Nonlinear Parameters Research Articles

Warm inflation with bulk viscous pressure for different solutions of an anisotropic universe

We study a warm inflationary model for different expansions assuming an anisotropic universe described by Bianchi I metric. The universe is filled with a scalar field or inflaton, radiation, and bulk viscous pressure. We carry out the inflationary analysis for different solutions of such universe in two different cases of the coefficient of dissipation Γ and the coefficient of bulk viscosity ξ as constant and variable parameters, respectively. We compare the obtained results with the recent observations, in order to find the observational constraints on the parameter space of the models. Moreover, we attempt to present a better judgment among the considered models by calculation of the non-linear parameter f NL describing the non-Gaussianity property of the models.

Toward Efficient and Unified Treatment of Static and Dynamic Correlations in Generalized Kohn-Sham Density Functional Theory.

Accurate description of the static correlation poses a persistent challenge in electronic structure theory, particularly when it has to be concurrently considered with the dynamic correlation. We develop here a method in the generalized Kohn-Sham density functional theory (DFT) framework, named R-xDH7-SCC15, which achieves an unprecedented accuracy in capturing the static correlation, while maintaining a good description of the dynamic correlation on par with the state-of-the-art DFT and wave function theory methods, all grounded in the same single-reference black-box methodology. Central to R-xDH7-SCC15 is a general-purpose static correlation correction (SCC) model applied to the renormalized XYG3-type doubly hybrid method (R-xDH7). The SCC model development involves a hybrid machine learning strategy that integrates symbolic regression with nonlinear parameter optimization, aiming to achieve a balance between generalization capability, numerical accuracy, and interpretability. Extensive benchmark studies confirm the robustness and broad applicability of R-xDH7-SCC15 across a diverse array of main-group chemical scenarios. Notably, it displays exceptional aptitude in accurately characterizing intricate reaction kinetics and dynamic processes in regions distant from equilibrium, where the influence of static correlation is most profound. Its capability to consistently and efficiently predict the whole energy profiles, activation barriers, and reaction pathways within a user-friendly "black-box" framework represents an important advance in the field of electronic structure theory.

Shadow and quasinormal modes of novel charged rotating black hole in Born–Infeld theory: Constraints from EHT results

This work investigates the shadow and quasinormal modes of a novel rotating Born–Infeld-type black hole. First, we study the effect of interaction between nonlinear electrodynamic fields and photons on shadow radius and show that it is less than the error of shadow measurements in Event Horizon Telescope (EHT) observations. Then, we obtain a rotating metric using the Newman–Janis algorithm, starting with the initial metric of the nonrotating novel Born–Infeld black hole solution. Next, we analyze the null geodesics to determine the celestial coordinates. The black hole’s shadow radius is determined by using celestial coordinates. The mass, spin, charge, and nonlinearity parameters all influence the shape and size of the black hole shadow. An increase in the spin parameter results in a gradual reduction in the size of black hole shadows and further distortion of the shadows. Furthermore, constraints on the spin and electric charge of black holes, as well as the nonlinearity parameter, are derived through the utilization of the shadow sizes of supermassive black holes Sagittarius (Sgr) A* and M87* obtained from observations of the EHT. Also, we investigate the correlation between the standard shadow radius and the equatorial and polar quasinormal modes for revolving black holes. Finally, we analyze the emission energy rate from the black hole based on different spacetime parameters. Our observation indicates that the emission energy rate decreases as the values of spin and nonlinearity parameters increase, keeping the charge-to-mass ratios of the Born–Infeld black hole constant.

Sleep stages detection based on analysis and optimisation of non-linear brain signal parameters

The analysis and detection of sleep stages continue to preoccupy researchers, particularly bioinformaticians and neurologists aiming to understand various aspects and functioning of the brain during sleep cycles. This understanding is crucial for developing systems capable of early diagnosis of sleep disorders and adapting these systems for use in operating rooms to monitor the brain activity of patients under sedation or anesthesia. In this study, we apply a set of methods to process and decompose the single-channel EEG neural signal into different brain waves such as beta, alpha, theta, and delta. We then focus on the analysis and optimization of the extracted non-linear features using Principal Component Analysis (PCA) to improve the performance and robustness of the classification of six sleep stages. Classifier validation is performed using the cross-validation method. The results show that when the dimensions of the combined non-linear features are reduced, the RF-PCA model achieves an accuracy of 95.2%, outperforming other models such as MLP, SVM, DT, and GB, as well as recent studies. These findings validate the effectiveness of the system, indicating its potential for embedded implementation in practical applications for sleep disorder diagnosis and monitoring.

