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FAST-MOVING PATTERN INTERFACES CLOSE TO A TURING INSTABILITY IN AN ASYMPTOTIC MODEL FOR THE THREE-DIMENSIONAL BÉNARD-MARANGONI PROBLEM

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arXiv 2024年

作者： Hilder, Bastian Jansen, Jonas Department of Mathematics Technische Universität München Boltzmannstrasse 3 Garching B. München 85748 Germany Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin53757 Germany

We study the bifurcation of planar patterns and fast-moving pattern interfaces in an asymptotic longwave model for the three-dimensional Bénard–Marangoni problem, which is close to a Turing instability. We derive the model from the full free-boundary Bénard–Marangoni problem for a thin liquid film on a heated substrate of low thermal conductivity via a lubrication approximation. This yields a quasilinear, fully coupled, mixed-order degenerate-parabolic system for the film height and temperature. As the Marangoni number M increases beyond a critical value M∗, the pure conduction state destabilises via a Turing(–Hopf) instability. Close to this critical value, we formally derive a system of amplitude equations which govern the slow modulation dynamics of square or hexagonal patterns. Using center manifold theory, we then study the bifurcation of square and hexagonal planar patterns. Finally, we construct planar fast-moving modulating travelling front solutions that model the transition between two planar patterns. The proof uses a spatial dynamics formulation and a center manifold reduction to a finite-dimensional invariant manifold, where modulating fronts appear as heteroclinic orbits. These modulating fronts facilitate a possible mechanism for pattern formation, as previously observed in *** Codes 35B36, 70K50, 35B32, 35Q35, 35K41, 35K59, 35K65, 35Q79, 76A20, 35B06, 34C37, 37L10 Copyright © 2024, The Authors. All rights reserved.

关键词： Thermal conductivity of liquids

Privacy Risk Assessment for Synthetic Longitudinal Health Data

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Privacy Risk Assessment for Synthetic Longitudinal Health Da...

69th Annual Meeting of the German Association of Medical Informatics, Biometry and Epidemiology, GMDS 2024

作者： Schneider, Julian Walter, Marvin Otte, Karen Meurers, Thierry Perrar, Ines Nöthlings, Ute Adams, Tim Fröhlich, Holger Prasser, Fabian Fluck, Juliane Kühnel, Lisa Knowledge Management ZB MED - Information Centre for Life Sciences Cologne Germany Medical Informatics Group Berlin Institute of Health at Charité - Universitätsmedizin Berlin Berlin Germany Institute of Nutritional and Food Sciences - Nutritional Epidemiology University of Bonn Bonn Germany Department of Bioinformatics Fraunhofer Institute for Algorithms and Scientific Computing SCAI Sankt Augustin Germany The Agricultural Faculty University of Bonn Bonn Germany Faculty of Technology Bielefeld University Bielefeld Germany

ISBN: (纸本)9781643685366

Introduction A modern approach to ensuring privacy when sharing datasets is the use of synthetic data generation methods, which often claim to outperform classic anonymization techniques in the trade-off between data utility and privacy. Recently, it was demonstrated that various deep learning-based approaches are able to generate useful synthesized datasets, often based on domain-specific analyses. However, evaluating the privacy implications of releasing synthetic data remains a challenging problem, especially when the goal is to conform with data protection guidelines. Methods Therefore, the recent privacy risk quantification framework Anonymeter has been built for evaluating multiple possible vulnerabilities, which are specifically based on privacy risks that are considered by the European Data Protection Board, i.e. singling out, linkability, and attribute inference. This framework was applied to a synthetic data generation study from the epidemiological domain, where the synthesization replicates time and age trends previously found in data collected during the DONALD cohort study (1312 participants, 16 time points). The conducted privacy analyses are presented, which place a focus on the vulnerability of outliers. Results The resulting privacy scores are discussed, which vary greatly between the different types of attacks. Conclusion Challenges encountered during their implementation and during the interpretation of their results are highlighted, and it is concluded that privacy risk assessment for synthetic data remains an open problem. © 2024 The Authors.

