Article
Engineering, Chemical
Hannes Bauer, Johannes Khinast
Summary: Twin-screw extruders are known for their good mixing performance, but the actual mixing mechanism remains largely unexplored due to the complexity of the screw geometry. This study uses Lagrangian Coherent Structures to understand laminar mixing in various elements of twin-screw extruders and offers a novel viewpoint for geometry optimization.
CHEMICAL ENGINEERING SCIENCE
(2022)
Article
Environmental Sciences
Anusmriti Ghosh, Kabir Suara, Scott W. McCue, Yingying Yu, Tarmo Soomere, Richard J. Brown
Summary: Coastal and estuarine ecosystems are heavily influenced by floating debris pollution, with robust techniques like Lagrangian coherent structures used to predict debris accumulation hotspots. A comprehensive study in Moreton Bay, Australia, identified 11 debris accumulation hotspots, with material accumulation occurring mainly during ebb tide and enhanced by wind. These hotspots, situated near islands and headlands, match areas with high historical debris collection, providing a useful tool for effective clean-up management.
SCIENCE OF THE TOTAL ENVIRONMENT
(2021)
Article
Engineering, Aerospace
Lin Sun, Fang Bian, Xiaoyu Lei, Delei Shi, Futing Bao
Summary: This paper proposes a new formula for calculating the contact area of two components in an arbitrary complex region, which can analyze the dynamic mixing process of the two components and evaluate the mixing efficiency. Based on the Lagrangian coherence structures, a new method to evaluate the mixing in ramjet engines is established, and the feasibility of using a lobed mixer in ramjet engines is studied. The study shows that the vortex induced by the lobed mixer can significantly increase the contact area between gas and air in the combustion chamber, effectively enhancing the mixing and combustion. The average mixing efficiency during the operation increased by 11.046% and the combustion efficiency increased by 8.318%.
AEROSPACE SCIENCE AND TECHNOLOGY
(2023)
Article
Environmental Sciences
Annalisa De Leo, Francesco Enrile, Alessandro Stocchino
Summary: This study aims to identify coherent trajectory patterns caused by vortex shedding in tidal environments, and single and multiple harmonics tides are replicated on a large-scale physical model. The dynamics of large-scale macro-vortices and stable and unstable manifolds within the flow are investigated using the Lagrangian Average Vorticity Deviation (LAVD) and Finite Time Lyapunov Exponents.
FRONTIERS IN MARINE SCIENCE
(2022)
Article
Mathematics, Applied
Aleksandar Badza, Trent W. Mattner, Sanjeeva Balasuriya
Summary: Lagrangian coherent structures (LCSs) are time-varying entities that capture the most influential transport features of a flow. This article systematically investigates whether LCS methods are self-consistent in their conclusions under the uncertainty of realistic Eulerian velocity data. The methods detecting full-dimensional coherent flow regions are found to be significantly more robust than those detecting lower-dimensional flow barriers.
PHYSICA D-NONLINEAR PHENOMENA
(2023)
Article
Mechanics
Jerke Eisma, Jerry Westerweel, Willem van de Water
Summary: In a turbulent boundary layer, a scalar emanating from a point source does not mix homogeneously, but is organized in large regions with little variation of concentration, known as uniform concentration zones. By measuring scalar concentration and the three-dimensional velocity field, researchers have identified these zones and found correlations with the rate of fluid parcel separation and strong shear in the velocity field. The study also compared methods to monitor the flow field history and found significant correlations with the edges of uniform concentration zones.
JOURNAL OF FLUID MECHANICS
(2021)
Review
Oceanography
Dimitrios Antivachis, Vassilios Vervatis, Sarantis Sofianos
Summary: The dynamics of fluid flows lead to persistent circulation features known as lagrangian coherent structures, which strongly control the advection of water masses. Lagrangian approaches and metrics are better suited for locating and delineating such structures and capturing their effects on the formation and dispersion of water masses. In this study, ocean velocity fields are analyzed using the framework of lagrangian coherent structures to investigate their impact on the motion and mixing of water masses in the Mediterranean Sea.
