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Borzi, A. (author), Wogrin, M. (author)Recent developments on multilevel schemes for open-loop optimal control problems with terminal observation governed by time-dependent reaction-diffusion systems are presented. The solution of optimality systems consisting of reaction-diffusion equations with opposite time orientation is discussed. Of particular importance in applications and for...conference paper 2006
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Müller, H. (author), Volkwein, S. (author)Proper orthogonal decomposition (POD) is a powerful technique for model reduction of linear and non-linear systems. It is based on a Galerkin type discretization with basis elements created from the system itself. In this work POD is used to derive low-order models for a so-called lambda-omega system that is a universal model to investigate two...conference paper 2006
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Hendriksen, W.E. (author)Living creatures exists for an important part out of soft material, such as skin, organs and cells, that are out-of-equilibrium formed by the self-assembly of molecular building blocks. Natural materials are continuously active with dynamic processes occurring, such as growth, shrinkage and transport mechanisms under the consumption of energy....doctoral thesis 2015
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Abdi, Bahareh (author)Atrial fibrillation (AF) is a common age-related cardiac arrhythmia. AF is characterized by rapid and irregular electrical activity of the heart leading to a higher risk of stroke and heart failure. During AF, the upper chambers of the heart, called atria, experience chaotic electrical wave propagation. However, despite the various mechanisms...doctoral thesis 2021
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Chen, J. (author)Cancer is known as one of the leading causes of death in the world with difficult<br/>diagnose at early stages, poor prognosis and high mortality. Animal-based<br/>experiments and clinical trials have always been the main approach for cancer<br/>research, albeit they may have limitations and ethical issues. Mathematicalmodeling<br/>as an...doctoral thesis 2020
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Lovrak, M. (author)Nature is full of life, which is driven by the numerous biochemical processes that occur in living organisms. Many motifs are universal regardless of species, such as enzymatic networks, self-assembly and reaction-diffusion. This work examines the development of novel soft functional materials via self-assembly and reaction-diffusion approaches....doctoral thesis 2018
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Rosso, M. (author), Van Steijn, V. (author), De Smet, L.C.P.M. (author), Sudhölter, E.J.R. (author), Kleijn, C.R. (author), Kreutzer, M.T. (author)A self-similar reaction front develops in reactive ion etching when the ions penetrate channels of shallow height h. This relates to the patterning of microchannels using a single-step etching and bonding, as described by Rhee et al. [Lab Chip 5, 102 (2005)] . Experimentally, we report that the front location scales as xf ? ht1/2 and the width...journal article 2011
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Bedeaux, D. (author), Ortiz de Zárate, J.M. (author), Pagonabarraga, I. (author), Sengers, J.V. (author), Kjelstrup, S. (author)In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature gradient, while still being far away from any...journal article 2011
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Würthner, Laeschkir (author), Brauns, Fridtjof (author), Pawlik, G. (author), Halatek, Jacob (author), Kerssemakers, J.W.J. (author), Dekker, C. (author), Frey, Erwin (author)Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological processes inherently involve multiple spatial and temporal scales and transition from one pattern to another...journal article 2022
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Zweifel, Lucian (author), Brauner, Christian (author), Teuwen, Julie J.E. (author), Dransfeld, C.A. (author)This study presents two novel methods for in situ characterization of the reaction-diffusion process during the co-curing of a polyetherimide thermoplastic interlayer with an epoxy-amine thermoset. The first method was based on hot stage experiments using a computer vision point tracker algorithm to detect and trace diffusion fronts, and the...journal article 2022
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Agresti, Antonio (author), Veraar, M.C. (author)In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases of nonlinear parabolic problems which are of quasi- or semilinear type. This first part is on local...journal article 2022
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Eichinger, Katharina (author), Gnann, M.V. (author), Kuehn, Christian (author)We investigate the stability of traveling-pulse solutions to the stochastic FitzHugh–Nagumo equations with additive noise. Special attention is given to the effect of small noise on the classical deterministically stable fast traveling pulse. Our method is based on adapting the velocity of the traveling wave by solving a scalar stochastic...journal article 2022
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Agresti, A. (author)This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion equations with mass control. It is known that strong solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an open question. Here we...journal article 2023
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Agresti, A. (author), Veraar, M.C. (author)In this paper we consider a class of stochastic reaction-diffusion equations. We provide local well-posedness, regularity, blow-up criteria and positivity of solutions. The key novelties of this work are related to the use transport noise, critical spaces and the proof of higher order regularity of solutions – even in case of non-smooth...journal article 2023
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Wang, Hucheng (author), Fu, Xiaoming (author), Gu, Guanyao (author), Bai, Shengyu (author), Li, Runlai (author), Zhong, Weimin (author), Guo, Xuhong (author), Eelkema, R. (author), van Esch, J.H. (author), Cao, Zhixing (author), Wang, Yiming (author)Living organisms are capable of dynamically changing their structures for adaptive functions through sophisticated reaction-diffusion processes. Here we show how active supramolecular hydrogels with programmable lifetimes and macroscopic structures can be created by relying on a simple reaction-diffusion strategy. Two hydrogel precursors ...journal article 2023
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Wu, F. (author), Halatek, Jacob (author), Reiter, Matthias (author), Kingma, Enzo (author), Frey, Erwin (author), Dekker, C. (author)Cells owe their internal organization to self-organized protein patterns, which originate and adapt to growth and external stimuli via a process that is as complex as it is little understood. Here, we study the emergence, stability, and state transitions of multistable Min protein oscillation patterns in live Escherichia coli bacteria during...journal article 2016
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Abdi, Bahareh (author), Hendriks, R.C. (author), van der Veen, A.J. (author), de Groot, Natasja M.S. (author)Finding the hidden parameters of the cardiac electrophysiological model would help to gain more insight on the mechanisms underlying atrial fibrillation, and subsequently, facilitate the diagnosis and treatment of the disease in later stages. In this work, we aim to estimate tissue conductivity from recorded electrograms as an indication of...journal article 2019
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Dang, Y. (author), Grundel, D.A.J. (author), Youk, H.O. (author)Cells form spatial patterns by coordinating their gene expressions. How a group of mesoscopic numbers (hundreds to thousands) of cells, without pre-existing morphogen gradients and spatial organization, self-organizes spatial patterns remains poorly understood. Of particular importance are dynamic spatial patterns such as spiral waves that...journal article 2020
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Daneshpour Aryadi, H. (author), Youk, H.O. (author)Communicating is crucial for cells to coordinate their behaviors. Immunological processes, involving diverse cytokines and cell types, are ideal for developing frameworks for modeling coordinated behaviors of cells. Here, we review recent studies that combine modeling and experiments to reveal how immune systems use autocrine, paracrine, and...review 2019