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Stably Stratified Atmospheric Boundary Layers: Event Detection and Classification for Turbulent Time Series
Get PDFThe atmospheric boundary layer is the lowest part of the atmosphere where life takes place. For understanding weather patterns affecting human lives a good understanding of the dynamics in this layer is required. One important process in the atmospheric boundary layer is turbulence. Decisions
that affect human life must be made daily based on predictions of turbulent flows. Hence it is fundamental to understand the physical processes behind it. But so far there are still many processes which are not fully understood and cannot be statistically modelled. This is especially true for the stably stratified atmospheric boundary layer which typically occurs during the night
or above cooler surfaces like glaciers. Apart from turbulence it includes small scale non turbulent motions of complex origins that are poorly understood by the scientific community. As stated in the paper by Vercauteren and Klein
(2015), the presence of such motions could affect turbulent mixing to a large extent if the thermal stratification is very high. Usual approaches which aim to recognize events in the atmospheric boundary layer assume certain physical processes and then search for a trace of these in the atmospheric time series. This can be acomplished by searching for certain geometries or large amplitudes. However, many events in atmospheric series result from yet
unidentified physical processes. Consequently a new approach is necessary.
A statistical method was recently developed by Kang et al. (2015a) to detect events in noisy time series. This method does not assume any underlying physical processes to extract events from the time series. Nevertheless, physical mechanisms can be investigated a posteriori by analyzing the extracted events. In this thesis we will analyse parts of the Snow-Horizontal Array Turbulence Study (SnoHATS) dataset (Bou-Zeid et al. (2010)) which was collected over a glacier by using a slightly modified version of this event detection
method. In their analysis, Kang et al. (2015) investigated events of a certain scale by defining a maximal duration of events, and filtering out small-scale variability. In this thesis, we will investigate different scales of motion by applying the method for multiple timescales. We will thereby
test the sensitivity of the method to technical criteria related to timescales of variability. In this thesis we will focus on scales from 1 to 30 minutes.
The rationale behind this choice of time window is that motions on scales between 1 and 30 minutes in stable conditions are typically dominated by wavelike motions, microfronts and other complex structures of unknown origin
(Mahrt, (2011)). We will refer to such motions as submesomotions in the rest of the thesis.
In chapter 2 the concept of turbulence in the atmospheric boundary layer is explained in more detail by first stating how we define turbulence and then illustrating the origin of turbulence in the atmospheric boundary layer. Afterwards,
in chapter 3, the dataset is described and in chapter 4 the steps in the event detection method by Kang et al. (2015a) are explained. The multiscale approach and the results from the event detection procedure are described in chapter 5
Machine Learning of coarse-grained Molecular Dynamics Force Fields
Get PDFAtomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models. Existing coarse-graining approaches define an effective interaction potential to match defined properties of high-resolution models or experimental data. In this paper, we reformulate coarse-graining as a supervised machine learning problem. We use statistical learning theory to decompose the coarse-graining error and cross-validation to select and compare the performance of different models. We introduce CGnets, a deep learning approach, that learns coarse-grained free energy functions and can be trained by a force matching scheme. CGnets maintain all physically relevant invariances and allow one to incorporate prior physics knowledge to avoid sampling of unphysical structures. We show that CGnets can capture all-atom explicit-solvent free energy surfaces with models using only a few coarse-grained beads and no solvent, while classical coarse-graining methods fail to capture crucial features of the free energy surface. Thus, CGnets are able to capture multi-body terms that emerge from the dimensionality reduction
Learning chemical reaction networks from trajectory data
No full textWe develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed,our method learns the propensity functions of the system with predetermined basis functions by maximizing the likelihood function of the trajectory data under l^1 sparse regularization. We demonstrate our method with numerical examples using synthetic data and carry out an asymptotic analysis of the proposed learning procedure in the infinite-data limit
Atmospheric Predictability: Revisiting the Inherent Finite-Time Barrier
Get PDFThe accepted idea that there exists an inherent finite-time barrier in deterministically predicting atmospheric flows originates from Edward N. Lorenz’s 1969 work based on two-dimensional (2D) turbulence. Yet, known analytic results on the 2D Navier–Stokes (N-S) equations suggest that one can skillfully predict the 2D N-S system indefinitely far ahead should the initial-condition error become sufficiently small, thereby presenting a potential conflict with Lorenz’s theory. Aided by numerical simulations, the present work reexamines Lorenz’s model and reviews both sides of the argument, paying particular attention to the roles played by the slope of the kinetic energy spectrum. It is found that when this slope is shallower than −3, the Lipschitz continuity of analytic solutions (with respect to initial conditions) breaks down as the model resolution increases, unless the viscous range of the real system is resolved—which remains practically impossible. This breakdown leads to the inherent finite-time limit. If, on the other hand, the spectral slope is steeper than −3, then the breakdown does not occur. In this way, the apparent contradiction between the analytic results and Lorenz’s theory is reconciled
Boltzmann Generators: Sampling Equilibrium States of Many-Body Systems with Deep Learning
