General Expansion Research Articles

Plane nonlinear shear wave propagation in transversely isotropic soft solids.

Nonlinear wave equations are obtained for the two plane shear wave modes in a transversely isotropic soft solid. The material is modeled using a general expansion of the strain energy density up to fourth order in strain. Whereas, in an isotropic soft solid, leading order nonlinearity for plane wave propagation appears at cubic order in strain, elastic anisotropy in a transversely isotropic material introduces nonlinear effects at quadratic order, including interaction between the modes of a wave with two displacement components. Expressions for second harmonic generation in an elliptically polarized wave field illustrate the low efficiency of nonlinear interactions between the two displacement components, which results from the disparity between propagation speeds of the two shear wave modes. Coupled wave equations with up to cubic nonlinearity are presented and then approximated to describe linearly polarized waves by neglecting interaction between modes. Evolution equations are obtained for linearly polarized progressive waves, and explicit expressions are given in terms of elastic moduli and propagation direction for the coefficients of leading order nonlinearity. Expressions are presented for up to third harmonic generation from a time-harmonic source.

DESCRIPTIVE COMPLEXITY IN CANTOR SERIES

AbstractA Cantor series expansion for a real number x with respect to a basic sequence $Q=(q_1,q_2,\dots )$ , where $q_i \geq 2$ , is a generalization of the base b expansion to an infinite sequence of bases. Ki and Linton in 1994 showed that for ordinary base b expansions the set of normal numbers is a $\boldsymbol {\Pi }^0_3$ -complete set, establishing the exact complexity of this set. In the case of Cantor series there are three natural notions of normality: normality, ratio normality, and distribution normality. These notions are equivalent for base b expansions, but not for more general Cantor series expansions. We show that for any basic sequence the set of distribution normal numbers is $\boldsymbol {\Pi }^0_3$ -complete, and if Q is $1$ -divergent then the sets of normal and ratio normal numbers are $\boldsymbol {\Pi }^0_3$ -complete. We further show that all five non-trivial differences of these sets are $D_2(\boldsymbol {\Pi }^0_3)$ -complete if $\lim _i q_i=\infty $ and Q is $1$ -divergent. This shows that except for the trivial containment that every normal number is ratio normal, these three notions are as independent as possible.

Structural components of income growth: an application to the evolution of the Spanish economy, 1980–2014

This paper analyses the structural and technical changes in Spain since the 1980s, using annual input–output tables. Specifically, a differential structural decomposition analysis (SDA) is applied to shifts in value-added, revealing eight different components and allowing the estimation of the impacts of technical change on the process of economic transformation on a sector-by-sector basis. We conclude that growth in the Spanish economy in recent decades was a mix of technological modernization and general economic expansion, although with some heterogeneity among sectors over time. High-technology services played a key role in modernization in the late 1980s and 1990s. In fact, the growth of High-technology, Medium-high-technology, Energy and Construction sectors accelerated through the 2008 crisis. Labour compensation and returns from capital followed different trends both during expansions and recessions, intensifying income inequality in Spain.

Hierarchical Bayesian framework for uncertainty reduction in the seismic fragility analysis of concrete gravity dams

Concrete gravity dams are critical infrastructures for communities to meet the basic human needs as well as rising standards of living. Most of the existing concrete gravity dams in Italy were built before the introduction of seismic regulations. Although no concrete gravity dams have as yet suffered a catastrophic collapse during or after a seismic event, their preservation remains a key aspect for communities, also in view of that older dams may have deteriorated to a critical level. For these reasons, researchers and practitioners in dam engineering are working to improve seismic fragility, and ultimately seismic risk, assessment procedures. Since no case histories are available, numerical modelling plays an important role, even though many uncertainties can affect the models and then the estimation of the seismic fragility.This paper presents a robust hierarchical Bayesian framework for the calibration of dynamic parameters of dam numerical models based on ambient vibrations, which allows an analyst to reduce uncertainties in the seismic fragility derivation. A probabilistic predictive model of the dam modal behaviour based on the general Polynomial Chaos Expansion is adopted in order to reduce the computational burden and a numerical algorithm for the solution of the inverse problem based on Markov Chain Monte Carlo is also presented.The proposed approach is applied to an existing large concrete gravity dam in Italy, and the effect of epistemic uncertainty reduction is finally evaluated in terms of fragility curves.