Effect of dark energy on photon orbits and thermodynamic phase transition for Hayward anti-de Sitter black holes

We investigate a black hole solution analogous to Hayward regular black holes with a negative cosmological constant surrounded by quintessence — the Hayward–Kiselev anti-de Sitter (AdS) black hole, derived from Einstein equations coupled with nonlinear electrodynamics. The solution reveals a singularity due to the quintessential dark energy, and we have outlined the conditions necessary for regularity. When pressure, e.g., P=0.016, the effect of quintessential dark energy results in an otherwise absent van der Waal phase transition and second-order phase transition. Interestingly, the impact of dark energy decreases critical temperature (Tc), whereas critical pressure (Pc) increases. Investigating the correlation between photon sphere radius and the first-order phase transition exhibited non-monotonic behaviour among the photon sphere radius, nonlinear charge parameter, temperature, and pressure under certain conditions. Variations in the photon sphere radius and impact parameter before and after the phase transition serve as order parameters. The critical exponents Δrps and Δups near the critical point consistently approach 1/2, suggesting that rps and ups can be order parameters for black hole phase transitions and indicating a potential universal gravitational relationship near the critical point within a black hole thermodynamic system. We also analysed the previously unexplored Kiselev-AdS black hole, which emerges as a particular case in the limit g→0.

Parameters estimation of complex solar photovoltaic models using bi-parameter coordinated updating L-SHADE with parameter decomposition method

Accurate estimation of unknown parameters of complex photovoltaic models is crucial to whether photovoltaic generators can efficiently convert energy. When a photovoltaic model has multiple diode branches, its complexity increases geometrically. To address the problems of high complexity and difficulty in estimation, this paper proposes an effective improved algorithm based on success-history adaptation differential evolution with linear population size reduction (L-SHADE)—Bi-parameter coordinated updating L-SHADE with parameter decomposition method (CSpL-SHADED). First in CSpL-SHADED, dynamic crossover rate ranking technology is developed to bridge the relationship between individuals and crossover rates, thereby improving effective mutation capabilities. In addition, a dynamic sub-population mechanism is also proposed to divide the entire population into multiple sub-populations so that they are evenly distributed in the search space, so the search ability of individuals in local areas is improved. Secondly, the unknown parameters of solar photovoltaic models of different complexity are effectively decomposed into linear and nonlinear parameters by the decomposition method. The nonlinear parameters are accurately estimated by CSpL-SHADED, and the linear parameters are calculated based on the constructed matrix equation. Through experiments on four solar photovoltaic models of different complexity, CSpL-SHADED showed strong competitiveness to varying degrees compared to the comparative algorithms.

Robust controller design and experimental validation based on bounded uncertainty for collaborative industrial robots.

In this paper, derived from the proportional-derivative control and robust control, a novel practical robust control method based on a dynamic feedforward model is established by taking six-axis motion cooperative industrial robots as the research object. The nonlinear friction, parameter uncertainty, and external disturbance are taken into consideration while establishing the dynamic model of the cooperative industrial robot. The method includes a proportional-derivative control and a robust control. Lyapunov theory is used to analyze the proposed controller, and it is shown that this method can guarantee uniformly bounded and uniformly final bounded systems. Simulation and experiment results show that the proposed controller is better than proportional-integral-derivative control and mode-based proportional-derivative control in stability tracking performance and robustness. In addition, the CSPACE platform for rapid controller prototyping may reduce the arduous programming effort and offer a lot of ease for the trials.

Census and properties of mesoscale eddies in the Kuril Basin of the Okhotsk Sea

High spatial-resolution satellite images show the presence of numerous eddies in the deep Kuril Basin of the Okhotsk Sea, where in-situ measurements acquired within eddies are relatively rare. We conducted the first altimetry-based systematic census of mesoscale eddies in the Kuril Basin in 1993–2021 using the automatic eddy tracking algorithm AMEDA. The dominance of cyclonic eddies over anticyclonic eddies was observed, which contradicts the common opinion that anticyclonic eddies prevail over cyclonic ones in the Kuril Basin. The paper focuses mainly on the long-lived eddies with the lateral size in the range from several tens of kilometers to some hundreds of kilometers and with the lifetime exceeding 30 days. It was found that these eddies are inhomogeneously distributed over the study area with high values of occurrence frequency in some domains. This is explained by the topographic features and peculiarities of the circulation in the Basin where Soya Warm Current water, Okhotsk Sea water and subarctic Pacific water circulate and mix. The fractions of these water masses and their seasonal and interannual variations within the surface cores of the eddy were estimated using a particle-tracking technique. The kinematic characteristics of these eddies have been computed as well. The vast majority of the anticyclonic and cyclonic eddies have the nonlinearity parameter exceeding one implying that the eddies in the Kuril Basin are coherent features transporting water with its properties. Peculiarities in distribution of formation, occurrence and decay locations have been analyzed. Our results have been compared with shipboard and buoy's observations and numerical simulation of eddies in the Kuril Basin.

