arXiv subjects

Christian Müller

Publications and source records attributed to Christian Müller.

At least 19 recordsLinked to original sources

arXiv2025

Stressability of Semi-Discrete Frameworks

In this paper we study the stressability of semi-discrete frameworks in the plane which are generated by a discrete sequence of smooth curves. We characterize their stressability property by the existence of stresses fulfilling certain difference-differential equation. In particular, we define a semi-discrete height function which we use to generate liftings. Furthermore, we show a semi-discrete analogue of the Maxwell-Cremona lifting property which implies that the stressable semi-discrete frameworks in the plane are precisely the orthogonal projections of semi-discrete conjugate surfaces in 3-space. Finally, we discuss geometric implications for frameworks with vanishing boundary forces and characterize the liftability of frameworks which only consist of two neighboring curves forming one strip.

math.MG↗

arXiv2025

Isometric Surfaces in Isotropic 3-Space

While the notion of isometric deformations of surfaces is straightforward for surfaces with Euclidean metric, a corresponding notion in isotropic space has been missing. By making Gauss' Theorema Egregium a necessary condition we develop a sensible notion of isometric surfaces in isotropic space. The well-known examples in Euclidean space, like isometries within the associated family of minimal surfaces, Bour's theorem, and Minding isometries, find their natural analogues in isotropic space. We also include an extensive treatment of infinitesimal flexibility, or infinitesimal deformation, of surfaces. We prove results for the isotropic displacement diagrams in analogy to its well-known counterparts in Euclidean space culminating in the existence of an isotropic Darboux wreath consisting of six surfaces. We show several interesting relations for special parametrizations involving Koenigs and Voss nets of smooth and discrete surfaces within the Darboux wreath and we encounter surfaces of constant Gaussian and mean curvature. At several occasions, we point to connections to statics as the isotropic space is a natural language to describe the Airy stress function.

math.DG↗

arXiv2025

Probing Glass Formation in Perylene Derivatives via Atomic Scale Simulations and Bayesian Regression

While the structural dynamics of chromophores are of interest for a range of applications, it is experimentally very challenging to resolve the underlying microscopic mechanisms. Glassy dynamics are also challenging for atomistic simulations due to the underlying dramatic slowdown over many orders of magnitude. Here, we address this issue by combining atomic scale simulations with autocorrelation function analysis and Bayesian regression, and apply this approach to a set of perylene derivatives as prototypical chromophores. The predicted glass transition temperatures and kinetic fragilities are in semi-quantitative agreement with experimental data. By analyzing the underlying dynamics via the normal vector autocorrelation function, we are able to connect the beta and alpha-relaxation processes in these materials to caged (or librational) dynamics and cooperative rotations of the molecules, respectively. The workflow presented in this work serves as a stepping stone toward understanding glassy dynamics in many-component mixtures of perylene derivatives and is readily extendable to other systems of chromophores.

cond-mat.mtrl-sci↗

arXiv2024

Discrete Lorentz surfaces and s-embeddings II: maximal surfaces

S-embeddings were introduced by Chelkak as a tool to study the conformal invariance of the thermodynamic limit of the Ising model. Moreover, Chelkak, Laslier and Russkikh introduced a lift of s-embeddings to Lorentz space, and showed that in the limit the lift converges to a maximal surface. They posed the question whether there are s-embeddings that lift to maximal surfaces already at the discrete level, before taking the limit. We answer this question in the positive. In a previous paper we identified a subclass of s-embeddings--isothermic s-embeddings--that lift to (discrete) S-isothermic surfaces, which were introduced by Bobenko and Pinkall as a discretization of isothermic surfaces. In this paper we identify a special class of isothermic s-embeddings that correspond to discrete S-maximal surfaces, translating an approach of Bobenko, Hoffmann and Springborn introduced for discrete S-minimal surfaces in Euclidean space. Additionally, each S-maximal surface comes with a 1-parameter family of associated surfaces that are isometric. This enables us to obtain an associated family of s-embeddings for each maximal s-embedding. We show that the Ising weights are constant in the associated family.