Diagnostic Species Diversity Pattern Can Provide Key Information on Vegetation Change: An Insight into High Mountain Habitats in Central Apennines

High mountain ecosystems are hotspots of biodiversity that are highly vulnerable to climate warming and land use change. In Europe, high mountain habitats are included in the EC Directive 92/43/EEC (Habitats Directive) and the identification of practices facilitating effective monitoring is crucial for meeting HD goals. We analyzed the temporal changes in species composition and diversity on high mountain EU habitats and explored if the subgroup of diagnostic species was able to summarize the comprehensive information on plant community variations. We performed a re-visitation study, using a set of 30 georeferenced historical plots newly collected after 20 years on two EU habitats (Galium magellense community growing on screes (8120 EU) and Trifolium thalii community of snowbeds (6170 EU)) in the Maiella National Park (MNP), which is one of the most threatened Mediterranean mountains in Europe. The presence of several endangered species and the availability of a botanical garden, a seed bank, and a nursery, make the MNP an excellent training ground to explore in situ and ex situ conservation strategies. We compared overall and diagnostic species richness patterns over time by rarefaction curves and described the singular aspects of species diversity (e.g., richness, Shannon index, Simpson index, and Berger–Parker index), by Rènyi’s diversity profiles. Diversity values consistently varied over time and across EU habitat types, with increasing values on scree communities and decreasing values on snowbeds. These changes could be associated with both land use change, through the increase of grazing pressure of Apennine chamois (Rupicapra pyrenaica ornata), which determined a rise of nitrophilous species in the scree community, and an increase of grasses at the expense of forbs in snowbeds, and to climate change, which promoted a general expansion of thermophilous species. Despite the two opposite, ongoing processes on the two plant communities studied, our results evidenced that diagnostic species and overall species followed the same trend of variation, demonstrating the potential of diagnostics for EU habitat monitoring. Our observations suggested that the re-visitation of historical plots and the implementation of frequent monitoring campaigns on diagnostic species can provide important data on species abundance and distribution patterns in these vulnerable ecosystems, supporting optimized in situ and ex situ conservation actions.

Tropical teleconnection impacts on Antarctic climate changes

Over the modern satellite era, substantial climatic changes have been observed in the Antarctic, including atmospheric and oceanic warming, ice sheet thinning and a general Antarctic-wide expansion of sea ice, followed by a more recent rapid loss. Although these changes, featuring strong zonal asymmetry, are partially influenced by increasing greenhouse gas emissions and stratospheric ozone depletion, tropical–polar teleconnections are believed to have a role through Rossby wave dynamics. In this Review, we synthesize understanding of tropical teleconnections to the Southern Hemisphere extratropics arising from the El Niño–Southern Oscillation, Interdecadal Pacific Oscillation and Atlantic Multidecadal Oscillation, focusing on the mechanisms and long-term climatic impacts. These teleconnections have contributed to observed Antarctic and Southern Ocean changes, including regional rapid surface warming, pre-2015 sea ice expansion and its sudden reduction thereafter, changes in ocean heat content and accelerated thinning of most of the Antarctic ice sheet. However, due to limited observations and inherent model biases, uncertainties remain in understanding and assessing the importance of these teleconnections versus those arising from greenhouse gases, ozone recovery and internal variability. Sustained pan-Antarctic efforts towards long-term observations, and more realistic dynamics and parameterizations in high-resolution climate models, offer opportunities to reduce these uncertainties.

