Article
Mechanics
Changze Zhao, Qian Wang, Haocheng Lu, Hua Liu
Summary: This study investigates the evolution of water entry cavity and the flow structures for a sphere interacting with periodic waves, using both numerical simulation and experimental validation. Large eddy simulation is applied to accurately capture the turbulent flow near the surface and within the cavity. An overset mesh-based numerical wave tank is developed to ensure high-resolution simulation of velocity fields. The experimental setup allows for precise control and validation of the computed results, showing good agreement between numerical and experimental results.
Article
Computer Science, Interdisciplinary Applications
Tiankui Zhang, Charles W. Wolgemuth
Summary: The dynamics of thin, membrane-like structures are crucial in cell biology, but simulating large scale deformations remains challenging due to spatial heterogeneity. A general computational framework has been developed to simulate the dynamics of membranes and vesicles, successfully predicting equilibrium shapes of multiphase vesicles.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Physics, Fluids & Plasmas
Wang Xiao, Kai Liu, John Lowengrub, Shuwang Li, Meng Zhao
Summary: This study investigates the dynamic wrinkling of three-dimensional vesicles in a time-dependent elongation flow using an immersed boundary method. The numerical results match well with the predictions of perturbation analysis, showing exponential relationships between the characteristic wavelength of wrinkles and the flow strength. The simulations of elongated vesicles are in good agreement with experimental results, and the analysis of morphological evolution using spherical harmonics reveals the importance of nonlinear effects in vesicle dynamics.
Article
Chemistry, Multidisciplinary
Veerendra Kumar Sharma, Jyoti Gupta, Harish Srinivasan, Himal Bhatt, Victoria Garcia Sakai, Subhankur Mitra
Summary: Curcumin significantly modulates the lateral diffusion of lipids in cell membrane, particularly in the ordered phase, enhancing membrane dynamics and potentially acting as an allosteric regulator of membrane functionality.
Article
Mathematics, Applied
Pith Peishu Xie
Summary: The introduction of new operators in the Operator axioms has led to the generation of new real numbers, resulting in new equations that extend traditional mathematical models. However, engineering computations often require approximate solutions for equations involving new operators to reflect intuitive order and equivalence relations. This paper introduces numerical computations using base-b expansions to approximate all real numbers.
Article
Engineering, Chemical
Jincheng Lou, Mark Dudley, Jingbo Wang, Yiming Liu, Tzahi Y. Cath, Craig S. Turchi, Michael B. Heeley, Eric M. V. Hoek, David Jassby, Nils Tilton
Summary: Membrane distillation (MD) is a thermal desalination process that can increase single-pass recovery by using composite membranes with a thermally conductive layer, but this also brings challenges in lateral heat conduction through the thin membrane.
JOURNAL OF MEMBRANE SCIENCE
(2023)
Article
Chemistry, Physical
Ritwick Kali, Scott T. Milner
Summary: This study analyzed the stability of PAP[5] embedded in PB-PEO membranes and found that stability is significantly influenced by the length of the hydrophobic block, hydration level, and the number of counterions. The analysis provides insights into molecular-scale pore-membrane interactions and guidance for designing improved PAP[5] embedded PB-PEO membranes for desalination.
MOLECULAR SYSTEMS DESIGN & ENGINEERING
(2022)
Article
Mathematics, Applied
Octavian Postavaru, Flavius Dragoi, Antonela Toma
Summary: In this paper, the authors explain the advantage of using the transformation x -> x(alpha) for solving numerically fractional differential equations. They also discuss a method to improve the accuracy of numerical results for delay fractional equations. The paper concludes with two numerical examples to illustrate their analysis.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2022)
Article
Chemistry, Multidisciplinary
Vadim Krivitsky, Adva Krivitsky, Valeria Mantella, Maya Ben-Yehuda Greenwald, Devanarayanan Siva Sankar, Jil Betschmann, Johannes Bader, Nicole Zoratto, Kento Schreier, Sarah Feiss, Dario Walker, Jorn Dengjel, Sabine Werner, Jean-Christophe Leroux
Summary: This study presents an electrochemical all-in-one device that can rapidly capture, load, and release extracellular vesicles (EVs). The device, composed of antibody-coated microstructured electrodes, effectively isolates EVs from various biofluids and improves EV loading with polyplexes. This portable device offers a lab-on-a-chip approach for efficient EV isolation and manipulation.
ADVANCED MATERIALS
(2023)
Article
Materials Science, Multidisciplinary
Aghil Igder, Wanling Cai, Xuan Luo, Ahmed H. M. Al-Antaki, Kasturi Vimalanathan, Alireza Keshavarz, Ataollah Nosrati, Colin L. Raston
Summary: Polysulfone ultrafiltration membranes were fabricated using a continuous flow micro-mixing process under high shear in a vortex fluidic device. The addition of graphene oxide further enhanced the permeability and rejection properties of the membranes. The vortex fluidic device processing showed shorter mixing time and resulted in membranes with higher porosity and permeability compared to conventional mixing.
