Spatial Decay Research Articles

A note on the temporal and spatial attenuation of ocean waves

We study attenuation of free waves in the homogeneous ocean. Using the Cauchy–Riemann relations and then energy equation, we derive a novel equation that relates temporal and spatial decay to the energy dissipation in the fluid. In particular, for spatially damped waves we find that the attenuation coefficient is inversely proportional to the group velocity. We discuss the consequences of this for continental shelf waves where the group velocity may tend to zero in wave number space, and hence the spatial attenuation coefficient may become infinitely large. We show that generally for a travelling wave solution, the spatial damping will remain unchanged in a frame of reference moving with the group velocity, revealing the different physics behind temporal wave damping and spatial wave damping.

Distance decay 2.0 - A global synthesis of taxonomic and functional turnover in ecological communities.

AimUnderstanding the variation in community composition and species abundances (i.e., β‐diversity) is at the heart of community ecology. A common approach to examine β‐diversity is to evaluate directional variation in community composition by measuring the decay in the similarity among pairs of communities along spatial or environmental distance. We provide the first global synthesis of taxonomic and functional distance decay along spatial and environmental distance by analysing 148 datasets comprising different types of organisms and environments.LocationGlobal.Time period1990 to present.Major taxa studiedFrom diatoms to mammals.MethodWe measured the strength of the decay using ranked Mantel tests (Mantel r) and the rate of distance decay as the slope of an exponential fit using generalized linear models. We used null models to test whether functional similarity decays faster or slower than expected given the taxonomic decay along the spatial and environmental distance. We also unveiled the factors driving the rate of decay across the datasets, including latitude, spatial extent, realm and organismal features.ResultsTaxonomic distance decay was stronger than functional distance decay along both spatial and environmental distance. Functional distance decay was random given the taxonomic distance decay. The rate of taxonomic and functional spatial distance decay was fastest in the datasets from mid‐latitudes. Overall, datasets covering larger spatial extents showed a lower rate of decay along spatial distance but a higher rate of decay along environmental distance. Marine ecosystems had the slowest rate of decay along environmental distances.Main conclusionsIn general, taxonomic distance decay is a useful tool for biogeographical research because it reflects dispersal‐related factors in addition to species responses to climatic and environmental variables. Moreover, functional distance decay might be a cost‐effective option for investigating community changes in heterogeneous environments.

Attenuation of agglomeration economies: Evidence from the universe of Chinese manufacturing firms

This paper quantifies industry-specific spatial attenuation of agglomeration economies by taking advantage of unique geocoded administrative data on the universe of Chinese manufacturing firms. The estimates of industry-level attenuation speed further allow us to systematically assess the goodness of fit of various spatial decay functional forms and to evaluate the micro-foundations that govern the decay patterns across industries. We obtain three main findings. First, agglomeration spillovers attenuate by about 90 percent on average from 0–1 km to 1–5 km in China, with large heterogeneity in the extent of attenuation ranging from 73 percent to 116 percent across industries. Second, the spatial decay speed is positively linked with proxies for knowledge spillovers and labor market pooling but is negatively linked with proxies for input sharing and the share of the state sector. Last, the inverse square distance decay function presents the best goodness of fit among the tested functional forms.

Location-aware neural graph collaborative filtering

Collaborative filtering (CF) is initiated by representing users and items as vectors and seeks to describe the relationship between users and items at a profound level, thus predicting users’ preferred behavior. To address the issue that previous research ignored higher-order geographical interactions hidden in users’ historical behaviors, this paper proposes a location-aware neural graph collaborative filtering model (LA-NGCF), which incorporates location information of items for improving prediction performance. The model characterizes the interactions between items based on spatial decay law from a graph perspective and designs two strategies to capture the interaction effects of users and items considering node heterogeneity. An optimized loss function with spatial distances of items is also developed in the model. Extensive experiments are conducted on three publicly available real-world datasets to examine the effectiveness of our model. Results show that LA-NGCF achieves competitive performances compared with several state-of-the-art models, which suggests that location information of items is beneficial for improving the performance of personalized recommendations. This paper offers an approach to incorporate weighted interactions between items into CF algorithms and enriches the methods of utilizing geographical information for artificial intelligence applications.