Invasion and Extirpation Potential of Native and Invasive Spartina Species Under Climate Change

Coastal areas host some of the planet’s most productive ecosystems, providing life-sustaining ecological services and several benefits to humankind, while also being some of the most threatened areas (e.g., by globalization, climate change, and biological invasion). Salt marshes are coastal habitats with a key role in food and shelter provisioning, sediment deposition, nutrient cycling and carbon storage. Spartina spp. is a genus of grass halophytes which occurs in salt marshes worldwide, and includes species with different invasive potential. We evaluated the effect of climate change in the distribution and invasion potential of five Spartina species (S. anglica, S. alterniflora, S. densiflora, S. patens, and S. maritima) at a global scale. Species distribution models (SDMs) were applied on species occurrence data and atmospheric environmental predictors (WorldClim 2.1) to project potential changes in habitat suitability and associated changes in distribution and species co-occurrence until the end of the century, across four Shared Socioeconomic Pathway scenarios (i.e., SSP1-2.6 to SSP5-8.5). Projections showed a global trend for increasing species co-occurrence, with a general range expansion potentiated by increasing pathway severity. This study suggests that Spartina species can potentially benefit from climate change, predicting poleward expansions in the Northern Hemisphere for most species, with results pointing at increased conflict and invasion potential in Northern Europe and East Asian shorelines, already under strong invasive pressure. S. anglica is projected to remain a successful invader, with more severe scenarios likely favoring greater expansions. S. alterniflora exhibits very low expansion comparatively, despite exhibiting the same northward distribution shift. SSP1-2.6 produced the smallest change to species co-occurrence, suggesting a smaller potential for invasion-related conflicts, although still registering a potential net expansion for the Genus. Despite their limitations, SDMs can help establish general trends in climate change ecology and inform policymakers and environmental agents to ensure the correct management of these habitats and, ultimately, ecosystems.

Luminosity distance and anisotropic sky-sampling at low redshifts: A numerical relativity study

Most cosmological data analysis today relies on the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) metric, providing the basis of the current standard cosmological model. Within this framework, interesting tensions between our increasingly precise data and theoretical predictions are coming to light. It is therefore reasonable to explore the potential for cosmological analysis outside of the exact FLRW cosmological framework. In this work we adopt the general luminosity-distance series expansion in redshift with no assumptions of homogeneity or isotropy. This framework will allow for a full model-independent analysis of near-future low-redshift cosmological surveys. We calculate the effective observational `Hubble', `deceleration', `curvature' and `jerk' parameters of the luminosity-distance series expansion in numerical relativity simulations of realistic structure formation, for observers located in different environments and with different levels of sky-coverage. With a `fairly-sampled' sky, we find 2% and 15% cosmic variance in the `Hubble' and `deceleration' parameters for scales of $200\text{ }\text{ }\mathrm{Mpc}/h$ (corresponding to density contrasts of $\ensuremath{\sim}0.1$ in the simulated model universe), respectively. On top of this, we find that typical observers measure maximal sky-variance of 7% and 550% in the same parameters, as compared to their analogies in the large scale FLRW model. Our work suggests the inclusion of low-redshift anisotropy in cosmological analysis could be important for drawing correct conclusions about our Universe.

A ring expansion strategy towards diverse azaheterocycles.

The development of innovative strategies for the synthesis of N-heterocyclic compounds is an important topic in organic synthesis. Ring expansion methods to form large N-heterocycles often involve the cycloaddition of strained aza rings with π bonds. However, in some cases such strategies suffer from some limitations owing to the difficulties in controlling the regioselectivity and the accessibility of specific π-bond synthons. Here, we report the development of a general ring expansion strategy that involves a formal cross-dimerization between three-membered aza heterocycles and three- and four-membered-ring ketones through synergistic bimetallic catalysis. These formal cross-dimerizations of two different strained rings are efficient and scalable, and provide a straightforward and broadly applicable means of assembling diverse N-heterocycles, such as 3-benzazepinones, dihydropyridinones and uracils, which are versatile units in numerous drugs and biologically active compounds. Preliminary mechanistic studies revealed that the C-C bond of strained ring ketones is first cleaved by the Pd0 species during the reaction.

Color, Loan Approval, and Crimes: The Dark Side of Mortgage Market Deregulation

This paper documents that racial differences in credit distribution during a general mortgage credit expansion can lead to unintended negative consequences on crime. Exploiting a federal mortgage market deregulation, we find a significant increase in mortgage approval to white borrowers, while the approval rate to black borrowers is unchanged. More importantly, the local housing boom induced by this credit expansion leads to an increase in money-related crime rates of black offenders. The results highlight an unintended adverse consequence of credit expansion on the welfare of the minorities.

