuler-Stiftung Tübingen,
DAAD (Deutscher Akademischer Austauschdienst
Existence, Uniqueness, and Numerical Modeling of Wine Fermentation Based on Integro-Differential Equations
No full textPredictive modeling is key for saving time and resources in manufacturing processes such as fermentation arising in food and chemical manufacturing. To make reliable predictions, realistic models representing the most important process features are required. Several models describing the white wine fermentation process already exist. However, all of these models lack a combination of features, such as the importance of oxygen at the beginning of the process, the consumption of sugar due to yeast activity, and the toxicity of alcohol on the yeast cells combined with the single-cell yeast dynamics. This work introduces a new population balance model representing all these features in one model. It is based on a system of highly nonlinear weakly hyperbolic partial/ordinary integro-differential equations which poses a number of theoretical and numerical challenges. This paper increases the understanding of the latter and of the process itself by combining theoretical with numerical investigations. Existence and uniqueness of solutions to a simplified problem are studied based on semigroup theory. For the numerical solution of the problem, a numerical methodology based on a finite volume scheme combined with a time implicit scheme is derived. The impact of the initial cell distribution on the dynamics is studied. The detailed model is compared to a simpler model based on ordinary differential equations. The observed differences for different initial cell distributions and distinct models turn out to be smaller than expected. The outcomes of this paper are specifically relevant for applied mathematicians, winemakers, and process engineers.ROENOBIO project by German Federal Ministry of Education and Research with contract number 05M2013UTA,
Research Training Group 2126 on Algorithmic Optimization funded by the German Research Foundatio
Mesoscopic simulations of inertial drag enhancement and polymer migration in viscoelastic solutions flowing around a confined array of cylinders
Get PDFWe study the flow around a periodic array of cylinders using a mesoscopic viscoelastic fluid that mimics polymeric solutions. We model our fluid employing a novel mesoscopic method based on Smoothed Dissipative Particle Dynamics and FENE springs. We characterize the static and dynamic properties of our model solutions and compare the results with theoretical predictions based on the Zimm model. After rheological characterization of the modeled solutions, we simulate the flow around a confined array of cylinders. The balance between inertia and elasticity in our simulations is studied using a wide range of Reynolds (Re) and Weissenberg (Wi) numbers. We find that increasing the flow rate reduces the drag coefficient on the cylinder up to a critical Re corresponding to a minimum. Thereafter, inertia becomes dominant and we encounter drag enhancement for all the solutions studied, including the Newtonian solvent. With the use of simple model for the viscous and inertial contributions to drag, we conclude that inertial effects are driving the increase in the drag experienced by the cylinder. In our simulations, we also observe migration of polymer chains away from the channel walls and in the wake of the cylinder. We conclude that stress gradients induced by the curvature of streamlines and convection of the depleted layers at the walls as the principal mechanisms driving the migration of chains. We find the extent of the migration correlates well with the viscoelastic Mach number (Ma = ReWi) suggesting that both elastic and inertial effects play a role in this phenomenon
Preference incorporation into many-objective optimization: An Ant colony algorithm based on interval outranking
No full textIn this paper, we enriched Ant Colony Optimization (ACO) with interval outranking to develop a novel multi-objective ACO optimizer to approach problems with many objective functions. This proposal is suitable if the preferences of the Decision Maker (DM) can be modeled through outranking relations. The introduced algorithm (Interval Outranking-based ACO, IO-ACO) is the first ant-colony optimizer that embeds an outranking model to bear vagueness and ill-definition of the DM's preferences. This capacity is the most differentiating feature of IO-ACO because this issue is highly relevant in practice. IO-ACO biases the search towards the Region of Interest (RoI), the privileged zone of the Pareto frontier containing the solutions that better match the DM's preferences. Two widely studied benchmarks were utilized to measure the efficiency of IO-ACO, i.e., the DTLZ and WFG test suites. Accordingly, IO-ACO was compared with four competitive multi-objective optimizers: The Indicator-based Many-Objective ACO, the Multi-objective Evolutionary Algorithm Based on Decomposition, the Reference Vector-Guided Evolutionary Algorithm using Improved Growing Neural Gas, and the Indicator-based Multi-objective Evolutionary Algorithm with Reference Point Adaptation. The numerical results show that IO-ACO approximates the RoI better than leading metaheuristics based on approximating the Pareto frontier alone
Wildfire Spreading: a new application of the Beta distribution
Get PDFThis dissertation is in the mathematical physics area, more specifically, applications
in the statistics field. The thesis, under the supervision of Dr. Gianni Pagnini, was carried out at
the BCAM - Basque Centre for Applied Mathematics in Bilbao, Spain. It is
the result of the continuous interaction with the team of Statistical Physics,
characterised by an international, stimulating and constantly growing environment.
The subject of this thesis is PROPAGATOR: a stochastic cellular automaton
model for forest fire spread simulation, conceived as a rapid method
for fire risk assessment.
The reason behind the popularity of cellular automata can be traced to their
simplicity, and to the enormous potential they hold in modeling complex systems,
in spite of their simplicity. Cellular automata can be viewed as a simple
model of a spatially extended decentralized system made up of a number of
individual components: cells. The communication between constituent cells
is limited to local interaction.
PROPAGATOR is a cellular automata model which simulates wildfire
spread through empirical laws that guarantee probabilistic outputs. This
algorithm, whose first version was released in 2009, is currently in use, along
with other software, although it is constantly being updated.