Assessing personal exposure to COVID-19 transmission in public indoor spaces based on fine-grained trajectory data: A simulation study

The coronavirus disease 2019 (COVID-19) pandemic has posed substantial challenges to worldwide health systems in quick response to epidemics. The assessment of personal exposure to COVID-19 in enclosed spaces is critical to identifying potential infectees and preventing outbreaks. However, traditional contact tracing methods rely heavily on a manual interview, which is costly and time consuming given the large population involved. With advanced indoor localisation techniques, it is possible to collect people's footprints accurately by locating their smartphones. This study presents a new framework for the assessment of personal exposure to COVID-19 carriers using their fine-grained trajectory data. An integral model was established to quantify the exposure risk, in which the spatial and temporal decay effects are simultaneously considered when modelling the airborne transmission of COVID-19. Regarding the obstacle effect of the indoor layout on airborne transmission, a weight graph based on the space syntax technique was further introduced to constrain the transmission strength between subspaces that are less inter-visible. The proposed framework was demonstrated by a simulation study, in which external comparison and internal analysis were conducted to justify its validity and robustness in different scenarios. Our method is expected to promote the efficient identification of potential infectees and provide an extensible spatial–temporal model to simulate different control measures and examine their effectiveness in a built environment.

Investigating Superdiffusive Shock Acceleration at a Parallel Shock with a Fractional Parker Equation for Energetic-particle Interaction with Small-scale Magnetic Flux Ropes

It has been suggested before that small-scale magnetic flux rope (SMFR) structures in the solar wind can temporarily trap energetic charged particles. We present the derivation of a new fractional Parker equation for energetic-particle interaction with SMFRs from our pitch-angle-dependent fractional diffusion-advection equation that can account for such trapping effects. The latter was derived previously in le Roux & Zank from the first principles starting with the standard focused transport equation. The new equation features anomalous advection and diffusion terms. It suggests that energetic-particle parallel transport occurs with a decaying efficiency of advection effects as parallel superdiffusion becomes more dominant at late times. Parallel superdiffusion can be linked back to underlying anomalous pitch-angle transport, which might be subdiffusive during interaction with quasi-helical coherent SMFRs. We apply the new equation to time-dependent superdiffusive shock acceleration at a parallel shock. The results show that the superdiffusive-shock-acceleration timescale is fractional, the net fractional differential particle flux is conserved across the shock ignoring particle injection at the shock, and the accelerated particle spectrum at the shock converges to the familiar power-law spectrum predicted by standard steady-state diffusive-shock-acceleration theory at late times. Upstream, as parallel superdiffusion progressively dominates the advection of energetic particles, their spatial distributions decay on spatial scales that grow with time. Furthermore, superdiffusive parallel shock acceleration is found to be less efficient if parallel anomalous diffusion is more superdiffusive, while perpendicular particle escape from the shock, thought to be subdiffusive during SMFR interaction, is reduced when increasingly subdiffusive.

Fast spatial behavior in higher order in time equations and systems

In this work, we consider the spatial decay for high-order parabolic (and combined with a hyperbolic) equation in a semi-infinite cylinder. We prove a Phragmén-Lindelöf alternative function and, by means of some appropriate inequalities, we show that the decay is of the type of the square of the distance to the bounded end face of the cylinder. The thermoelastic case is also considered when the heat conduction is modeled using a high-order parabolic equation. Though the arguments are similar to others usually applied, we obtain new relevant results by selecting appropriate functions never considered before.

Elastic criterion for shear-banding instability in amorphous solids.

In amorphous solids, plastic flow is prone to localization into shear bands via an avalanche of shear-transformation (ST) rearrangements of constituent atoms or particles. However, such banding instability still remains a lack of direct experimental evidence. Using a real 3D colloidal glass under shear as proof of principle, we study STs' avalanches into shear banding that is controlled by strain rates. We demonstrate that, accompanying the emergent shear banding, the elastic response fields of the system, typical of a quadrupole for shear and a centrosymmetry for dilatation, lose the Eshelby-type spatial symmetry; instead, a strong correlation appears preferentially along the banding direction. By quantifying the fields' spatial decay, we identify an elastic criterion for the shear-banding instability, that is, the strongly correlated length of dilatation is smaller than the full length of shear correlation. Specifically, ST-induced free volume has to be confined within the elastic shear domain of ST so that those STs can self-organize to trigger shear banding. This physical picture is directly visualized by tracing the real-space evolution of local dilatation and ST particles. The present work unites the two classical mechanisms: free volume and STs, for the fundamental understanding of shear banding in amorphous solids.