PROGRESS IN OCEANOGRAPHY
(2023)
Article
Mechanics
Xiaoning Wang, Jianchun Wang, Shiyi Chen
Summary: This study investigates the effects of compressibility on the statistics and coherent structures of a temporally developing mixing layer through numerical simulations. The results show that as the convective Mach number increases, the streamwise dissipation becomes more effective in suppressing turbulent kinetic energy. At low convective Mach numbers, the mixing layer is accompanied by spanwise Kelvin-Helmholtz rollers, while at higher convective Mach numbers, large-scale high- and low-speed structures dominate. The study also reveals a correlation between high-shearing motions on top of low-speed structures and the clustering of small-scale vortical structures.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Physics, Multidisciplinary
M. Danish Siddiqi, Meraj A. Khan, Amira A. Ishan, S. K. Chaubey
Summary: This research focuses on investigating anti-invariant Lorentzian submersions and Lagrangian Lorentzian submersions from Lorentzian concircular structure (LCS)(n) manifolds to semi-Riemannian manifolds, showing that their horizontal distributions are not integrable and fibers are not totally geodesic. It concludes that if the Reeb vector field is horizontal, the anti-invariant and LLS cannot be harmonic.
FRONTIERS IN PHYSICS
(2022)
Article
Engineering, Chemical
Linna Jin, Yuhui Cao
Summary: This study applied the improved delayed detached-eddy simulation (IDDES) method to predict turbulent mixing in a confined impinging-jet mixer. The results showed good agreement with experimental data and provided insights on the coherent structures and their effects on turbulence statistics and mixing efficiency.
CHEMICAL ENGINEERING SCIENCE
(2022)
Article
Engineering, Multidisciplinary
Zhihao Qian, Moubin Liu, Lihua Wang, Chuanzeng Zhang
Summary: In this study, a novel and accurate numerical technique based on the Lagrangian-Eulerian Stabilized Collocation Method (LESCM) is proposed for computing Finite Time Lyapunov Exponents (FTLEs) in viscous incompressible flows. This technique surpasses the accuracy of pure Lagrangian particle methods and provides an accurate way of detecting complex Lagrangian Coherent Structures (LCSs) in flow fields. By harnessing the efficiency of LESCM, MATLAB can handle up to 16 million particles with ease, eliminating the need for parallel computation techniques.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mechanics
Nikolas Olson Aksamit
Summary: We introduce a mapping method that quantifies and visualizes the full geometry of three-dimensional deformation in fluid flows using Cauchy-Green strain tensor eigenvalues. The mapping system visualizes the role of all three eigenvalues in a single plot, providing a comprehensive understanding of the fluid deformation. We also provide methods to visualize the degree of approximation of limiting deformation states and tools to quantify differences between flows based on the compositional geometry of invariant manifolds.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Engineering, Multidisciplinary
Hang Cheng, Jie Shen, YiZhao Zhang, Quan Zhou, Kai Leong Chong, YuLu Liu, ZhiMing Lu
Summary: This paper investigates the Lagrangian coherent structures (LCSs) and their heat-transport mechanism in turbulent Rayleigh-Benard convection. The results show a power-law relationship between Nusselt number and Rayleigh number, and the presence of lobe structures that play a significant role in heat transport. Furthermore, most thermal plumes transport along the LCSs, while only a few mix with the turbulent background.
SCIENCE CHINA-TECHNOLOGICAL SCIENCES
(2022)
Article
Computer Science, Interdisciplinary Applications
Jack Tyler, Alexander Wittig
Summary: This paper introduces a novel method called DA-LCS for the numerical calculation of hyperbolic Lagrangian Coherent Structures using Differential Algebra, which improves the accuracy of structure identification and uncovers additional dynamic behavior.
JOURNAL OF COMPUTATIONAL SCIENCE
(2022)
Article
Physics, Fluids & Plasmas
Dan Lucas, Tatsuya Yasuda
Summary: Time-delayed feedback control is a method to stabilize periodic orbits in chaotic dynamical systems, and it can also be applied to stabilize coherent structures in fluid turbulence. The odd-number limitation of this method can be overcome in fluid problems by utilizing the symmetries of the system, leading to the discovery of eight additional coherent structures that can be stabilized.
PHYSICAL REVIEW FLUIDS
(2022)
Article
Engineering, Mechanical
Shobhit Jain, George Haller
Summary: Invariant manifolds are important constructs for understanding nonlinear phenomena in dynamical systems, particularly in mechanical systems. However, their use has been limited to low-dimensional academic examples, and challenges exist in computing them for realistic engineering structures described by finite element models.