math.DG↗

arXiv2024

Klein-Arnold tensegrities

In this paper, we introduce new classes of infinite and combinatorially periodic tensegrities, derived from algebraic multidimensional continued fractions in the sense of F. Klein. We describe the stress coefficients on edges through integer invariants of these continued fractions, as initiated by V.I. Arnold, thereby creating a novel connection between geometric rigidity theory and the geometry of continued fractions. Remarkably, the new classes of tensegrities possess rational self-stress coefficients. To establish the self-stressability of the frameworks, we present a projective version of the classical Maxwell-Cremona lifting principle, a result of independent interest.

math.CO↗

arXiv2024

Discrete Lorentz surfaces and s-embeddings I: isothermic surfaces

S-embeddings were introduced by Chelkak as a tool to study the conformal invariance of the thermodynamic limit of the Ising model. Moreover, Chelkak, Laslier and Russkikh introduced a lift of s-embeddings to Lorentz space, and showed that in the limit the lift converges to a maximal surface. They posed the question whether there are s-embeddings that lift to maximal surfaces already at the discrete level, before taking the limit. This paper is the first in a two paper series, in which we answer that question in the positive. In this paper we introduce a correspondence between s-embeddings (incircular nets) and congruences of touching Lorentz spheres. This geometric interpretation of s-embeddings enables us to apply the tools of discrete differential geometry. We identify a subclass of s-embeddings -- isothermic s-embeddings -- that lift to (discrete) S-isothermic surfaces, which were introduced by Bobenko and Pinkall. S-isothermic surfaces are the key component that will allow us to obtain discrete maximal surfaces in the follow-up paper. Moreover, we show here that the Ising weights of an isothermic s-embedding are in a subvariety.

math.DG↗

arXiv2024

Reliable Student: Addressing Noise in Semi-Supervised 3D Object Detection

Semi-supervised 3D object detection can benefit from the promising pseudo-labeling technique when labeled data is limited. However, recent approaches have overlooked the impact of noisy pseudo-labels during training, despite efforts to enhance pseudo-label quality through confidence-based filtering. In this paper, we examine the impact of noisy pseudo-labels on IoU-based target assignment and propose the Reliable Student framework, which incorporates two complementary approaches to mitigate errors. First, it involves a class-aware target assignment strategy that reduces false negative assignments in difficult classes. Second, it includes a reliability weighting strategy that suppresses false positive assignment errors while also addressing remaining false negatives from the first step. The reliability weights are determined by querying the teacher network for confidence scores of the student-generated proposals. Our work surpasses the previous state-of-the-art on KITTI 3D object detection benchmark on point clouds in the semi-supervised setting. On 1% labeled data, our approach achieves a 6.2% AP improvement for the pedestrian class, despite having only 37 labeled samples available. The improvements become significant for the 2% setting, achieving 6.0% AP and 5.7% AP improvements for the pedestrian and cyclist classes, respectively.

cs.CV↗

arXiv2023

A differential approach to Maxwell-Cremona liftings

In 1864, J. C. Maxwell introduced a link between self-stressed frameworks in the plane and piecewise linear liftings to 3-space. This connection has found numerous applications in areas such as discrete geometry, control theory and structural engineering. While there are some generalisations of this theory to liftings of $d$-complexes in $d$-space, extensions for liftings of frameworks in $d$-space for $d\geq 3$ have been missing. In this paper, we introduce and study differential liftings on general graphs using differential forms associated with the elements of the homotopy groups of the complements to the frameworks. Such liftings play the role of integrands for the classical notion of liftings for planar frameworks. We show that these differential liftings have a natural extension to self-stressed frameworks in higher dimensions. As a result we generalise the notion of classical liftings to both graphs and multidimensional $k$-complexes in $d$-space ($k=2,\ldots, d$). Finally we discuss a natural representation of generalised liftings as real-valued functions on Grassmannians.

math.MG↗

arXiv2023

Significance of Elastic Coupling for Stresses and Leakage in Frictional Contacts

We study how the commonly neglected coupling of normal and in-plane elastic response affects tribological properties when Hertzian or randomly rough indenters slide past an elastic body. Compressibility-induced coupling is found to substantially increase maximum tensile stresses, which cause materials to fail, and to decrease friction such that Amontons law is violated macroscopically even when it holds microscopically. Confinement-induced coupling increases friction and enlarges domains of high tension. Moreover, both types of coupling affect the gap topography and thereby leakage. Thus, coupling can be much more than a minor perturbation of a mechanical contact.