Well-Posedness for the Dispersive Hunter–Saxton Equation

Abstract This article represents a 1st step toward understanding the well-posedness of the dispersive Hunter–Saxton equation, which arises in the study of nematic liquid crystals. Although the equation has formal similarities with the KdV equation, the lack of $L^2$ control gives it a quasilinear character. Further, the lack of spatial decay obstructs access to dispersive tools, including local smoothing estimates. Here, we give the 1st proof of local and global well-posedness for the Cauchy problem. Secondly, we improve our well-posedness results with respect to the low regularity of the initial data. The key techniques we use include constructing modified energies to realize a normal form analysis in our quasilinear setting, and frequency envelopes to prove continuous dependence with respect to the initial data.

Formation of the spatial structure of pump radiation in the focal plane of a lens for different types of stimulated light scattering

Experiments of our earlier work on the study of stimulated thermal scattering of the second harmonic of neodymium laser radiation in toluene are reproduced in order to confirm the put forward hypothesis about the nature of the laser beam structure decay in the focal plane of a short-focus lens. Experiments were carried out under similar conditions, but with a liquid (CCl4), in which there is no two-photon absorption of the second harmonic radiation from a neodymium laser. A conclusion is made that the spatial structure decay of the laser beam of the second harmonic of the Nd : YAG laser radiation focused by short-focus lenses with a numerical aperture NA ∼ 0.1 in toluene is associated with two-photon absorption.

Small‐scale spatiotemporal variability and distance–decay relationships in intertidal micro‐ and meiobenthic assemblages

AbstractCompositional similarity generally decreases with increasing geographic distance between sites (distance decay of similarity, DDS). Two non‐exclusive mechanisms have been proposed to explain this pattern: increasing differences in environmental conditions and pure spatial effects of dispersal limitation. On regional and global scales, environmental selection is considered the major factor for microbial assemblages, whereas pure spatial effects are generally more profound for larger organisms with limited dispersal ability. We investigated the DDS relationships at a small spatial scale (decimeters ‐ tens of meters) for three groups of benthic organisms differing in body size: diatoms and flagellates (DF), ciliates (CL), and harpacticoids (HA). All groups demonstrated definite DDS relationships. The pure spatial effects were strongest for the smallest‐size protists (DF), relatively weaker for CL and negligible for HA. In contrast, environmental factors (i.e., the differences in sediment properties) were more important for the HA and CL assemblages than for DF assemblages. In addition, we revealed a considerable temporal component of DDS relationships. First, similarity decreased with the time interval between sampling events (“temporal DDS”). Second, the average spatial similarity itself increased with time. These effects were significant for DF and CL only but were weak or undetectable for HA. Thus, our results are opposite to those commonly observed at larger (regional or global) scales. We suppose that the DDS relationships obtained at different spatial scales, despite formal similarity, reflect different phenomena driven by different mechanisms. At the geographical scale, species distribution patterns are mainly driven by long‐distance dispersal processes operated at the population level and dependent on their size‐related traits, which, taken in common, offer the advantage of small‐sized groups. The local‐scale distribution is primarily determined by individual motility and within‐habitat environmental heterogeneity. Small protists are relatively less motile, finely perceived and, therefore, have higher rates of spatial decay.

Non-radial finite time blow-up for the fourth-order nonlinear Schrödinger equations

We revisit the finite time blow-up for the fourth-order Schrödinger equation with focusing inhomogeneous nonlinearity −|x|−2|u|4nu. By exploiting localized virial estimates and spatial decay of the nonlinearity, we prove the finite time blow-up of non-radial solutions with negative energy. Our result is the first one dealing with the existence of non-radial blow-up solutions to the fourth-order Schrödinger equations.

The spatial decay of human capital externalities - A functional regression approach with precise geo-referenced data

This paper analyzes human capital externalities from high-skilled workers by applying functional regression to precise geocoded register data. Functional regression enables us to describe the concentration of high-skilled workers around workplaces as continuous curves and to efficiently estimate a spillover function determined by distance. Furthermore, our rich panel data allow us to address the sorting of workers and disentangle human capital externalities from supply effects by using an extensive set of time-varying fixed effects. Our estimates reveal that human capital externalities attenuate with increasing distance and disappear after 25 km. Externalities from the immediate neighborhood of an establishment are twice as large as externalities from surroundings 10 km away.