NONLINEAR DYNAMICS
(2022)
Article
Multidisciplinary Sciences
Mattia Cenedese, Joar Axas, Bastian Baeuerlein, Kerstin Avila, George Haller
Summary: This study develops a data-driven reduced modeling method for non-linear, high-dimensional physical systems, which reconstructs and predicts the dynamics of the full physical system. The method demonstrates accurate predictive ability on experimental data.
NATURE COMMUNICATIONS
(2022)
Article
Multidisciplinary Sciences
Lidia Martinez, Pablo Merino, Gonzalo Santoro, Jose I. Martinez, Stergios Katsanoulis, Jesse Ault, Alvaro Mayoral, Luis Vazquez, Mario Accolla, Alexandre Dazzi, Jeremie Mathurin, Ferenc Borondics, Enrique Blazquez-Blazquez, Nitzan Shauloff, Rosa Lebron-Aguilar, Jesus E. Quintanilla-Lopez, Raz Jelinek, Jose Cernicharo, Howard A. Stone, Victor A. de la Pena O'Shea, Pedro L. de Andres, George Haller, Gary J. Ellis, Jose A. Martin-Gago
Summary: The study proposes an alternative gas phase process for the synthesis of long hydrocarbon chains using atomic carbon and molecular hydrogen precursors in an inert carrier gas, without the use of metal catalysts. Under mild reaction conditions, efficient C-C chain growth was achieved with the presence of CH2 and H radicals, leading to the production of unbranched alkanes micrometers in length.
NATURE COMMUNICATIONS
(2021)
Correction
Mathematics, Applied
George Haller, Nikolas Aksamit, Alex P. Encinas-Bartos
Article
Mechanics
Nikolas O. Aksmit, George Haller
Summary: Using the recent theory of diffusive momentum transport, this study identifies internal barriers in wall-bounded turbulence. These barriers, formed by the invariant manifolds of the velocity field, block the viscous part of the instantaneous momentum flux in the flow. The study introduces new diagnostic tools and normalized trajectory metrics to provide unprecedented visualizations of objective coherent structures.
JOURNAL OF FLUID MECHANICS
(2022)
Article
Engineering, Mechanical
Mingwu Li, George Haller
Summary: In Part I of this paper, the authors constructed reduced-order models for harmonically excited mechanical systems with internal resonances using spectral submanifold theory. By locating the solution branches of equilibria of the corresponding reduced-order model, they were able to extract forced response curves formed by periodic orbits of the full system. In Part II, the authors use bifurcations of the equilibria of the reduced-order model to predict bifurcations of the periodic response of the full system, specifically predicting the existence of two-dimensional and three-dimensional quasi-periodic attractors and repellers in periodically forced mechanical systems of arbitrary dimension.
NONLINEAR DYNAMICS
(2022)
Article
Multidisciplinary Sciences
M. Cenedese, J. Axas, H. Yang, M. Eriten, G. Haller
Summary: This paper reviews a data-driven nonlinear model reduction methodology based on spectral submanifolds, which can be used to reduce the dimensionality of nonlinear systems and provide accurate predictions.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Multidisciplinary Sciences
Thomas Breunung, Florian Kogelbauer, George Haller
Summary: Invariant manifolds are crucial for understanding the dynamical behavior of nonlinear mechanical systems and reducing the model order. However, their applicability under random external forcing is still unclear. In this paper, we clarify the role of deterministic invariant manifolds, specifically normally hyperbolic invariant manifolds and spectral submanifolds, when small white noise excitation is added, and demonstrate our results on several mechanical systems.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Physics, Fluids & Plasmas
Balint Kaszas, Mattia Cenedese, George Haller
Summary: This study derives low-dimensional models using data-driven methods to describe transitions among exact coherent states in plane Couette flow. These models can accurately predict off-SSM transitions that were not used in their training.
PHYSICAL REVIEW FLUIDS
(2022)
Article
Mathematics, Applied
Alex P. Encinas-Bartos, Nikolas O. Aksamit, George Haller
Summary: This study employs a recently developed single-trajectory Lagrangian diagnostic tool to visualize oceanic vortices from sparse drifter data. The authors developed a general algorithm based on this tool to extract approximate eddy boundaries and found that it outperforms other available methodologies for eddy detection.
