arXiv subjects

Andreas Rätz

Publications and source records attributed to Andreas Rätz.

6 recordsLinked to original sources

arXiv2026

A Class AAA Solar Testbed for Reproducible Long-Term Characterization of Energy-Harvesting Systems

Energy harvesting promises maintenance-free operation of wireless sensor nodes but introduces strong dependencies on stochastic and deployment-specific environmental conditions. In particular, solar-powered systems are highly sensitive to variations in irradiance and spectral composition, which complicates system-level design, parameter tuning, and reliable verification. This work presents a solar testbed in which active control via Hardware-in-the-Loop (HIL) enables stable and repeatable illumination conditions for evaluating ultra-low-power energy harvesting systems. The proposed LED-based solar testbed provides spectrally configurable illumination over a wide dynamic range, from 5.7 mW/m2 to 908 kW/m2. It achieves Class AAA performance according to IEC 60904-9, with a spectral match below 1.3% and a spatial non-uniformity below 1.28% over a 16.5 cm x 16.5 cm test area. The long-term irradiance instability remains below 0.6%. Closed-loop control using integrated illuminance and spectral sensors ensures high temporal stability, while a temperature-controlled DUT stage supports long-term experiments. Experimental results demonstrate high repeatability and suitability for systematic laboratory characterization of solar energy harvesting systems.

eess.SY↗

arXiv2019

A new Diffuse-interface approximation of the Willmore flow

Standard diffuse approximations of the Willmore flow often lead to intersecting phase boundaries that in many cases do not correspond to the intended sharp interface evolution. Here we introduce a new two-variable diffuse approximation that includes a rather simple but efficient penalization of the deviation from a quasi-one dimensional structure of the phase fields. We justify the approximation property by a Gamma convergence result for the energies and a matched asymptotic expansion for the flow. Ground states of the energy are shown to be one-dimensional, in contrast to the presence of saddle solutions for the usual diffuse approximation. Finally we present numerical simulations that illustrate the approximation property and apply our new approach to problems where the usual approach leads to an undesired behavior.

math.AP↗

arXiv2015

A coupled surface-Cahn--Hilliard bulk-diffusion system modeling lipid raft formation in cell membranes

We propose and investigate a model for lipid raft formation and dynamics in biological membranes. The model describes the lipid composition of the membrane and an interaction with cholesterol. To account for cholesterol exchange between cytosol and cell membrane we couple a bulk-diffusion to an evolution equation on the membrane. The latter describes a relaxation dynamics for an energy taking lipid-phase separation and lipid-cholesterol interaction energy into account. It takes the form of an (extended) Cahn--Hilliard equation. Different laws for the exchange term represent equilibrium and non-equilibrium models. We present a thermodynamic justification, analyze the respective qualitative behavior and derive asymptotic reductions of the model. In particular we present a formal asymptotic expansion near the sharp interface limit, where the membrane is separated into two pure phases of saturated and unsaturated lipids, respectively. Finally we perform numerical simulations and investigate the long-time behavior of the model and its parameter dependence. Both the mathematical analysis and the numerical simulations show the emergence of raft-like structures in the non-equilibrium case whereas in the equilibrium case only macrodomains survive in the long-time evolution.

math.AP↗

arXiv2013

Symmetry breaking in a bulk-surface reaction-diffusion model for signaling networks

Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and a flux term in the membrane equations. A specific model of this form was recently proposed by the authors for the GTPase cycle in cells. We investigate here a putative role of diffusive instabilities in cell polarization. By a linearized stability analysis we identify two different mechanisms. The first resembles a classical Turing instability for the membrane subsystem and requires (unrealistically) large differences in the lateral diffusion of activator and substrate. The second possibility on the other hand is induced by the difference in cytosolic and lateral diffusion and appears much more realistic. We complement our theoretical analysis by numerical simulations that confirm the new stability mechanism and allow to investigate the evolution beyond the regime where the linearization applies.

math.AP↗

arXiv2013

Colliding Interfaces in Old and New Diffuse-interface Approximations of Willmore-flow

This paper is concerned with diffuse-interface approximations of the Willmore flow. We first present numerical results of standard diffuse-interface models for colliding one dimensional interfaces. In such a scenario evolutions towards interfaces with corners can occur that do not necessarily describe the adequate sharp-interface dynamics. We therefore propose and investigate alternative diffuse-interface approximations that lead to a different and more regular behavior if interfaces collide. These dynamics are derived from approximate energies that converge to the $L^1$-lower-semicontinuous envelope of the Willmore energy, which is in general not true for the more standard Willmore approximation.

math.AP↗

arXiv2011

Turing instabilities in a mathematical model for signaling networks

GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell polarity. As feedback loops contribute to the GTPase cycle and as the coupling between membrane-bound and cytoplasmic processes introduces different diffusion coefficients a Turing mechanism is a natural candidate for this symmetry breaking. We formulate a mathematical model that couples a reaction-diffusion system in the inner volume to a reaction-diffusion system on the membrane via a flux condition and an attachment/detachment law at the membrane. We present a reduction to a simpler non-local reaction-diffusion model and perform a stability analysis and numerical simulations for this reduction. Our model in principle does support Turing instabilities but only if the lateral diffusion of inactivated GTPase is much faster than the diffusion of activated GTPase.

math.AP↗