Nonlinear Scaling Research Articles

Effects of peculiar velocities on the morphological properties of large-scale structure

It is known that the large-scale structure (LSS) mapped by a galaxy redshift survey is subject to distortions by galaxies' peculiar velocities. Besides the signatures generated in common N-point statistics, such as the anisotropy in the galaxy 2-point correlation function, the peculiar velocities also induce distinct features in LSS's morphological properties, which are fully described by four Minkowski functionals (MFs), i.e., the volume, surface area, integrated mean curvature and Euler characteristic (or genus). In this work, by using large suite of N-body simulations, we present and analyze these important features in the MFs of LSS on both (quasi-)linear and non-linear scales, with a focus on the latter. We also find the MFs can give competitive constraints on cosmological parameters compared to the power spectrum, probablly due to the non-linear information contained. For galaxy number density similar to the DESI BGS galaxies, the constraint on $\sigma_8$ from the MFs with one smoothing scale can be better by $\sim 50\%$ than from the power spectrum. These findings are important for the cosmological applications of MFs of LSS, and probablly open up a new avenue for studying the peculiar velocity field itself.

Robust image similarity metric method for SAR images

Synthetic aperture radar (SAR) image similarity metric is at the core of SAR image interpretation techniques, however, it is still a challenging task due to complex nonlinear intensity, scale, and rotation differences between SAR images and other remote sensing images. This letter addresses this problem by proposing a novel similarity metric method for SAR images using structure and shape properties. The magnitude and orientation representation of the phase congruency model is first built based on the local phase of images. Then a new scale and rotation-invariant local binary pattern (SRI-LBP) descriptor is proposed using local structure and shape information. Finally, a similarity metric is defined using the symmetry Kullback Leibler divergence (SKLD) of the SRI-LBP descriptors. Numerical experiment results verify its robustness in terms of nonlinear intensity, scale, and rotation differences.

Efficient imaging method for multireceiver SAS

With the Loffeld's bistatic formula, the point target reference spectrum (PTRS) of multireceiver synthetic aperture sonar (SAS) can be decomposed into the quasi monostatic term and bistatic deformation (BD) term. The former term is analogous to the monostatic SAS PTRS while the latter one describes the bistatic phase introduced by the bistatic displacement between the transmitter and receiver. The multireceiver SAS echo signal can be transformed into monostatic SAS equivalent data after correcting the BD term. Based on the range sub-block processing method, this data transformation is conducted by using the preprocessing step. Then, fast imaging processors based on monostatic SAS system can be directly exploited to process the monostatic SAS equivalent data. In this paper, the authors mainly focus on the application of non-linear chirp scaling algorithm. At last, the simulations and real data are used to validate the presented method. The processing results show that the imaging performance of presented method is nearly close to that of traditional method. Besides, the imaging efficiency is highly improved compared to the phase centre approximation (PCA) method.

Mapping Active Site Geometry to Activity in Immobilized Frustrated Lewis Pair Catalysts.

The immobilization of molecular catalysts imposes spatial constraints on their active site. We reveal that in bifunctional catalysis such constraints can also be utilized as an appealing handle to boost intrinsic activity through judicious control of the active site geometry. To demonstrate this, we develop a pragmatic approach, based on nonlinear scaling relationships, to map the spatial arrangements of the acid–base components of frustrated Lewis pairs (FLPs) to their performance in the catalytic hydrogenation of CO2. The resulting activity map shows that fixing the donor–acceptor centers at specific distances and locking them into appropriate orientations leads to an unforeseen many‐fold increase in the catalytic activity of FLPs compared to their unconstrained counterparts.

Mapping Active Site Geometry to Activity in Immobilized Frustrated Lewis Pair Catalysts

AbstractThe immobilization of molecular catalysts imposes spatial constraints on their active site. We reveal that in bifunctional catalysis such constraints can also be utilized as an appealing handle to boost intrinsic activity through judicious control of the active site geometry. To demonstrate this, we develop a pragmatic approach, based on nonlinear scaling relationships, to map the spatial arrangements of the acid–base components of frustrated Lewis pairs (FLPs) to their performance in the catalytic hydrogenation of CO2. The resulting activity map shows that fixing the donor–acceptor centers at specific distances and locking them into appropriate orientations leads to an unforeseen many‐fold increase in the catalytic activity of FLPs compared to their unconstrained counterparts.