Affective Implications of Human-Animal Relationship on Pig Welfare: Integrating Non-Linear Heart Rate Variability Measures.

The human-animal relationship is crucial for animal welfare. Gentle handling enhances pigs' comfort while rough handling causes fear and stress. This study examined how different human-animal relationship qualities affect the behavior and heart rate variability (linear and non-linear parameters) of 36 nursery pigs. Over six weeks, pigs experienced positive (n = 12), minimal (n = 12), or negative (n = 12) human handling. Their responses to handlers were then assessed in an experimental arena with four phases: habituation, exposure to the handler standing and sitting, and forced interaction. Pigs subjected to negative handling exhibited increased fear-related behaviors, spending less time in contact with the handler. They also exhibited heightened stress responses, with greater LF/HF ratio and Lmean values compared with positively handled pigs. Conversely, gently handled pigs displayed affiliative behaviors, accepting more strokes, and higher parasympathetic activation, indicated by greater RMSSD/SDNN and SampEn values, suggesting a more positive affective state. Minimally handled pigs exhibited some behavioral similarities to gently handled pigs, although physiological data indicated that the interaction was likely more rewarding for the gently handled pigs. These results emphasize the impact of human-animal relationships on pig welfare and highlight the value of incorporating non-linear heart rate variability parameters in such evaluations.

Influence of ZnMn2O4/CuCo2O4 nano-fillers on the optical and electrical properties PVA/CMC/PEG blended polymers

(1-x)ZnMn2O4/xCuCo2O4 samples were synthesized by the co-precipitation method while polyvinyl alcohol/carboxymethyl cellulose/polyethylene glycol (PVA/CMC/PEG) blended polymer were fabricated by the casting method. Rietveld refinement analysis was used to determine the crystallite size and phase percentages for each composition were determined for all samples. The morphology and structure of PVA/CMC/PEG/(1-x)ZnMn2O4/xCuCo2O4 blends were examined using scanning electron microscopy and x-ray diffraction techniques. The reflectance and transmittance spectra were examined for blended polymers using a diffused reflectance spectrophotometer. Using LCR meter, the prepared blend films' dielectric properties were evaluated. When the blend is loaded with 0.9ZnMn2O4/0.1CuCo2O4, the lowest transmittance values (29–47 %) in the visible region are reached. As the CuCo2O4 doping levels became 10 % in the filler, the smallest direct and indirect energy gap values of 5.4 and (4.47, 1.9, 1.65) eV were attained, respectively. The linear and nonlinear optical parameters affected by the amount of CuCo2O4 in the filler samples. The optical conductivity of the doped blend reached its maximum value at x = 0.15. The CIE chromaticity diagrams revealed that the blends have varying degrees of blue color. The addition of (1-x)ZnMn2O4/xCuCo2O4 fillers improves the energy storage capability of the blends without raising the energy dissipation. The highest value of AC conductivity was achieved with the blend containing 0.9ZnMn2O4/0.1CuCo2O4. Nyquist plot revealed that the ionic conductivity increased as a result of doping. The obtained results suggest that the doped PVA/CMC/PEG/(1-x)ZnMn2O4/xCuCo2O4 blends might be used in a variety of industrial applications, including solar cell technology.

