Non-constant Coupling Research Articles

Cosmological fluids with boundary term couplings

Cosmological models can be studied effectively using dynamical systems techniques. Starting from Brown’s formulation of the variational principle for relativistic fluids, we introduce new types of couplings involving a perfect fluid, a scalar field, and boundary terms. We describe three different coupling models, one of which turns out to be particularly relevant for cosmology. Its behaviour is similar to that of models in which dark matter decays into dark energy. In particular, for a constant coupling, the model mimics well-known dynamical dark energy models while the non-constant couplings offer a rich dynamical structure, unseen before. We are able to achieve this richness whilst working in a two-dimensional phase space. This is a significant advantage which allows us to provide a clear physical interpretation of the key features and draw analogies with previously studied models.

Normalized solutions to a Schrödinger–Bopp–Podolsky system under Neumann boundary conditions

In this paper, we study a Schrödinger–Bopp–Podolsky (SBP) system of partial differential equations in a bounded and smooth domain of [Formula: see text] with a nonconstant coupling factor. Under a compatibility condition on the boundary data we deduce existence of solutions by means of the Ljusternik–Schnirelmann theory.

Surface operators in the 6d N = (2, 0) theory

The 6d theory has natural surface operator observables, which are akin in many ways to Wilson loops in gauge theories. We propose a definition of a ‘locally BPS’ surface operator and study its conformal anomalies, the analog of the conformal dimension of local operators. We study the abelian theory and the holographic dual of the large N theory refining previously used techniques. Introducing non-constant couplings to the scalar fields allows for an extra anomaly coefficient, which we find in both cases to be related to one of the geometrical anomaly coefficients, suggesting a general relation due to supersymmetry. We also comment on surfaces with conical singularities.

Improved physiological noise regression in fNIRS: A multimodal extension of the General Linear Model using temporally embedded Canonical Correlation Analysis

For the robust estimation of evoked brain activity from functional Near-Infrared Spectroscopy (fNIRS) signals, it is crucial to reduce nuisance signals from systemic physiology and motion. The current best practice incorporates short-separation (SS) fNIRS measurements as regressors in a General Linear Model (GLM). However, several challenging signal characteristics such as non-instantaneous and non-constant coupling are not yet addressed by this approach and additional auxiliary signals are not optimally exploited. We have recently introduced a new methodological framework for the unsupervised multivariate analysis of fNIRS signals using Blind Source Separation (BSS) methods. Building onto the framework, in this manuscript we show how to incorporate the advantages of regularized temporally embedded Canonical Correlation Analysis (tCCA) into the supervised GLM. This approach allows flexible integration of any number of auxiliary modalities and signals. We provide guidance for the selection of optimal parameters and auxiliary signals for the proposed GLM extension. Its performance in the recovery of evoked HRFs is then evaluated using both simulated ground truth data and real experimental data and compared with the GLM with short-separation regression. Our results show that the GLM with tCCA significantly improves upon the current best practice, yielding significantly better results across all applied metrics: Correlation (HbO max. +45%), Root Mean Squared Error (HbO max. −55%), F-Score (HbO up to 3.25-fold) and p-value as well as power spectral density of the noise floor. The proposed method can be incorporated into the GLM in an easily applicable way that flexibly combines any available auxiliary signals into optimal nuisance regressors. This work has potential significance both for conventional neuroscientific fNIRS experiments as well as for emerging applications of fNIRS in everyday environments, medicine and BCI, where high Contrast to Noise Ratio is of importance for single trial analysis.

Standing Waves for Nonautonomous Klein-Gordon-Maxwell Systems

We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many standing waves.