Article
Mechanics
Stergios Katsanoulis, Florian Kogelbauer, Roshan Kaundinya, Jesse Ault, George Haller
Summary: Instantaneous features of three-dimensional velocity fields can be visualized most directly through streamsurfaces, but it is often unclear which streamsurfaces to choose given the infinite possibilities passing through each point. However, vector fields with a non-degenerate first integral can define a continuous family of streamsurfaces, while vortical regions in generic vector fields may have local first integrals over a discrete set of streamtubes. In this study, a method is introduced to construct such first integrals from velocity data and it is shown that their level sets accurately frame vortical features in known examples.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Mathematics, Applied
George Haller, Balint Kaszas, Aihui Liu, Joar Axas
Summary: A primary spectral submanifold (SSM) is the smoothest nonlinear continuation of a nonresonant spectral subspace E, providing a low-dimensional, smooth model in polynomial form for system dynamics. However, previous limitations required the SSM to be spanned by eigenvectors of the same stability type, and the nonlinear behavior of interest may be far from the smoothest continuation of a subspace. Here, we overcome these limitations by constructing a class of SSMs that contain invariant manifolds with mixed internal stability types and lower smoothness class arising from fractional powers.
Article
Mechanics
Balint Kaszas, Tiemo Pedergnana, George Haller
Summary: For an arbitrary velocity field v defined on a finite, fixed spatial domain, we determine the closest rigid-body velocity field vRB to v in the L2 norm. The resulting deformation velocity component, vd = v - vRB, is found to be frame-indifferent and physically observable. This implies that the momentum, energy, vorticity, enstrophy, and helicity of the flow are all frame-indifferent when computed from the deformation velocity component vd.
EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
(2023)
Article
Mechanics
Nikolas O. Aksamit, Robert Hartmann, Detlef Lohse, George Haller
Summary: Mathematical developments in the theory of objective coherent structures have improved our understanding of the material organization of complex fluid flows. However, there is limited investigation into these objectively defined transport barriers in 3-D unsteady flows with complicated spatiotemporal dynamics. Our study utilizes simulations to uncover the interplay between different types of barriers in turbulent rotating Rayleigh-Bénard convection.
JOURNAL OF FLUID MECHANICS
(2023)
Article
Environmental Sciences
Nikolas O. Aksamit, Ben Kravitz, Douglas G. MacMartin, George Haller
Summary: Stratospheric sulfate aerosol geoengineering involves temporarily intervening in the climate system to reduce global temperature by optimizing diffusion through strategic injection locations. Utilizing time-varying diffusion barriers can increase global coverage and slow aerosol growth, impacting radiative forcing effects in the long term. Further research is needed to accurately predict the long-term effects on radiative forcing and explore the potential benefits of this approach for cooling the planet.
ATMOSPHERIC CHEMISTRY AND PHYSICS
(2021)
Article
Mathematics, Applied
Melanie Kobras, Valerio Lucarini, Maarten H. P. Ambaum
Summary: In this study, a minimal dynamical system derived from the classical Phillips two-level model is introduced to investigate the interaction between eddies and mean flow. The study finds that the horizontal shape of the eddies can lead to three distinct dynamical regimes, and these regimes undergo transitions depending on the intensity of external baroclinic forcing. Additionally, the study provides insights into the continuous or discontinuous transitions of atmospheric properties between different regimes.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Shu-hong Xue, Yun-yun Yang, Biao Feng, Hai-long Yu, Li Wang
Summary: This research focuses on the robustness of multiplex networks and proposes a new index to measure their stability under malicious attacks. The effectiveness of this method is verified in real multiplex networks.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Julien Nespoulous, Guillaume Perrin, Christine Funfschilling, Christian Soize
Summary: This paper focuses on optimizing driver commands to limit energy consumption of trains under punctuality and security constraints. A four-step approach is proposed, involving simplified modeling, parameter identification, reformulation of the optimization problem, and using evolutionary algorithms. The challenge lies in integrating uncertainties into the optimization problem.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Alain Bourdier, Jean-Claude Diels, Hassen Ghalila, Olivier Delage
Summary: In this article, the influence of a turbulent atmosphere on the growth of modulational instability, which is the cause of multiple filamentation, is studied. It is found that considering the stochastic behavior of the refractive index leads to a decrease in the growth rate of this instability. Good qualitative agreement between analytical and numerical results is obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Ling An, Liming Ling, Xiaoen Zhang
Summary: In this paper, an integrable fractional derivative nonlinear Schrodinger equation is proposed and a reconstruction formula of the solution is obtained by constructing an appropriate Riemann-Hilbert problem. The explicit fractional N-soliton solution and the rigorous verification of the fractional one-soliton solution are presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Marzia Bisi, Nadia Loy
