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
| 24.10.24 | Tomas Kasemets, Dr | |
Industry Talk on LADE | ||
| 14:30 Uhr s.t., Minkowski-Raum, 05-119, Staudingerweg 7 | ||
|
| 20.11.24 | Alexander 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 | ||
|
| 22.11.24 | Alina Chertock, Prof. Dr. | |
Many important scientific problems involve several sources of uncertainties, such as
model parameters and initial and boundary conditions. Quantifying these uncertainties
is essential for many applications since it helps to conduct sensitivity analysis and
provides guidance for improving the models. The design of reliable numerical methods
for models with uncertainties has seen a lot of activity lately. One of the most popular
methods is Monte Carlo-type simulations, which are generally good but inefficient due
to the large number of realizations required. In addition to Monte Carlo methods, a
widely used approach for solving partial differential equations with uncertainties is the
generalized polynomial chaos (gPC), where stochastic processes are represented in
terms of orthogonal polynomials series of random variables. It is well-known that gPC-
based methods, which are spectral-type methods, exhibit fast convergence when the
solution depends smoothly on random parameters. However, their application to
nonlinear systems of conservation/balance laws still encounters some significant
difficulties. The latter is related to the presence of discontinuities that may develop in
numerical solutions in finite time, triggering the appearance of aliasing errors and
Gibbs-type phenomena. This talk will provide an overview of numerical methods for
models with uncertainties and explore strategies to address the challenges
encountered when applying these methods to nonlinear hyperbolic systems of
conservation and balance laws. | ||
| 14:15 Uhr s.t., Hilbert room, 05-426, Staudingerweg 9 | ||
|
| 05.12.24 | Jürgen 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 | ||
|
zukünftige Termine
| 16.01.25 | Hendrik Ranocha, Prof. Dr. | |
Compressible computational fluid dynamics (CFD) is an active and
fruitful area of research. In this talk, we will focus on time
integration methods optimized for CFD applications. We will briefly
review the classical Courant-Friedrichs-Lewy (CFL) constraint and
present error-based time step size control as an alternative. In
particular, we will discuss how the design of the methods influences
their efficiency and robustness. Combining theoretical analysis with a
data-driven approach, we will present new optimized time integration
methods for compressible CFD applications that are available in
open-source software. | ||
| 14:30 Uhr s.t., Minkowski-Raum, 05-119, Staudingerweg 7, at Zoom | ||
|
| 30.01.25 | René 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 | ||
|
| 13.02.25 | Frauke 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 L. Stelzl | Lukas Stelzl |