Nonlinear time-dependent behavior of rheodictic polymers: A theoretical and experimental investigation

The present study examined the nonlinear time-dependent behavior of rheodictic polymers, a class of noncrosslinked materials that exhibit flow. Such behavior was addressed with extended Schapery's nonlinear viscoelastic model by introducing new physical quantities, i.e., the flow term Φflow and corresponding nonlinear shift parameter g2,flow. While Φflow portrays irrecoverable deformation, g2,flow depicts a nonlinear contribution to flow acceleration. This theory was accompanied by analytical and experimental methodologies for identifying all the parameters in the linear and nonlinear viscoelastic domains. Predictions of long-term time-dependent behavior (in shear) at various stress states show excellent agreement with the experimental data, i.e., within 5% error, obtained for polycarbonate at 130°C. Surprisingly, the newly introduced g2,flow indicates that flow retardation occurs with increasing stress, implying that a highly deformed entangled system hinders molecular reptation/disentanglement. Nevertheless, the proposed extension of Schapery's nonlinear viscoelastic model not only allows accurate predictions of the nonlinear time-dependent behavior of rheodictic polymers but also enables a detailed outlook on the underlying molecular mechanisms under severe environmental and loading conditions.

Analysis of the tri-hybrid Maxwell nanofluid flow with temperature-dependent thermophysical characteristics on static and dynamic surfaces employing Levenberg-Marquardt artificial neural networks

Using the Levenberg-Marquardt Artificial Neural Network (LM-ANN) model, this study applies computational neuroscience to the analysis of flow, heat, and mass transport characteristics. The novel characteristics of MHD Maxwell tri-hybrid nanofluid passing through static and moving wedge with temperature-dependent thermophysical properties (thermal conductivity, viscosity, diffusivity, and electrical field) in permeable, radiative, and mixed convection processes are investigated in this paper. Nonlinear PDEs are transformed into nonlinear ODEs using similarity variables. A dataset for the LM-ANN is generated across various scenarios by varying parameters such as the temperature-dependent viscosity parameter ( 0.07 − 0.1 ) , variable diffusivity parameter ( 0.4 − 2.5 ) , thermal buoyancy parameter ( 0.1 − 0.5 ) , nonlinear thermal buoyancy parameter ( 0.2 − 0.5 ) , thermal radiation ( 1 − 1.5 ) , buoyancy ratio parameter ( 0.2 − 0.5 ) , chemical reaction parameter ( 1 − 3 ) , and Schmidt number ( 1 − 3 ) using the Bvp5c numerical algorithm. The testing, training, and validation procedure of LM-ANN is utilized to examine the estimated solutions of specific situations, and the proposed algorithm is then validated. After that, the proposed LM-ANN is validated using regression analysis, MSE, and histogram analysis. The prescribed approach impeccably mirrors the recommended and cited findings, evincing a precision level within the realm of 10−9. Results indicate that increasing the permeability parameter from 1 to 1.2 and the temperature-dependent thermal conductivity parameter from 0.4 to 2.5 enhances the Nusselt number. Additionally, increasing the chemical reaction parameter from 1 to 3 leads to an increase in the Sherwood number. The significance of this study lies in its potential applications in industries such as aerospace, chemical processing, and energy systems, where efficient heat and mass transfer processes are crucial. For instance, the findings can be applied to enhance cooling techniques in high-performance aerospace components, optimize reactor designs in chemical plants, and improve thermal management in power generation systems.

Enhancing structural integrity of refractories during manufacturing through integration of UPV and acoustic nonlinearity measurements

ABSTRACT This paper addresses the critical need for robust quality assurance in commercial refractories, emphasizing the role of Ultrasonic Pulse Velocity (UPV) testing in assessing material integrity. Traditionally, UPV testing has become a standard practice for evaluating refractory, ceramic, and concrete materials after production. However, this study introduces an innovative approach by advocating the integration of UPV tests at an intermediate stage prior to temperature curing. The primary objective is to predict the performance of refractory samples under compressive loading, examine intrinsic damages, and analyse ultrasonic characteristics in both time and frequency domains. Experimental investigations introduce damages, including artificial voids simulating various defect types, both before and during heat treatment. Analysis of UPV, Root Mean Squared (RMS) values of frequency spectra, and the acoustic nonlinearity parameter (ANP) reveals substantial differences between healthy and damaged regions. The mean UPV and RMS values consistently decrease in damaged regions, indicating sensitivity to defect severity. The ANP is sensitive to damage size, especially with higher frequency transducers detecting subtle changes more effectively. These findings emphasise the potential for proactive testing at an intermediate stage in the manufacturing process, enhancing the structural integrity and overall quality of refractory materials.

