arXiv subjects

Henning U. Voss

Publications and source records attributed to Henning U. Voss.

16 recordsLinked to original sources

arXiv2025

Quasilattices of the Spectre monotile

The Spectre is a family of recently discovered aperiodic monotiles that tile the plane only in non-periodic ways, and novel physical phenomena have been predicted for planar systems made of aperiodic monotiles. It is shown that point decorations of Tile(1,1), the base tile for all Spectres, supports the generation of a large variety of non-periodic quasilattices, in contrast to Bravais-lattices in which all point decorations would be periodic. A lattice generating function is introduced as a mapping from point decorations to quasilattice space, and investigated systematically. It is found that some lattices result from the properties of nearest-neighbor distances of point decorations, and that other lattices show near-periodicity in projections along one of the symmetry axes of the tiling. It is concluded that the lattice generating function can serve as a template for the design of physical potential landscapes that can be controlled by the point decoration as a parameter.

physics.gen-ph↗

arXiv2024

A tiling algorithm for the aperiodic monotile Tile(1,1)

An algorithm is provided to tile the plane with the aperiodic monotile Tile(1,1) recently discovered by Smith et al. (2023). Their geometric construction guidelines are expanded into a numerical MATLAB algorithm. The intention is to remove a possible obstacle for researchers interested in applications of this fundamental tiling of the plane.

math-ph↗

arXiv2024

Moiré patterns of space-filling curves

It is shown on the examples of Moore and Gosper curves that two spatially shifted or twisted, pre-asymptotic space-filling curves can produce large-scale superstructures akin to moiré patterns. To study physical phenomena emerging from these patterns, a geometrical coupling coefficient based on the Neumann integral is introduced. It is found that moiré patterns appear most defined at the peaks of those coefficients. A physical interpretation of these coefficients as a measure for inductive coupling between radiofrequency resonators leads to a design principle for strongly overlapping resonators with vanishing mutual inductance, which might be interesting for applications in MRI. These findings are demonstrated in graphical, numerical, and physical experiments.

physics.app-ph↗

arXiv2023

Real-time motion amplification on mobile devices

A simple motion amplification algorithm suitable for real-time applications on mobile devices, including smartphones, is presented. It is based on motion enhancement by moving average differencing (MEMAD), a temporal high-pass filter for video streams. MEMAD can amplify small moving objects or subtle motion in larger objects. It is computationally sufficiently simple to be implemented in real time on smartphones. In the specific implementation as an Android phone app, MEMAD is demonstrated on examples chosen such as to motivate applications in the engineering, biological, and medical sciences.

cs.GR↗

arXiv2022

The transient route to resonance

The periodically driven harmonic oscillator with damping is one of the most elementary and trusted models in physics and normally applied in its steady state, disregarding specific initial conditions and associated transients. For example, steady state solutions are already sufficient to describe resonance. In some applications transient solutions might play a role though, and a review of these might be useful. In order to characterize the transients of the harmonic oscillator, its winding number is graphed in dependence of initial conditions. These visualizations show a complexity of the transients of the harmonic oscillator that are not readily evident from the inspection of the model alone.

physics.class-ph↗

arXiv2020

Recovery of eigenvectors from eigenvalues in systems of coupled harmonic oscillators

The eigenvector-eigenvalue identity relates the eigenvectors of a Hermitian matrix to its eigenvalues and the eigenvalues of its principal submatrices in which the jth row and column have been removed. We show that one-dimensional arrays of coupled resonators, described by square matrices with real eigenvalues, provide simple physical systems where this formula can be applied in practice. The subsystems consist of arrays with the jth resonator removed, and thus can be realized physically. From their spectra alone, the oscillation modes of the full system can be obtained. This principle of successive single resonator deletions is demonstrated in two experiments of coupled radiofrequency resonator arrays with greater-than-nearest neighbor couplings, in which the spectra are measured with a network analyzer. Both the Hermitian as well as a non-Hermitian case are covered in the experiments. In both cases the experimental eigenvector estimates agree well with numerical simulations if certain consistency conditions imposed by system symmetries are taken into account. In the Hermitian case, these estimates are obtained from resonance spectra alone without knowledge of the system parameters. It remains an interesting problem of physical relevance to find conditions under which the full non-Hermitian eigenvector set can be obtained from the spectra alone.