Impact of Tourism Receipts, FDI and Energy Usage on Economic Growth in South Asia

Purpose: The study examines the significant and direct influence of FDI and tourism income on economic growth in selected South Asian countries. . Design/Methodology/Approach: The study has made use of ARDL regression methodology to analyze the influence of tourism receipts, FDI and energy usage on economic growth.Findings: This study shows a strong long-term FDI, tourist receipts, and energy links, whereas the effects of these variables are less valuable in the short term.Implications/Originality/Value: It is generally recognized that FDI accompanies general economic expansion, the development of tourism, and the use of energy around the globe. However, several empirical outcomes have been disclosed in a long-standing discussion.

Performant implementation of the atomic cluster expansion (PACE) and application to copper and silicon

The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code PACE that is suitable for use in large-scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in PACE shifts a previously established Pareto front for machine learning interatomic potentials toward faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.

Spin-orbit torques in strained PtMnSb from first principles

We compute spin-orbit torques (SOTs) in strained PtMnSb from first principles. We consider both tetragonal strain and shear strain. We find a strong linear dependence of the field-like SOTs on these strains, while the antidamping SOT is only moderately sensitive to shear strain and even insensitive to tetragonal strain. We also study the dependence of the SOT on the magnetization direction. In order to obtain analytical expressions suitable for fitting our numerical \textit{ab-initio} results we derive a general expansion of the SOT in terms of all response tensors that are allowed by crystal symmetry. Our expansion includes also higher-order terms beyond the usually considered lowest order. We find that the dependence on the strain is much smaller for the higher-order terms than for the lowest order terms. In order to judge the sensitivity of the SOT on the exchange correlation potential we compute the SOT in both GGA and LDA. We find that the higher-order terms depend significantly on the exchange-correlation potential, while the lowest order terms are insensitive to it. Since the higher-order terms are small in comparison to the lowest order terms the total SOT is insensitive to the exchange correlation potential in strained PtMnSb.

Uncertainty Quantification of GEKO Model Coefficients on Compressible Flows

In the present work, supersonic flows over an axisymmetric base and a 24-deg compression ramp are investigated using the generalized k - ω (GEKO) model implemented in the commercial software, ANSYS FLUENT. GEKO is a two-equation model based on the k - ω formulation, and some specified model coefficients can be tuned depending on the flow characteristics. Uncertainty quantification (UQ) analysis is incorporated to quantify the uncertainty of the model coefficients and to calibrate the coefficients. The Latin hypercube sampling (LHS) method is used for sampling independent input parameters as a uniform distribution. A metamodel is constructed based on general polynomial chaos expansion (gPCE) using ordinary least squares (OLS). The influential coefficient closure is obtained by using Sobol indices. The affine invariant ensemble algorithm (AIES) is selected to characterize the posterior distribution via Markov chain Monte Carlo sampling. Calibrated model coefficients are extracted from posterior distributions obtained through Bayesian inference, which is based on the point-collocation nonintrusive polynomial chaos (NIPC) method. Results obtained through calibrated model coefficients by Bayesian inference show superior prediction with available experimental measurements than those from original model ones.

Galaxy shape statistics in the effective field theory

Intrinsic galaxy alignments yield an important contribution to the observed statistics of galaxy shapes. The general bias expansion for galaxy sizes and shapes in three dimensions has been recently described by Vlah, Chisari & Schmidt using the general perturbative effective field theory (EFT) framework, in analogy to the clustering of galaxies. In this work, we present a formalism that uses the properties of spherical tensors to project galaxy shapes onto the observed sky in the flat-sky approximation, and compute the two-point functions at next-to-leading order as well as the leading-order three-point functions of galaxy shapes and number counts. The resulting expressions are given in forms that are convenient for efficient numerical implementation. For a source redshift distribution typical of Stage IV surveys, we find that nonlinear intrinsic alignment contributions to galaxy shape correlations become relevant at angular wavenumbers l ≳ 100.