Analysis of the Characteristics of Cross-Regional Patient Groups and Differences in Hospital Service Utilization in Beijing.

When medical diagnostic difficulties occur at local hospitals, seeking high-quality services across regions becomes a priority for many patients. Traditional statistical methods in health care are unable to account for spatial characteristics such as outflow place or distributions of disease type and patient ages in the context of an increasing number of cross-regional groups; thus, these methods are incapable of studying service utilization differences among hospitals. From a geographic perspective, we analyzed the spatial characteristics of cross-regional patient groups who travelled from other places to Beijing and the spatial decay patterns in the actual service utilization of different hospitals in Beijing by using geographic calculations, geographic visualizations, and distance decay functions. We found the following results: (1) It is feasible to study patients’ cross-regional mobility from a geographical perspective. Through interdisciplinary integration, we can explore laws and conclusions that cannot be examined by traditional statistical methods in health care. (2) The characteristics of cross-regional patients who travelled from other places to Beijing were as follows: (a) Most patients came from northern China, and neoplasm treatment was the main demand of cross-regional patients; (b) patients 40–65 years old were the main cross-regional treatment group, and the average age of patients from northern regions and certain eastern coastal cities was relatively high. (3) The exponential distance decay function was the best of all five distance decay functions in fitting the distribution of cross-regional patient mobility to hospitals of different levels, types, and functional areas. The results of applying this function and the centrality calculation method showed that hospital service utilization was least affected by distance and that average radial distances (AR) were greatest in tertiary hospitals (distance decay coefficient β = 0.0786, AR = 664.70 km), traditional Chinese medicine hospitals (β = 0.0752, AR = 743.52 km), and hospitals in urban extension areas (β = 0.0782, AR = 693.29 km). Our results can serve as a reference for research concerning the allocation of medical resources and patients’ choices regarding medical treatment.

A prediction method for spatially decaying freestream turbulence

A simple set of equations, capable of quantifying and predicting the spatial decay of freestream turbulence (FST) is derived in the current study. The prediction equations are based on the inviscid estimate of the turbulent kinetic energy (TKE) dissipation rate. The new set of model equations includes the integral length scale and the turbulent kinetic energy as variables and is superior to the previous set of decay equations because, unlike those, they are not dependent on any physical grid parameters (b or M). This new set of equations, when compared and validated against 17 sets (2 active grids, 2 multi-scale grids, 9 square-cross-sectioned grids and 4 circular cross-sectioned grids) of previous, well-accepted, experimental data, including those relating to grid-generated turbulence and covering a wide range of turbulent Reynolds number (ReLu 0) (7.5 × 101 to 6.9 × 104), where Lu 0 is the initial integral length scale, showed very good agreement (within ±15%). This set of correlation equations can be used to estimate the local and/or initial turbulent kinetic energy and integral length scale (Lu ) in an FST flow and to locate the region within a flow domain where nearly-constant turbulence conditions are expected to prevail.

Direct comparison of three-terminal and four-terminal Hanle effects in the persistent photoconductor Al0.3Ga0.7As:Si

The electronic rendition of the Hanle effect, which is interpreted as the ensemble dephasing of a spin accumulation in the semiconductor under a perpendicular magnetic field, has been one of the most widely utilized and effective methods of measuring spin lifetime, spin accumulation, and spin transport in semiconductors. However, the origin of the Hanle magnetoresistance in the three-terminal (3T) setup has been intensively questioned both theoretically and experimentally; this is in contrast to the nonlocal four-terminal (NL-4T) measurement, which is accepted as reflecting spin accumulation and its spatial decay in metals and semiconductors alike. Here, we present results from 3T and NL-4T Hanle measurements on the same spin injection and detection devices with an ${\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}:\mathrm{Si}$ semiconducting channel. The use of ${\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}:\mathrm{Si}$, a persistent photoconductor, enables examination of the evolution of both types of Hanle signals with varying carrier density in the channel on one and the same device via in situ photodoping. We observe that the 3T and NL-4T Hanle signals exhibit similar Lorentzian line shapes, and thus yield similar spin lifetimes at all carrier densities. Moreover, the amplitudes of both types of Hanle signals are found to be consistent with each other, showing a similar exponential decrease with carrier density and in agreement with the Valet-Fert theory, in contrast to devices with artificial oxide barriers. These observations provide compelling evidence that in devices in which the spin injectors and detectors are engineered to minimize the presence of localized states, the 3T Hanle measurements provide a reliable probe of the spin accumulation and its dynamics in the semiconductor channel.

