Seminar über Theorie der Kondensierten Materie/ Weiche Materie und Statistische Physik

Programm für das Wintersemester 2024/2025

Thursdays, 14:30 Uhr s.t.

F. Schmid / G. Settanni / P. Virnau / L. Stelzl
Minkowski-Raum, 05-119, Staudingerweg 7

24.10.24Tomas Kasemets, Dr
Industry Talk on LADE
14:30 Uhr s.t., Minkowski-Raum, 05-119, Staudingerweg 7

zukünftige Termine
20.11.24Alexander Kurganov, Prof. Dr.
I will present semi-discrete path-conservative central-upwind (PCCU) schemes for ideal and shallow water magnetohydrodynamics (MHD) equations. These schemes possess several important properties: they locally preserve the divergence-free constraint, they do not rely on any (approximate) Riemann problem solver, and they robustly producehigh-resolution and non- oscillatory results. The derivation of the schemes is based on the Godunov-Powell nonconservative modifications of the studied MHD systems. The local divergence-free property is enforced by augmenting the modified systems with the evolution equations for the corresponding derivatives of the magnetic field components. These derivatives are then used to design a special piecewise linear reconstruction of the magnetic field, which guarantees a non- oscillatory nature of the resulting scheme. In addition, the proposed PCCU discretization accounts for the jump of the nonconservative product terms across cell interfaces, thereby ensuring stability. I will also discuss the extension of the proposed schemes to magnetic rotating shallow water equations. The new scheme is both well-balanced and exactly preserves the divergence- free condition of the magnetic field. The well-balanced property is enforced by applying a flux globalization approach within the PCCU scheme. As a result, both still- and moving- water equilibria can be exactly preserved at the discrete level. The proposed PCCU schemes are tested on several benchmarks. The obtained numerical results illustrate the performance of the new schemes, their robustness, and their ability not only to achieve high resolution, but also preserve the positivity of computed quantities such as density, pressure, and water depth. The talk is based on joint works with Alina Chertock (North Carolina State University, USA), Michael Redle (RWTH Aachen University, Germany),Kailiang Wu (Southern University of Science and Technology, China) and Vladimir Zeitlin (Sorbonne University, France).
10:15 Uhr s.t., Hilbert-Raum, 05-426, Staudingerweg 9

05.12.24Jürgen Horbach, Prof. Dr.
We consider a class of non-standard, two-dimensional (2D) Hamiltonian models that may show features of active particle dynamics, and therefore, we refer to these models as active Hamiltonian (AH) systems. The idea is to consider a spin fluid where -- on top of spin-spin and particle-particle interactions -- spins are coupled to the particle's velocities via a vector potential. Continuous spin variables interact with each other as in a standard $XY$ model. Typically, the AH models exhibit non-standard thermodynamic properties (e.g.~for temperature and pressure) and equations of motion with non-standard forces. This implies that the derivation of symplectic algorithms to numerically solve Hamilton's equations of motion, as well as the thermostatting for these systems, is not straightforward. However, one can make use of the fact that for Hamiltonian systems the equipartition theorem holds, providing a clear definition of temperature (note, however, that the temperature is not given by the average kinetic energy in this case) [1]. We derive a symplectic integration scheme and propose a Nos\'e-Poincar\'e thermostat, providing a correct sampling in the canonical ensemble [2]. Results for two different AH models are presented: (i) A model proposed by Casiulis et al. [3] shows transition from a fluid at high temperature to a cluster phase at low temperature where, due to the coupling of velocities and spins, a center-of-mass motion of the cluster occurs. The claim in Ref. [3] that this cluster motion is reminiscent of real flocks of birds has been challenged by Cavagna et al. [4]. (ii) We propose an AH model where spins and velocities are coupled such that as a result particles feel a generalized Lorentz force. We show that our model leads to a collective motion of particle clusters that is closer to the behavior of flocks of birds. [1] K. Huang, Statistical Mechanics (John Wiley \& Sons, New York, 1987). [2] A. Bhattacharya, J. Horbach, and S. Karmakar, arXiv:2409.14864 (2024). [3] M. Casiulis, M. Tarzia, L. F. Cugliandolo, and O. Dauchot, Phys. Rev. Lett. {\bf 124}, 198001 (2020). [4] A. Cavagna, I. Giardina, and M. Viale, arXiv:1912.07056 (2019).
14:30 Uhr s.t., Minkowski-Raum, 05-119, Staudingerweg 7, at Zoom