cond-mat.soft↗

arXiv2023

Revealing the co-action of viscous and multistability hysteresis in an adhesive, nominally flat punch: A combined numerical and experimental study

Viscoelasticity is well known to cause significant hysteresis of crack closure and opening when an elastomer is brought in and out of contact with a flat, rigid, adhesive counterface. A separate origin of adhesive hysteresis is small-scale, elastic multistability. Here, we study a system in which both mechanisms act concurrently. Specifically, we compare the simulated and experimentally measured time evolution of the interfacial force and the real contact area between a soft elastomer and a rigid, flat punch, to which small-scale, single-sinusoidal roughness is added. To this end, we further the Green's function molecular dynamics method and extend recently developed imaging techniques to elucidate the rate- and preload-dependence of the pull-off process. Our results reveal that hysteresis is much enhanced when the saddle points of the topography come into contact, which, however, is impeded by viscoelastic forces and may require sufficiently large preloads. A similar coaction of viscous- and multistability effects is expected to occur in macroscopic polymer contacts and to be relevant, e.g., for pressure-sensitive adhesives and modern adhesive gripping devices.

cond-mat.soft↗

arXiv2022

Charge transport in doped conjugated polymers for organic thermoelectrics

Research on conjugated polymers for thermoelectric applications has made tremendous progress in recent years, which is accompanied by surging interest in molecular doping as a means to achieve the high electrical conductivities that are required. A detailed understanding of the complex relationship between the doping process, the structural as well as energetic properties of the polymer films, and the resulting thermoelectric behavior is slowly emerging. This review summarizes recent developments and strategies that permit enhancing the electrical conductivity of p- and n-type conjugated polymers via molecular doping. The impact of the chemical design of both the polymer and the dopant, the processing conditions, and the resulting nanostructure on the doping efficiency and stability of the doped state are discussed. Attention is paid to the interdependence of the electrical and thermal transport characteristics of semiconductor host-dopant systems and the Seebeck coefficient. Strategies that permit to improve the thermoelectric performance, such as an uniaxial alignment of the polymer backbone in both bulk and thin film geometries, manipulation of the dielectric constant of the polymer, and the variation of the dopant size, are explored. A combination of theory and experiment is predicted to yield new chemical design principles and processing schemes that will ultimately give rise to the next generation of organic thermoelectric materials.

physics.chem-ph↗

arXiv2021

CamLessMonoDepth: Monocular Depth Estimation with Unknown Camera Parameters

Perceiving 3D information is of paramount importance in many applications of computer vision. Recent advances in monocular depth estimation have shown that gaining such knowledge from a single camera input is possible by training deep neural networks to predict inverse depth and pose, without the necessity of ground truth data. The majority of such approaches, however, require camera parameters to be fed explicitly during training. As a result, image sequences from wild cannot be used during training. While there exist methods which also predict camera intrinsics, their performance is not on par with novel methods taking camera parameters as input. In this work, we propose a method for implicit estimation of pinhole camera intrinsics along with depth and pose, by learning from monocular image sequences alone. In addition, by utilizing efficient sub-pixel convolutions, we show that high fidelity depth estimates can be obtained. We also embed pixel-wise uncertainty estimation into the framework, to emphasize the possible applicability of this work in practical domain. Finally, we demonstrate the possibility of accurate prediction of depth information without prior knowledge of camera intrinsics, while outperforming the existing state-of-the-art approaches on KITTI benchmark.

cs.CV↗

arXiv2021

Low-power/high-gain flexible complementary circuits based on printed organic electrochemical transistors