quant-ph↗

arXiv2020

A Conjugate-Gradient Approach to the Parameter Estimation Problem of Magnetic Resonance Advection Imaging

We consider the inverse problem of estimating the spatially varying pulse wave velocity in blood vessels in the brain from dynamic MRI data, as it appears in the recently proposed imaging technique of Magnetic Resonance Advection Imaging (MRAI). The problem is formulated as a linear operator equation with a noisy operator and solved using a conjugate gradient type approach. Numerical examples on experimental data show the usefulness and advantages of the developed algorithm in comparison to previously proposed methods.

math.NA↗

arXiv2019

Machine Discovery of Partial Differential Equations from Spatiotemporal Data

The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which physical terms are necessary and which can be removed (because they are physically negligible in the sense that they do not affect the dynamics too much) from a pool of candidate functions. The method is built on the recent development of Sparse Bayesian Learning; which enforces the sparsity in the to-be-identified PDEs, and therefore can balance the model complexity and fitting error with theoretical guarantees. Without leveraging prior knowledge or assumptions in the discovery process, we use an automated approach to discover ten types of PDEs, including the famous Navier-Stokes and sine-Gordon equations, from simulation data alone. Moreover, we demonstrate our data-driven discovery process with the Complex Ginzburg-Landau Equation (CGLE) using data measured from a traveling-wave convection experiment. Our machine discovery approach presents solutions that has the potential to inspire, support and assist physicists for the establishment of physical laws from measured spatiotemporal data, especially in notorious fields that are often too complex to allow a straightforward establishment of physical law, such as biophysics, fluid dynamics, neuroscience or nonlinear optics.

stat.ML↗

arXiv2019

Topological modes in radiofrequency resonator arrays

Topological properties of solid states have sparked considerable recent interest due to their importance in the physics of lattices with a non-trivial basis and their potential in the design of novel materials. Here we describe an experimental and an accompanying numerical toolbox to create and analyze topological states in coupled radiofrequency resonator arrays. The arrays are coupled harmonic oscillator systems that are very easily constructed, offer a variety of geometric configurations, and whose eigenfunctions and eigenvalues are amenable to detailed analysis. These systems offer well defined analogs to coupled oscillator systems in general in that they are characterized by resonances whose frequency spectra depend on the individual resonators, the interactions between them, and the geometric and topological symmetries and boundary conditions. In particular, we describe an experimental analog of a small one-dimensional system, with excellent agreement with theory. The numerical part of the toolbox allows for simulations of larger mesoscopic systems with a semi-continuous band structure, in which all resonators still exhibit individual signatures. Systematic parameter variation yields an astonishing richness of band structures in this simple linear system, allowing for further explorations into novel phenomena of topological modes.

physics.app-ph↗

arXiv2018

Hypersampling of pseudo-periodic signals by analytic phase projection

A method to upsample insufficiently sampled experimental time series of pseudo-periodic signals is proposed. The result is an estimate of the pseudo-periodic cycle underlying the signal. This hypersampling requires a sufficiently sampled reference signal that defines the pseudo-periodic dynamics. The time series and reference signal are combined by projecting the time series values to the analytic phase of the reference signal. The resulting estimate of the pseudo-periodic cycle has a considerably higher effective sampling rate than the time series. The procedure is applied to time series of MRI images of the human brain. As a result, the effective sampling rate could be increased by three orders of magnitude. This allows for capturing the waveforms of the very fast cerebral pulse waves traversing the brain. Hypersampling is numerically compared to the more commonly used retrospective gating. An outlook regarding EEG and optical recordings of brain activity as the reference signal is provided.