Epiphytic fungal communities vary by substrate type and at submetre spatial scales.

Fungal species have numerous important environmental functions. Where these functions occur will depend on how fungi are spatially distributed, but the spatial structures of fungal communities are largely unknown, especially in understudied hyperdiverse tropical tree canopy systems. Here we explore fungal communities in a Costa Rican tropical rainforest canopy, with a focus on local-scale spatial structure and substrate specificity of fungi. Samples of ~1cm3 were collected from 135 points along five adjacent tree branches, with intersample distances from 1 to 800cm, and dissected into four substrates: outer host tree bark, inner bark, dead bryophytes and living bryophytes. We sequenced the ITS2 region to characterize total fungal communities. Fungal community composition and diversity varied among substrate types, even when multiple substrates were in direct contact. Fungi were most diverse in living bryophytes, with 39% of all operational taxonomic units (OTUs) found exclusively in this substrate, and the least diverse in inner bark. Fungal communities had significant positive spatial autocorrelation and distance decay of similarity only at distances less than 1m. Similarity among samples declined by half in less than 10cm, and even at these short distances, similarities were low with few OTUs shared among samples. These results indicate that community turnover is high and occurs at very small spatial scales, with any two locations sharing very few fungi in common. High heterogeneity of fungal communities in space and among substrates may have implications for the distributions, population dynamics and diversity of other tree canopy organisms, including epiphytic plants.

Ranked diffusion, delta Bose gas, and Burgers equation.

We study the diffusion of N particles in one dimension interacting via a drift proportional to their rank. In the attractive case (self-gravitating gas) a mapping to the Lieb-Liniger quantum model allows one to obtain stationary time correlations, return probabilities, and the decay rate to the stationary state. The rank field obeys a Burgers equation, which we analyze. It allows one to obtain the stationary density at large N in an external potential V(x) (in the repulsive case). In the attractive case the decay rate to the steady state is found to depend on the initial condition if its spatial decay is slow enough. Coulomb gas methods allow one to study the final equilibrium at large N.

Kidney Cancer Risk Associated with Historic Groundwater Trichloroethylene Contamination.

Trichloroethylene (TCE) is a well-documented kidney carcinogen based on a substantial body of evidence including mechanistic and animal studies, as well as reports from occupational settings. However, the cancer risks for those in residential exposures such as TCE contamination in groundwater are much less clear. The objective of this study was to perform a detailed spatio-temporal analysis of estimated residential TCE exposure in New Hampshire, US. We identified kidney cancer cases (n = 292) and age-, gender-matched controls (n = 448) from the Dartmouth-Hitchcock Health System and queried a commercial financial database for address histories. We used publically available data on TCE levels in groundwater measured at contaminated sites in New Hampshire and then modeled the spatial dispersion and temporal decay. We overlaid geospatial residential locations of cases and controls with yearly maps of estimated TCE levels to estimate median exposures over the 5, 10, and 15-year epochs before diagnosis. The 50th–75th percentile of estimated residential exposure over a 15-year period was associated with increased kidney cancer risk (adjusted Odds Ratio (OR) 1.78 95% CI 1.05–3.03), compared to <50th percentile. This finding supports the need for groundwater monitoring of TCE contaminated sites to identify potential public health risks.

Information Structures of the Kalman Filter for the Elastic Wave Equation

We study the Kalman Filter for the linear elastic wave equation over the real line with spatially distributed partial state measurements. The dynamics of the filter are described by a spatial convolution operator with asymptotic exponential spatial decay rate. This decay rate dictates how measurements from different spatial locations must be exchanged to implement the filter: faster spatial decay implies local measurements are more relevant and the filter is more “decentralized”; slower decay implies farther measurements also become relevant and the filter is more “centralized”. Using dimensional analysis, we demonstrate that this decay rate is a function of one dimensionless group defined from system parameters, such as wave speed and noise variances. We find a critical value of such dimensionless group for which the Kalman Filter is completely decentralized.