Summary: This paper proposes and investigates general kinetic models with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. The mathematical properties of the kinetic model are proved, and the quasi-invariant asymptotic regime is studied and compared with other models. Numerical tests are performed to demonstrate the time evolution of distribution functions and macroscopic fields.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Carlos A. Pires, David Docquier, Stephane Vannitsem
Summary: This study presents a general theory for computing information transfers in nonlinear stochastic systems driven by deterministic forcings and additive and/or multiplicative noises. It extends the Liang-Kleeman framework of causality inference to nonlinear cases based on information transfer across system variables. The study introduces an effective method called the 'Causal Sensitivity Method' (CSM) for computing the rates of Shannon entropy transfer between selected causal and consequential variables. The CSM method is robust, cheaper, and less data-demanding than traditional methods, and it opens new perspectives on real-world applications.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Feiting Fan, Minzhi Wei
Summary: This paper focuses on the existence of periodic and solitary waves for a quintic Benjamin-Bona-Mahony (BBM) equation with distributed delay and diffused perturbation. By transforming the corresponding traveling wave equation into a three-dimensional dynamical system and applying geometric singular perturbation theory, the existence of periodic and solitary waves are established. The uniqueness of periodic waves and the monotonicity of wave speed are also analyzed.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Wangbo Luo, Yanxiang Zhao
Summary: We propose a generalized Ohta-Kawasaki model to study the nonlocal effect on pattern formation in binary systems with long-range interactions. In the 1D case, the model displays similar bubble patterns as the standard model, but Fourier analysis reveals that the optimal number of bubbles for the generalized model may have an upper bound.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Corentin Correia, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
Summary: The emergence of clustering of rare events is due to periodicity, where fast returns to target sets lead to a bulk of high observations. In this research, we explore the potential of a new mechanism to create clustering of rare events by linking observable functions to a finite number of points belonging to the same orbit. We show that with the right choice of system and observable, any given cluster size distribution can be obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Enyu Fan, Changpin Li
Summary: This paper numerically studies the Allen-Cahn equations with different kinds of time fractional derivatives and investigates the influences of time derivatives on the solutions of the considered models.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Yuhang Zhu, Yinghao Zhao, Chaolin Song, Zeyu Wang
Summary: In this study, a novel approach called Time-Variant Reliability Updating (TVRU) is proposed, which integrates Kriging-based time-dependent reliability with parallel learning. This method enhances risk assessment in complex systems, showcasing exceptional efficiency and accuracy.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Chiara Cecilia Maiocchi, Valerio Lucarini, Andrey Gritsun, Yuzuru Sato
Summary: The predictability of weather and climate is influenced by the state-dependent nature of atmospheric systems. The presence of special atmospheric states, such as blockings, is associated with anomalous instability. Chaotic systems, like the attractor of the Lorenz '96 model, exhibit heterogeneity in their dynamical properties, including the number of unstable dimensions. The variability of unstable dimensions is linked to the presence of finite-time Lyapunov exponents that fluctuate around zero. These findings have implications for understanding the structural stability and behavior modeling of high-dimensional chaotic systems.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Christian Klein, Goksu Oruc
Summary: A numerical study on the fractional Camassa-Holm equations is conducted to construct smooth solitary waves and investigate their stability. The long-time behavior of solutions for general localized initial data from the Schwartz class of rapidly decreasing functions is also studied. Additionally, the appearance of dispersive shock waves is explored.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Vasily E. Tarasov
Summary: This paper extends the standard action principle and the first Noether theorem to consider the general form of nonlocality in time and describes dissipative and non-Lagrangian nonlinear systems. The general fractional calculus is used to handle a wide class of nonlocalities in time compared to the usual fractional calculus. The nonlocality is described by a pair of operator kernels belonging to the Luchko set. The non-holonomic variation equations of the Sedov type are used to describe the motion equations of a wide class of dissipative and non-Lagrangian systems. Additionally, the equations of motion are considered not only with general fractional derivatives but also with general fractional integrals. An application example is presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