GaiaEarly Data Release 3

Context.GaiaEarly Data Release 3 (GaiaEDR3) provides accurate astrometry for about 1.6 million compact (QSO-like) extragalactic sources, 1.2 million of which have the best-quality five-parameter astrometric solutions.Aims.The proper motions of QSO-like sources are used to reveal a systematic pattern due to the acceleration of the solar systembarycentre with respect to the rest frame of the Universe. Apart from being an important scientific result by itself, the acceleration measured in this way is a good quality indicator of theGaiaastrometric solution.Methods.Theeffect of the acceleration was obtained as a part of the general expansion of the vector field of proper motions in vector spherical harmonics (VSH). Various versions of the VSH fit and various subsets of the sources were tried and compared to get the most consistent result and a realistic estimate of its uncertainty. Additional tests with theGaiaastrometric solution were used to get a better idea of the possible systematic errors in the estimate.Results.Our best estimate of the acceleration based onGaiaEDR3 is (2.32 ± 0.16) × 10−10m s−2(or 7.33 ±0.51 km s−1Myr−1) towardsα= 269.1° ± 5.4°,δ= −31.6° ± 4.1°, corresponding to a proper motion amplitude of 5.05 ±0.35μas yr−1. This is in good agreement with the acceleration expected from current models of the Galactic gravitational potential. We expect that futureGaiadata releases will provide estimates of the acceleration with uncertainties substantially below 0.1μas yr−1.

Modeling the Potential Future Distribution of Anthrax Outbreaks under Multiple Climate Change Scenarios for Kenya.

The climate is changing, and such changes are projected to cause global increase in the prevalence and geographic ranges of infectious diseases such as anthrax. There is limited knowledge in the tropics with regards to expected impacts of climate change on anthrax outbreaks. We determined the future distribution of anthrax in Kenya with representative concentration pathways (RCP) 4.5 and 8.5 for year 2055. Ecological niche modelling (ENM) of boosted regression trees (BRT) was applied in predicting the potential geographic distribution of anthrax for current and future climatic conditions. The models were fitted with presence-only anthrax occurrences (n = 178) from historical archives (2011–2017), sporadic outbreak surveys (2017–2018), and active surveillance (2019–2020). The selected environmental variables in order of importance included rainfall of wettest month, mean precipitation (February, October, December, July), annual temperature range, temperature seasonality, length of longest dry season, potential evapotranspiration and slope. We found a general anthrax risk areal expansion i.e., current, 36,131 km2, RCP 4.5, 40,012 km2, and RCP 8.5, 39,835 km2. The distribution exhibited a northward shift from current to future. This prediction of the potential anthrax distribution under changing climates can inform anticipatory measures to mitigate future anthrax risk.

Late-order terms of second order ODEs in terms of pre-factors

Factorial over a power approach is one of the fundamental techniques for deriving the late-order terms in the asymptotic approximation of integrals and differential equations. To our knowledge, although many differential equations depending on small or large parameters are addressed thoroughly and intensively by this approach in the literature to date, no explicit formula of the general representation of singularly-perturbed second order inhomogeneous ODEs in the form of this paper has yet been discussed generally in terms of their pre-factors. In this paper, we obtain a leading order asymptotic formula of the general asymptotic expansions suitable for the particular type of ODE by its pre-factors.

Tricomi’s Method for the Laplace Transform and Orthogonal Polynomials

Tricomi’s method for computing a set of inverse Laplace transforms in terms of Laguerre polynomials is revisited. By using the more recent results about the inversion and the connection coefficients for the series of orthogonal polynomials, we find the possibility to extend the Tricomi method to more general series expansions. Some examples showing the effectiveness of the considered procedure are shown.

1+3 -Newton-Cartan system and Newton-Cartan cosmology

We perform a covariant $1+3$ split of the Newton-Cartan equations. The resulting 3-dimensional system of equations, called the $1+3$-Newton-Cartan equations, is structurally equivalent to the $1+3$-Einstein equations. In particular it features the momentum constraint, and a choice of adapted coordinates corresponds to a choice of shift vector. We show that these equations reduce to the classical Newton equations without the need for special Galilean coordinates. The solutions to the $1+3$-Newton-Cartan equations are equivalent to the solutions of the classical Newton equations if space is assumed to be compact or if fall-off conditions at infinity are assumed. We then show that space expansion arises as a fundamental field in Newton-Cartan theory, and not by construction as in the classical formulation of Newtonian cosmology. We recover the Buchert-Ehlers theorem for the general expansion law in Newtonian cosmology.