Theoretical ecology | EPFL Graph Search

Theoretical ecology is the scientific discipline devoted to the study of ecological systems using theoretical methods such as simple conceptual models, mathematical models, computational simulations, and advanced data analysis. Effective models improve understanding of the natural world by revealing how the dynamics of species populations are often based on fundamental biological conditions and processes. Further, the field aims to unify a diverse range of empirical observations by assuming that common, mechanistic processes generate observable phenomena across species and ecological environments. Based on biologically realistic assumptions, theoretical ecologists are able to uncover novel, non-intuitive insights about natural processes. Theoretical results are often verified by empirical and observational studies, revealing the power of theoretical methods in both predicting and understanding the noisy, diverse biological world. The field is broad and includes foundations in applie

Cyclic thermomechanical behaviour of pile-soil interface and design methods for energy pile foundations

Elena Ravera

Energy piles are shallow geothermal systems integrated into structures already required for structural functions of civil works that provide both geothermal energy supply and structural support to the built environments. This research work is driven by the need to convey scientifically based answers that meet the needs of practice for the thermomechanical design of energy piles. Two main challenges are part of this thesis: (i) the understanding of the mechanism that govern the behaviour of energy pile-soil interface and (ii) the development of theoretical methods for design purposes. The multifunctional roles of this technology require to investigate new thermomechanical effects related to daily and seasonal temperature variations during their lifetime, thermally induced effects on pile and soil behaviour, as well as structure-pile-soil interaction. The failure mechanism at the pile-soil interface subjected to cyclic thermal loads is investigated from experimental and constitutive perspectives. The effects of thermal cycling and negative temperatures on pile-soil interface behaviour are presented. Experimental procedures and constitutive models for more advanced design analyses are proposed to help develop reliable long-term predictions of the behaviour and performance of energy pile groups. The results suggest that (i) there is no reduction of the shear strength of the fine-grained soil-concrete interface when subjected to cyclic thermal loading in saturated condition, and (ii) no analysis can be considered complete for a robust design of the system without addressing the risk of freezing. The utility of developing theoretical methods enables the examination of complex practical problems in a systematic, albeit approximate, way for routine design. The majority of theoretical procedures has been originally presented for conventional pile groups with some of them modified to address the different type of loads characterising energy pile groups. However, some gaps are still present in the literature especially with regard to the analysis of pile-soil-slab interactions under thermal loads and the analysis of stress-strain behaviour of energy piles in a group. The development of theoretical methods aims to provide analysis tools for the design of energy piles with respect to the previously mentioned shortcomings. Two methods, the interaction factor method and the load transfer method are mathematically formulated to expand and enrich the framework of available analytical and semi-analytical methods. (i) The interaction factor method integrates the available formulation of the method and allows the analysis of the displacement interaction under a broad range of design conditions addressing the pile-soil-slab interactions. (ii) The load transfer method provides a semi-analytical solution to study the thermomechanical response of an energy pile in a group.

EPFL2021

Numerical Approximation of Flows in Random Porous Media

Francesco Tesei

The objective of this thesis is to develop efficient numerical schemes to successfully tackle problems arising from the study of groundwater flows in a porous saturated medium; we deal therefore with partial differential equations(PDE) having random coefficients and we are interested in computing statistics related to specific quantities of interest (QoI), e.g. a linear functional of the solution of the PDE or the solution itself. We mainly consider the approximation of the pressure in the medium through a stochastic Darcy problem with random lognormally distributed permeability relying on Matérn-type covariance functions to take into account a wide range of possible smoothness of the permeability field. Once the problem has been reformulated in terms of a countable number of random variables, we analyze sparse grid polynomial approximations of the QoI. We propose different strategies to exploit the anisotropicity of the QoI with respect to the different random entries; to this end we consider a priori'' and a posteriori'' strategies to drive the exploration of the multi-index set that defines the sparse grid, associating a profit to each multi-index either by using explicit theoretical estimates or by actually solving the PDE and computing on the fly the corresponding sparse grid interpolant. We show on several numerical examples the effectiveness of this strategy in treating the case of smooth permeability fields. In order to cover also the case of rough input permeabilities we consider, instead, Multi Level Monte Carlo techniques based on the use of a suitable control variate. Such a control variate is obtained from the solution of an auxiliary Darcy problem with a regularized input permeability which leads to pressure distributions that are smoother and less oscillatory than the original ones, but still highly correlated with them. We use then a sparse grid approximation to compute effectively the mean of the control variate and provide explicit bounds for the corresponding estimator as well as a complexity result. We also consider groundwater transport problems and focus, in particular, on arrival times properly defined starting from particle trajectories driven by the stochastic Darcy velocity and subject to molecular diffusion taking place at porous level. In this case, by using suitable PDEs whose solution can be linked to specific expectations (with respect to all Brownian motions) thanks to the famous Feynman-Kac formula, we compute statistics of such arrival times, e.g. their expected value or the probability of exiting the physical domain in a given time horizon. We discuss several scenarios and readapt the methodologies previously developed involving adaptive sparse grid stochastic collocation and Monte Carlo type schemes to this case.

EPFL2016

Stark coefficients for highly excited rovibrational states of H2O

Oleg Aseev, Oleg Boyarkine, Maxim Grechko, Thomas Rizzo

Quantum beat spectroscopy is combined with triple-resonance vibrational overtone excitation to measure the Stark coefficients (SCs) of the water molecule for 28 rovibrational levels lying from 27 600 to 41 000 cm−1. These data provide a stringent test for assessing the accuracy of the available potential energy surfaces (PESs) and dipole moment surfaces (DMSs) of this benchmark molecule in this energy region, which is inaccessible by direct absorption. SCs, calculated using the combination of a high accuracy, spectroscopically determined PES and a recent ab initio DMS, are within the 1% accuracy of available experimental data for levels below 25 000 cm−1 , and within 4.5% for coefficients associated with levels up to 35000 cm−1. However, the error in the computed coefficients is over 60% for the very high rovibrational states lying just below the lowest dissociation threshold, due, it seems, to lack of a high accuracy PES in this region. The comparative analysis sug-gests further steps, which may bring the theoretical predictions closer to the experimental accuracy.