ACS APPLIED POLYMER MATERIALS
(2022)
Article
Biochemistry & Molecular Biology
Hsin-Yu Chang, Hsiang-Chi Tsai, Yu Jane Sheng, Heng-Kwong Tsao
Summary: Hybrid membranes containing lipids and A(x)B(y)A(z) triblock copolymers show improved biocompatibility and mechanical stability. In this study, the conformations and stability of asymmetric membranes composed of triblock copolymers were investigated using dissipative particle dynamics. The behavior of loop-shaped and bridge-shaped copolymers in the membranes depended on the interactions between the hydrophobic B-blocks and lipid heads. Different approaches were proposed to achieve thermodynamically stable asymmetric membranes, including symmetrization arrest and the use of asymmetric triblock copolymers.
Article
Chemistry, Physical
Minoru Nakano, Hiroyuki Nakao, Shigeharu Yoshida, Masakazu Fukuda, Manjiro Imai, Keisuke Ikeda
Summary: This study investigates the dynamic changes of lipids with membrane curvature, revealing that lipids in membranes with high positive curvature have unique packing properties, resulting in enhanced hydrophobic hydration and increased activation entropy. These findings provide important insights into the functions and structural changes of biomembranes.
JOURNAL OF PHYSICAL CHEMISTRY LETTERS
(2022)
Article
Multidisciplinary Sciences
Anabel-Lise Le Roux, Caterina Tozzi, Nikhil Walani, Xarxa Quiroga, Dobryna Zalvidea, Xavier Trepat, Margarita Staykova, Marino Arroyo, Pere Roca-Cusachs
Summary: BAR proteins reshape low-curvature membrane templates through a mechanochemical phase transition, depending on the initial template shape and involving a progressive transition between distinct local states.
NATURE COMMUNICATIONS
(2021)
Article
Chemistry, Physical
Suraj Verma, Namasivayam Dhenadhayalan, King-Chuen Lin
Summary: The effect of gradual cholesterol increase on the dynamics of DOPC and DPPC membranes was investigated using single-molecule fluorescence correlation spectroscopy. The results showed that the rigidity of DOPC membranes increased with increasing cholesterol concentration, while the rigidity of DPPC membranes decreased.
JOURNAL OF MOLECULAR LIQUIDS
(2022)
Article
Biophysics
Gilia Cristine Marques Ruiz, Luis Fernando do Carmo Morato, Wallance Moreira Pazin, Francesco Milano, Carlos Jose Leopoldo Constantino, Ludovico Valli, Livia Giotta
Summary: The study demonstrates the interaction between the hormone 17 alpha-ethinylestradiol (EE2) and lipid monolayers and bilayers in cell membrane models, contributing to the understanding of EE2's effects on fluid membranes.
COLLOIDS AND SURFACES B-BIOINTERFACES
(2021)
Article
Mathematics, Applied
Weizhu Bao, Harald Garcke, Robert Nurnberg, Quan Zhao
Summary: This research focuses on the evolution of two-dimensional curve networks and three-dimensional surface clusters. Surface diffusion is used to describe the motion of interfaces, and a parametric finite element method based on a suitable variational formulation is proposed. The method maintains volume conservation and energy stability, preserving the fundamental geometric structures of the flow. It also has excellent properties in terms of mesh point distribution.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Automation & Control Systems
Harald Garcke, Paul Huettl, Christian Kahle, Patrik Knopf, Tim Laux
Summary: We optimize the selection of eigenvalues of the Laplace operator with boundary conditions by modifying the shape of the domain. This is done using a phase-field function to represent the shapes to be minimized. The modified Laplace operator introduces phase-field dependent coefficients to extend the eigenvalue problem on a fixed design domain. We formulate this as an optimal control problem with PDE constraints, where the phase-field function acts as the control. We establish necessary optimality conditions and derive the sharp interface limit for this problem, and present numerical simulations.
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2023)
Article
Mathematics, Applied
Helmut Abels, Felicitas Buerger, Harald Garcke
Summary: We prove the existence of a short-time solution for a system involving a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. The mean curvature flow is scaled with a dependent term defined on the surface, coupled with a diffusion equation for that quantity. Our proof utilizes a splitting ansatz, solving both equations separately through linearization and contraction arguments. This result is formulated for immersed hypersurfaces and provides a uniform lower bound on the existence time, allowing for small changes in the initial value of the height function.
