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Transition paths of marine debris and the stability of the garbage patches
Get PDFABSTRACT
We used transition path theory (TPT) to infer “reactive” pathways of floating marine debris trajectories. The TPT analysis was applied on a
pollution-aware time-homogeneous Markov chain model constructed from trajectories produced by satellite-tracked undrogued buoys from
the National Oceanic and Atmospheric Administration’s Global Drifter Program. The latter involved coping with the openness of the system
in physical space, which further required an adaptation of the standard TPT setting. Directly connecting pollution sources along coastlines
with garbage patches of varied strengths, the unveiled reactive pollution routes represent alternative targets for ocean cleanup efforts. Among
our specific findings we highlight: constraining a highly probable pollution source for the Great Pacific garbage patch; characterizing the
weakness of the Indian Ocean gyre as a trap for plastic waste; and unveiling a tendency of the subtropical gyres to export garbage toward the
coastlines rather than to other gyres in the event of anomalously intense winds
Non-Markovian modeling of protein folding
Get PDFWe extract the folding free energy landscape and the time-
dependent friction function, the two ingredients of the gener-
alized Langevin equation (GLE), from explicit-water molecular
dynamics (MD) simulations of the α-helix forming polypeptide
alanine9 for a one-dimensional reaction coordinate based on the
sum of the native H-bond distances. Folding and unfolding times
from numerical integration of the GLE agree accurately with
MD results, which demonstrate the robustness of our GLE-based
non-Markovian model. In contrast, Markovian models do not
accurately describe the peptide kinetics and in particular, cannot
reproduce the folding and unfolding kinetics simultaneously, even
if a spatially dependent friction profile is used. Analysis of the
GLE demonstrates that memory effects in the friction significantly
speed up peptide folding and unfolding kinetics, as predicted by
the Grote–Hynes theory, and are the cause of anomalous diffusion
in configuration space. Our methods are applicable to any reac-
tion coordinate and in principle, also to experimental trajectories
from single-molecule experiments. Our results demonstrate that a
consistent description of protein-folding dynamics must account
for memory friction effects
Large deviations for Markov jump processes with uniformly diminishing rates
Get PDFABSTRACT. We prove a large-deviation principle (LDP) for the sample paths of jump Markov processes in the small noise
limit when, possibly, all the jump rates vanish uniformly, but slowly enough, in a region of the state space. We further discuss
the optimality of our assumptions on the decay of the jump rates. As a direct application of this work we relax the assumptions
needed for the application of LDPs to, e.g., Chemical Reaction Network dynamics, where vanishing reaction rates arise
naturally particularly the context of mass action kinetics
Toward a Numerical Laboratory for Investigations of Gravity Wave–Mean Flow Interactions in the Atmosphere
No full textIdealized integral studies of the dynamics of atmospheric inertia–gravity waves (IGWs) from their sources in the troposphere (e.g., by spontaneous emission from jets and fronts) to dissipation and mean flow effects at higher altitudes could contribute to a better treatment of these processes in IGW parameterizations in numerical weather prediction and climate simulation. It seems important that numerical codes applied for this purpose are efficient and focus on the essentials. Therefore, a previously published staggered-grid solver for f-plane soundproof pseudoincompressible dynamics is extended here by two main components. These are 1) a semi-implicit time stepping scheme for the integration of buoyancy and Coriolis effects, and 2) the incorporation of Newtonian heating consistent with pseudoincompressible dynamics. This heating function is used to enforce a temperature profile that is baroclinically unstable in the troposphere and it allows the background state to vary in time. Numerical experiments for several benchmarks are compared against a buoyancy/Coriolis-explicit third-order Runge–Kutta scheme, verifying the accuracy and efficiency of the scheme. Preliminary mesoscale simulations with baroclinic wave activity in the troposphere show intensive small-scale wave activity at high altitudes, and they also indicate there the expected reversal of the zonal-mean zonal winds.