In fact, the first version was requested by the Italian Civil Protection, but
later it became part of the ANYWHERE project. This project, active from
June 2016 to December 2019, was funded under the EU’s research and innovation
funding program Horizon 2020 (H2020), which aimed to improve
emergency management and response to high-impact weather and climate
events such as floods, landslides, swells, snowfalls, forest fires, heat waves
and droughts.
As part of the ANYWHERE project, Propagator was rewritten in Python.
The version we worked with is the 2020 version, but an updated 2022 version is already available.
The main aim of this work was to understand the distribution of the
wildfire propagation. As can be seen from Propagator input parameters,
the propagation depends on different factors: ignition point, wind speed and
direction, as well as fuel moisture content and firebreaks-fire fighting strategies.
Wind is recognized to be by far the most important factor in the entire
problem of forest fire propagation. In this paper, we analyzed four different
situations varying initial conditions, in particular we changed wind speed:
0 km/h, 10 km/h, 20 km/h, 30 km/h. However, the phenomenon of fire
spotting and firebreaks-fire fighting strategies were not taken into consideration.
By modifying the code, it was possible to obtain the output required to
achieve the desired result. The conclusion we came to is that the distribution
of a wildfire spreading is described by the beta distribution.
This allows us, for the first time, to attribute a new application of the beta
function: describing the propagation of a process studied using a cellular
automaton algorithm.
The thesis is organised as follows:
In the first chapter, there is an introduction to special functions. In
particular, their role in applied mathematics is analyzed, followed by
a discussion of the two most commonly used special functions: the
Gamma function and the Beta function.
• In the second chapter, the PROPAGATOR model was introduced following
the article "PROPAGATOR: An Operational Cellular-Automata
Based Wildfire Simulator" by A. Trucchia.
• The third chapter contains the analysis carried out on the output data.
A discussion of the obtained results and suitable observations can be
found in the conclusions.
• There are three appendixes containing:
– Appendix A: the lines of code we wrote to carry out the analysis.
– Appendix B: explanation of the software, apps and routines used,
with particular reference to the Hypathia server.
– Appendix C: discussion on stochastic processes carried out as an
approach and preparation for the subsequent work with Propagator
Fire-spotting generated fires. Part II: The role of flame geometry and slope
Get PDFThis is the second part of a series of two papers concerning fire-spotting generated fires. While, in the first part, we focus on the impact of macro-scale factors on the growth of the burning area by considering the atmospheric stability conditions, in the present study we focus on the impact of meso-scale factors by considering the effects of the flame geometry and terrain slope. First, we discuss the phenomenological power law that relates flame length and fireline intensity by reporting literature data, analysing a formula originally proposed by Albini, and deriving an alternative formula based on the energy conservation principle. Subsequently, we extend the physical fire-spotting parametrisation RandomFront adopted in the first part by including flame geometry and slope. Numerical examples show that fire-spotting is affected by flame geometry and, therefore, cannot be neglected in simplified fire-spread models used in operational software codes for wild- fire propagation. Meanwhile, we observe that terrain slope enhances the spread of a fire at a higher rate than the augmentation of fire-spotting generated fires, such that a rapid merging occurs among independent fires.BERC 2014–2017
BERC 2018–2021
SEV-2013-0323
MTM2016-76016-R
PID2019-107685RB-I00
PhD grant “La Caixa 2014”
On the interfacial lithium dynamics in Li7La3Zr2O12:poly(ethylene oxide) (LiTFSI) composite polymer-ceramic solid electrolytes under strong polymer phase confinement
Get PDFA better molecular-level understanding of Li+ diffusion through ceramic/polymer interfaces is key to designing high-performance composite solid-state electrolytes for all-solid-state batteries. By considering as a case study a composite electrolyte constituted by Li+ conductive Ga3+ doped-Li7La3Zr2O12 (LLZO) garnet fillers embedded within a poly(ethylene oxide) and lithium bis(trifluoromethanesulfonyl) imide polymer matrix (PEO(LiTFSI)), we investigate Li+ interfacial dynamics at conditions of high polymer confinement, with large filler particles in a fully amorphous polymer phase. Such confinement scenario is aimed to capture the conditions near the percolation threshold, at which conductivity enhancement is often reported. Using molecular dynamics simulations combined with the generalized shadow hybrid Monte Carlo method and umbrella sampling calculations, we explain why the hopping towards the polymer phase of the Li+ sitting on the LLZO surface is thermodynamically hindered while hopping of Li+ from the polymer to the LLZO is kinetically slowed-down by rigidified polymer near the interface. In addition, we demonstrate how the overlap of LLZO-bound polymer chains at high confinement leads to a decrease of Li+ diffusivity within the interstitial space. We put forward that these insights are relevant to interpreting the variation of ionic conductivity as a function of volume fraction and filler particle sizes also below the glass transition temperature of the polymer, at the typical operating conditions of lithium-ion batteries.Ikerbasque COVID-1
ENERGY CONSERVATION FOR 2D EULER WITH VORTICITY IN L(log L)α*
Get PDFIn these notes we discuss the conservation of the energy for weak solutions of the twodimensional incompressible Euler equations. Weak solutions with vorticity in (Formula presented) with p > 3/2 are always conservative, while for less integrable vorticity the conservation of the energy may depend on the approximation method used to construct the solution. Here we prove that the canonical approximations introduced by DiPerna and Majda provide conservative solutions when the initial vorticity is in the class L(logL)α with α > 1/2