Exploring the optical and electrical features of PVA/CMC/PPy/MWCNTs blended polymers

The objective of this study is to create nanocomposite films using polyvinyl alcohol (PVA), sodium carboxymethyl cellulose (CMC), polypyrrole (PPy) and Multi-walled carbon nanotubes (MWCNTs). These nanocomposites show potential for use in a range of optoelectronics devices. The structure and morphology of PVA/CMC/PPy/x wt % MWCNTs blends were explored using X-ray diffraction and scanning electron microscope techniques. In the visible range, the transmittance lowered from 78 to 87 % (PVA/CMC/PPy blend) to 3–5 % (x = 0.25 wt % MWCNTs). The transmittance in the UV range decreased significantly, approaching zero, for the blend containing 0.25 wt % MWCNTs. The material improves the absorption of UV–visible light and efficiently prevents the penetration of UV–visible light. When the concentration of MWCNTs reached 0.05 in the doped blend, the reflectance value improved considerably. The addition of MWCNTs to the PVA/CMC/PPy composite leads to a reduction in the optical bandgap values. The lowest direct and indirect band gaps are (4.98, 4.36) eV and (4.52, 3.19, 2.68, 1.18) eV, respectively, accomplished when the MWCNTs content was 0.2 wt %. A blend containing 0.15 wt % MWCNTs resulted in the highest values of refractive index and nonlinear optical parameters. In the visible light spectrum, the blend with 0.25 wt% MWCNTs had the best optical conductivity values. Doped blends can be used in optoelectronic or photocatalytic applications depended on the amount of MWCNTs doped. The current-voltage characteristics and logarithm of the current density and square root of the electric field strength of PVA/CMC/PPy/x wt % MWCNTs blended polymers at various temperatures were investigated.

The role of Bi incorporation on the optical dispersion parameters of binary Se–In chalcogenide glass films as encouraging materials for photovoltaic implementations

The bulk form of Se78In(22-x)Bix (x = 0, 4, 8, and 12 at.%) was produced with melt-quench technology. Subsequently, thin films of these compositions were produced through the thermal evaporation method under vacuum conditions. Analysis via diffraction of X-rays confirmed the disordered character of the resulting films. The refractive index (n) and extinction coefficient (k) were computed using optical transmission T(λ) and reflection R(λ) data. Analysis of optical constants revealed that the optical energy gap Egopt decreases while the Urbach tail Eu augments as the Bi content increases. Other related constants were determined and investigated in relation to variations in Bi content. The outcomes of our study were compared with those published previously. Non-linear parameters were calculated and discussed for the investigated films.

Group-Action-Based S-box Generation Technique for Enhanced Block Cipher Security and Robust Image Encryption Scheme

Data security is one of the biggest concerns in the modern world due to advancements in technology, and cryptography ensures that the privacy, integrity, and authenticity of such information are safeguarded in today’s digitally connected world. In this article, we introduce a new technique for the construction of non-linear components in block ciphers. The proposed S-box generation process is a transformational procedure through which the elements of a finite field are mapped onto highly nonlinear permutations. This transformation is achieved through a series of algebraic and combinatorial operations. It involves group actions on some pairs of two Galois fields to create an initial S-box Pr Sbox, which induces a rich algebraic structure. The post S-box Po Sbox, which is derived from heuristic group-based optimization, leads to high nonlinearity and other important cryptographic parameters. The proposed S-box demonstrates resilience against various attacks, making the system resistant to statistical vulnerabilities. The investigation reveals remarkable attributes, including a nonlinearity score of 112, an average Strict Avalanche Criterion score of 0.504, and LAP (Linear Approximation Probability) score of 0.062, surpassing well-established S-boxes that exhibit desired cryptographic properties. This novel methodology suggests an encouraging approach for enhancing the security framework of block ciphers. In addition, we also proposed a three-step image encryption technique comprising of Row Permutation, Bitwise XOR, and block-wise substitution using Po Sbox. These operations contribute to adding more levels of randomness, which improves the dispersion across the cipher image and makes it equally intense. Therefore, we were able to establish that the approach works to mitigate against statistical and cryptanalytic attacks. The PSNR, UACI, MSE, NCC, AD, SC, MD, and NAE data comparisons with existing methods are also provided to prove the efficiency of the encryption algorithm.