An empirical nonlinear power spectrum overdensity response

Context.The overdensity inside a cosmological sub-volume and the tidal fields from its surroundings affect the matter distribution of the region. The resulting difference between the local and global power spectra is characterized by the response function.Aims.Our aim is to provide a new, simple, and accurate formula for the power spectrum overdensity response at highly nonlinear scales based on the results of cosmological simulations and paying special attention to the lognormal nature of the density field.Methods.We measured the dark matter power spectrum amplitude as a function of the overdensity (δW) inN-body simulation subsamples. We show that the response follows a power-law form in terms of (1 + δW), and we provide a new fit in terms of the variance,σ(L), of a sub-volume of sizeL.Results.Our fit has a similar accuracy and a comparable complexity to second-order standard perturbation theory on large scales, but it is also valid for nonlinear (smaller) scales, where perturbation theory needs higher-order terms for a comparable precision. Furthermore, we show that the lognormal nature of the overdensity distribution causes a previously unidentified bias: the power spectrum amplitude for a subsample with an average density is typically underestimated by about −2σ2. Although this bias falls to the sub-percent level above characteristic scales of 200 Mpc h−1, taking it into account improves the accuracy of estimating power spectra from zoom-in simulations and smaller high-resolution surveys embedded in larger low-resolution volumes.

SVM Based Intrusion Detection Method with Nonlinear Scaling and Feature Selection

Intrusion is one of major security issues of internet with the rapid growth in smart and Internet of Thing (IoT) devices, and it becomes important to detect attacks and set out alarm in IoT systems. In this paper, the support vector machine (SVM) and principal component analysis (PCA) based method is used to detect attacks in smart IoT systems. SVM with nonlinear scheme is used for intrusion classification and PCA is adopted for feature selection on the training and testing datasets. Experiments on the NSL-KDD dataset show that the test accuracy of the proposed method can reach 82.2% with 16 features selected from PCA for binary-classification which is almost the same as the result obtained with all the 41 features; and the test accuracy can achieve 78.3% with 29 features selected from PCA for multi-classification while 79.6% without feature selection. The Denial of Service (DoS) attack detection accuracy of the proposed method can achieve 8.8% improvement compared with existing artificial neural network based method.

Spatial scaling of gregarious host populations and nonlinearities in infectious disease transmission.

Research Highlight: Lunn, T. J., Peel, A. J., Eby, P., Brooks, R., Plowright, R. K., Kessler, M. K., & McCallum, H. (2021). Counterintuitive scaling between population abundance and local density: Implications for modelling transmission of infectious diseases in bat populations. Journal of Animal Ecology, https://doi.org/10.1111/1365-2656.13634. Quantifying the transmission of an infectious disease is often difficult and for natural animal systems it can be a major challenge. Animals move over time and space changing their degree of aggregation and rate of contact, which, in turn, affects the risk of infection and the onward spread of the pathogen. Capturing the fundamentals of these processes requires the identification of both the correct spatial scale at which the processes take place and what constitutes a meaningful host population unit. Lunn et al. collected data on the gregarious Pteropus (flying foxes) bats from roost sites in Australia and investigated whether total bat abundance at the roost level, the spatial scale commonly used to model pathogen spread in bat populations, was representative of bat measurements at the tree level, the scale at which pathogen transmission between bats most likely occurs. Their findings showed that bat population measurements at the sub-plot level were strong predictors for potential transmission at the tree scale, while roost-level measurements were less robust. This study suggests that bat abundance at roost is inadequate to capture the gregarious structure of bat populations and the fundamental processes of transmission at lower scale.

Studying Interstellar Turbulence Driving Scales Using the Bispectrum

We demonstrate the utility of the bispectrum, the Fourier three-point correlation function, for studying driving scales of magnetohydrodynamic (MHD) turbulence in the interstellar medium. We calculate the bispectrum by implementing a parallelized Monte Carlo direct measurement method, which we have made publicly available. In previous works, the bispectrum has been used to identify nonlinear scaling correlations and break degeneracies in lower-order statistics like the power spectrum. We find that the bicoherence, a related statistic which measures phase coupling of Fourier modes, identifies turbulence-driving scales using density and column density fields. In particular, it shows that the driving scale is phase-coupled to scales present in the turbulent cascade. We also find that the presence of an ordered magnetic field at large scales enhances phase coupling as compared to a pure hydrodynamic case. We therefore suggest the bispectrum and bicoherence as tools for searching for non-locality for wave interactions in MHD turbulence.