16.01.25Hendrik Ranocha, Prof. Dr.
tba
14:30 Uhr s.t., Minkowski-Raum, 05-119, Staudingerweg 7, at Zoom

30.01.25René van Roij, Prof. Dr.
Title: Circuits of Microfluidic Memristors: Computing with Aqueous Electrolytes Speaker: René van Roij, Institute for Theoretical Physics, Utrecht University, The Netherlands Abstract: In this online talk we will discuss recent advances in our understanding of the physics of cone-shaped microfluidic channels under static and pulsatile voltage- and pressure drops. On the basis of Poisson-Nernst-Planck-Stokes equations for transport of aqueous electrolytes through channels carrying a surface charge, we will provide a theoretical explanation for the experimentally observed diode-like current rectification of these channels. At steady electric driving this rectification involves salt depletion or accumulation in the channel depending on the sign of the applied voltage [1], and this effect also explains the observed pressure-sensitivity of the electric conductance. An extension towards an applied AC voltage predicts these channels to be tunable between diodes at low frequencies ωτ<<1, memristors (resistors with memory) at intermediate frequencies ωτ ~ 1, and Ohmic resistors at high frequency ωτ>>1 , with a characteristic (memory retention) time τ proportional to the square of the channel length [2]. We predict that Hodgkin- Huxley-inspired iontronic circuits of short (fast) and long (slow) conical channels yield neuromorphic responses akin to (trains of) action potentials [2] and several other neuronic spiking modes [3]. Next, we show theoretically and experimentally that a tapered microfluidic channel filled with an aqueous nearly close-packed dispersion of colloidal charged spheres is a much stronger memristor than the channel with only surface charges on the channel wall [4]. Upon applying a train of four positive (negative) voltage pulses, each pulse representing a binary “1” (“0”), we map the hexadecimal number represented by this train on an analog channel conductance, which offers opportunities for reservoir computing -we give a proof of principle for the case of recognizing hand-written digits [4]. Finally we will also discuss recent and ongoing work on iontronic information processing. We exploit the mobility of the medium (water) by considering simultaneously applied pulsatile pressure and voltage signals to increase the bandwidth [5]. Finally, the versatile ionic nature of the charge carriers allows for Langmuir-like ionic exchange reaction kinetics on the channel surface [6]. We show that this can give rise to direct iontronic analogues of synaptic long-term potentiation and coincidence detection of electric and chemical signals [7], which are both ingredients for brain-like (Hebbian) learning. References: [1] W.Q. Boon, T. Veenstra, M. Dijkstra, and R. van Roij, Pressure-sensitive ion conduction in a conical channel: optimal pressure and geometry, Physics of Fluids 34, 101701 (2022). [2] T.M. Kamsma, W.Q. Boon, T. ter Rele, C. Spitoni, and R. van Roij, Iontronic Neuromorphic Signaling with Conical Microfluidic Memristors, Phys. Rev. Lett. 130, 268401 (2023). [3] T.M Kamsma, E. A. Rossing, C. Spitoni, and R. van Roij, Advanced iontronic spiking modes with multiscale diffusive dynamics in a fluidic circuit, Neuromorph. Comput. Eng. 4 024003 (2024). [4] T.M. Kamsma, J. Kim, K. Kim, W.Q. Boon, C. Spitoni, J. Park, and R. van Roij, Brain-inspired computing with fluidic iontronic nanochannels, PNAS 121, e23202242121 (2024). [5] A. Barnaveli, T.M. Kamsma, W.Q. Boon, and R. van Roij, Pressure-gated microfluidic memristor for pulsatile information processing, arXiv:2404.15006. [6] W.Q. Boon. M. Dijkstra, and R. van Roij, Coulombic Surface-Ion Interactions Induce Nonlinear and Chemistry-Specific Charging Kinetics, Phys. Rev. Lett. 130, 058001 (2023). [7] T.M. Kamsma, M. Klop, W.Q. Boon, C. Spitoni, and R. van Roij, arXiv:2406.03195
14:30 Uhr s.t., Minkowski-Raum, 05-119, Staudingerweg 7, at Zoom

13.02.25Frauke Gräter, Prof. Dr.
Enhancing scale-bridging simulations by machine learning – or substituting them altogether?
14:30 Uhr s.t., Minkowski-Raum, 05-119, Staudingerweg 7, at Zoom

Koordination: Kontakt:

F. Schmid
friederike.schmid@uni-mainz.de

P. Virnau
virnau@uni-mainz.de

L. Stelzl
lstelzl@uni-mainz.de

Lukas Stelzl
lstelzl@uni-mainz.de