On more insightful dimensionless numbers for computational viscoelastic rheology

Abrupt contraction flows involving viscoelastic fluids represent a longstanding computational challenge within the field of non-Newtonian fluid mechanics. Despite the apparent simplicity of the geometry, these flows have given rise to intricate discussions in the study of viscoelastic phenomena. This study aims to re-examine the numerical solutions for flows through abrupt contractions, offering a fresh interpretation through the lens of reformulated dimensionless numbers. These numbers are designed to consider the characteristic shear rate of the problem, providing a more comprehensive understanding of the underlying dynamics.When investigating models with intermediate levels of complexity, such as the Giesekus and Phan-Thien-Tanner constitutive equations, the usual comparison with the corresponding Oldroyd-B model becomes inadequate because it tends to rely on the nominal relaxation time (λ) and the nominal total viscosity (η) instead of their effective counterparts when defining the Reynolds number (Re), the Weissenberg number (Wi) and the ratio of solvent to total viscosities (β) (β plays a role only in rheological models involving a solvent contribution). If these dimensionless numbers are tailored to account for the characteristic shear rate specific to the problem under investigation, the choice of the corresponding Oldroyd-B flow, at the adequate values of Re, Wi, and β allows for significantly better quantification of the correct effects of nonlinear viscoelasticity of the original model.We show the conventional approach tends to overemphasize the role of the nonlinear parameter in nonlinear constitutive equations, like the Giesekus and PTT models, when examining standard abrupt contraction flow outputs such as the Couette correction and vortex size. This overestimation occurs because the conventional method does not allow the Reynolds and Weissenberg numbers (and possibly β) to carry the portion of the nonlinear effect that can potentially be captured by the linear Oldroyd-B model through the use of characteristic shear rate-based values. We believe the present approach provides a better perspective of the role played by the nonlinear parameter and its extension to more general flows is also discussed.

Structural, optical and electrical conduction characteristics of PMMA/PVAc/TBAI blended polymers

This study aims to create tetra-n-butylammonium iodide (TBAI) doped poly(methyl methacrylate) (PMMA)/polyvinyl acetate (PVAc) blended polymers for utilize in a diversity of optoelectronic applications. By the casting technique, the films of (PMMA/PVAc/x wt % TBAI) were formed. The structure and morphology characteristics of the blended materials were studied using X-ray diffraction and scanning electron microscopy techniques. The optical transmittance declined to a minimum value when the blend was loaded with 38 wt % TBAI. The blend containing 38 % TBAI exhibits the highest reflectance values in the visible range. The lowest direct optical bandgap energies (4.20 eV) and indirect optical bandgap energies (3.71 eV, 3.13 eV) were achieved when TBAI reached 38 wt%. The addition of TBAI leads to an enhancement of the refractive index values of PMMA/PVAc in the visible spectrum. The effect of TBAI doping amount on the optical dielectric constant, energy loss functions, optical conductivity, nonlinear optical parameters and emitted color of the host blend was explored. The maximum values of the optical dielectric constant and energy loss functions were achieved after the TBAI level reached 38 wt%. The three non-linear optical (NLO) parameters for PMMA/PVAc blended polymers were enhanced as the amount of TBAI increased. An increase in voltage (V) or temperature results in a significant increase in electric current (I). Raising the amount of TBAI doping also caused the electric current to rise irregularly, with the exception of the blend with x = 11 %, where it fell. The samples exhibited the non-ohmic characteristics of the current-voltage (I–V) properties. The conduction mechanism of all blended materials was studied in detail. Finally, the outcomes supported the optical and electric properties studies, which suggested that a range of nanoelectronics applications could make use of the PMMA/PVAc/x weight percent TBAI blended polymers.

Intermodulation spectroscopy and the nonlinear response of two-level systems in superconducting coplanar-waveguide resonators

Two-level system (TLS) loss typically limits the coherence of superconducting quantum circuits. The loss induced by TLS defects is nonlinear, resulting in quality factors with a strong dependence on the circulating microwave power. We observe frequency mixing due to this nonlinearity by applying a two-tone drive to a coplanar waveguide resonator and measuring the intermodulation products using a multifrequency lock-in technique. This intermodulation spectroscopy method provides an efficient approach to characterizing TLS loss in superconducting circuits. Using harmonic balance reconstruction, we recover the nonlinear parameters of the device-TLS interaction, which are in good agreement with the standard tunneling model for TLSs. Published by the American Physical Society 2024

Mini-Workshop: Nonlinear Approximation of High-dimensional Functions in Scientific Computing

Approximation techniques for high dimensional PDEs are crucial for contemporary scientific computing tasks and gained momentum in recent years due to the renewed interest in neural networks. It seems that especially nonlinear parametrizations will play an essential role in efficient and tractable approximations of high dimensional problems. We held a mini-workshop on the relation and possible synergy of neural networks and tensor product approximation. To reliably evaluate the prospect of different numerical experiments, the traditional talks were accompanied by live coding sessions.