Cosmology in the non-linear regime: the small scale miracle

Interest is rising in exploiting the full shape information of the galaxy power spectrum, and in pushing analyses to smaller non-linear scales. Here I use the halo model to quantify the information content in the tomographic angular power spectrum of galaxies Cℓgal(iz) for the future high-resolution surveys Euclid and SKA2. I study how this information varies as a function of the scale cut applied, either with angular cut ℓmax or physical cut kmax. For this, I use analytical covariances with the most complete census of non-Gaussian terms, which proves to be critical. I find that the Fisher information on most cosmological and astrophysical parameters shows a striking behaviour. Beyond the perturbative regime, we first get decreasing returns: the information continues to rise but the slope slows down until reaching saturation. The location of this plateau, at k ∼ 2 Mpc−1, is slightly beyond the reach of current modelling methods and depends to some extent on the parameter and redshift bin considered. I explain the origin of this plateau, which is due to non-linear effects both on the power spectrum, and more importantly on non-Gaussian covariance terms. Then, pushing further, we see the information rising again in the highly non-linear regime, with a steep slope. This is the small-scale miracle, for which I give my interpretation and discuss the properties. There are suggestions that it may be possible to disentangle this information from the astrophysical content, and improve dark energy constraints. Finally, more hints are shown that high-order statistics may yield significant improvements over the power spectrum in this regime, with the improvements increasing with kmax.

Cosmology with cosmic web environments

We undertake the first comprehensive and quantitative real-space analysis of the cosmological information content in the environments of the cosmic web (voids, filaments, walls, and nodes) up to non-linear scales,k = 0.5hMpc−1. Relying on the large set ofN-body simulations from the Quijote suite, the environments are defined through the eigenvalues of the tidal tensor and the Fisher formalism is used to assess the constraining power of the spectra derived in each of the four environments and their combination. Our results show that there is more information available in the environment-dependent power spectra – both individually and when combined – than in the matter power spectrum. By breaking some key degeneracies between parameters of the cosmological model such asMν–σ8or Ωm–σ8, the power spectra computed in identified environments improve the constraints on cosmological parameters by factors of ∼15 for the summed neutrino massMνand ∼8 for the matter density Ωmover those derived from the matter power spectrum. We show that these tighter constraints are obtained for a wide range of the maximum scale, fromkmax = 0.1hMpc−1to highly non-linear regimes withkmax = 0.5hMpc−1. We also report an eight times higher value of the signal-to-noise ratio for the combination of environment-dependent power spectra than for the matter spectrum. Importantly, we show that all the results presented here are robust to variations of the parameters defining the environments, suggesting a robustness to the definition we chose to extract them.

Myoelectric Pattern Recognition Performance Enhancement Using Nonlinear Features.

The multichannel electrode array used for electromyogram (EMG) pattern recognition provides good performance, but it has a high cost, is computationally expensive, and is inconvenient to wear. Therefore, researchers try to use as few channels as possible while maintaining improved pattern recognition performance. However, minimizing the number of channels affects the performance due to the least separable margin among the movements possessing weak signal strengths. To meet these challenges, two time-domain features based on nonlinear scaling, the log of the mean absolute value (LMAV) and the nonlinear scaled value (NSV), are proposed. In this study, we validate the proposed features on two datasets, the existing four feature extraction methods, variable window size, and various signal-to-noise ratios (SNR). In addition, we also propose a feature extraction method where the LMAV and NSV are grouped with the existing 11 time-domain features. The proposed feature extraction method enhances accuracy, sensitivity, specificity, precision, and F1 score by 1.00%, 5.01%, 0.55%, 4.71%, and 5.06% for dataset 1, and 1.18%, 5.90%, 0.66%, 5.63%, and 6.04% for dataset 2, respectively. Therefore, the experimental results strongly suggest the proposed feature extraction method, for taking a step forward with regard to improved myoelectric pattern recognition performance.