Fabienne 1, Elena 1, Rupert Klein2, and Ulrich Achatz
On the algebra and groups of incompressible vortex dynamics
Get PDFAn algebraic representation for 2D and 3D incompressible, inviscid fluid
motion based on the continuous Nambu representation of Helmholtz vorticity
equation is introduced. The Nambu brackets of conserved quantities generate a
Lie algebra. Physically,we introducematrix representations for the components
of the linear momentum (2D and 3D), the circulation (2D) and the total flux
of vorticity (3D). These quantities form the basis of the vortex-Heisenberg Lie
algebra.Applying thematrix commutator to the basismatrices leads to the same
physical relations as the Nambu bracket for this quantities expressed classically
as functionals. Using the matrix representation of the Lie algebra we derive the
matrix and vector representations for the nilpotent vortex-Heisenberg groups
that we denote by VH(2) and VH(3). It turns out that VH(2) is a covering group
of the classical Heisenberg group for mass point dynamics. VH(3) can be seen
as central extension of the abelian group of translations. We further introduce
the Helmholtz vortex group V(3), where additionally the angular momentum
is included. Regarding application-oriented aspects, the novel matrix representation
might be useful for numerical investigations of the group, whereas
the vector representation of the group might provide a better process-related
understanding of vortex flows.
Keywords: Nambu mechanics, fluid dynamics, vorticity equation, algebra
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∗Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons
Attribution 4.0 licence. Any further distribution of this work must maintain attribution
to the author(s) and the title of the work, journal citation and DOI.
1751-8121
Investigation of water-mediated intermolecular interactions with the adaptive resolution simulation technique
No full textAbstract
We use the adaptive resolution simulation (AdResS) technique to estimate the region in space where water-mediated effects in molecule–molecule interactions are relevant. AdResS is employed to identify the region around the solute (solvation shell) where the atomistic details of the hydrogen bonding network are relevant while outside water plays the role of a thermodynamic bath that can be described at simplified macroscopic level. The consequence is that for the interaction of two solutes the intermolecular distance at which water mediated effects start to be relevant is represented by the sum of the radii of the two respective solvation shells identified via AdResS. The hypothesis formulated above will be proven by calculating the solute-solute potential of mean force for different solutes. As test molecules we use amino acids derived from fragments of the FCHo2-F-BAR domain protein; this choice stems from the fact that the current results, beside proving the technical capability of AdResS in this context, may provide data for future actual coarse-grained models
EDP-convergence for nonlinear fast–slow reaction systems with detailed balance
No full textWe consider nonlinear reaction systems satisfying mass-action kinetics with slow and fast reactions. It is known that the fast-reaction-rate limit can be described by an ODE with Lagrange multipliers and a set of nonlinear constraints that ask the fast reactions to be in equilibrium. Our aim is to study the limiting gradient structure which is available if the reaction system satisfies the detailed-balance condition. The gradient structure on the set of concentration vectors is given in terms of the relative Boltzmann entropy and a cosh-type dissipation potential. We show that a limiting or effective gradient structure can be rigorously derived via EDP-convergence, i.e. convergence in the sense of the energy-dissipation principle for gradient flows. In general, the effective entropy will no longer be of Boltzmann type and the reactions will no longer satisfy mass-action kinetics
SCORE: Smart Consensus Of RNA Expression—a consensus tool for detecting differentially expressed genes in bacteria
No full textRNA-sequencing (RNA-Seq) is the current method of choice for studying bacterial transcriptomes. To date, many computational pipelines have been developed to predict differentially expressed genes from RNA-Seq data, but no gold-standard has been widely accepted. We present the Snakemake-based tool Smart Consensus Of RNA Expression (SCORE) which uses a consensus approach founded on a selection of well-established tools for differential gene expression analysis. This allows SCORE to increase the overall prediction accuracy and to merge varying results into a single, human-readable output. SCORE performs all steps for the analysis of bacterial RNA-Seq data, from read preprocessing to the overrepresentation analysis of significantly associated ontologies. Development of consensus approaches like SCORE will help to streamline future RNA-Seq workflows and will fundamentally contribute to the creation of new gold-standards for the analysis of these types of data.
Availability and implementation:
https://github.com/SiWolf/SCORE
Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading
No full textAgent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation model leads to a significant gain in computational efficiency, while preserving important dynamical properties. Based on a precise mathematical description of spatio-temporal ABMs, we present two different metapopulation approaches (stochastic and piecewise deterministic) and discuss the approximation steps between the different models within this framework. Especially, we show how the stochastic metapopulation model results from a Galerkin projection of the underlying ABM onto a finite-dimensional ansatz space. Finally, we utilize our modeling framework to provide a conceptual model for the spreading of COVID-19 that can be scaled to real-world scenarios