physics.med-ph↗

arXiv2017

A universal negative group delay filter for the prediction of band-limited signals

A filter for universal real-time prediction of band-limited signals is presented. The filter consists of multiple time-delayed feedback terms in order to accomplish anticipatory coupling, which again leads to a negative group delay for frequencies in the baseband. The universality of the filter arises from its property that it does not rely on a specific model of the signal. Specifically, as long as the signal to be predicted is band-limited with a known cutoff frequency, the filter order, the only parameter of the filter, follows and the filter predicts the signal in real time up to a prediction horizon that depends on the cutoff frequency, too. It is worked out in detail how signal prediction arises from the negative group delay of the filter. Its properties, including stability, are investigated theoretically, by numerical simulations, and by application to a physiological signal. Possible control and signal processing applications of this filter are discussed.

cs.SD↗

arXiv2016

A simple predictor based on delay-induced negative group delay

A very simple linear signal predictor that uses past predicted values rather than past signal values for prediction is presented. Man-made or natural systems utilizing this predictor would not require a memory of input signal values but only of already predicted, internalized states. This delay-induced negative group delay (DINGD) predictor affords real-time prediction of signals without the need for a specific signal model. Its properties are derived analytically and are numerically tested on various types of broadband input data.

physics.data-an↗

arXiv2016

The leaky integrator with recurrent inhibition as a predictor

It is shown that the leaky integrator, the basis for many neuronal models, possesses a negative group delay when a time-delayed recurrent inhibition is added to it. By means of this negative group delay, the leaky integrator becomes a predictor for some frequency components of the input signal. The prediction properties are derived analytically and an application to a local field potential is provided.

q-bio.NC↗

arXiv2016

A negative group delay model for feedback-delayed manual tracking

We propose that feedback-delayed manual tracking performance is limited by fundamental constraints imposed by the physics of negative group delay. To test this hypothesis, the results of an experiment in which subjects demonstrate both reactive and predictive dynamics are modeled by a linear system with delay-induced negative group delay. Although one of the simplest real-time predictors conceivable, this model explains key components of experimental observations. Most notably, it explains the observation that prediction time linearly increases with feedback delay, up to a certain point when tracking performance deteriorates. It also explains the transition from reactive to predictive behavior with increasing feedback delay. The model contains only one free parameter, the feedback gain, which has been fixed by comparison with one set of experimental observations for the reactive case. Our model provides quantitative predictions that can be tested in further experiments.

nlin.AO↗

arXiv2015

Signal prediction by anticipatory relaxation dynamics

Real-time prediction of signals is a task often encountered in control problems as well as by living systems. Here a model-free prediction approach based on the coupling of a linear relaxation-delay system to a smooth, stationary signal is described. The resulting anticipatory relaxation dynamics (ARD) is a frequency-dependent predictor of future signal values. ARD not only approximately predicts signals on average but can anticipate the occurrence of signal peaks, too. This can be explained by recognizing ARD as an input/output system with negative group delay. It is completely characterized, including its prediction horizon, by its analytically given frequency response function.

nlin.AO↗

arXiv2009

Classical Mobius-Ring Resonators Exhibit Fermion-Boson Rotational Symmetry

The behavior of coupled harmonic oscillators in systems with specified boundary conditions is typically characterized by resonances whose frequency spectra represent harmonics according to properties of the individual oscillators, the interactions between them, and the overall symmetry of the system. Here it is demonstrated that classical one- and two-dimensional radiofrequency resonators constrained to a Mobius topology are the formal partners of cylindrical ring resonators, and specifically give rise to half-integral harmonic excitations that are orthogonal to the integral excitations of a ring. In particular, the half-integral harmonics are formally invariant under rotations at a minimum of 4pi rather than 2pi radians, in analogy to the rotational symmetry of fermions in quantum mechanics. The results offer a pathway for discovery in other physical systems as well as the design of novel materials and electronic instrumentation.

physics.class-ph↗