Hadron collider probes of the quartic couplings of gluons to the photon and Z boson

We explore the experimental sensitivities of measuring the gg → Zγ process at the LHC to the dimension-8 quartic couplings of gluon pairs to the Z boson and photon, in addition to comparing them with the analogous sensitivities in the gg → γγ process. These processes can both receive contributions from 4 different CP-conserving dimension-8 operators with distinct Lorentz structures that contain a pair of gluon field strengths, {hat{G}}_{mu v}^a , and a pair of electroweak SU(2) gauge field strengths, {W}_{mu v}^i , as well as 4 similar operators containing a pair of {hat{G}}_{mu v}^a and a pair of U(1) gauge field strengths, Bμν. We calculate the scattering angular distributions for gg → Zγ and the Z → overline{f}f decay angular distributions for these 4 Lorentz structures, as well as the Standard Model background. We analyze the sensitivity of ATLAS measurements of the Z(→ ℓ+ℓ−, overline{nu}nu , overline{q}q )γ final states with integrated luminosities up to 139 fb−1 at sqrt{s} = 13 TeV, showing that they exclude values ≲ 2 TeV for the dimension-8 operator scales, and compare the Zγ sensitivity with that of an ATLAS measurement of the γγ final state. We present combined Zγ and γγ constraints on the scales of dimension-8 SMEFT operators and γγ constraints on the nonlinearity scale of the Born-Infeld extension of the Standard Model. We also estimate the sensitivities to dimension-8 operators of experiments at possible future proton-proton colliders with centre-of-mass energies of 25, 50 and 100 TeV, and discuss possible measurements of the Z spin and angular correlations.

Multiscale Modeling and Experimental Characterization for Enhancement in Electrical, Mechanical, and Thermal Performances of Lithium-Ion Battery

Lithium-ion batteries are the thriving energy storage device in multiple fields, including automobiles, smart energy grids, and telecommunication. Due to its high complexity in the electrochemical–electrical–thermal system, there are certain non-linear spatiotemporal scales for measuring the performance of lithium-ion batteries. The fusion of experimental and modeling approaches was used in this study to enhance the performance of lithium-ion batteries. This article helps to evaluate the properties of the LiMn2O4 cathode material for Li-ion batteries and also characterize the crystalline nature, morphological structure, and ionic and electronic conductivity of the electrode material using an experimental approach. In addition, a new computational model was designed and formulated to support various other models for computational investigation. This simulation was designed to analyze the one-dimensional structure of coin cell batteries and to evaluate electrochemical and thermal performances. All computational performances have been validated with the help of experimental techniques and also provide multiple benchmarks for future integration of experimental and computational approaches.

Thermo-optical numerical modal analysis of multicore fibers for high power lasers and amplifiers

Lasers for modern industrial and research applications are required to provide a high average beam power and at the same time be reliable, efficient, and compact. Rare-earth doped single-mode fiber lasers are the most promising solution. Large mode area fibers are effectively used to reduce nonlinear effects and scaling up the beam power which is now bounded by thermal effects. A new cutting-edge approach to the issue involves the use of Multi-Core Fibers (MCFs), coherently combining several lower power beams into a higher power one, and thus pushing the threshold of nonlinearities and transverse mode instabilities to higher power. The amplification process involves heat generation in the doped cores due to quantum defect, which propagates radially and creates a temperature gradient across the fiber cross-section. Even though the cores are optically uncoupled, the refractive index gradient due to thermo-optical effects could cause cross-talk and core mode coupling. In this work, we numerically analyze the performances of 9-core MCFs for high power fiber lasers by taking into account the coupling and bending effects due to the heat load generated by the quantum defect between pump and laser radiation. MCFs show very low sensitivity to heat load and bending, with effectively single-mode behaviour up to 15 μm core diameter (effective area 181 μm2) and down to 35 μm pitch.

Dimensionality of Iterative Methods: The Adimensional Scale Invariant Steffensen (ASIS) Method

The dimensionality of parameters and variables is a fundamental issue in physics but is mostly ignored from a mathematical point of view. Difficulties arising from dimensional inconsistency are overcome by scaling analysis and, often, both concepts, dimensionality and scaling, are confused. In the particular case of iterative methods for solving nonlinear equations, dimensionality and scaling affect their robustness: While some classical methods, such as Newton’s, are adimensional and scale independent, some other iterations such as Steffensen’s are not; their convergence depends on scaling, and their evaluation needs a dimensional congruence. In this paper, we introduce the concept of an adimensional form of a function in order to study the behavior of iterative methods, thus correcting, if possible, some pathological features. From this adimensional form, we will devise an adimensional and scale invariant method based on Steffensen’s, which we will call the ASIS method.