关键词： Differential privacy

On Dark Stars, Planck Cores and the Nature of Dark Matter 23

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On Dark Stars, Planck Cores and the Nature of Dark Matter

23rd Workshop What Comes Beyond the Standard Models

作者： Nikitin, I. Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin53757 Germany

Dark stars are compact massive objects, described by Einstein gravitational field equations with matter. The type we consider possesses no event horizon, instead, there is a deep gravitational well with a very strong redshift factor. Observationally, dark stars can be identified with black holes. Inside dark stars, Planck density of matter is reached, Planck cores are formed, where the equations are modified by quantum gravity. In the paper, several models of dark stars with Planck cores are considered, resulting in the following hypothesis on the composition of dark matter. The galaxies are flooded with low-energetic radiation from the dark stars. The particle type can be photons and gravitons from the Standard Model, can also be a new type of massless particles. The model estimations show that the extremely large redshift factor z ∼ 1049 and the emission wavelength λ0 ∼ 1014m can be reached. The particles are not registered directly in the existing dark matter experiments. They come in a density sufficient to explain the observable rotation curves. The emission has a geometric dependence of density on radius ρ ∼ r−2, producing flat rotation curves. The distribution of sources also describes the deviations from the flat shape. The model provides a good fit of experimental rotation curves. Outbreaks caused by a fall of an external object on a dark star lead to emission wavelength shifted towards smaller values. The model estimations give the outbreak wavelength λ ∼ 1m compatible with fast radio bursts. The paper raises several principal questions. White holes with Planck core appear to be stable. Galactic rotation curves in the considered setup do not depend on the matter type. Inside the galaxy, dark matter can be of hot radial type. At cosmological distances, it can behave like the cold uniform type. © 2020 DMFA zaloznistvo. All rights reserved.

关键词： Stars

Knowledge Detection and Discovery using Semantic Graph Embeddings on Large Knowledge Graphs generated on Text Mining Results 15

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Knowledge Detection and Discovery using Semantic Graph Embed...

15th Federated Conference on Computer Science and Information Systems, FedCSIS 2020

作者： Dorpinghaus, Jens Jacobs, Marc Bonn Germany Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin Germany

ISBN: (纸本)9788395541674

Knowledge graphs play a central role in big data integration, especially for connecting data from different domains. Bringing unstructured texts, e.g. from scientific literature, into a structured, comparable format is one of the key assets. Here, we use knowledge graphs in the biomedical domain working together with text mining based document data for knowledge extraction and retrieval from text and natural language structures. For example cause and effect models, can potentially facilitate clinical decision making or help to drive research towards precision medicine. However, the power of knowledge graphs critically depends on context information. Here we provide a novel semantic approach towards a context enriched biomedical knowledge graph utilizing data integration with linked data applied to language technologies and text mining. This graph concept can be used for graph embedding applied in different approaches, e.g with focus on topic detection, document clustering and knowledge discovery. We discuss algorithmic approaches to tackle these challenges and show results for several applications like search query finding and knowledge discovery. The presented remarkable approaches lead to valuable results on large knowledge graphs. © 2020 Polish Information Processing Society - as it is since 2011.

关键词： Knowledge graph

Optimization of Retrieval algorithms on Large Scale Knowledge Graphs 15

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Optimization of Retrieval Algorithms on Large Scale Knowledg...

15th Federated Conference on Computer Science and Information Systems, FedCSIS 2020

作者： Dorpinghaus, Jens Stefan, Andreas Bonn Germany Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin Germany

ISBN: (纸本)9788395541674

Knowledge graphs have been shown to play an important role in recent knowledge mining and discovery, for example in the field of life sciences or bioinformatics. Although a lot of research has been done on the field of query optimization, query transformation and of course in storing and retrieving large scale knowledge graphs the field of algorithmic optimization is still a major challenge and a vital factor in using graph databases. Few researchers have addressed the problem of optimizing algorithms on large scale labeled property graphs. Here, we present two optimization approaches and compare them with a naive approach of directly querying the graph database. The aim of our work is to determine limiting factors of graph databases like Neo4j and we describe a novel solution to tackle these challenges. For this, we suggest a classification schema to differ between the complexity of a problem on a graph database. We evaluate our optimization approaches on a test system containing a knowledge graph derived biomedical publication data enriched with text mining data. This dense graph has more than 71M nodes and 850M relationships. The results are very encouraging and- depending on the problem-we were able to show a speedup of a factor between 44 and 3839. © 2020 Polish Information Processing Society - as it is since 2011.