JOURNAL OF EVOLUTION EQUATIONS
(2023)
Article
Mathematics, Applied
Harald Garcke, Kei Fong Lam, Robert Nurnberg, Andrea Signori
Summary: This paper analyzes a phase field approach for structural topology optimization, which innovatively penalizes overhangs (design regions that require underlying support structures during construction) with anisotropic energy functionals. Convex and non-convex examples are provided, with the latter showcasing oscillatory behavior along the object boundary termed the dripping effect in the literature. Rigorous mathematical analysis is presented for the structural topology optimization problem with convex and non-continuously-differentiable anisotropies, deriving the first order necessary optimality condition using subdifferential calculus. Via formally matched asymptotic expansions, the approach is connected with previous works in the literature based on a sharp interface shape optimization description. Several numerical results are provided to demonstrate the advantages of the proposed approach in penalizing overhang developments.
APPLIED MATHEMATICS AND OPTIMIZATION
(2023)
Article
Mathematics
Helmut Abels, Felicitas Buerger, Harald Garcke
Summary: This paper studies a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. The properties of solutions are analyzed, focusing on the qualitative evolution of the surface in relation to the mean curvature flow. It is shown that the surface area strictly decreases and an example of a surface that exists for infinite times is given. Mean convexity is conserved while convexity is not. An embedded hypersurface that develops a self-intersection over time is constructed. The interpretation of the equations as a gradient flow is also provided. (c) 2022 Elsevier Inc. All rights reserved.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Harald Garcke, Patrik Knopf, Robert Nuernberg, Quan Zhao
Summary: This paper presents a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in R-d for d is an element of {2,3}. The model includes the anisotropic Cahn-Hilliard equation, a degenerate mobility function, and suitable boundary conditions. By regularizing the model and using asymptotic expansions, the sharp-interface limit is obtained, which includes the anisotropic surface diffusion flow, Young's law, and zero-flux condition at the contact line. Weak solutions are shown to exist for the regularized model. Numerical results demonstrate the excellent agreement between the proposed diffuse-interface model and its sharp-interface limit.
JOURNAL OF NONLINEAR SCIENCE
(2023)
Article
Computer Science, Interdisciplinary Applications
Harald Garcke, Robert Nuernberg, Quan Zhao
Summary: In this paper, we study the numerical approximation of a sharp-interface model for two-phase flow. We propose structure-preserving finite element methods that satisfy volume preservation and energy decay on the discrete level. For the evolving fluid interface, we use parametric finite element approximations and introduce an implicit tangential velocity for better interface mesh quality. Two different approaches, unfitted and fitted finite element methods, are considered for the two-phase Navier-Stokes equations. Numerical results are presented to demonstrate the accuracy and efficiency of the introduced methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Robert Nuernberg
Summary: In this paper, a fully discrete approximation for solidification and liquidation of materials with negligible specific heat is introduced and analyzed. The model is a two-sided Mullins-Sekerka problem. The discretization uses finite elements in space and an independent parameterization of the moving free boundary. Unconditional stability and exact volume conservation are proven for the introduced scheme. Several numerical simulations, including simulations for nearly crystalline surface energies, demonstrate the practicality and accuracy of the presented numerical method.
JOURNAL OF NUMERICAL MATHEMATICS
(2023)
Article
Automation & Control Systems
Harald Garcke, Kei Fong Lam, Robert Nurnberg, Andrea Signori
Summary: This work addresses the problem of structural topology optimization for 4D printing using the phase field approach. It involves a two-step process where a 3D object with multi-material active composites is first created and external loads are applied. Then, the object deforms in response to a change in environmental stimulus and removal of loads. The challenge is to find the optimal distribution of materials to achieve the desired configuration in the programmed stage. The problem is formulated as a PDE-constrained minimization problem and necessary conditions for minimizers are derived.
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
(2023)
Article
Mathematics
Laura Carini, Max Jensen, Robert Nurnberg
Summary: We propose a deep learning method for solving partial differential equations that arise as gradient flows. The method relies on the Brezis-Ekeland principle, which defines an objective function to be minimized and is well-suited for machine learning using deep neural networks. We describe the method in a general framework and demonstrate its application with an example implementation for the heat equation in dimensions two to seven.
ARCHIVUM MATHEMATICUM
(2023)
Article
Mathematics
Klaus Deckelnick, Robert Nuernberg
Summary: Based on a recent novel formulation of parametric anisotropic curve shortening flow, we analyze a fully discrete numerical method for this geometric evolution equation. The method utilizes piecewise linear finite elements in space and a backward Euler approximation in time. We establish the existence and uniqueness of a discrete solution, as well as an unconditional stability property. Numerical computations support the theoretical results and demonstrate the practicality of our method.
ARCHIVUM MATHEMATICUM
(2023)