Cosmological direct detection of dark energy: Non-linear structure formation signatures of dark energy scattering with visible matter

Abstract We consider the recently proposed possibility that dark energy (DE) and baryons may scatter through a pure momentum exchange process, leaving the background evolution unaffected. Earlier work has shown that, even for barn-scale cross-sections, the imprints of this scattering process on linear cosmological observables is too tiny to be observed. We therefore turn our attention to non-linear scales, and for the first time investigate the signatures of DE-baryon scattering on the non-linear formation of cosmic structures, by running a suite of large N-body simulations. The observables we extract include the non-linear matter power spectrum, halo mass function, and density and baryon fraction profiles of haloes. We find that in the non-linear regime the signatures of DE-baryon scattering are significantly larger than their linear counterparts, due to the important role of angular momentum in collapsing structures, and potentially observable. The most promising observables in this sense are the baryon density and baryon fraction profiles of haloes, which can potentially be constrained by a combination of kinetic Sunyaev–Zeldovich (SZ), thermal SZ, and weak lensing measurements. Overall, our results indicate that future prospects for cosmological and astrophysical direct detection of non-gravitational signatures of dark energy are extremely bright.

Neural Networks as Optimal Estimators to Marginalize Over Baryonic Effects

Abstract Many different studies have shown that a wealth of cosmological information resides on small, nonlinear scales. Unfortunately, there are two challenges to overcome to utilize that information. First, we do not know the optimal estimator that will allow us to retrieve the maximum information. Second, baryonic effects impact that regime significantly and in a poorly understood manner. Ideally, we would like to use an estimator that extracts the maximum cosmological information while marginalizing over baryonic effects. In this work we show that neural networks can achieve that when considering some simple scenarios. We made use of data where the maximum amount of cosmological information is known: power spectra and 2D Gaussian density fields. We also contaminate the data with simplified baryonic effects and train neural networks to predict the value of the cosmological parameters. For this data, we show that neural networks can (1) extract the maximum available cosmological information, (2) marginalize over baryonic effects, and (3) extract cosmological information that is buried in the regime dominated by baryonic physics. We also show that neural networks learn the priors of the data they are trained on, affecting their extrapolation properties. We conclude that a promising strategy to maximize the scientific return of cosmological experiments is to train neural networks on state-of-the-art numerical simulations with different strengths and implementations of baryonic effects.

An improved synthetic aperture radar‐scale invariant feature transform algorithm for interferometric imaging radar altimeter image registration

Interferometric imaging radar altimeter (InIRA) integrating synthetic aperture radar (SAR) and synthetic aperture radar interferometry (InSAR) is a new type of radar altimeter. InIRA will be widely adopted in marine scientific research and surface water topography measurements. Owing to the geometric distortion of InIRA images, there are difficulties in feature point extraction and matching, making InIRA registration challenging. Here, an improved SAR-scale invariant feature transform (SIFT, SAR-SIFT) algorithm is proposed to address these difficulties. First, a modified Harris non-linear scale space is constructed using the Harris function and non-linear scale space, and extracted the feature points according to the SAR-SIFT algorithm. Second, the orbital parameters of InIRA are used to calculate the geographic coordinates of each feature point by Hermit interpolation. Subsequently, a geographic-coordinate-based method is proposed to match the feature points. The results show that the proposed algorithm gained more correct matches and improved the registration accuracy by 13% and 16.7% compared with the SIFT and SAR-SIFT algorithms, respectively, and was 18% more time efficient than the SAR-SIFT algorithm. The experiments demonstrate that the proposed algorithm outperforms the SAR-SIFT algorithm for InIRA image registration in terms of accuracy and efficiency.

Structural similitude for a scaled rotor system considering stiffness characteristics of bolted joints

Rotor system with bolted joints is widely used in aero-engine, and has the features of large axial span, high-degrees of freedom, and nonlinearity. There exist several researches on similitude of rotor systems, but these studies mainly focus on the simple and linear systems. The similitude investigation for the rotor system considering bolted joints has not been conducted. To fill this gap, a method to obtain the scaling laws for low-pressure (LP) compressor are presented based on the generalized and fundamental equations of substructures (bolted joint, shaft, and disk), which considers the nonlinearity of bolted joints and different materials. The dynamic model of the LP compressor considering the nonlinearity produced by bolted joints is established. Moreover, the effect of bolted joints on the LP compressor is investigated to illustrate the necessity for considering bolted joints in similitude procedure. In order to ensure the similitude of nonlinear dynamic characteristics, the scaling factors are divided into the linear and nonlinear scaling factors, where the nonlinear scaling factors are used to put the bolted joint into similitude. The results show that the natural frequencies, vibration responses, frequency components, and stability can be predicted accurately by scaled models, even the models are made of relatively cheap materials.