The ability to accurately extract low-amplitude voltage signals is crucial in several fields, ranging from single-use diagnostics and medical technology to robotics and the Internet of Things. The organic electrochemical transistor, which features large transconductance values at low operation voltages, is ideal for monitoring small signals. Its large transconductance translates small gate voltage variations into significant changes in the drain current. However, a current-to-voltage conversion is further needed to allow proper data acquisition and signal processing. Low power consumption, high amplification, and manufacturability on flexible and low-cost carriers are also crucial and highly anticipated for targeted applications. Here, we report low-power and high-gain flexible circuits based on printed complementary organic electrochemical transistors (OECTs). We leverage the low threshold voltage of both p-type and n-type enhancement-mode OECTs to develop complementary voltage amplifiers that can sense voltages as low as 100 $μ$V, with gains of 30.4 dB and at a power consumption < 2.7 $μ$W (single-stage amplifier). At the optimal operating conditions, the voltage gain normalized to power consumption reaches 169 dB/$μ$W, which is > 50 times larger than state-of-the-art OECT-based amplifiers. In a two-stage configuration, the complementary voltage amplifiers reach a DC voltage gain of 193 V/V, which is the highest among emerging CMOS-like technologies operating at supply voltages below 1 volt. Our findings demonstrate that flexible complementary circuits based on printed OECTs define a power-efficient platform for sensing and amplifying low-amplitude voltage signals in several emerging beyond-silicon applications.

cond-mat.mtrl-sci↗

arXiv2021

Bots Don't Mind Waiting, Do They? Comparing the Interaction With Automatically and Manually Created Pull Requests

As a maintainer of an open source software project, you are usually happy about contributions in the form of pull requests that bring the project a step forward. Past studies have shown that when reviewing a pull request, not only its content is taken into account, but also, for example, the social characteristics of the contributor. Whether a contribution is accepted and how long this takes therefore depends not only on the content of the contribution. What we only have indications for so far, however, is that pull requests from bots may be prioritized lower, even if the bots are explicitly deployed by the development team and are considered useful. One goal of the bot research and development community is to design helpful bots to effectively support software development in a variety of ways. To get closer to this goal, in this GitHub mining study, we examine the measurable differences in how maintainers interact with manually created pull requests from humans compared to those created automatically by bots. About one third of all pull requests on GitHub currently come from bots. While pull requests from humans are accepted and merged in 72.53% of all cases, this applies to only 37.38% of bot pull requests. Furthermore, it takes significantly longer for a bot pull request to be interacted with and for it to be merged, even though they contain fewer changes on average than human pull requests. These results suggest that bots have yet to realize their full potential.

cs.SE↗

arXiv2021

High thermoelectric power factor of poly(3-hexylthiophene) through in-plane alignment and doping with a molybdenum dithiolene complex

Here we report a record thermoelectric power factor of up to 160 $μ$ W m-1 K-2 for the conjugated polymer poly(3-hexylthiophene) (P3HT). This result is achieved through the combination of high-temperature rubbing of thin films together with the use of a large molybdenum dithiolene p-dopant with a high electron affinity. Comparison of the UV-vis-NIR spectra of the chemically doped samples to electrochemically oxidized material reveals an oxidation level of 10%, i.e. one polaron for every 10 repeat units. The high power factor arises due to an increase in the charge-carrier mobility and hence electrical conductivity along the rubbing direction. We conclude that P3HT, with its facile synthesis and outstanding processability, should not be ruled out as a potential thermoelectric material.

physics.app-ph↗

arXiv2021

Geometric criteria for realizability of tensegrities in higher dimensions

In this paper we study a classical Maxwell question on the existence of self-stresses for frameworks, which are called tensegrities. We give a complete answer on geometric conditions of at most $(d+1)$-valent tensegrities in $\mathbb{R}^d$ both in terms of discrete multiplicative 1-forms and in terms of "meet" and "join" operations in the Grassmann-Cayley algebra.

math.CO↗

arXiv2020

Equilibrium stressability of multidimensional frameworks

We prove an equilibrium stressability criterium for trivalent multidimensional tensegrities. The criterium appears in different languages: (1) in terms of stress monodromies, (2) in terms of surgeries, (3) in terms of exact discrete 1-forms, and (4) in Cayley algebra terms.

math.MG↗

arXiv2020

Discrete Curvature and Torsion from Cross-Ratios

Motivated by a Möbius invariant subdivision scheme for polygons, we study a curvature notion for discrete curves where the cross-ratio plays an important role in all our key definitions. Using a particular Möbius invariant point-insertion-rule, comparable to the classical four-point-scheme, we construct circles along discrete curves. Asymptotic analysis shows that these circles defined on a sampled curve converge to the smooth curvature circles as the sampling density increases. We express our discrete torsion for space curves, which is not a Möbius invariant notion, using the cross-ratio and show its asymptotic behavior in analogy to the curvature.

math.DG↗