关键词： Knowledge graph

Feature-based prediction of properties of cross-linked epoxy polymers by molecular dynamics and machine learning techniques

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arXiv 2023年

作者： Sindu, B.S. Hamaekers, Jan Special and Multifunctional Structures Laboratory CSIR-Structural Engineering Research Centre Taramani Tamil Nadu Chennai600113 India Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt AugustinD-53757 Germany

Epoxy polymers are used in wide range of applications. The properties and performance of epoxy polymers depend upon various factors like the type of constituents and their proportions used and other process parameters. The conventional way of developing epoxy polymers is usually labor-intensive and may not be fully efficient, which has resulted in epoxy polymers having a limited performance range due to the use of predetermined blend combinations, compositions and development parameters. Hence, in order to experiment with more design parameters, robust and easy computational techniques need to be established. To this end, we developed and analyzed in this study a new machine learning (ML) based approach to predict the mechanical properties of epoxy polymers based on their basic structural features. The results from molecular dynamics (MD) simulations have been used to derive the ML model. The salient feature of our work is that for the development of epoxy polymers based on EPON-862, several new hardeners were explored in addition to the conventionally used ones. The influence of additional parameters like the proportion of curing agent used and the extent of curing on the mechanical properties of epoxy polymers were also investigated. This method can be further extended by providing the epoxy polymer with the desired properties through knowledge of the structural characteristics of its constituents. The findings of our study can thus lead toward development of efficient design methodologies for epoxy polymeric systems. © 2023, CC BY-NC-ND.

关键词： Molecular dynamics

On dark stars, planck cores and the nature of dark matter

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arXiv 2021年

作者： Nikitin, Igor Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin53757 Germany

关键词： Galaxies

Galactic model with a phase transition from dark matter to dark energy

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arXiv 2021年

作者： Nikitin, Igor Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin53757 Germany

This work continues the construction of a recently proposed model of dark matter stars. In this model, dark matter quanta are sterile massless particles that are emitted from the central regions of the galaxy in the radial direction. As a result, at large distances r from the center of the galaxy, the mass density of dark matter has the form ρ ∼ r−2, in contrast to the homogeneous model ρ = Const. In the cosmological context, the homogeneous model with massless particles corresponds to the radiation epoch of the expansion of the universe, while the proposed inhomogeneous model turns out to be equivalent to ΛCDM. In this paper, scenarios will be considered in which the radial emission of dark matter is brought into hydrostatic equilibrium with a uniform background. It is shown that solutions exist if the uniform background has an equation of state typical for dark energy. Thus, this model describes a phase transition from dark matter inside the galaxy to dark energy outside of it. The specific mechanism for such a transition could be Bose-Einstein condensation. In addition, the question of what happens if dark matter particles are not sterile, for example, are photons of the Standard Model, is considered. © 2021, CC BY.

关键词： Galaxies

Wormholes and Teleporters

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arXiv 2021年

作者： Nikitin, Igor Fraunhofer Institute for Algorithms and Scientific Computing Schloss Birlinghoven Sankt Augustin53757 Germany

In general relativity, there is a class of solutions that currently do not have observed analogues, but on which the theory is shaped, giving an understanding what is fundamentally possible within its framework. Such solutions include wormholes, tunnels that connect distant regions in spacetime. Although not a single wormhole has yet been discovered, there is a large number of works devoted to their study, thanks to which wormholes as a class of solutions become firmly established in modern science. In this paper, we consider two topologically nontrivial types of solutions related to wormholes. First: Wormholes that can open and close. In this relation, we will discuss topological censorship theorems, which under certain conditions prohibit changing topology. We will also discuss known ways to circumvent these theorems. Using analytical and numerical methods, as well as visualization, we will construct an example of an opening and closing wormhole with the dimensions of the central black hole in the Milky Way galaxy. Our construction continues the work by Kardashev, Novikov and Shatskiy, in which a static wormhole with the same parameters was considered. The second type is a modification of Visser's dihedral wormhole solution for a dynamic case, which can be considered as a model of a teleportation event. © 2021, CC BY.

关键词： Topology