A new blind source separation framework for signal analysis and artifact rejection in functional Near-Infrared Spectroscopy

In the analysis of functional Near-Infrared Spectroscopy (fNIRS) signals from real-world scenarios, artifact rejection is essential. However, currently there exists no gold-standard. Although a plenitude of methodological approaches implicitly assume the presence of latent processes in the signals, elaborate Blind-Source-Separation methods have rarely been applied. A reason are challenging characteristics such as Non-instantaneous and non-constant coupling, correlated noise and statistical dependencies between signal components. We present a novel suitable BSS framework that tackles these issues by incorporating A) Independent Component Analysis methods that exploit both higher order statistics and sample dependency, B) multimodality, i.e., fNIRS with accelerometer signals, and C) Canonical-Correlation Analysis with temporal embedding. This enables analysis of signal components and rejection of motion-induced physiological hemodynamic artifacts that would otherwise be hard to identify. We implement a method for Blind Source Separation and Accelerometer based Artifact Rejection and Detection (BLISSA2RD). It allows the analysis of a novel n-back based cognitive workload paradigm in freely moving subjects, that is also presented in this manuscript. We evaluate on the corresponding data set and simulated ground truth data, making use of metrics based on 1st and 2nd order statistics and SNR and compare with three established methods: PCA, Spline and Wavelet-based artifact removal. Across 17 subjects, the method is shown to reduce movement induced artifacts by up to two orders of magnitude, improves the SNR of continuous hemodynamic signals in single channels by up to 10dB, and significantly outperforms conventional methods in the extraction of simulated Hemodynamic Response Functions from strongly contaminated data. The framework and methods presented can serve as an introduction to a new type of multivariate methods for the analysis of fNIRS signals and as a blueprint for artifact rejection in complex environments beyond the applied paradigm.

Gauge theories on spheres with 16 supercharges and non-constant couplings

We construct a class of theories with 16 supersymmetries on spheres of dimension nine and less. The gauge coupling and mass terms for the scalar fields depend on the polar angle away from the north pole. Assuming finite coupling on the north pole, this leads to zero coupling at the south pole for d > 4 and infinite coupling at the south pole for d < 4. The underlying supersymmetry algebra of these theories is shown to be isomorphic to the Poincaré superalgebra in d-dimensions. We also give a localization procedure which leads to nontrivial results for d = 2.

Klein–Gordon–Maxwell Systems with Nonconstant Coupling Coefficient

Abstract We study a Klein–Gordon–Maxwell system in a bounded spatial domain under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many static solutions.

Two coupled nonlinear Schrödinger equations involving a non-constant coupling coefficient

In this paper, we study the existence and multiplicity of vector positive solutions for two coupled nonlinear Schrödinger equations involving a non-constant coupling coefficient.

Effects of nonconstant coupling through nonlinear magnetics in electromagnetic vibration energy harvesters

This article discusses how a nonhomogeneous magnetic field with a nonconstant flux gradient affects the behavior of electromagnetic vibration energy harvesters. Based on simulations, the authors show that this nonlinearity enables to increase the output power and bandwidth but not to effectively limit the oscillator vibration amplitude. The impact, however, depends on various system parameters, especially the mechanical damping. Comparing the results to an energy-harvesting prototype, one can conclude that, in practice, the linear model based on a homogeneous magnetic field provides a good estimate. The authors finally give suggestions about magnetic fields that are beneficial for energy harvesting.

Spectra of soft ring graphs

We discuss a ring-shaped soft quantum wire modelled by δ interaction supported by the ring with a generally nonconstant coupling strength. We derive the condition which determines the discrete spectrum of such systems, and analyse the dependence of the eigenvalues and eigenfunctions on the coupling and ring geometry. In particular, we illustrate that a random component in the coupling leads to a localization. The discrete spectrum is also investigated in the situation when the ring is placed into a homogeneous magnetic field or threaded by an Aharonov–Bohm flux and the system exhibits persistent currents. (Some figures in this article are in colour only in the electronic version)

On the validity of simple two-state electronic transition models

The locations and widths of the transition zones for the Landau-Zener and the Demkov model are calculated in a straightforward way. A single transition near a diabatic curve crossing (Landau-Zener model) is found to be related to two transition zones located on either side of the crossing. A single transition between parallel diabatic states induced by an exponentially varying coupling potential (Demkov model) is found to be related to a single transition zone. For low collision velocities the transition zones are determined by the adiabatic potential energy difference and are independent of the collision velocity for both systems. For high velocities the zones are found to depend on the velocity. Finally, the validity of the Landau-Zener model is investigated for non-constant coupling potentials.