Get PDFComputing equilibrium states in condensed-matter many-body systems, such as solvated proteins, is a long-standing challenge. Lacking methods for generating statistically independent equilibrium samples directly, vast computational effort is invested for simulating these system in small steps, e.g., using Molecular Dynamics. Combining deep learning and statistical mechanics, we here develop Boltzmann Generators, that are shown to generate statistically independent samples of equilibrium states of representative condensed matter systems and complex polymers. Boltzmann Generators use neural networks to learn a coordinate transformation of the complex configurational equilibrium distribution to a distribution that can be easily sampled. Accurate computation of free energy differences, and discovery of new system states are demonstrated, providing a new statistical mechanics tool that performs orders of magnitude faster than standard simulation methods
Machine Learning Can Predict the Timing and Size of Analog Earthquakes
Get PDFDespite the growing spatiotemporal density of geophysical observations at subduction zones, predicting the timing and size of future earthquakes remains a challenge. Here we simulate multiple seismic cycles in a laboratory‐scale subduction zone. The model creates both partial and full margin ruptures, simulating magnitude M_w 6.2–8.3 earthquakes with a coefficient of variation in recurrence intervals of 0.5, similar to real subduction zones. We show that the common procedure of estimating the next earthquake size from slip‐deficit is unreliable. On the contrary, machine learning predicts well the timing and size of laboratory earthquakes by reconstructing and properly interpreting the spatiotemporally complex loading history of the system. These results promise substantial progress in real earthquake forecasting, as they suggest that the complex motion recorded by geodesists at subduction zones might be diagnostic of earthquake imminence
Modeling of Drug Diffusion Based on Concentration Profiles in Healthy and Damaged Human Skin
No full textBased on experimental drug concentration profiles in healthy as well as tape-stripped ex vivo human skin, we model the penetration of the antiinflammatory drug dexamethasone into the skin layers by the one-dimensional generalized diffusion equation. We estimate the position-dependent free-energy and diffusivity profiles by solving the conjugated minimization problem, in which the only inputs are concentration profiles of dexamethasone in skin at three consecutive penetration times. The resulting free-energy profiles for damaged and healthy skin show only minor differences. In contrast, the drug diffusivity in the first 10 μm of the upper skin layer of damaged skin is 200-fold increased compared to healthy skin, which reflects the corrupted barrier function of tape-stripped skin. For the case of healthy skin, we examine the robustness of our method by analyzing the behavior of the extracted skin parameters when the number of input and output parameters are reduced. We also discuss techniques for the regularization of our parameter extraction method
Network measures of mixing
No full textTransport and mixing processes in �uid �ows can be studied directly from Lagrangian trajectory data, such as those obtained from particle
tracking experiments. Recent work in this context highlights the application of graph-based approaches, where trajectories serve as nodes and
some similarity or distance measure between them is employed to build a (possibly weighted) network, which is then analyzed using spectral
methods. Here, we consider the simplest case of an unweighted, undirected network and analytically relate local network measures such as
node degree or clustering coe�cient to �ow structures. In particular, we use these localmeasures to divide the family of trajectories into groups
of similar dynamical behavior via manifold learning methods
Global well-posedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes
No full textIn this work we study the global solvability of the primitive equations for the atmosphere coupled to moisture dynamics with phase changes for warm clouds, where water is present in the form of water vapor and in the liquid state as cloud water and rain water. This moisture model contains closures for the phase changes condensation and evaporation, as well as the processes of autoconversion of cloud water into rainwater and the collection of cloud water by the falling rain droplets. It has been used by Klein and Majda in \cite{KM} and corresponds to a basic form of the bulk microphysics closure in the spirit of Kessler \cite{Ke} and Grabowski and Smolarkiewicz \cite{GS}. The moisture balances are strongly coupled to the thermodynamic equation via the latent heat associated to the phase changes. In \cite{HKLT} we assumed the velocity field to be given and proved rigorously the global existence and uniqueness of uniformly bounded solutions of the moisture balances coupled to the thermodynamic equation. In this paper we present the solvability of a full moist atmospheric flow model, where the moisture model is coupled to the primitive equations of atmospherical dynamics governing the velocity field. For the derivation of a priori estimates for the velocity field we thereby use the ideas of Cao and Titi \cite{CT}, who succeeded in proving the global solvability of the primitive equations
Rationalization of the Membrane Permeability Differences in a Series of Analogue Cyclic Decapeptides
No full textCyclization and selected backbone N-methylations are found to be often necessary but not sufficient conditions for peptidic drugs to have a good bioavailability. Thus, the design of cyclic peptides with good passive membrane permeability and good solubility remains a challenge. The backbone scaffold of a recently published series of cyclic decapeptides with six selected backbone N-methylations was designed to favor the adoption of a closed conformation with β-turns and four transannular hydrogen bonds. Although this conformation was indeed adopted by the peptides as determined by NMR measurements, substantial differences in the membrane permeability were observed. In this
work, we aim to rationalize the impact of discrete side chain modifications on membrane permeability for six of these cyclic decapeptides. The thermodynamic and kinetic properties were investigated using molecular dynamics simulations and Markov state modeling in water and chloroform. The study highlights the influence that side-chain modifications can have on the
backbone conformation. Peptides with a D-proline in the β-turns were more likely to adopt, even in water, the closed conformation with transannular hydrogen bonds, which facilitates transition through the membrane. The population of the closed conformation in water was found to correlate positively with PAMPA log Pe